1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
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32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
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54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
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126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
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156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command default
168 \pdf_title "LyX's Math Manual"
169 \pdf_author "LyX Team, Uwe Stöhr"
170 \pdf_subject "LyX-documentation about math"
171 \pdf_keywords "LyX, Mathed"
173 \pdf_bookmarksnumbered true
174 \pdf_bookmarksopen true
175 \pdf_bookmarksopenlevel 1
176 \pdf_breaklinks false
180 \pdf_pdfusetitle false
181 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
184 \use_package amsmath 2
185 \use_package amssymb 2
186 \use_package cancel 1
188 \use_package mathdots 1
189 \use_package mathtools 2
190 \use_package mhchem 1
191 \use_package stackrel 1
192 \use_package stmaryrd 1
193 \use_package undertilde 0
195 \cite_engine_type default
199 \paperorientation portrait
205 \notefontcolor #0000ff
212 \paragraph_separation skip
215 \math_numbering_side default
216 \quotes_style english
220 \paperpagestyle plain
225 \tracking_changes true
226 \output_changes false
229 \html_be_strict false
230 \author -563046850 "Jean-Marc LASGOUTTES"
237 's detailed Math manual
241 by the \SpecialChar LyX
246 \begin_layout Plain Layout
248 If you have comments or error corrections, please send them to the \SpecialChar LyX
253 \begin_inset CommandInset href
255 name "lyx-docs@lists.lyx.org"
256 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
268 \begin_inset Note Note
271 \begin_layout Plain Layout
278 \begin_inset Newline newline
282 \begin_inset Newline newline
290 \begin_layout Standard
291 \begin_inset CommandInset toc
292 LatexCommand tableofcontents
299 \begin_layout Standard
300 \begin_inset Note Note
303 \begin_layout Plain Layout
304 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
307 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
314 If they are not installed the document can be exported anyway but the sections
315 where the packages are required will not appear in the output.
320 ; if it is not installed, this file cannot be exported.
323 \begin_layout Plain Layout
324 The latest PDF-version of this document can be found here:
325 \begin_inset Newline newline
330 https://wiki.lyx.org/LyX/Manuals#Math
338 \begin_layout Standard
339 \begin_inset Newpage newpage
345 \begin_layout Section
349 \begin_layout Standard
350 This document explains \SpecialChar LyX
351 's math features and is furthermore a collection
352 of \SpecialChar LaTeX
353 -commands used for mathematical characters and constructs.
354 The explanations are designed for the usage of commands.
355 It is therefore required that you have read the section
366 \begin_layout Standard
367 Most of the characters and many constructs explained in this manual are
368 also accessible via the menu
372 \SpecialChar menuseparator
388 But everybody who has to write lots of formulas will notice that it is
389 much faster to use commands instead of the math toolbar.
390 Therefore this manual is focused on commands but also mentions the correspondin
391 g toolbar buttons when available.
394 \begin_layout Standard
395 If not specially mentioned the commands are only available within formulas.
396 To be able to use all commands explained in this document, the option
400 must be checked in the document settings (menu
402 Document\SpecialChar menuseparator
403 Settings\SpecialChar menuseparator
414 \begin_layout Plain Layout
417 Use AMS math package automatically
423 \begin_layout Plain Layout
432 -math when math constructs are found that are supported by \SpecialChar LyX
441 \begin_layout Standard
442 This document doesn't list all
446 \begin_layout Plain Layout
459 \begin_layout Plain Layout
464 \begin_layout Plain Layout
473 -math commands is in the file
476 \begin_inset CommandInset href
479 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
486 , which is part of every \SpecialChar LaTeX
487 standard installation.
492 for lucidity reasons.
495 \begin_layout Section
499 \begin_layout Standard
500 To create an inline formula
501 \begin_inset Index idx
504 \begin_layout Plain Layout
510 that is embedded into a text line, use one of the shortcuts
516 or the toolbar button
523 \begin_inset Newline newline
526 To create a display style formula
527 \begin_inset Index idx
530 \begin_layout Plain Layout
531 Formula ! display style
536 which will appear bigger, has a different format, and will be in a separate
537 paragraph, use one of these shortcuts:
546 \begin_layout Standard
547 To change a display style formula to an inline formula, set the cursor into
548 the formula and use one of the shortcuts
556 Edit\SpecialChar menuseparator
557 Math\SpecialChar menuseparator
561 The same way is used to change an inline formula to a display style formula.
564 \begin_layout Standard
565 To display parts of an inline formula in the size of a display style formula,
573 \begin_inset Index idx
576 \begin_layout Plain Layout
585 Then a new blue box appears in which the desired formula part is inserted.
588 \begin_layout Standard
589 Only inline formulas are allowed inside tables.
592 \begin_layout Standard
597 can be turned on in the menu
599 View\SpecialChar menuseparator
603 When you click there on
604 \begin_inset Quotes eld
608 \begin_inset Quotes erd
611 the toolbar will be shown permanently at the bottom; this state is visualized
616 menu with a checkmark.
617 When you click in this state again on
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
633 is only shown when the cursor is within a formula; this state is visualized
634 by the renaming of the menu entry from
635 \begin_inset Quotes eld
639 \begin_inset Quotes erd
643 \begin_inset Quotes eld
651 \begin_inset Quotes erd
657 \begin_layout Standard
660 \begin_inset Index idx
663 \begin_layout Plain Layout
670 is invoked by pressing the toolbar button
678 Insert\SpecialChar menuseparator
690 \begin_layout Standard
691 To change the \SpecialChar LaTeX
693 \begin_inset Index idx
696 \begin_layout Plain Layout
705 Document\SpecialChar menuseparator
706 Settings\SpecialChar menuseparator
716 \begin_layout Standard
717 To edit matrices, case differentiations and multiline formulas subsequently,
720 Edit\SpecialChar menuseparator
725 Edit\SpecialChar menuseparator
727 \begin_inset space \thinspace{}
731 \begin_inset space \thinspace{}
741 When lines and columns are swapped via the menu, the column or line where
742 the cursor is in is exchanged with the column to the right or the line
744 Is the cursor in the last column or row, the exchange is done with the
745 column to the left or the line above.
748 \begin_layout Standard
749 To write text in formulas
753 \begin_layout Plain Layout
754 For multiline formulas the command
761 \begin_inset CommandInset ref
763 reference "subsec:Text-in-multiline"
777 \begin_inset Index idx
780 \begin_layout Plain Layout
787 \begin_inset Index idx
790 \begin_layout Plain Layout
797 This mode is invoked with the shortcut
803 or by the insertion of the command
810 \begin_inset Index idx
813 \begin_layout Plain Layout
822 The text appears black in \SpecialChar LyX
823 and can therefore be distinguished from the
824 other formula parts which appear blue.
825 In the output mathematical text is set upright, in contrary to other formula
829 \begin_layout Subsection*
833 \begin_layout Standard
834 Most of the \SpecialChar LaTeX
835 -commands for math constructs have the following scheme:
838 \begin_layout Standard
854 \begin_layout Standard
855 A command always starts with a backslash
856 \begin_inset Quotes gld
866 \begin_inset Quotes grd
870 To omit optional arguments, also omit the associated brackets.
871 The braces around the required arguments are named in this document as
874 \begin_inset Index idx
877 \begin_layout Plain Layout
885 If you add in a formula a left brace to a command name, \SpecialChar LyX
887 creates a \SpecialChar TeX
889 In all other cases \SpecialChar TeX
890 braces are created in formulas with the command
898 braces appear red in \SpecialChar LyX
899 , in contrary to normal braces which appear blue.
901 mode no command is needed to get \SpecialChar TeX
904 braces don't appear in the output.
907 \begin_layout Standard
908 When commands without arguments, like commands for symbols are entered in
910 mode, a space character must
914 be behind the command to end it.
915 This space doesn't appear in the output.
916 When the space should appear in the output, the space must be followed
917 by a protected space in normal text.
920 \begin_layout Standard
921 A protected space is inserted with
924 arg "command-alternatives space-insert protected ; math-space"
930 \begin_layout Subsection*
931 \begin_inset Newpage newpage
937 \begin_layout Itemize
939 \begin_inset space \textvisiblespace{}
942 denotes a space character to be input.
945 \begin_layout Itemize
947 \begin_inset Formula $\to$
950 denotes the usage of the corresponding arrow key on the keyboard.
955 key can often be used instead of
956 \begin_inset Formula $\to$
960 \begin_inset Formula $\downarrow$
968 \begin_inset Formula $\leftarrow$
972 \begin_inset Formula $\uparrow$
978 \begin_layout Subsection*
982 \begin_layout Standard
984 \begin_inset Float table
991 \begin_layout Plain Layout
993 \begin_inset Caption Standard
995 \begin_layout Plain Layout
996 \begin_inset CommandInset label
998 name "tab:Available-units"
1010 \begin_layout Plain Layout
1012 \begin_inset Tabular
1013 <lyxtabular version="3" rows="13" columns="2">
1014 <features booktabs="true" tabularvalignment="middle">
1015 <column alignment="center" valignment="top">
1016 <column alignment="center" valignment="top" width="0pt">
1018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1021 \begin_layout Plain Layout
1027 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1030 \begin_layout Plain Layout
1038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1041 \begin_layout Plain Layout
1047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1050 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1061 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1070 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1081 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1090 \begin_layout Plain Layout
1092 \begin_inset space \thinspace{}
1096 \begin_inset space \thinspace{}
1106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1109 \begin_layout Plain Layout
1115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1118 \begin_layout Plain Layout
1120 \begin_inset space \thinspace{}
1124 \begin_inset space \thinspace{}
1134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1137 \begin_layout Plain Layout
1143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1146 \begin_layout Plain Layout
1148 \begin_inset space \thinspace{}
1152 \begin_inset space \thinspace{}
1162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1165 \begin_layout Plain Layout
1171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1174 \begin_layout Plain Layout
1176 \begin_inset space \thinspace{}
1180 \begin_inset space \thinspace{}
1190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1193 \begin_layout Plain Layout
1199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1202 \begin_layout Plain Layout
1204 \begin_inset space \thinspace{}
1208 \begin_inset space \thinspace{}
1218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1221 \begin_layout Plain Layout
1227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1230 \begin_layout Plain Layout
1232 \begin_inset space \thinspace{}
1236 \begin_inset Formula $\approx$
1240 \begin_inset space \thinspace{}
1250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1253 \begin_layout Plain Layout
1259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1262 \begin_layout Plain Layout
1264 \begin_inset space \thinspace{}
1268 \begin_inset space \thinspace{}
1278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1281 \begin_layout Plain Layout
1287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1290 \begin_layout Plain Layout
1294 \begin_inset Quotes eld
1300 \begin_inset Quotes erd
1310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1313 \begin_layout Plain Layout
1319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1322 \begin_layout Plain Layout
1324 \begin_inset Quotes eld
1332 \begin_inset Quotes erd
1342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1345 \begin_layout Plain Layout
1351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1354 \begin_layout Plain Layout
1356 \begin_inset space \thinspace{}
1360 \begin_inset Formula $\nicefrac{1}{18}$
1364 \begin_inset space \thinspace{}
1385 \begin_layout Standard
1386 \begin_inset Newpage newpage
1392 \begin_layout Section
1396 \begin_layout Subsection
1398 \begin_inset Index idx
1401 \begin_layout Plain Layout
1408 \begin_inset Index idx
1411 \begin_layout Plain Layout
1418 \begin_inset Index idx
1421 \begin_layout Plain Layout
1426 \begin_layout Plain Layout
1437 \begin_layout Plain Layout
1450 \begin_inset Index idx
1453 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1469 \begin_layout Plain Layout
1484 \begin_layout Standard
1485 Indices are created with an underscore
1486 \begin_inset Quotes eld
1490 \begin_inset Quotes erd
1493 or via the math toolbar button
1496 arg "math-subscript"
1499 , exponents with a caret
1500 \begin_inset Quotes eld
1504 \begin_inset Quotes erd
1507 or via the math toolbar button
1510 arg "math-superscript"
1516 \begin_layout Standard
1518 \begin_inset Tabular
1519 <lyxtabular version="3" rows="4" columns="2">
1520 <features booktabs="true" tabularvalignment="middle">
1521 <column alignment="center" valignment="top" width="0pt">
1522 <column alignment="center" valignment="top" width="0pt">
1524 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1527 \begin_layout Plain Layout
1533 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1536 \begin_layout Plain Layout
1544 <cell alignment="center" valignment="top" usebox="none">
1547 \begin_layout Plain Layout
1553 <cell alignment="center" valignment="top" usebox="none">
1556 \begin_layout Plain Layout
1557 \begin_inset Formula $B_{V}$
1566 <row topspace="1.5mm">
1567 <cell alignment="center" valignment="top" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B^{V}$
1589 <row topspace="1.5mm">
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1593 \begin_layout Plain Layout
1595 \begin_inset space \textvisiblespace{}
1603 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $B^{A}$
1623 \begin_layout Standard
1624 As the caret is in some languages an accent, vowels will be accentuated
1625 in this case and not set as exponents
1629 \begin_layout Plain Layout
1630 Depending on the used keyboard settings this can also happen for characters
1637 To get exponents in this case, press
1641 after the caret as in the last example.
1644 \begin_layout Subsection
1646 \begin_inset CommandInset label
1648 name "subsec:Fractions"
1653 \begin_inset Index idx
1656 \begin_layout Plain Layout
1665 \begin_layout Standard
1666 Fractions are generated with the command
1673 \begin_inset Index idx
1676 \begin_layout Plain Layout
1684 or via the math toolbar button
1687 arg "math-insert \\frac"
1691 The font size is adjusted automatically, depending on whether the fraction
1692 is in an inline or display style formula.
1693 With the math toolbar button
1696 arg "math-insert \\frac-square"
1699 you can select different fraction types.
1702 \begin_layout Standard
1710 \begin_inset Index idx
1713 \begin_layout Plain Layout
1721 a fraction can be created that always has the size of a display style formula.
1729 \begin_inset Index idx
1732 \begin_layout Plain Layout
1740 the fraction appears always with the size of an inline formula.
1744 \begin_layout Standard
1745 A line with the fraction
1746 \begin_inset Formula $\frac{1}{2}$
1749 that was created with the command
1758 \begin_layout Standard
1759 A line with the fraction
1760 \begin_inset Formula $\dfrac{1}{2}$
1763 that was created with the command
1772 \begin_layout Standard
1774 \begin_inset Tabular
1775 <lyxtabular version="3" rows="4" columns="2">
1776 <features booktabs="true" tabularvalignment="middle">
1777 <column alignment="center" valignment="top" width="0pt">
1778 <column alignment="center" valignment="top" width="0pt">
1780 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1783 \begin_layout Plain Layout
1789 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1792 \begin_layout Plain Layout
1799 <row topspace="1.5mm">
1800 <cell alignment="center" valignment="top" usebox="none">
1803 \begin_layout Plain Layout
1807 \begin_inset space \textvisiblespace{}
1811 \begin_inset Formula $\downarrow$
1819 <cell alignment="center" valignment="top" usebox="none">
1822 \begin_layout Plain Layout
1823 \begin_inset Formula $\frac{A}{B}$
1832 <row topspace="2mm">
1833 <cell alignment="center" valignment="top" usebox="none">
1836 \begin_layout Plain Layout
1840 \begin_inset space \textvisiblespace{}
1844 \begin_inset Formula $\downarrow$
1852 <cell alignment="center" valignment="top" usebox="none">
1855 \begin_layout Plain Layout
1856 \begin_inset Formula $\dfrac{A}{B}$
1865 <row topspace="2mm" bottomspace="1mm">
1866 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1869 \begin_layout Plain Layout
1873 \begin_inset space \textvisiblespace{}
1879 \begin_inset space \textvisiblespace{}
1883 \begin_inset Formula $\downarrow$
1887 \begin_inset Formula $\downarrow\downarrow$
1895 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1898 \begin_layout Plain Layout
1899 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1915 \begin_layout Standard
1916 \begin_inset VSpace bigskip
1920 \begin_inset Newpage newpage
1923 For nested fractions the command
1930 \begin_inset Index idx
1933 \begin_layout Plain Layout
1943 \begin_inset VSpace -3mm
1949 \begin_layout Standard
1950 \begin_inset Formula
1952 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1953 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1961 \begin_layout Standard
1962 The command for the example above is:
1965 \begin_layout Standard
1971 \begin_inset space \textvisiblespace{}
1975 \begin_inset Formula $\downarrow$
1981 \begin_inset space \textvisiblespace{}
1987 \begin_inset space \textvisiblespace{}
1991 \begin_inset Formula $\downarrow$
1995 \begin_inset Formula $\downarrow$
2001 \begin_layout Standard
2002 \begin_inset VSpace medskip
2008 \begin_layout Standard
2015 sets the fraction always in the size of a displayed formula, also when
2016 it is part of another fraction.
2019 \begin_layout Standard
2020 It is possible to specify the alignment of the numerator.
2027 is used to left align it, the command
2040 centers the numerator.
2041 These fractions demonstrate the different alignments:
2044 \begin_layout Standard
2047 \begin_inset Formula
2049 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2057 \begin_layout Standard
2058 \begin_inset Note Greyedout
2061 \begin_layout Plain Layout
2078 are no real \SpecialChar LaTeX
2079 commands but represent the command
2083 cfrac[alignment]{numerator}{denominator}
2086 Therefore you cannot use them in \SpecialChar TeX
2095 \begin_layout Standard
2096 \begin_inset VSpace medskip
2099 It is often advantageous to combine
2112 \begin_inset Formula
2114 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2122 \begin_layout Standard
2123 For inline fractions with a sloped fraction stroke you can use the command
2131 \begin_inset Index idx
2134 \begin_layout Plain Layout
2143 \begin_inset Formula $\nicefrac{5}{31}$
2153 \begin_inset Index idx
2156 \begin_layout Plain Layout
2165 \begin_inset Formula $\unitfrac{5}{31}$
2168 There is furthermore the command
2174 that offers to write a fraction in combination with a number:
2175 \begin_inset Formula $\unitfrac[2]{1}{3}$
2181 \begin_layout Standard
2182 \begin_inset Note Greyedout
2185 \begin_layout Plain Layout
2196 is not a real \SpecialChar LaTeX
2197 command but the command
2198 \begin_inset Newline newline
2205 unitfrac[number]{numerator}{denominator}
2208 Therefore you cannot use it in \SpecialChar TeX
2217 \begin_layout Standard
2218 How to define own fractions where the fraction stroke can be changed, is
2220 \begin_inset CommandInset ref
2222 reference "subsec:Self-defined-Fractions"
2229 \begin_layout Standard
2230 Multiline fractions are explained in
2231 \begin_inset CommandInset ref
2233 reference "subsec:Multiline-Fractions"
2240 \begin_layout Subsection
2242 \begin_inset Index idx
2245 \begin_layout Plain Layout
2254 \begin_layout Standard
2255 Square roots are created with
2262 \begin_inset Index idx
2265 \begin_layout Plain Layout
2273 or the math toolbar button
2276 arg "math-insert \\sqrt"
2279 , all other roots with the command
2286 \begin_inset Index idx
2289 \begin_layout Plain Layout
2297 or with the math toolbar button
2300 arg "math-insert \\root"
2306 \begin_layout Standard
2308 \begin_inset Tabular
2309 <lyxtabular version="3" rows="3" columns="2">
2310 <features booktabs="true" tabularvalignment="middle">
2311 <column alignment="center" valignment="top" width="0pt">
2312 <column alignment="center" valignment="top" width="0pt">
2314 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2317 \begin_layout Plain Layout
2323 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2326 \begin_layout Plain Layout
2333 <row topspace="1mm">
2334 <cell alignment="center" valignment="top" usebox="none">
2337 \begin_layout Plain Layout
2341 \begin_inset space \textvisiblespace{}
2349 <cell alignment="center" valignment="top" usebox="none">
2352 \begin_layout Plain Layout
2353 \begin_inset Formula $\sqrt{A-B}$
2362 <row topspace="1mm">
2363 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2366 \begin_layout Plain Layout
2370 \begin_inset space \textvisiblespace{}
2374 \begin_inset Formula $\downarrow$
2382 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2385 \begin_layout Plain Layout
2386 \begin_inset Formula $\sqrt[3]{A-B}$
2402 \begin_layout Standard
2403 A square root can also be created with
2409 when the root index field is left empty.
2412 \begin_layout Standard
2413 With certain indices the distance to the root is too small, like in this
2415 \begin_inset Formula $\sqrt[\beta]{B}$
2419 \begin_inset Newline newline
2423 \begin_inset Formula $\beta$
2427 To avoid this, the commands
2434 \begin_inset Index idx
2437 \begin_layout Plain Layout
2452 \begin_inset Index idx
2455 \begin_layout Plain Layout
2463 are used with the following scheme:
2466 \begin_layout Standard
2480 \begin_layout Standard
2481 Distance is the number of Big Points (unit bp;
2482 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2485 ), that the index should be moved to the left or top, resp..
2486 The commands are written to the index.
2487 This way the command
2488 \begin_inset Newline newline
2498 \begin_inset Formula $\to$
2504 \begin_inset Formula $\to$
2510 \begin_inset space \textvisiblespace{}
2514 \begin_inset Formula $\to$
2518 \begin_inset Newline newline
2523 produces a correct typeset formula:
2524 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2530 \begin_layout Subsection
2531 Binomial Coefficients
2532 \begin_inset Index idx
2535 \begin_layout Plain Layout
2536 Binomial coefficients
2544 \begin_layout Standard
2545 Binomial coefficients are inserted with the command
2552 \begin_inset Index idx
2555 \begin_layout Plain Layout
2563 or with the submenu of the math toolbar button
2566 arg "math-insert \\frac-square"
2582 there are the commands
2589 \begin_inset Index idx
2592 \begin_layout Plain Layout
2607 \begin_inset Index idx
2610 \begin_layout Plain Layout
2619 For other brackets around binomial coeficients there are the commands
2626 \begin_inset Index idx
2629 \begin_layout Plain Layout
2644 \begin_inset Index idx
2647 \begin_layout Plain Layout
2658 \begin_layout Standard
2660 \begin_inset Tabular
2661 <lyxtabular version="3" rows="6" columns="2">
2662 <features booktabs="true" tabularvalignment="middle">
2663 <column alignment="center" valignment="top" width="0pt">
2664 <column alignment="center" valignment="top" width="0pt">
2666 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2669 \begin_layout Plain Layout
2675 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2678 \begin_layout Plain Layout
2685 <row topspace="1mm">
2686 <cell alignment="center" valignment="top" usebox="none">
2689 \begin_layout Plain Layout
2693 \begin_inset space \textvisiblespace{}
2697 \begin_inset Formula $\downarrow$
2705 <cell alignment="center" valignment="top" usebox="none">
2708 \begin_layout Plain Layout
2709 \begin_inset Formula $\binom{A}{B}$
2718 <row topspace="2mm">
2719 <cell alignment="center" valignment="top" usebox="none">
2722 \begin_layout Plain Layout
2726 \begin_inset space \textvisiblespace{}
2730 \begin_inset Formula $\downarrow$
2738 <cell alignment="center" valignment="top" usebox="none">
2741 \begin_layout Plain Layout
2742 \begin_inset Formula $\dbinom{A}{B}$
2751 <row topspace="2mm" bottomspace="0.5mm">
2752 <cell alignment="center" valignment="top" usebox="none">
2755 \begin_layout Plain Layout
2759 \begin_inset space \textvisiblespace{}
2763 \begin_inset Formula $\downarrow$
2771 <cell alignment="center" valignment="top" usebox="none">
2774 \begin_layout Plain Layout
2775 \begin_inset Formula $\tbinom{A}{B}$
2784 <row topspace="1mm">
2785 <cell alignment="center" valignment="top" topline="true" usebox="none">
2788 \begin_layout Plain Layout
2792 \begin_inset space \textvisiblespace{}
2796 \begin_inset Formula $\downarrow$
2804 <cell alignment="center" valignment="top" topline="true" usebox="none">
2807 \begin_layout Plain Layout
2808 \begin_inset Formula ${A \brack B}$
2817 <row topspace="2mm" bottomspace="0.5mm">
2818 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2821 \begin_layout Plain Layout
2825 \begin_inset space \textvisiblespace{}
2829 \begin_inset Formula $\downarrow$
2837 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2840 \begin_layout Plain Layout
2841 \begin_inset Formula ${A \brace B}$
2857 \begin_layout Subsection
2858 Case Differentiations
2859 \begin_inset Index idx
2862 \begin_layout Plain Layout
2863 Case differentiations
2871 \begin_layout Standard
2873 \begin_inset Tabular
2874 <lyxtabular version="3" rows="3" columns="2">
2875 <features booktabs="true" tabularvalignment="middle">
2876 <column alignment="center" valignment="top" width="0pt">
2877 <column alignment="center" valignment="top" width="0pt">
2879 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2882 \begin_layout Plain Layout
2888 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2891 \begin_layout Plain Layout
2899 <cell alignment="center" valignment="top" usebox="none">
2902 \begin_layout Plain Layout
2906 \begin_inset space \textvisiblespace{}
2910 \begin_inset Formula $\to$
2914 \begin_inset Index idx
2917 \begin_layout Plain Layout
2930 <cell alignment="center" valignment="top" usebox="none">
2933 \begin_layout Plain Layout
2934 \begin_inset Formula $\begin{cases}
2944 <row topspace="1.5mm">
2945 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2948 \begin_layout Plain Layout
2952 \begin_inset space \textvisiblespace{}
2958 arg "newline-insert newline"
2966 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2969 \begin_layout Plain Layout
2970 \begin_inset Formula $\begin{cases}
2971 A & \textrm{for }x>0\\
2972 B & \textrm{for }x=0
2989 \begin_layout Standard
2996 or pressing the math toolbar button
2999 arg "math-insert \\cases"
3002 you can create new lines with the shortcut
3005 arg "newline-insert newline"
3008 or the table toolbar button
3011 arg "tabular-feature append-row"
3017 \begin_layout Standard
3024 is also available via the menu
3026 Insert\SpecialChar menuseparator
3027 Math\SpecialChar menuseparator
3033 \begin_layout Subsection
3035 \begin_inset Index idx
3038 \begin_layout Plain Layout
3047 \begin_layout Standard
3055 \begin_inset Index idx
3058 \begin_layout Plain Layout
3066 every character can be displayed canceled.
3067 The characters are quasi accentuated by a slash.
3070 \begin_layout Standard
3072 \begin_inset Tabular
3073 <lyxtabular version="3" rows="4" columns="2">
3074 <features booktabs="true" tabularvalignment="middle">
3075 <column alignment="center" valignment="top" width="0pt">
3076 <column alignment="center" valignment="top" width="0pt">
3078 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3081 \begin_layout Plain Layout
3087 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3090 \begin_layout Plain Layout
3098 <cell alignment="center" valignment="top" usebox="none">
3101 \begin_layout Plain Layout
3109 <cell alignment="center" valignment="top" usebox="none">
3112 \begin_layout Plain Layout
3113 \begin_inset Formula $\not=$
3123 <cell alignment="center" valignment="top" usebox="none">
3126 \begin_layout Plain Layout
3136 <cell alignment="center" valignment="top" usebox="none">
3139 \begin_layout Plain Layout
3140 \begin_inset Formula $\not\le$
3150 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3153 \begin_layout Plain Layout
3163 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3166 \begin_layout Plain Layout
3167 \begin_inset Formula $\not\parallel$
3183 \begin_layout Standard
3184 The last example shows that not all negations look good.
3185 Therefore there are special commands for some negations (see
3186 \begin_inset CommandInset ref
3188 reference "subsec:Mathematical-Symbols"
3193 \begin_inset CommandInset ref
3195 reference "sec:Relations"
3202 \begin_layout Subsection
3204 \begin_inset CommandInset label
3206 name "subsec:Placeholders"
3211 \begin_inset Index idx
3214 \begin_layout Plain Layout
3221 \begin_inset Index idx
3224 \begin_layout Plain Layout
3225 Chemical characters ! Isotopes
3231 \begin_inset Index idx
3234 \begin_layout Plain Layout
3239 \begin_layout Plain Layout
3250 \begin_layout Plain Layout
3265 \begin_layout Standard
3267 \begin_inset space \thinspace{}
3271 \begin_inset space \space{}
3278 \begin_layout Plain Layout
3279 Typesetting isotopes and chemical symbols is described in
3280 \begin_inset CommandInset ref
3282 reference "subsec:Chemical-Symbols-and"
3291 the following problem occurs:
3294 \begin_layout Standard
3296 \begin_inset Tabular
3297 <lyxtabular version="3" rows="2" columns="2">
3298 <features booktabs="true" tabularvalignment="middle">
3299 <column alignment="center" valignment="top" width="0pt">
3300 <column alignment="center" valignment="top" width="0pt">
3302 <cell alignment="center" valignment="top" usebox="none">
3305 \begin_layout Plain Layout
3306 Indices created with sub- and superscripts:
3311 <cell alignment="center" valignment="top" usebox="none">
3314 \begin_layout Plain Layout
3315 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3324 <row topspace="1.5mm">
3325 <cell alignment="center" valignment="top" usebox="none">
3328 \begin_layout Plain Layout
3334 <cell alignment="center" valignment="top" usebox="none">
3337 \begin_layout Plain Layout
3338 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3354 \begin_layout Standard
3355 The shorter index is by default placed below or above the first character
3356 of the longer index.
3357 To avoid this there is the command
3364 \begin_inset Index idx
3367 \begin_layout Plain Layout
3375 or the math toolbar button
3376 \begin_inset space \thinspace{}
3383 \begin_layout Plain Layout
3384 can be found in the submenu of the toolbar button
3387 arg "math-insert \\space"
3401 that creates one or more phantom characters.
3408 a small blue box appears that is superposed with two red arrows.
3409 The arrows indicate that the complete width and height of the box content
3410 will be created as placeholder.
3411 Phantom characters are accordingly placeholders with the size of the characters.
3414 \begin_layout Standard
3416 \begin_inset Tabular
3417 <lyxtabular version="3" rows="4" columns="2">
3418 <features booktabs="true" tabularvalignment="middle">
3419 <column alignment="center" valignment="top" width="0pt">
3420 <column alignment="center" valignment="top" width="0pt">
3422 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3425 \begin_layout Plain Layout
3431 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3434 \begin_layout Plain Layout
3441 <row topspace="1.5mm">
3442 <cell alignment="center" valignment="top" usebox="none">
3445 \begin_layout Plain Layout
3447 \begin_inset space \textvisiblespace{}
3453 \begin_inset space \textvisiblespace{}
3457 \begin_inset Formula $\to$
3461 \begin_inset space \textvisiblespace{}
3469 <cell alignment="center" valignment="top" usebox="none">
3472 \begin_layout Plain Layout
3473 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3482 <row topspace="1.5mm" bottomspace="0.5mm">
3483 <cell alignment="center" valignment="top" usebox="none">
3486 \begin_layout Plain Layout
3488 \begin_inset space \textvisiblespace{}
3494 \begin_inset space \textvisiblespace{}
3498 \begin_inset Formula $\to$
3502 \begin_inset space \textvisiblespace{}
3510 <cell alignment="center" valignment="top" usebox="none">
3513 \begin_layout Plain Layout
3514 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3523 <row topspace="1.5mm" bottomspace="0.5mm">
3524 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3527 \begin_layout Plain Layout
3531 \begin_inset space \textvisiblespace{}
3537 \begin_inset space \textvisiblespace{}
3541 \begin_inset Formula $\to$
3545 \begin_inset space \textvisiblespace{}
3553 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3556 \begin_layout Plain Layout
3557 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3573 \begin_layout Standard
3574 Furthermore there are the commands
3581 \begin_inset Index idx
3584 \begin_layout Plain Layout
3605 \begin_inset Index idx
3608 \begin_layout Plain Layout
3629 creates only space for the maximal height of the characters in the box
3630 but not for its width.
3637 creates only space for the width of the box content.
3638 Therefore the boxes of both commands have only one red arrow.
3641 \begin_layout Standard
3642 For example the command
3647 \begin_inset space \textvisiblespace{}
3654 creates space for the height of the integral sign,
3658 \begin_layout Plain Layout
3665 creates an integral sign, see
3666 \begin_inset CommandInset ref
3668 reference "subsec:Big-Operators"
3677 because this is the larger character.
3678 An example application is in
3679 \begin_inset CommandInset ref
3681 reference "subsec:Multiline-Brackets"
3688 \begin_layout Standard
3689 Placeholders can also be used for text when they are inserted via the menu
3692 Insert\SpecialChar menuseparator
3693 Formatting\SpecialChar menuseparator
3699 \begin_layout Standard
3701 \begin_inset Newline newline
3705 \begin_inset Phantom Phantom
3708 \begin_layout Plain Layout
3717 \begin_layout Subsection
3719 \begin_inset Index idx
3722 \begin_layout Plain Layout
3729 \begin_inset Index idx
3732 \begin_layout Plain Layout
3733 Formula ! underlined
3741 \begin_layout Standard
3743 \begin_inset Tabular
3744 <lyxtabular version="3" rows="4" columns="2">
3745 <features booktabs="true" tabularvalignment="middle">
3746 <column alignment="center" valignment="top" width="0pt">
3747 <column alignment="center" valignment="top" width="0pt">
3749 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3752 \begin_layout Plain Layout
3758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3761 \begin_layout Plain Layout
3768 <row topspace="2mm">
3769 <cell alignment="center" valignment="top" usebox="none">
3772 \begin_layout Plain Layout
3776 \begin_inset space \textvisiblespace{}
3780 \begin_inset Index idx
3783 \begin_layout Plain Layout
3796 <cell alignment="center" valignment="top" usebox="none">
3799 \begin_layout Plain Layout
3800 \begin_inset Formula $\overline{A+B}$
3809 <row bottomspace="1mm">
3810 <cell alignment="center" valignment="top" usebox="none">
3813 \begin_layout Plain Layout
3817 \begin_inset space \textvisiblespace{}
3821 \begin_inset Index idx
3824 \begin_layout Plain Layout
3837 <cell alignment="center" valignment="top" usebox="none">
3840 \begin_layout Plain Layout
3841 \begin_inset Formula $\underline{A+B}$
3850 <row topspace="2mm" bottomspace="1mm">
3851 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3854 \begin_layout Plain Layout
3858 \begin_inset space \textvisiblespace{}
3864 \begin_inset space \textvisiblespace{}
3872 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3875 \begin_layout Plain Layout
3876 \begin_inset Formula $\overline{\underline{A+B}}$
3892 \begin_layout Standard
3893 In the last example it doesn't matter if first
3908 \begin_layout Standard
3909 To double underline use
3918 \begin_layout Standard
3919 It is possible to place up to 6 lines above or below characters.
3922 \begin_layout Standard
3923 \begin_inset VSpace bigskip
3926 Custom lines can be created using the command
3933 \begin_inset Index idx
3936 \begin_layout Plain Layout
3944 which has the following scheme:
3947 \begin_layout Standard
3952 rule[vertical offset]{length}{thickness}
3955 \begin_layout Standard
3956 The optional vertical offset shifts the line upwards (or downwards, when
3957 the value is negative).
3959 \begin_inset CommandInset ref
3961 reference "tab:Available-units"
3965 can be used for the values.
3966 Here are two example lines created with the commands
3967 \begin_inset Newline newline
3974 rule[-2ex]{3cm}{2pt}
3985 \begin_layout Standard
3987 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3993 \begin_layout Standard
4000 can also be used for text when a line is inserted via the menu
4002 Insert\SpecialChar menuseparator
4003 Formatting\SpecialChar menuseparator
4005 \begin_inset space ~
4013 \begin_layout Standard
4015 \begin_inset CommandInset line
4026 \begin_layout Subsection
4028 \begin_inset CommandInset label
4030 name "subsec:Ellipses"
4035 \begin_inset Index idx
4038 \begin_layout Plain Layout
4047 \begin_layout Standard
4048 There are different types of ellipses available.
4052 \begin_layout Plain Layout
4053 In the math toolbar in the submenu of the button
4056 arg "math-insert \\ldots"
4064 For listings dots at the baseline are used (
4071 \begin_inset Index idx
4074 \begin_layout Plain Layout
4082 ), while for operations dots are needed that are on the same height as the
4090 \begin_inset Index idx
4093 \begin_layout Plain Layout
4102 When using the command
4109 \begin_inset Index idx
4112 \begin_layout Plain Layout
4120 , \SpecialChar LaTeX
4121 decides on the basis of the next character what type is used.
4124 \begin_layout Standard
4126 \begin_inset Tabular
4127 <lyxtabular version="3" rows="9" columns="2">
4128 <features booktabs="true" tabularvalignment="middle">
4129 <column alignment="center" valignment="top" width="0pt">
4130 <column alignment="center" valignment="top" width="0pt">
4132 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4135 \begin_layout Plain Layout
4141 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4144 \begin_layout Plain Layout
4152 <cell alignment="center" valignment="top" usebox="none">
4155 \begin_layout Plain Layout
4157 \begin_inset space \textvisiblespace{}
4163 \begin_inset space \textvisiblespace{}
4171 <cell alignment="center" valignment="top" usebox="none">
4174 \begin_layout Plain Layout
4175 \begin_inset Formula $A_{1},\dots,A_{n}$
4185 <cell alignment="center" valignment="top" usebox="none">
4188 \begin_layout Plain Layout
4190 \begin_inset space \textvisiblespace{}
4196 \begin_inset space \textvisiblespace{}
4204 <cell alignment="center" valignment="top" usebox="none">
4207 \begin_layout Plain Layout
4208 \begin_inset Formula $A_{1}+\dots+A_{n}$
4218 <cell alignment="center" valignment="top" usebox="none">
4221 \begin_layout Plain Layout
4223 \begin_inset space \textvisiblespace{}
4229 \begin_inset space \textvisiblespace{}
4237 <cell alignment="center" valignment="top" usebox="none">
4240 \begin_layout Plain Layout
4241 \begin_inset Formula $A_{1},\ldots,A_{n}$
4251 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4254 \begin_layout Plain Layout
4256 \begin_inset space \textvisiblespace{}
4262 \begin_inset space \textvisiblespace{}
4270 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4273 \begin_layout Plain Layout
4274 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4284 <cell alignment="center" valignment="top" usebox="none">
4287 \begin_layout Plain Layout
4295 <cell alignment="center" valignment="top" usebox="none">
4298 \begin_layout Plain Layout
4299 \begin_inset Formula $\vdots$
4309 <cell alignment="center" valignment="top" usebox="none">
4312 \begin_layout Plain Layout
4320 <cell alignment="center" valignment="top" usebox="none">
4323 \begin_layout Plain Layout
4324 \begin_inset Formula $\ddots$
4334 <cell alignment="center" valignment="top" usebox="none">
4337 \begin_layout Plain Layout
4345 <cell alignment="center" valignment="top" usebox="none">
4348 \begin_layout Plain Layout
4349 \begin_inset Formula $\iddots$
4359 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4362 \begin_layout Plain Layout
4364 \begin_inset space \thinspace{}
4367 matrix with the different dots
4372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4375 \begin_layout Plain Layout
4376 \begin_inset Formula $\begin{array}{ccc}
4377 A_{11} & \cdots & A_{1m}\\
4378 \vdots & \ddots & \vdots\\
4379 A_{n1} & \cdots & A_{nm}
4396 \begin_layout Standard
4397 The ellipses available in menu
4399 Insert\SpecialChar menuseparator
4401 \begin_inset space ~
4415 \begin_layout Standard
4416 \begin_inset VSpace medskip
4425 , one of the options
4427 Use mathdots package (automatically)
4429 must be set in the document settings under
4432 \begin_inset space ~
4438 \begin_inset Newline newline
4443 Use mathdots package
4445 will improve the appearance of all dots in the documents if their font
4446 style or size is not the default.
4449 \begin_layout Standard
4450 \begin_inset VSpace medskip
4453 Specially for matrices there are ellipses that span over several columns.
4454 They are created with the command
4461 \begin_inset Index idx
4464 \begin_layout Plain Layout
4472 , that has the following scheme:
4475 \begin_layout Standard
4480 hdotsfor[distance]{number of columns}
4483 \begin_layout Standard
4484 The number of columns specifies how many columns should be spanned.
4485 Distance is a factor for the distance between the dots.
4488 \begin_layout Standard
4489 In the following matrix the command
4495 was inserted in the first box of the second line, to get an ellipsis with
4496 a dot distance twice as long as with the command
4503 \begin_inset Formula
4505 \left(\begin{array}{cccc}
4514 Note that the matrix fields that should be spanned must be empty, otherwise
4515 you get \SpecialChar LaTeX
4519 \begin_layout Standard
4520 \begin_inset VSpace bigskip
4523 Furthermore you can fill with the command
4530 \begin_inset Index idx
4533 \begin_layout Plain Layout
4541 the rest of a line with dots.
4542 The effect of these commands is the same as with
4549 \begin_inset CommandInset ref
4551 reference "subsec:Variable-Space"
4558 \begin_layout Standard
4559 For example the command
4564 \begin_inset space \textvisiblespace{}
4572 \begin_layout Standard
4573 \begin_inset Formula $A\dotfill B$
4579 \begin_layout Standard
4586 there is for a line the command
4593 \begin_inset Index idx
4596 \begin_layout Plain Layout
4607 \begin_layout Standard
4608 \begin_inset Formula $A\hrulefill B$
4614 \begin_layout Standard
4615 To use the commands for text, they have to be inserted in \SpecialChar TeX
4619 \begin_layout Section
4621 \begin_inset CommandInset label
4628 \begin_inset Index idx
4631 \begin_layout Plain Layout
4640 \begin_layout Standard
4641 Matrices can be inserted via the math toolbar button
4644 arg "dialog-show mathmatrix"
4649 Insert\SpecialChar menuseparator
4650 Math\SpecialChar menuseparator
4654 In the matrix dialog you can specify the number of columns and rows, the
4655 alignment and the decoration.
4656 The vertical alignment is only of importance for matrices in inline formulas:
4659 \begin_layout Standard
4660 The first matrix is top
4661 \begin_inset Formula $\begin{array}[t]{cccc}
4669 \begin_inset Formula $\begin{array}{cccc}
4676 and the third bottom
4677 \begin_inset Formula $\begin{array}[b]{cccc}
4687 \begin_layout Standard
4688 The horizontal alignment specifies how the column entries should be aligned.
4689 It is set by entering a letter for every column.
4694 denotes left aligned,
4703 To create for example a 4
4708 \begin_inset space ~
4711 matrix where the first column is left aligned, the second and third are
4712 centered and the last one is right aligned, one enters for the horizontal
4718 Normally in a matrix all columns are centered, therefore the default for
4726 \begin_layout Standard
4727 Horizontal alignment:
4730 \begin_layout Standard
4736 \begin_inset Formula $\begin{array}{lll}
4748 \begin_inset Formula $\begin{array}{ccc}
4760 \begin_inset Formula $\begin{array}{rrr}
4770 \begin_layout Standard
4771 To add or delete rows and columns subsequently, the math toolbar buttons
4775 arg "tabular-feature append-row"
4781 arg "tabular-feature delete-row"
4785 \begin_inset space \thinspace{}
4790 Edit\SpecialChar menuseparator
4794 New rows can also be created with
4797 arg "newline-insert newline"
4803 \begin_layout Standard
4804 \begin_inset VSpace bigskip
4808 \change_deleted -563046850 1563190969
4812 \change_inserted -563046850 1563190971
4818 \change_deleted -563046850 1563192602
4820 \change_inserted -563046850 1563192607
4823 parentheses in the selected style around the matrix
4824 \change_inserted -563046850 1563192780
4829 style, suitable for an inline matrix like this one
4830 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
4832 \end{smallmatrix}\bigr)$
4839 \change_inserted -563046850 1563192943
4840 Here the parentheses have been added manually using commands
4853 \begin_layout Standard
4855 \change_deleted -563046850 1563192735
4858 Alternatively, parentheses can can
4859 \change_deleted -563046850 1563192971
4862 be created with the commands
4869 \begin_inset Index idx
4872 \begin_layout Plain Layout
4887 \begin_inset Index idx
4890 \begin_layout Plain Layout
4901 \begin_inset space ~
4907 \begin_inset CommandInset ref
4909 reference "subsec:Automatic-Bracket-Size"
4913 , or by using the following commands:
4914 \begin_inset VSpace medskip
4920 \begin_layout Standard
4921 \begin_inset space \hfill{}
4925 \begin_inset Tabular
4926 <lyxtabular version="3" rows="4" columns="2">
4927 <features booktabs="true" tabularvalignment="middle">
4928 <column alignment="center" valignment="top" width="0pt">
4929 <column alignment="center" valignment="top">
4931 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4934 \begin_layout Plain Layout
4940 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4943 \begin_layout Plain Layout
4950 <row topspace="1.5mm">
4951 <cell alignment="center" valignment="top" usebox="none">
4954 \begin_layout Plain Layout
4958 \begin_inset space \textvisiblespace{}
4966 \begin_inset space \thinspace{}
4974 <cell alignment="center" valignment="top" usebox="none">
4977 \begin_layout Plain Layout
4978 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4979 0 & \textrm{-}\mathrm{i}\\
4981 \end{array}\end{bmatrix}$
4990 <row topspace="1.5mm" bottomspace="0.5mm">
4991 <cell alignment="center" valignment="top" usebox="none">
4994 \begin_layout Plain Layout
4998 \begin_inset space \textvisiblespace{}
5006 \begin_inset space \thinspace{}
5014 <cell alignment="center" valignment="top" usebox="none">
5017 \begin_layout Plain Layout
5018 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5019 0 & \textrm{-}\mathrm{i}\\
5021 \end{array}\end{Bmatrix}$
5031 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5034 \begin_layout Plain Layout
5038 \begin_inset space \textvisiblespace{}
5046 \begin_inset space \thinspace{}
5054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5057 \begin_layout Plain Layout
5058 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5059 0 & \textrm{-}\mathrm{i}\\
5061 \end{array}\end{pmatrix}$
5075 \begin_inset space \hfill{}
5079 \begin_inset Tabular
5080 <lyxtabular version="3" rows="4" columns="2">
5081 <features booktabs="true" tabularvalignment="middle">
5082 <column alignment="center" valignment="top" width="0pt">
5083 <column alignment="center" valignment="top">
5085 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5088 \begin_layout Plain Layout
5094 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5097 \begin_layout Plain Layout
5104 <row topspace="1.5mm">
5105 <cell alignment="center" valignment="top" usebox="none">
5108 \begin_layout Plain Layout
5112 \begin_inset space \textvisiblespace{}
5120 \begin_inset space \thinspace{}
5128 <cell alignment="center" valignment="top" usebox="none">
5131 \begin_layout Plain Layout
5132 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5133 0 & \textrm{-}\mathrm{i}\\
5135 \end{array}\end{vmatrix}$
5144 <row topspace="1.5mm" bottomspace="0.5mm">
5145 <cell alignment="center" valignment="top" usebox="none">
5148 \begin_layout Plain Layout
5152 \begin_inset space \textvisiblespace{}
5160 \begin_inset space \thinspace{}
5168 <cell alignment="center" valignment="top" usebox="none">
5171 \begin_layout Plain Layout
5172 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5173 0 & \textrm{-}\mathrm{i}\\
5175 \end{array}\end{Vmatrix}$
5185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5188 \begin_layout Plain Layout
5192 \begin_inset space \textvisiblespace{}
5200 \begin_inset space \thinspace{}
5208 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5211 \begin_layout Plain Layout
5212 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5213 0 & \textrm{-}\mathrm{i}\\
5215 \end{array}\end{matrix}$
5229 \begin_inset space \hfill{}
5235 \begin_layout Standard
5236 \begin_inset VSpace medskip
5240 \begin_inset space \thinspace{}
5244 \begin_inset space \space{}
5253 is inserted, a blue box appears between two vertical lines where the matrix
5255 \begin_inset Newline newline
5258 Note that decorated matrices ignore the vertical alignment.
5261 \begin_layout Standard
5262 \begin_inset VSpace bigskip
5265 As all multiline formulas are matrices, the length
5272 \begin_inset Index idx
5275 \begin_layout Plain Layout
5283 that is described in
5284 \begin_inset CommandInset ref
5286 reference "subsec:Column-Separation"
5290 can also be used to change the column separation of matrices.
5293 \begin_layout Standard
5294 To change the row separation, the command
5301 \begin_inset Index idx
5304 \begin_layout Plain Layout
5313 It is used as follows:
5316 \begin_layout Standard
5323 arraystretch}{stretch factor}
5324 \begin_inset Index idx
5327 \begin_layout Plain Layout
5338 \begin_layout Standard
5345 assigns the stretch factor to the predefined command
5353 \begin_inset space \thinspace{}
5357 \begin_inset space \space{}
5360 the row separation, use the factor 2.
5361 This is then used for all following matrices.
5362 To go back to the original separation, assign the factor 1 to
5371 \begin_layout Standard
5372 To set matrices into a text line, the command
5379 \begin_inset Index idx
5382 \begin_layout Plain Layout
5391 When it is inserted a blue box with two dashed lines appears.
5392 In this box the matrix is inserted.
5395 \begin_layout Standard
5397 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5399 \end{smallmatrix}\right)$
5405 \begin_layout Section
5406 Brackets and Delimiters
5407 \begin_inset Index idx
5410 \begin_layout Plain Layout
5417 \begin_inset Index idx
5420 \begin_layout Plain Layout
5429 \begin_layout Subsection
5430 Vertical Brackets and Delimiters
5431 \begin_inset Index idx
5434 \begin_layout Plain Layout
5443 \begin_layout Standard
5444 \begin_inset space \hfill{}
5448 \begin_inset Tabular
5449 <lyxtabular version="3" rows="9" columns="2">
5450 <features booktabs="true" tabularvalignment="middle">
5451 <column alignment="center" valignment="top" width="0pt">
5452 <column alignment="center" valignment="top" width="0pt">
5454 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5457 \begin_layout Plain Layout
5463 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5466 \begin_layout Plain Layout
5474 <cell alignment="center" valignment="top" usebox="none">
5477 \begin_layout Plain Layout
5483 <cell alignment="center" valignment="top" usebox="none">
5486 \begin_layout Plain Layout
5487 \begin_inset Formula $($
5497 <cell alignment="center" valignment="top" usebox="none">
5500 \begin_layout Plain Layout
5506 <cell alignment="center" valignment="top" usebox="none">
5509 \begin_layout Plain Layout
5510 \begin_inset Formula $\{$
5520 <cell alignment="center" valignment="top" usebox="none">
5523 \begin_layout Plain Layout
5529 <cell alignment="center" valignment="top" usebox="none">
5532 \begin_layout Plain Layout
5533 \begin_inset Formula $[$
5543 <cell alignment="center" valignment="top" usebox="none">
5546 \begin_layout Plain Layout
5554 <cell alignment="center" valignment="top" usebox="none">
5557 \begin_layout Plain Layout
5558 \begin_inset Formula $\langle$
5568 <cell alignment="center" valignment="top" usebox="none">
5571 \begin_layout Plain Layout
5579 <cell alignment="center" valignment="top" usebox="none">
5582 \begin_layout Plain Layout
5583 \begin_inset Formula $\lceil$
5593 <cell alignment="center" valignment="top" usebox="none">
5596 \begin_layout Plain Layout
5604 <cell alignment="center" valignment="top" usebox="none">
5607 \begin_layout Plain Layout
5608 \begin_inset Formula $\lfloor$
5618 <cell alignment="center" valignment="top" usebox="none">
5621 \begin_layout Plain Layout
5627 <cell alignment="center" valignment="top" usebox="none">
5630 \begin_layout Plain Layout
5631 \begin_inset Formula $/$
5641 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5644 \begin_layout Plain Layout
5650 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5653 \begin_layout Plain Layout
5654 \begin_inset Formula $|$
5668 \begin_inset space \hfill{}
5672 \begin_inset Tabular
5673 <lyxtabular version="3" rows="9" columns="2">
5674 <features booktabs="true" tabularvalignment="middle">
5675 <column alignment="center" valignment="top" width="0pt">
5676 <column alignment="center" valignment="top" width="0pt">
5678 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5681 \begin_layout Plain Layout
5687 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5690 \begin_layout Plain Layout
5698 <cell alignment="center" valignment="top" usebox="none">
5701 \begin_layout Plain Layout
5707 <cell alignment="center" valignment="top" usebox="none">
5710 \begin_layout Plain Layout
5711 \begin_inset Formula $)$
5721 <cell alignment="center" valignment="top" usebox="none">
5724 \begin_layout Plain Layout
5730 <cell alignment="center" valignment="top" usebox="none">
5733 \begin_layout Plain Layout
5734 \begin_inset Formula $\}$
5744 <cell alignment="center" valignment="top" usebox="none">
5747 \begin_layout Plain Layout
5753 <cell alignment="center" valignment="top" usebox="none">
5756 \begin_layout Plain Layout
5757 \begin_inset Formula $]$
5767 <cell alignment="center" valignment="top" usebox="none">
5770 \begin_layout Plain Layout
5778 <cell alignment="center" valignment="top" usebox="none">
5781 \begin_layout Plain Layout
5782 \begin_inset Formula $\rangle$
5792 <cell alignment="center" valignment="top" usebox="none">
5795 \begin_layout Plain Layout
5803 <cell alignment="center" valignment="top" usebox="none">
5806 \begin_layout Plain Layout
5807 \begin_inset Formula $\rceil$
5817 <cell alignment="center" valignment="top" usebox="none">
5820 \begin_layout Plain Layout
5828 <cell alignment="center" valignment="top" usebox="none">
5831 \begin_layout Plain Layout
5832 \begin_inset Formula $\rfloor$
5842 <cell alignment="center" valignment="top" usebox="none">
5845 \begin_layout Plain Layout
5855 <cell alignment="center" valignment="top" usebox="none">
5858 \begin_layout Plain Layout
5859 \begin_inset Formula $\backslash$
5869 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5872 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5883 \begin_layout Plain Layout
5884 \begin_inset Formula $\|$
5898 \begin_inset space \hfill{}
5904 \begin_layout Standard
5907 \begin_inset Note Greyedout
5910 \begin_layout Plain Layout
5923 \begin_inset Index idx
5926 \begin_layout Plain Layout
5934 must be used for the backslash, because the command
5942 produces a line break there.
5950 \begin_layout Standard
5951 For all characters listed above the size can be adjusted with the commands
5952 described in the following two subsections.
5953 When using these commands, the characters < and > can directly be used
5954 instead of the commands
5969 \begin_layout Subsubsection
5971 \begin_inset CommandInset label
5973 name "subsec:Manual-Bracket-Size"
5978 \begin_inset Index idx
5981 \begin_layout Plain Layout
5982 Bracket size ! manual
5990 \begin_layout Standard
5991 The bracket size can be specified manually by the \SpecialChar LaTeX
5999 \begin_inset Index idx
6002 \begin_layout Plain Layout
6035 denotes the smallest and
6041 the largest bracket size.
6044 \begin_layout Standard
6045 These commands are used to emphasize levels of brackets:
6048 \begin_layout Standard
6050 \begin_inset Tabular
6051 <lyxtabular version="3" rows="2" columns="2">
6052 <features booktabs="true" tabularvalignment="middle">
6053 <column alignment="center" valignment="top" width="0pt">
6054 <column alignment="center" valignment="top" width="0pt">
6056 <cell alignment="center" valignment="top" usebox="none">
6059 \begin_layout Plain Layout
6060 all brackets in the same size:
6065 <cell alignment="center" valignment="top" usebox="none">
6068 \begin_layout Plain Layout
6069 \begin_inset Formula $((A+B)(A-B))^{C}$
6078 <row topspace="2mm">
6079 <cell alignment="center" valignment="top" usebox="none">
6082 \begin_layout Plain Layout
6088 <cell alignment="center" valignment="top" usebox="none">
6091 \begin_layout Plain Layout
6092 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6108 \begin_layout Standard
6109 For the second formula the command
6116 \begin_inset space \textvisiblespace{}
6124 \begin_layout Standard
6125 Here is an overview about all bracket sizes:
6128 \begin_layout Standard
6145 \begin_inset space \textvisiblespace{}
6153 \begin_inset space \textvisiblespace{}
6157 \begin_inset space \textvisiblespace{}
6167 \begin_layout Standard
6169 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6175 \begin_layout Standard
6182 -commands there is the variant
6189 \begin_inset Index idx
6192 \begin_layout Plain Layout
6200 that adds a bit more space between the bracket and its content, and the
6214 \begin_inset Index idx
6217 \begin_layout Plain Layout
6227 , that don't add additional space.
6232 at the end of the command
6238 is for a left bracket; for a right bracket this will be replaced by an
6244 A left or right bracket can each be an opening or closing bracket.
6247 \begin_layout Standard
6248 In the following table is a comparison of the variants:
6251 \begin_layout Standard
6253 \begin_inset Tabular
6254 <lyxtabular version="3" rows="5" columns="2">
6255 <features booktabs="true" tabularvalignment="middle">
6256 <column alignment="center" valignment="top" width="0pt">
6257 <column alignment="center" valignment="middle">
6259 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6262 \begin_layout Plain Layout
6268 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6271 \begin_layout Plain Layout
6278 <row topspace="2mm">
6279 <cell alignment="center" valignment="top" usebox="none">
6282 \begin_layout Plain Layout
6292 \begin_inset space \textvisiblespace{}
6302 <cell alignment="center" valignment="top" usebox="none">
6305 \begin_layout Plain Layout
6306 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6315 <row topspace="2mm">
6316 <cell alignment="center" valignment="top" usebox="none">
6319 \begin_layout Plain Layout
6329 \begin_inset space \textvisiblespace{}
6339 <cell alignment="center" valignment="top" usebox="none">
6342 \begin_layout Plain Layout
6343 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6352 <row topspace="2mm" bottomspace="0.5mm">
6353 <cell alignment="center" valignment="top" usebox="none">
6356 \begin_layout Plain Layout
6366 \begin_inset space \textvisiblespace{}
6376 <cell alignment="center" valignment="top" usebox="none">
6379 \begin_layout Plain Layout
6380 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6389 <row topspace="1.5mm" bottomspace="0.5mm">
6390 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6393 \begin_layout Plain Layout
6405 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6425 \begin_layout Subsubsection
6426 Automatic Bracket Size
6427 \begin_inset CommandInset label
6429 name "subsec:Automatic-Bracket-Size"
6434 \begin_inset Index idx
6437 \begin_layout Plain Layout
6438 Bracket size ! automatic
6446 \begin_layout Standard
6447 Brackets with variable size can be inserted with the commands
6454 \begin_inset Index idx
6457 \begin_layout Plain Layout
6472 \begin_inset Index idx
6475 \begin_layout Plain Layout
6483 or via the math toolbar button
6486 arg "dialog-show mathdelimiter"
6502 the wanted bracket must be inserted.
6503 The bracket size will then automatically be calculated for the output.
6506 \begin_layout Standard
6508 normal bracket: The command
6515 \begin_inset space \textvisiblespace{}
6519 \begin_inset Formula $\downarrow$
6523 \begin_inset space \textvisiblespace{}
6529 \begin_inset Formula
6539 \begin_layout Standard
6541 multiline bracket: The command
6550 \begin_inset space \textvisiblespace{}
6554 \begin_inset Formula $\downarrow$
6558 \begin_inset space \textvisiblespace{}
6566 \begin_inset Formula
6568 \ln\left(\frac{A}{C}\right)
6576 \begin_layout Standard
6592 \begin_inset space ~
6598 This has the advantage that you can see in \SpecialChar LyX
6599 immediately the real bracket
6600 size and that the matching right bracket will be created too.
6601 \begin_inset Newline newline
6604 The command for the last example would then be:
6615 \begin_inset space \textvisiblespace{}
6619 \begin_inset Formula $\downarrow$
6625 \begin_layout Standard
6626 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6627 For example the command
6634 \begin_inset space \textvisiblespace{}
6638 \begin_inset Formula $\downarrow$
6642 \begin_inset space \textvisiblespace{}
6652 \begin_inset Formula
6654 \left.\frac{A}{B}\right\}
6673 will be converted by \SpecialChar LyX
6674 to brackets in the right size when the document is
6675 reloaded and an omitted bracket will appear as dashed line.
6678 \begin_layout Standard
6679 \begin_inset VSpace bigskip
6682 Because all popular \SpecialChar LaTeX
6683 distributions use e\SpecialChar TeX
6684 , an extension to \SpecialChar LaTeX
6693 \begin_inset Index idx
6696 \begin_layout Plain Layout
6704 is additionally available for all brackets and limits.
6705 With this command the height of the following character is adapted to the
6706 one of the surrounding brackets, what is e.
6707 \begin_inset space \thinspace{}
6711 \begin_inset space \space{}
6714 needed for physical vectors:
6715 \begin_inset Formula
6717 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6722 For physical vectors there is a special \SpecialChar LaTeX
6723 -package, described in
6724 \begin_inset CommandInset ref
6726 reference "subsec:Physical-Vectors"
6733 \begin_layout Subsection
6735 \begin_inset Index idx
6738 \begin_layout Plain Layout
6739 Brackets ! horizontal
6747 \begin_layout Standard
6749 \begin_inset Tabular
6750 <lyxtabular version="3" rows="4" columns="2">
6751 <features booktabs="true" tabularvalignment="middle">
6752 <column alignment="center" valignment="top" width="0pt">
6753 <column alignment="center" valignment="top" width="0pt">
6755 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6758 \begin_layout Plain Layout
6764 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6767 \begin_layout Plain Layout
6775 <cell alignment="center" valignment="top" usebox="none">
6778 \begin_layout Plain Layout
6782 \begin_inset space \textvisiblespace{}
6786 \begin_inset space \textvisiblespace{}
6790 \begin_inset Index idx
6793 \begin_layout Plain Layout
6806 <cell alignment="center" valignment="top" usebox="none">
6809 \begin_layout Plain Layout
6810 \begin_inset Formula $\overbrace{A+B}^{3}$
6819 <row topspace="2mm">
6820 <cell alignment="center" valignment="top" usebox="none">
6823 \begin_layout Plain Layout
6827 \begin_inset space \textvisiblespace{}
6831 \begin_inset space \textvisiblespace{}
6835 \begin_inset Index idx
6838 \begin_layout Plain Layout
6851 <cell alignment="center" valignment="top" usebox="none">
6854 \begin_layout Plain Layout
6855 \begin_inset Formula $\underbrace{A+B}_{5}$
6865 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6868 \begin_layout Plain Layout
6872 \begin_inset space \textvisiblespace{}
6878 \begin_inset space \textvisiblespace{}
6882 \begin_inset space \textvisiblespace{}
6886 \begin_inset space \textvisiblespace{}
6890 \begin_inset space \textvisiblespace{}
6894 \begin_inset space \textvisiblespace{}
6898 \begin_inset space \textvisiblespace{}
6906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6909 \begin_layout Plain Layout
6910 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6926 \begin_layout Standard
6927 In the last example it doesn't matter if
6939 is inserted at first.
6942 \begin_layout Standard
6943 \begin_inset VSpace medskip
6949 \begin_layout Standard
6950 If you set in the document settings under
6953 \begin_inset space ~
6963 \begin_inset Index idx
6966 \begin_layout Plain Layout
6967 Packages ! mathtools
6975 \begin_inset space ~
6980 , you have access to square backets:
6983 \begin_layout Standard
6985 \begin_inset Tabular
6986 <lyxtabular version="3" rows="4" columns="2">
6987 <features booktabs="true" tabularvalignment="middle">
6988 <column alignment="center" valignment="top" width="0pt">
6989 <column alignment="center" valignment="top" width="0pt">
6991 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6994 \begin_layout Plain Layout
7000 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7003 \begin_layout Plain Layout
7011 <cell alignment="center" valignment="top" usebox="none">
7014 \begin_layout Plain Layout
7042 \begin_inset space \textvisiblespace{}
7046 \begin_inset Index idx
7049 \begin_layout Plain Layout
7062 <cell alignment="center" valignment="top" usebox="none">
7065 \begin_layout Plain Layout
7066 \begin_inset Formula $\overbracket{A+B}^{3}$
7075 <row topspace="2mm">
7076 <cell alignment="center" valignment="top" usebox="none">
7079 \begin_layout Plain Layout
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset Index idx
7114 \begin_layout Plain Layout
7139 <cell alignment="center" valignment="top" usebox="none">
7142 \begin_layout Plain Layout
7143 \begin_inset Formula $\underbracket{A+B}_{5}$
7153 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7156 \begin_layout Plain Layout
7162 \begin_inset space \textvisiblespace{}
7166 \begin_inset space \textvisiblespace{}
7170 \begin_inset space \textvisiblespace{}
7174 \begin_inset space \textvisiblespace{}
7178 \begin_inset space \textvisiblespace{}
7186 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7189 \begin_layout Plain Layout
7190 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7206 \begin_layout Standard
7219 you can change the thickness of the bracket's stroke by specifying the
7220 desired thickness in square brackets behind the command:
7223 \begin_layout Standard
7225 \begin_inset Tabular
7226 <lyxtabular version="3" rows="3" columns="2">
7227 <features booktabs="true" tabularvalignment="middle">
7228 <column alignment="center" valignment="top" width="0pt">
7229 <column alignment="center" valignment="top" width="0pt">
7231 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7234 \begin_layout Plain Layout
7240 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7243 \begin_layout Plain Layout
7251 <cell alignment="center" valignment="top" usebox="none">
7254 \begin_layout Plain Layout
7284 \begin_inset space \textvisiblespace{}
7292 <cell alignment="center" valignment="top" usebox="none">
7295 \begin_layout Plain Layout
7296 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7305 <row topspace="2mm">
7306 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7309 \begin_layout Plain Layout
7339 \begin_inset space \textvisiblespace{}
7347 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7350 \begin_layout Plain Layout
7351 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7367 \begin_layout Standard
7368 \begin_inset VSpace bigskip
7371 When brackets should overlap each other, multiline formulas, as described
7373 \begin_inset CommandInset ref
7375 reference "sec:Multiline-Formulas"
7380 \begin_inset Formula
7382 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7383 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7388 In the first row the formula is inserted together with the first brace.
7389 It is hereby important that the space command
7393 \begin_layout Plain Layout
7394 Space commands are explained in
7395 \begin_inset CommandInset ref
7397 reference "subsec:Predefined-Space"
7412 is inserted before the first
7413 \begin_inset Formula $d$
7416 , because the brace that ends behind the
7417 \begin_inset Formula $q$
7420 prevents that the following
7421 \begin_inset Quotes eld
7425 \begin_inset Quotes erd
7428 is surrounded by space.
7432 \begin_layout Plain Layout
7433 because a bracket is not handled as a character, see
7434 \begin_inset CommandInset ref
7436 reference "subsec:Binary-Operators"
7445 In the second row the second brace is inserted.
7446 As it should begin before the
7447 \begin_inset Formula $b$
7462 \begin_layout Plain Layout
7470 \begin_inset CommandInset ref
7472 reference "subsec:Placeholders"
7481 This space is needed because the
7482 \begin_inset Quotes eld
7486 \begin_inset Quotes erd
7489 is also surrounded by space in the formula.
7490 The brace is placed under the command
7499 \begin_layout Standard
7500 It gets more complicated when brackets overlap each other above and under
7501 the formula, like in the following example:
7505 \begin_layout Plain Layout
7517 \begin_inset Formula
7519 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7520 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7529 \begin_layout Plain Layout
7540 The first formula row is the same as the second row of the previous example,
7541 with the difference that the brace is above.
7542 The second row contains the formula together with the second brace.
7543 To avoid that there is space between the upper brace in the first row and
7544 the formula, the row spacing needs to be reduced.
7545 This is not easily possible due to a bug in \SpecialChar LyX
7550 \begin_layout Plain Layout
7551 \begin_inset CommandInset href
7553 name "LyX-bug #1505"
7554 target "https://www.lyx.org/trac/ticket/1505"
7564 As a solution for the problem, the global formula row separation
7571 \begin_inset Index idx
7574 \begin_layout Plain Layout
7582 must be changed to -6
7583 \begin_inset space \thinspace{}
7586 pt before the formula with the command
7602 is set back after the formula to the standard value of 3
7603 \begin_inset space \thinspace{}
7606 pt using the same command.
7607 More about the row separation in formulas is explained in
7608 \begin_inset CommandInset ref
7610 reference "subsec:Line-Separation"
7617 \begin_layout Section
7619 \begin_inset Index idx
7622 \begin_layout Plain Layout
7631 \begin_layout Standard
7632 Arrows can be inserted via the math toolbar button
7635 arg "math-insert \\leftarrow"
7638 or the commands listed in the following subsections.
7641 \begin_layout Subsection
7643 \begin_inset Index idx
7646 \begin_layout Plain Layout
7655 \begin_layout Standard
7656 \begin_inset space \hfill{}
7660 \begin_inset Tabular
7661 <lyxtabular version="3" rows="8" columns="2">
7662 <features booktabs="true" tabularvalignment="middle">
7663 <column alignment="center" valignment="top" width="0pt">
7664 <column alignment="center" valignment="top" width="0pt">
7666 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7669 \begin_layout Plain Layout
7675 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7678 \begin_layout Plain Layout
7686 <cell alignment="center" valignment="top" usebox="none">
7689 \begin_layout Plain Layout
7697 <cell alignment="center" valignment="top" usebox="none">
7700 \begin_layout Plain Layout
7701 \begin_inset Formula $\gets$
7711 <cell alignment="center" valignment="top" usebox="none">
7714 \begin_layout Plain Layout
7722 <cell alignment="center" valignment="top" usebox="none">
7725 \begin_layout Plain Layout
7726 \begin_inset Formula $\Leftarrow$
7736 <cell alignment="center" valignment="top" usebox="none">
7739 \begin_layout Plain Layout
7747 <cell alignment="center" valignment="top" usebox="none">
7750 \begin_layout Plain Layout
7751 \begin_inset Formula $\longleftarrow$
7761 <cell alignment="center" valignment="top" usebox="none">
7764 \begin_layout Plain Layout
7772 <cell alignment="center" valignment="top" usebox="none">
7775 \begin_layout Plain Layout
7776 \begin_inset Formula $\Longleftarrow$
7786 <cell alignment="center" valignment="top" usebox="none">
7789 \begin_layout Plain Layout
7797 <cell alignment="center" valignment="top" usebox="none">
7800 \begin_layout Plain Layout
7801 \begin_inset Formula $\leftharpoonup$
7811 <cell alignment="center" valignment="top" usebox="none">
7814 \begin_layout Plain Layout
7822 <cell alignment="center" valignment="top" usebox="none">
7825 \begin_layout Plain Layout
7826 \begin_inset Formula $\leftharpoondown$
7836 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7839 \begin_layout Plain Layout
7847 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7850 \begin_layout Plain Layout
7851 \begin_inset Formula $\hookleftarrow$
7865 \begin_inset space \hfill{}
7869 \begin_inset Tabular
7870 <lyxtabular version="3" rows="8" columns="2">
7871 <features booktabs="true" tabularvalignment="middle">
7872 <column alignment="center" valignment="top" width="0pt">
7873 <column alignment="center" valignment="top" width="0pt">
7875 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7878 \begin_layout Plain Layout
7884 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7887 \begin_layout Plain Layout
7895 <cell alignment="center" valignment="top" usebox="none">
7898 \begin_layout Plain Layout
7906 <cell alignment="center" valignment="top" usebox="none">
7909 \begin_layout Plain Layout
7910 \begin_inset Formula $\to$
7920 <cell alignment="center" valignment="top" usebox="none">
7923 \begin_layout Plain Layout
7931 <cell alignment="center" valignment="top" usebox="none">
7934 \begin_layout Plain Layout
7935 \begin_inset Formula $\Rightarrow$
7945 <cell alignment="center" valignment="top" usebox="none">
7948 \begin_layout Plain Layout
7956 <cell alignment="center" valignment="top" usebox="none">
7959 \begin_layout Plain Layout
7960 \begin_inset Formula $\longrightarrow$
7970 <cell alignment="center" valignment="top" usebox="none">
7973 \begin_layout Plain Layout
7981 <cell alignment="center" valignment="top" usebox="none">
7984 \begin_layout Plain Layout
7985 \begin_inset Formula $\Longrightarrow$
7995 <cell alignment="center" valignment="top" usebox="none">
7998 \begin_layout Plain Layout
8006 <cell alignment="center" valignment="top" usebox="none">
8009 \begin_layout Plain Layout
8010 \begin_inset Formula $\rightharpoonup$
8020 <cell alignment="center" valignment="top" usebox="none">
8023 \begin_layout Plain Layout
8031 <cell alignment="center" valignment="top" usebox="none">
8034 \begin_layout Plain Layout
8035 \begin_inset Formula $\rightharpoondown$
8045 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8048 \begin_layout Plain Layout
8056 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8059 \begin_layout Plain Layout
8060 \begin_inset Formula $\hookrightarrow$
8074 \begin_inset space \hfill{}
8080 \begin_layout Standard
8081 \begin_inset space \hfill{}
8085 \begin_inset Tabular
8086 <lyxtabular version="3" rows="6" columns="2">
8087 <features booktabs="true" tabularvalignment="middle">
8088 <column alignment="center" valignment="top" width="0pt">
8089 <column alignment="center" valignment="top" width="0pt">
8091 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8094 \begin_layout Plain Layout
8100 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8103 \begin_layout Plain Layout
8111 <cell alignment="center" valignment="top" usebox="none">
8114 \begin_layout Plain Layout
8122 <cell alignment="center" valignment="top" usebox="none">
8125 \begin_layout Plain Layout
8126 \begin_inset Formula $\leftrightarrow$
8136 <cell alignment="center" valignment="top" usebox="none">
8139 \begin_layout Plain Layout
8147 <cell alignment="center" valignment="top" usebox="none">
8150 \begin_layout Plain Layout
8151 \begin_inset Formula $\Leftrightarrow$
8161 <cell alignment="center" valignment="top" usebox="none">
8164 \begin_layout Plain Layout
8172 <cell alignment="center" valignment="top" usebox="none">
8175 \begin_layout Plain Layout
8176 \begin_inset Formula $\longleftrightarrow$
8186 <cell alignment="center" valignment="top" usebox="none">
8189 \begin_layout Plain Layout
8197 <cell alignment="center" valignment="top" usebox="none">
8200 \begin_layout Plain Layout
8201 \begin_inset Formula $\Longleftrightarrow$
8211 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8214 \begin_layout Plain Layout
8222 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8225 \begin_layout Plain Layout
8226 \begin_inset Formula $\rightleftharpoons$
8240 \begin_inset space \hspace{}
8245 \begin_inset space \hfill{}
8249 \begin_inset Tabular
8250 <lyxtabular version="3" rows="5" columns="2">
8251 <features booktabs="true" tabularvalignment="middle">
8252 <column alignment="center" valignment="top" width="0pt">
8253 <column alignment="center" valignment="top" width="0pt">
8255 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8258 \begin_layout Plain Layout
8264 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8267 \begin_layout Plain Layout
8275 <cell alignment="center" valignment="top" usebox="none">
8278 \begin_layout Plain Layout
8286 <cell alignment="center" valignment="top" usebox="none">
8289 \begin_layout Plain Layout
8290 \begin_inset Formula $\mapsto$
8300 <cell alignment="center" valignment="top" usebox="none">
8303 \begin_layout Plain Layout
8311 <cell alignment="center" valignment="top" usebox="none">
8314 \begin_layout Plain Layout
8315 \begin_inset Formula $\longmapsto$
8325 <cell alignment="center" valignment="top" usebox="none">
8328 \begin_layout Plain Layout
8336 <cell alignment="center" valignment="top" usebox="none">
8339 \begin_layout Plain Layout
8340 \begin_inset Formula $\leadsto$
8350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8353 \begin_layout Plain Layout
8361 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8364 \begin_layout Plain Layout
8365 \begin_inset Formula $\dasharrow$
8379 \begin_inset space \hfill{}
8385 \begin_layout Standard
8386 \begin_inset VSpace medskip
8389 Arrows used as accents like e.
8390 \begin_inset space \thinspace{}
8394 \begin_inset space \space{}
8397 vector arrows are listed in
8398 \begin_inset CommandInset ref
8400 reference "sec:Accents"
8407 \begin_layout Standard
8408 \begin_inset VSpace bigskip
8411 Furthermore there are the labeled arrows
8412 \begin_inset Index idx
8415 \begin_layout Plain Layout
8428 \begin_inset Index idx
8431 \begin_layout Plain Layout
8446 \begin_inset Index idx
8449 \begin_layout Plain Layout
8456 \begin_layout Plain Layout
8471 When inserting one of these commands in a formula, an arrow with two blue
8472 boxes appear where the label can be inserted.
8473 The length of the arrow adapts to the label width.
8476 \begin_layout Standard
8478 \begin_inset Tabular
8479 <lyxtabular version="3" rows="3" columns="2">
8480 <features booktabs="true" tabularvalignment="middle">
8481 <column alignment="center" valignment="top" width="0pt">
8482 <column alignment="center" valignment="top" width="0pt">
8484 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8487 \begin_layout Plain Layout
8493 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8496 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" usebox="none">
8507 \begin_layout Plain Layout
8511 \begin_inset space \textvisiblespace{}
8515 \begin_inset Formula $\downarrow$
8519 \begin_inset Formula $\to$
8527 <cell alignment="center" valignment="top" usebox="none">
8530 \begin_layout Plain Layout
8531 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8540 <row topspace="2mm">
8541 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8544 \begin_layout Plain Layout
8548 \begin_inset space \textvisiblespace{}
8552 \begin_inset Formula $\downarrow$
8556 \begin_inset Formula $\to$
8564 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8567 \begin_layout Plain Layout
8568 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8584 \begin_layout Standard
8585 \begin_inset VSpace medskip
8591 \begin_layout Standard
8592 If you set in the document settings under
8595 \begin_inset space ~
8605 \begin_inset Index idx
8608 \begin_layout Plain Layout
8609 Packages ! mathtools
8617 \begin_inset space ~
8622 , you have access to the following labeled arrows:
8625 \begin_layout Standard
8626 \begin_inset Newpage newpage
8632 \begin_layout Standard
8634 \begin_inset space \hspace*{\fill}
8638 \begin_inset Tabular
8639 <lyxtabular version="3" rows="7" columns="2">
8640 <features booktabs="true" tabularvalignment="middle">
8641 <column alignment="center" valignment="top" width="0pt">
8642 <column alignment="center" valignment="top" width="0pt">
8644 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8647 \begin_layout Plain Layout
8653 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8656 \begin_layout Plain Layout
8664 <cell alignment="center" valignment="top" usebox="none">
8667 \begin_layout Plain Layout
8687 <cell alignment="center" valignment="top" usebox="none">
8690 \begin_layout Plain Layout
8691 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8700 <row topspace="2mm">
8701 <cell alignment="center" valignment="top" usebox="none">
8704 \begin_layout Plain Layout
8724 <cell alignment="center" valignment="top" usebox="none">
8727 \begin_layout Plain Layout
8728 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8737 <row topspace="2mm">
8738 <cell alignment="center" valignment="top" usebox="none">
8741 \begin_layout Plain Layout
8761 <cell alignment="center" valignment="top" usebox="none">
8764 \begin_layout Plain Layout
8765 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8774 <row topspace="2mm">
8775 <cell alignment="center" valignment="top" usebox="none">
8778 \begin_layout Plain Layout
8798 <cell alignment="center" valignment="top" usebox="none">
8801 \begin_layout Plain Layout
8802 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8811 <row topspace="2mm">
8812 <cell alignment="center" valignment="top" usebox="none">
8815 \begin_layout Plain Layout
8835 <cell alignment="center" valignment="top" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8848 <row topspace="2mm">
8849 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8852 \begin_layout Plain Layout
8872 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8875 \begin_layout Plain Layout
8876 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8890 \begin_inset space \hspace*{\fill}
8894 \begin_inset Tabular
8895 <lyxtabular version="3" rows="7" columns="2">
8896 <features booktabs="true" tabularvalignment="middle">
8897 <column alignment="center" valignment="top" width="0pt">
8898 <column alignment="center" valignment="top" width="0pt">
8900 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8903 \begin_layout Plain Layout
8909 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8912 \begin_layout Plain Layout
8920 <cell alignment="center" valignment="top" usebox="none">
8923 \begin_layout Plain Layout
8943 <cell alignment="center" valignment="top" usebox="none">
8946 \begin_layout Plain Layout
8947 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8956 <row topspace="2mm">
8957 <cell alignment="center" valignment="top" usebox="none">
8960 \begin_layout Plain Layout
8980 <cell alignment="center" valignment="top" usebox="none">
8983 \begin_layout Plain Layout
8984 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8993 <row topspace="2mm">
8994 <cell alignment="center" valignment="top" usebox="none">
8997 \begin_layout Plain Layout
9017 <cell alignment="center" valignment="top" usebox="none">
9020 \begin_layout Plain Layout
9021 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9030 <row topspace="2mm">
9031 <cell alignment="center" valignment="top" usebox="none">
9034 \begin_layout Plain Layout
9054 <cell alignment="center" valignment="top" usebox="none">
9057 \begin_layout Plain Layout
9058 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9067 <row topspace="2mm">
9068 <cell alignment="center" valignment="top" usebox="none">
9071 \begin_layout Plain Layout
9091 <cell alignment="center" valignment="top" usebox="none">
9094 \begin_layout Plain Layout
9095 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9104 <row topspace="2mm">
9105 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9108 \begin_layout Plain Layout
9128 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9131 \begin_layout Plain Layout
9132 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9146 \begin_inset space \hspace*{\fill}
9152 \begin_layout Standard
9153 The command scheme is for all these arrows:
9156 \begin_layout Standard
9158 \begin_inset Tabular
9159 <lyxtabular version="3" rows="2" columns="2">
9160 <features booktabs="true" tabularvalignment="middle">
9161 <column alignment="center" valignment="top" width="0pt">
9162 <column alignment="center" valignment="top" width="0pt">
9164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9167 \begin_layout Plain Layout
9173 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9176 \begin_layout Plain Layout
9183 <row bottomspace="0.5mm">
9184 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9187 \begin_layout Plain Layout
9190 xleftrightarrow[x=a]
9193 \begin_inset Formula $\to$
9201 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9204 \begin_layout Plain Layout
9205 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9221 \begin_layout Subsection
9222 Vertical and diagonal Arrows
9223 \begin_inset Index idx
9226 \begin_layout Plain Layout
9233 \begin_inset Index idx
9236 \begin_layout Plain Layout
9245 \begin_layout Standard
9246 \begin_inset space \hfill{}
9250 \begin_inset Tabular
9251 <lyxtabular version="3" rows="7" columns="2">
9252 <features booktabs="true" tabularvalignment="middle">
9253 <column alignment="center" valignment="top" width="0pt">
9254 <column alignment="center" valignment="top" width="0pt">
9256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9259 \begin_layout Plain Layout
9265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9268 \begin_layout Plain Layout
9276 <cell alignment="center" valignment="top" usebox="none">
9279 \begin_layout Plain Layout
9287 <cell alignment="center" valignment="top" usebox="none">
9290 \begin_layout Plain Layout
9291 \begin_inset Formula $\uparrow$
9301 <cell alignment="center" valignment="top" usebox="none">
9304 \begin_layout Plain Layout
9312 <cell alignment="center" valignment="top" usebox="none">
9315 \begin_layout Plain Layout
9316 \begin_inset Formula $\Uparrow$
9326 <cell alignment="center" valignment="top" usebox="none">
9329 \begin_layout Plain Layout
9337 <cell alignment="center" valignment="top" usebox="none">
9340 \begin_layout Plain Layout
9341 \begin_inset Formula $\updownarrow$
9351 <cell alignment="center" valignment="top" usebox="none">
9354 \begin_layout Plain Layout
9362 <cell alignment="center" valignment="top" usebox="none">
9365 \begin_layout Plain Layout
9366 \begin_inset Formula $\Updownarrow$
9376 <cell alignment="center" valignment="top" usebox="none">
9379 \begin_layout Plain Layout
9387 <cell alignment="center" valignment="top" usebox="none">
9390 \begin_layout Plain Layout
9391 \begin_inset Formula $\Downarrow$
9401 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9404 \begin_layout Plain Layout
9412 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9415 \begin_layout Plain Layout
9416 \begin_inset Formula $\downarrow$
9430 \begin_inset space \hfill{}
9434 \begin_inset Tabular
9435 <lyxtabular version="3" rows="5" columns="2">
9436 <features booktabs="true" tabularvalignment="middle">
9437 <column alignment="center" valignment="top" width="0pt">
9438 <column alignment="center" valignment="top" width="0pt">
9440 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9443 \begin_layout Plain Layout
9449 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9452 \begin_layout Plain Layout
9460 <cell alignment="center" valignment="top" usebox="none">
9463 \begin_layout Plain Layout
9471 <cell alignment="center" valignment="top" usebox="none">
9474 \begin_layout Plain Layout
9475 \begin_inset Formula $\nearrow$
9485 <cell alignment="center" valignment="top" usebox="none">
9488 \begin_layout Plain Layout
9496 <cell alignment="center" valignment="top" usebox="none">
9499 \begin_layout Plain Layout
9500 \begin_inset Formula $\searrow$
9510 <cell alignment="center" valignment="top" usebox="none">
9513 \begin_layout Plain Layout
9521 <cell alignment="center" valignment="top" usebox="none">
9524 \begin_layout Plain Layout
9525 \begin_inset Formula $\swarrow$
9535 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9538 \begin_layout Plain Layout
9546 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9549 \begin_layout Plain Layout
9550 \begin_inset Formula $\nwarrow$
9564 \begin_inset space \hfill{}
9570 \begin_layout Standard
9571 \begin_inset VSpace medskip
9574 Vertical arrows can be used also as delimiters together with the commands
9576 \begin_inset CommandInset ref
9578 reference "subsec:Manual-Bracket-Size"
9583 \begin_inset CommandInset ref
9585 reference "subsec:Automatic-Bracket-Size"
9592 \begin_layout Section
9594 \begin_inset CommandInset label
9601 \begin_inset Index idx
9604 \begin_layout Plain Layout
9613 \begin_layout Standard
9614 Accents can be inserted via the math toolbar button
9617 arg "math-insert \\hat"
9620 or the commands listed in the following subsections.
9623 \begin_layout Subsection
9624 Accents for one Character
9628 \begin_layout Plain Layout
9641 \begin_layout Plain Layout
9643 \begin_inset CommandInset ref
9645 reference "subsec:Accents-in-Text"
9658 \begin_layout Plain Layout
9666 \begin_inset Note Note
9669 \begin_layout Plain Layout
9676 is used to avoid that the footnote appears in the PDF-bookmark.
9679 \begin_layout Plain Layout
9687 \begin_inset CommandInset ref
9689 reference "subsec:Formulas-in-Section"
9699 \begin_inset CommandInset label
9701 name "subsec:Accents-for-one"
9706 \begin_inset Index idx
9709 \begin_layout Plain Layout
9710 Accents ! for one character
9718 \begin_layout Standard
9719 \begin_inset space \hfill{}
9723 \begin_inset Tabular
9724 <lyxtabular version="3" rows="8" columns="2">
9725 <features booktabs="true" tabularvalignment="middle">
9726 <column alignment="center" valignment="top" width="0pt">
9727 <column alignment="center" valignment="top" width="0pt">
9729 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9732 \begin_layout Plain Layout
9738 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9741 \begin_layout Plain Layout
9748 <row topspace="1.5mm">
9749 <cell alignment="center" valignment="top" usebox="none">
9752 \begin_layout Plain Layout
9756 \begin_inset space \textvisiblespace{}
9764 <cell alignment="center" valignment="top" usebox="none">
9767 \begin_layout Plain Layout
9768 \begin_inset Formula $\dot{A}$
9777 <row topspace="1.5mm">
9778 <cell alignment="center" valignment="top" usebox="none">
9781 \begin_layout Plain Layout
9785 \begin_inset space \textvisiblespace{}
9793 <cell alignment="center" valignment="top" usebox="none">
9796 \begin_layout Plain Layout
9797 \begin_inset Formula $\ddot{A}$
9806 <row topspace="1.5mm">
9807 <cell alignment="center" valignment="top" usebox="none">
9810 \begin_layout Plain Layout
9814 \begin_inset space \textvisiblespace{}
9822 <cell alignment="center" valignment="top" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\dddot{A}$
9835 <row topspace="1.5mm">
9836 <cell alignment="center" valignment="top" usebox="none">
9839 \begin_layout Plain Layout
9843 \begin_inset space \textvisiblespace{}
9851 <cell alignment="center" valignment="top" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\ddddot{A}$
9864 <row topspace="1.5mm">
9865 <cell alignment="center" valignment="top" usebox="none">
9868 \begin_layout Plain Layout
9872 \begin_inset space \textvisiblespace{}
9876 \begin_inset Index idx
9879 \begin_layout Plain Layout
9890 <cell alignment="center" valignment="top" usebox="none">
9893 \begin_layout Plain Layout
9894 \begin_inset Formula $\vec{A}$
9903 <row topspace="1.5mm">
9904 <cell alignment="center" valignment="top" usebox="none">
9907 \begin_layout Plain Layout
9911 \begin_inset space \textvisiblespace{}
9919 <cell alignment="center" valignment="top" usebox="none">
9922 \begin_layout Plain Layout
9923 \begin_inset Formula $\bar{A}$
9932 <row topspace="1.5mm">
9933 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9936 \begin_layout Plain Layout
9940 \begin_inset space \textvisiblespace{}
9948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9951 \begin_layout Plain Layout
9952 \begin_inset Formula $\mathring{A}$
9966 \begin_inset space \hfill{}
9970 \begin_inset Tabular
9971 <lyxtabular version="3" rows="7" columns="2">
9972 <features booktabs="true" tabularvalignment="middle">
9973 <column alignment="center" valignment="top" width="0pt">
9974 <column alignment="center" valignment="top" width="0pt">
9976 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9979 \begin_layout Plain Layout
9985 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9988 \begin_layout Plain Layout
9995 <row topspace="1.5mm">
9996 <cell alignment="center" valignment="top" usebox="none">
9999 \begin_layout Plain Layout
10003 \begin_inset space \textvisiblespace{}
10011 <cell alignment="center" valignment="top" usebox="none">
10014 \begin_layout Plain Layout
10015 \begin_inset Formula $\tilde{A}$
10024 <row topspace="1.5mm">
10025 <cell alignment="center" valignment="top" usebox="none">
10028 \begin_layout Plain Layout
10032 \begin_inset space \textvisiblespace{}
10040 <cell alignment="center" valignment="top" usebox="none">
10043 \begin_layout Plain Layout
10044 \begin_inset Formula $\hat{A}$
10053 <row topspace="1.5mm">
10054 <cell alignment="center" valignment="top" usebox="none">
10057 \begin_layout Plain Layout
10061 \begin_inset space \textvisiblespace{}
10069 <cell alignment="center" valignment="top" usebox="none">
10072 \begin_layout Plain Layout
10073 \begin_inset Formula $\check{A}$
10082 <row topspace="1.5mm">
10083 <cell alignment="center" valignment="top" usebox="none">
10086 \begin_layout Plain Layout
10090 \begin_inset space \textvisiblespace{}
10098 <cell alignment="center" valignment="top" usebox="none">
10101 \begin_layout Plain Layout
10102 \begin_inset Formula $\acute{A}$
10111 <row topspace="1.5mm">
10112 <cell alignment="center" valignment="top" usebox="none">
10115 \begin_layout Plain Layout
10119 \begin_inset space \textvisiblespace{}
10127 <cell alignment="center" valignment="top" usebox="none">
10130 \begin_layout Plain Layout
10131 \begin_inset Formula $\grave{A}$
10140 <row topspace="1.5mm">
10141 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10144 \begin_layout Plain Layout
10148 \begin_inset space \textvisiblespace{}
10156 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10159 \begin_layout Plain Layout
10160 \begin_inset Formula $\breve{A}$
10174 \begin_inset space \hfill{}
10180 \begin_layout Standard
10181 \begin_inset VSpace bigskip
10187 \begin_layout Standard
10188 You can directly insert accents like é to formulas.
10190 will transform them to the corresponding accent command.
10192 \begin_inset Index idx
10195 \begin_layout Plain Layout
10201 it is better to insert a quotation mark before the vowel.
10202 These two characters are then treated by \SpecialChar LaTeX
10207 character when the formula part with the umlaut is marked as German.
10215 \begin_inset Quotes eld
10219 \begin_inset Quotes erd
10222 umlauts are created as demonstrated in the following example:
10225 \begin_layout Standard
10226 \begin_inset VSpace -2mm
10232 \begin_layout Standard
10234 \begin_inset Tabular
10235 <lyxtabular version="3" rows="3" columns="2">
10236 <features booktabs="true" tabularvalignment="middle">
10237 <column alignment="center" valignment="top" width="0pt">
10238 <column alignment="center" valignment="top">
10240 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10243 \begin_layout Plain Layout
10249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10252 \begin_layout Plain Layout
10260 <cell alignment="center" valignment="top" usebox="none">
10263 \begin_layout Plain Layout
10264 \begin_inset Quotes grd
10272 <cell alignment="center" valignment="top" usebox="none">
10275 \begin_layout Plain Layout
10276 \begin_inset space \hspace{}
10283 \begin_inset Formula $"i$
10292 <row topspace="1.5mm">
10293 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10296 \begin_layout Plain Layout
10300 \begin_inset space \textvisiblespace{}
10308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10311 \begin_layout Plain Layout
10312 \begin_inset Formula $\ddot{i}$
10328 \begin_layout Standard
10329 Another advantage to
10335 is that umlauts can directly be converted to mathematical text because
10336 the accent commands above are
10342 in mathematical text
10345 To convert an accented character to mathematical text, only the character
10346 under the accent may be converted.
10347 This applies also for all other conversions, e.
10348 \begin_inset space \thinspace{}
10352 \begin_inset space \space{}
10358 \begin_layout Standard
10359 In mathematical text, umlauts and other accented characters can directly
10363 \begin_layout Standard
10364 \begin_inset VSpace bigskip
10370 \begin_layout Standard
10372 also supports a tilde under the character if the \SpecialChar LaTeX
10378 \begin_inset Index idx
10381 \begin_layout Plain Layout
10382 Packages ! undertilde
10387 is installed on your system:
10390 \begin_layout Standard
10394 \begin_layout Plain Layout
10404 \begin_inset Note Note
10407 \begin_layout Plain Layout
10408 The following table will only be displayed when the \SpecialChar LaTeX
10421 \begin_layout Standard
10424 \begin_inset Tabular
10425 <lyxtabular version="3" rows="2" columns="2">
10426 <features booktabs="true" tabularvalignment="middle">
10427 <column alignment="center" valignment="top" width="0pt">
10428 <column alignment="center" valignment="top" width="0pt">
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10457 \begin_inset space \textvisiblespace{}
10465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10468 \begin_layout Plain Layout
10469 \begin_inset Formula $\utilde{A}$
10485 \begin_layout Standard
10489 \begin_layout Plain Layout
10499 \begin_inset Note Note
10502 \begin_layout Plain Layout
10503 The following will be displayed when the \SpecialChar LaTeX
10516 \begin_layout Standard
10517 You need to install the \SpecialChar LaTeX
10522 to see the rest of this subsection in the output.
10525 \begin_layout Standard
10529 \begin_layout Plain Layout
10541 \begin_layout Standard
10542 \begin_inset Newpage newpage
10548 \begin_layout Subsection
10549 Accents for several Characters
10550 \begin_inset Index idx
10553 \begin_layout Plain Layout
10554 Accents ! for several characters
10562 \begin_layout Standard
10563 \begin_inset space \hfill{}
10567 \begin_inset Tabular
10568 <lyxtabular version="3" rows="5" columns="2">
10569 <features booktabs="true" tabularvalignment="middle">
10570 <column alignment="center" valignment="top" width="0pt">
10571 <column alignment="center" valignment="top" width="0pt">
10573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10576 \begin_layout Plain Layout
10582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10585 \begin_layout Plain Layout
10592 <row topspace="1.5mm">
10593 <cell alignment="center" valignment="top" usebox="none">
10596 \begin_layout Plain Layout
10600 \begin_inset space \textvisiblespace{}
10608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10611 \begin_layout Plain Layout
10612 \begin_inset Formula $\overleftarrow{A=B}$
10621 <row topspace="1.5mm">
10622 <cell alignment="center" valignment="top" usebox="none">
10625 \begin_layout Plain Layout
10629 \begin_inset space \textvisiblespace{}
10637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10640 \begin_layout Plain Layout
10641 \begin_inset Formula $\underleftarrow{A=B}$
10650 <row topspace="1.5mm">
10651 <cell alignment="center" valignment="top" usebox="none">
10654 \begin_layout Plain Layout
10658 \begin_inset space \textvisiblespace{}
10666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10669 \begin_layout Plain Layout
10670 \begin_inset Formula $\overleftrightarrow{A=B}$
10679 <row topspace="1.5mm" bottomspace="1mm">
10680 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10683 \begin_layout Plain Layout
10686 underleftrightarrow
10687 \begin_inset space \textvisiblespace{}
10695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10698 \begin_layout Plain Layout
10699 \begin_inset Formula $\underleftrightarrow{A=B}$
10713 \begin_inset space \hfill{}
10717 \begin_inset Tabular
10718 <lyxtabular version="3" rows="5" columns="2">
10719 <features booktabs="true" tabularvalignment="middle">
10720 <column alignment="center" valignment="top" width="0pt">
10721 <column alignment="center" valignment="top" width="0pt">
10723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10726 \begin_layout Plain Layout
10732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10735 \begin_layout Plain Layout
10742 <row topspace="1.5mm">
10743 <cell alignment="center" valignment="top" usebox="none">
10746 \begin_layout Plain Layout
10750 \begin_inset space \textvisiblespace{}
10758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10761 \begin_layout Plain Layout
10762 \begin_inset Formula $\overrightarrow{A=B}$
10771 <row topspace="1.5mm">
10772 <cell alignment="center" valignment="top" usebox="none">
10775 \begin_layout Plain Layout
10779 \begin_inset space \textvisiblespace{}
10787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10790 \begin_layout Plain Layout
10791 \begin_inset Formula $\underrightarrow{A=B}$
10800 <row topspace="1.5mm">
10801 <cell alignment="center" valignment="top" usebox="none">
10804 \begin_layout Plain Layout
10808 \begin_inset space \textvisiblespace{}
10816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10819 \begin_layout Plain Layout
10820 \begin_inset Formula $\widetilde{A=B}$
10829 <row topspace="1.5mm" bottomspace="1mm">
10830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10833 \begin_layout Plain Layout
10837 \begin_inset space \textvisiblespace{}
10845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10848 \begin_layout Plain Layout
10849 \begin_inset Formula $\widehat{A=B}$
10863 \begin_inset space \hfill{}
10869 \begin_layout Standard
10870 \begin_inset VSpace medskip
10873 With these commands as many characters as you like can be accented.
10886 will only be set in the output with a length of three characters, as shown
10887 in the following example:
10888 \begin_inset Formula
10890 \widetilde{A+B=C-D}
10898 \begin_layout Standard
10906 \begin_inset Index idx
10909 \begin_layout Plain Layout
10924 \begin_inset Index idx
10927 \begin_layout Plain Layout
10935 described in the previous subsection it is also possible to accent several
10942 \begin_inset space \textvisiblespace{}
10946 \begin_inset Formula $\downarrow$
10952 \begin_inset Formula
10954 \underset{***}{A=B}
10962 \begin_layout Section
10964 \begin_inset CommandInset label
10966 name "subsec:Space"
10971 \begin_inset Index idx
10974 \begin_layout Plain Layout
10983 \begin_layout Subsection
10985 \begin_inset CommandInset label
10987 name "subsec:Predefined-Space"
10992 \begin_inset Index idx
10995 \begin_layout Plain Layout
10996 Space ! horizontal ! predefined
11004 \begin_layout Standard
11005 Sometimes it is necessary to insert horizontal space into a formula.
11006 This is done by inserting a protected space (shortcut
11009 arg "command-alternatives space-insert protected ; math-space"
11014 \begin_inset Quotes eld
11020 \begin_inset space \textvisiblespace{}
11026 \begin_inset Quotes erd
11029 appears and by pressing
11033 several times one can select one of eight different space sizes.
11034 The spaces can also be inserted using the math toolbar button
11037 arg "math-insert \\space"
11040 or special commands.
11041 Independent from the inserted command, one can select the size again by
11049 \begin_layout Standard
11052 \begin_inset Tabular
11053 <lyxtabular version="3" rows="6" columns="3">
11054 <features booktabs="true" tabularvalignment="middle">
11055 <column alignment="center" valignment="top">
11056 <column alignment="center" valignment="top" width="15col%">
11057 <column alignment="center" valignment="top">
11059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11062 \begin_layout Plain Layout
11068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11071 \begin_layout Plain Layout
11081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11084 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11106 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11115 \begin_layout Plain Layout
11116 \begin_inset Formula $A\,B$
11126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11140 \begin_layout Plain Layout
11146 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11149 \begin_layout Plain Layout
11150 \begin_inset Formula $A\:B$
11160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11174 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11183 \begin_layout Plain Layout
11184 \begin_inset Formula $A\;B$
11194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11197 \begin_layout Plain Layout
11205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11208 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11217 \begin_layout Plain Layout
11218 \begin_inset Formula $A\quad B$
11228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11231 \begin_layout Plain Layout
11239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11242 \begin_layout Plain Layout
11248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11251 \begin_layout Plain Layout
11252 \begin_inset Formula $A\qquad B$
11266 \begin_inset space \hfill{}
11270 \begin_inset Tabular
11271 <lyxtabular version="3" rows="6" columns="3">
11272 <features booktabs="true" tabularvalignment="middle">
11273 <column alignment="center" valignment="top">
11274 <column alignment="center" valignment="top" width="15col%">
11275 <column alignment="center" valignment="top">
11277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11280 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11302 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11333 \begin_layout Plain Layout
11334 \begin_inset Formula $A\hfill B$
11344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11358 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11367 \begin_layout Plain Layout
11368 \begin_inset Formula $A\hspace*{1em}B$
11378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11381 \begin_layout Plain Layout
11389 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11392 \begin_layout Plain Layout
11398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11401 \begin_layout Plain Layout
11402 \begin_inset Formula $A\hspace{1em}B$
11412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11415 \begin_layout Plain Layout
11419 \begin_inset space \textvisiblespace{}
11427 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11430 \begin_layout Plain Layout
11436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11439 \begin_layout Plain Layout
11440 \begin_inset Formula $A\ B$
11450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11453 \begin_layout Plain Layout
11461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11464 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11473 \begin_layout Plain Layout
11474 \begin_inset Formula $A\!B$
11490 \begin_layout Standard
11492 \begin_inset space ~
11496 \begin_inset space \thinspace{}
11500 \begin_inset space \thinspace{}
11503 7 are variable spaces which are explained in
11504 \begin_inset CommandInset ref
11506 reference "subsec:Variable-Space"
11512 \begin_inset space ~
11515 9 seems to produce no space.
11516 It is displayed red in \SpecialChar LyX
11517 contrary to the other sizes, because it is a negative
11519 There are two more negative spaces:
11522 \begin_layout Standard
11524 \begin_inset Tabular
11525 <lyxtabular version="3" rows="3" columns="3">
11526 <features booktabs="true" tabularvalignment="middle">
11527 <column alignment="center" valignment="middle" width="6.8cm">
11528 <column alignment="center" valignment="top" width="0pt">
11529 <column alignment="center" valignment="top" width="0pt">
11531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11534 \begin_layout Plain Layout
11540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11543 \begin_layout Plain Layout
11551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11554 \begin_layout Plain Layout
11564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11567 \begin_layout Plain Layout
11572 keystrokes after inserting the protected space
11577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11580 \begin_layout Plain Layout
11586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11589 \begin_layout Plain Layout
11597 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11600 \begin_layout Plain Layout
11606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11609 \begin_layout Plain Layout
11610 \begin_inset Formula $A\negmedspace B$
11618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11621 \begin_layout Plain Layout
11622 \begin_inset Formula $A\negthickspace B$
11638 \begin_layout Standard
11639 Negative spaces can lead to characters overlapping each other.
11640 Thus they can be used to enforce ligatures, which are e.
11641 \begin_inset space \thinspace{}
11645 \begin_inset space \space{}
11648 useful for summation operators:
11651 \begin_layout Standard
11653 \begin_inset Tabular
11654 <lyxtabular version="3" rows="3" columns="2">
11655 <features booktabs="true" tabularvalignment="middle">
11656 <column alignment="center" valignment="top" width="0pt">
11657 <column alignment="center" valignment="top">
11659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11662 \begin_layout Plain Layout
11668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11671 \begin_layout Plain Layout
11679 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11682 \begin_layout Plain Layout
11688 \begin_inset space \textvisiblespace{}
11696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11699 \begin_layout Plain Layout
11700 \begin_inset Formula $\sum\sum f_{kl}$
11710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11713 \begin_layout Plain Layout
11721 \begin_inset space \textvisiblespace{}
11729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11732 \begin_layout Plain Layout
11733 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11749 \begin_layout Standard
11751 \begin_inset VSpace medskip
11757 \begin_layout Standard
11759 Relations like for example equal signs, are always surrounded by space.
11760 To suppress this, the equal sign is placed into a \SpecialChar TeX
11762 The following example demonstrates this:
11765 \begin_layout Standard
11767 \begin_inset Tabular
11768 <lyxtabular version="3" rows="2" columns="2">
11769 <features tabularvalignment="middle">
11770 <column alignment="center" valignment="top" width="0pt">
11771 <column alignment="center" valignment="top" width="0pt">
11773 <cell alignment="center" valignment="top" usebox="none">
11776 \begin_layout Plain Layout
11782 <cell alignment="center" valignment="top" usebox="none">
11785 \begin_layout Plain Layout
11786 \begin_inset Formula $A=B$
11796 <cell alignment="center" valignment="top" usebox="none">
11799 \begin_layout Plain Layout
11800 equation without space
11805 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11808 \begin_layout Plain Layout
11809 \begin_inset Formula $A{=}B$
11825 \begin_layout Standard
11827 The command for the last formula is:
11832 \begin_inset Formula $\to$
11838 \begin_layout Standard
11839 \begin_inset VSpace bigskip
11845 \begin_layout Standard
11846 Spaces are needed for physical units, because the space between the value
11847 and the unit is the smallest one and not a normal space.
11848 For units in text, the smallest space is inserted via the menu
11850 Insert\SpecialChar menuseparator
11851 Formatting\SpecialChar menuseparator
11853 \begin_inset space ~
11861 arg "space-insert thin"
11867 \begin_layout Standard
11868 An example to visualize the difference:
11871 \begin_layout Standard
11872 \begin_inset Tabular
11873 <lyxtabular version="3" rows="2" columns="2">
11874 <features tabularvalignment="middle">
11875 <column alignment="left" valignment="top">
11876 <column alignment="left" valignment="top">
11878 <cell alignment="center" valignment="top" usebox="none">
11881 \begin_layout Plain Layout
11883 \begin_inset Formula $\cdot$
11891 <cell alignment="center" valignment="top" usebox="none">
11894 \begin_layout Plain Layout
11895 space between value and unit
11902 <cell alignment="center" valignment="top" usebox="none">
11905 \begin_layout Plain Layout
11907 \begin_inset space \thinspace{}
11911 \begin_inset Formula $\cdot$
11919 <cell alignment="center" valignment="top" usebox="none">
11922 \begin_layout Plain Layout
11923 smallest space between value and unit
11936 \begin_layout Subsection
11941 \begin_layout Plain Layout
11954 \begin_layout Plain Layout
11955 for vertical space in formulas see
11956 \begin_inset CommandInset ref
11958 reference "subsec:Line-Separation"
11971 \begin_layout Plain Layout
11979 \begin_inset Note Note
11982 \begin_layout Plain Layout
11985 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11988 \begin_layout Plain Layout
11991 texorpdfstring is in section
11992 \begin_inset CommandInset ref
11994 reference "subsec:Formulas-in-Section"
12004 \begin_inset CommandInset label
12006 name "subsec:Variable-Space"
12011 \begin_inset Index idx
12014 \begin_layout Plain Layout
12015 Space ! horizontal ! variable
12023 \begin_layout Standard
12024 Space with a defined length can be inserted with the command
12031 \begin_inset Index idx
12034 \begin_layout Plain Layout
12044 \begin_inset Quotes eld
12050 \begin_inset space \textvisiblespace{}
12056 \begin_inset Quotes erd
12060 The length can be specified by left-clicking on the
12061 \begin_inset Quotes eld
12067 \begin_inset space \textvisiblespace{}
12073 \begin_inset Quotes erd
12077 The length may also be negative.
12078 When a space would be the first character in a line it would be omitted.
12079 To force its output use the command
12091 or left-click on the
12092 \begin_inset Quotes eld
12098 \begin_inset space \textvisiblespace{}
12104 \begin_inset Quotes erd
12107 and check the option
12112 \begin_inset Newline newline
12115 To insert as much space as is available, the command
12122 \begin_inset Index idx
12125 \begin_layout Plain Layout
12136 \begin_layout Standard
12138 \begin_inset Tabular
12139 <lyxtabular version="3" rows="4" columns="2">
12140 <features booktabs="true" tabularvalignment="middle">
12141 <column alignment="center" valignment="top" width="0pt">
12142 <column alignment="center" valignment="top">
12144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12147 \begin_layout Plain Layout
12155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12158 \begin_layout Plain Layout
12166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12169 \begin_layout Plain Layout
12173 \begin_inset space \textvisiblespace{}
12179 \begin_inset space \thinspace{}
12187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12190 \begin_layout Plain Layout
12191 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12204 \begin_layout Plain Layout
12208 \begin_inset space \textvisiblespace{}
12214 \begin_inset space \thinspace{}
12222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12225 \begin_layout Plain Layout
12226 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12239 \begin_layout Plain Layout
12243 \begin_inset space \textvisiblespace{}
12251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12254 \begin_layout Plain Layout
12255 \begin_inset Formula $A=A\hfill B=B$
12271 \begin_layout Standard
12272 In the last example the available space is given by the longest column entry
12274 In an inline formula the space depends on the length of the line in which
12282 Thus, when the line uses the full width, no space will be created.
12289 only has an effect on displayed formulas when the formula style
12294 (Formula styles are explained in
12295 \begin_inset CommandInset ref
12297 reference "sec:Formula-Styles"
12304 \begin_layout Standard
12311 , there are the commands
12323 that fill the space with a pattern, see
12324 \begin_inset CommandInset ref
12326 reference "subsec:Ellipses"
12333 \begin_layout Standard
12334 For text, variable space can be inserted via the menu
12336 Insert\SpecialChar menuseparator
12337 Formatting\SpecialChar menuseparator
12339 \begin_inset space ~
12347 \begin_layout Standard
12348 This is a line with
12349 \begin_inset space \hspace{}
12354 \begin_inset space \thinspace{}
12360 \begin_layout Standard
12361 This is a line with
12362 \begin_inset space \hfill{}
12368 \begin_layout Subsection
12369 Space besides inline Formulas
12370 \begin_inset Index idx
12373 \begin_layout Plain Layout
12374 Space ! besides inline formulas
12382 \begin_layout Standard
12383 The space that surrounds inline formulas can be adjusted with the length
12391 \begin_inset Index idx
12394 \begin_layout Plain Layout
12403 The value of a length is set with the command
12410 \begin_inset Index idx
12413 \begin_layout Plain Layout
12421 which has the following scheme:
12424 \begin_layout Standard
12429 setlength{length name}{value}
12432 \begin_layout Standard
12440 \begin_inset space \thinspace{}
12446 \begin_layout Standard
12456 \begin_layout Standard
12457 is inserted in \SpecialChar TeX
12460 \begin_inset space \thinspace{}
12463 mm space will now be set around all inline formulas:
12467 \begin_layout Plain Layout
12481 \begin_layout Standard
12482 This is a line with an inline formula
12483 \begin_inset Formula $A=B$
12487 \begin_inset space \thinspace{}
12490 mm surrounding space.
12494 \begin_layout Plain Layout
12508 \begin_layout Standard
12509 To return to the predefined value,
12515 is set to the value 0
12516 \begin_inset space \thinspace{}
12522 \begin_layout Standard
12523 \begin_inset Newpage newpage
12529 \begin_layout Section
12531 \begin_inset Index idx
12534 \begin_layout Plain Layout
12541 \begin_inset Index idx
12544 \begin_layout Plain Layout
12549 \begin_layout Plain Layout
12560 \begin_layout Plain Layout
12575 \begin_layout Standard
12576 Boxes for text are described in chapter
12583 \begin_inset space ~
12591 \begin_layout Subsection
12593 \begin_inset CommandInset label
12595 name "subsec:Boxes-with-Frame"
12600 \begin_inset Index idx
12603 \begin_layout Plain Layout
12612 \begin_layout Standard
12613 It is possible to frame a formula or part of one with the commands
12620 \begin_inset Index idx
12623 \begin_layout Plain Layout
12638 \begin_inset Index idx
12641 \begin_layout Plain Layout
12652 \begin_layout Standard
12653 When one of these commands is inserted in a formula, a blue box appears
12654 within a frame to enter formula parts.
12661 an additional formula has to be created by
12665 within this box, because the box content will otherwise be treated as mathemati
12673 is used, a new formula is automatically created inside the frame.
12676 \begin_layout Standard
12683 is not suitable to frame displayed formulas because the formula will always
12684 be set in the size of the text.
12691 is in contrary not suitable to frame inline formulas, because the formula
12692 will always be set in the size of a displayed formula.
12695 \begin_layout Standard
12709 \begin_inset Index idx
12712 \begin_layout Plain Layout
12720 where additionally the frame width and the alignment can be specified.
12727 is used in the following scheme:
12730 \begin_layout Standard
12735 framebox[frame width][position]{box content}
12738 \begin_layout Standard
12739 The position can either be
12756 right aligns the formula in the box.
12757 When no position is given, the formula will be centered.
12758 \begin_inset Newline newline
12761 If no width is given, also no position can be given.
12762 In this case the frame width is adjusted to the box content like for
12771 \begin_layout Standard
12778 is inserted, a box appears containing three blue boxes.
12779 The first two boxes are surrounded by brackets and denote the two optional
12781 The third box is for formula parts like for
12790 \begin_layout Standard
12792 \begin_inset Tabular
12793 <lyxtabular version="3" rows="5" columns="2">
12794 <features booktabs="true" tabularvalignment="middle">
12795 <column alignment="center" valignment="top" width="0pt">
12796 <column alignment="center" valignment="top">
12798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12801 \begin_layout Plain Layout
12807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12810 \begin_layout Plain Layout
12817 <row topspace="1.5mm">
12818 <cell alignment="center" valignment="top" usebox="none">
12821 \begin_layout Plain Layout
12825 \begin_inset space \textvisiblespace{}
12835 \begin_inset space \textvisiblespace{}
12843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12846 \begin_layout Plain Layout
12847 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12856 <row topspace="1.5mm">
12857 <cell alignment="center" valignment="top" usebox="none">
12860 \begin_layout Plain Layout
12864 \begin_inset space \textvisiblespace{}
12870 \begin_inset space \textvisiblespace{}
12878 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12881 \begin_layout Plain Layout
12882 \begin_inset Formula $\boxed{\int A=B}$
12891 <row topspace="1.5mm">
12892 <cell alignment="center" valignment="top" usebox="none">
12895 \begin_layout Plain Layout
12899 \begin_inset space \textvisiblespace{}
12907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12910 \begin_layout Plain Layout
12911 \begin_inset Formula $A+\fbox{B}$
12920 <row topspace="1.5mm" bottomspace="1mm">
12921 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12924 \begin_layout Plain Layout
12928 \begin_inset space \textvisiblespace{}
12932 \begin_inset Formula $\to$
12936 \begin_inset Formula $\to$
12946 \begin_inset space \textvisiblespace{}
12950 \begin_inset Formula $\downarrow$
12958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12961 \begin_layout Plain Layout
12962 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12978 \begin_layout Standard
12979 The frame thickness can also be adjusted.
12980 To do this the following commands have to be inserted in \SpecialChar TeX
12985 \begin_layout Standard
12995 \begin_inset Quotes eld
12999 \begin_inset Quotes erd
13013 \begin_inset Quotes eld
13017 \begin_inset Quotes erd
13023 \begin_layout Standard
13024 \begin_inset Quotes eld
13028 \begin_inset Quotes erd
13031 specifies the minimal distance between the frame and the first character
13033 An example for this is the following framed formula:
13037 \begin_layout Plain Layout
13049 \begin_inset Formula
13056 Before this formula the commands
13059 \begin_layout Standard
13081 \begin_layout Standard
13082 were inserted in \SpecialChar TeX
13084 The given values are used for all following boxes.
13087 \begin_layout Standard
13088 To return to the standard frame size, the command
13091 \begin_layout Standard
13116 \begin_layout Plain Layout
13130 \begin_layout Standard
13131 is inserted in \SpecialChar TeX
13132 mode before the next formula.
13135 \begin_layout Subsection
13136 Boxes without Frame
13137 \begin_inset CommandInset label
13139 name "subsec:Boxes-without-Frame"
13144 \begin_inset Index idx
13147 \begin_layout Plain Layout
13148 Boxes ! without frame
13156 \begin_layout Standard
13157 For boxes without a frame there are the following box commands:
13164 \begin_inset Index idx
13167 \begin_layout Plain Layout
13182 \begin_inset Index idx
13185 \begin_layout Plain Layout
13200 \begin_inset Index idx
13203 \begin_layout Plain Layout
13214 \begin_layout Standard
13221 a box can be super- or subscripted.
13222 But in contrary to normal super- and subscripting, the characters in the
13223 box keep their font size.
13230 is used in the following scheme:
13233 \begin_layout Standard
13238 raisebox{height}{box content}
13241 \begin_layout Standard
13242 When the box should contain a formula, an extra formula is needed like for
13253 \begin_inset Note Greyedout
13256 \begin_layout Plain Layout
13267 this extra formula is created by pressing
13271 twice instead of once because \SpecialChar LyX
13272 doesn't yet support
13286 \begin_layout Standard
13288 \begin_inset Tabular
13289 <lyxtabular version="3" rows="4" columns="2">
13290 <features booktabs="true" tabularvalignment="middle">
13291 <column alignment="center" valignment="top" width="0pt">
13292 <column alignment="center" valignment="top">
13294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13297 \begin_layout Plain Layout
13303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13306 \begin_layout Plain Layout
13314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13317 \begin_layout Plain Layout
13321 \begin_inset Formula $\to$
13327 \begin_inset Formula $\to$
13335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13338 \begin_layout Plain Layout
13339 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13352 \begin_layout Plain Layout
13356 \begin_inset Formula $\to$
13362 \begin_inset Formula $\to$
13370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13373 \begin_layout Plain Layout
13374 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13387 \begin_layout Plain Layout
13391 \begin_inset Formula $\to$
13407 \begin_inset space \textvisiblespace{}
13415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13418 \begin_layout Plain Layout
13419 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13435 \begin_layout Standard
13460 , with the difference that there is no frame.
13463 \begin_layout Subsection
13465 \begin_inset CommandInset label
13467 name "subsec:Colored-Boxes"
13472 \begin_inset Index idx
13475 \begin_layout Plain Layout
13484 \begin_layout Standard
13485 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13494 \begin_layout Plain Layout
13495 The \SpecialChar LaTeX
13500 is part of every \SpecialChar LaTeX
13501 standard installation.
13507 \begin_inset Index idx
13510 \begin_layout Plain Layout
13516 has to be loaded in the \SpecialChar LaTeX
13517 -preamble with the line
13521 \begin_layout Plain Layout
13522 When text is colored somewhere in the document with a predefined color,
13524 loads the \SpecialChar LaTeX
13530 Thus it is possible that the package is loaded twice, but this does not
13537 \begin_inset Note Note
13540 \begin_layout Plain Layout
13541 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13550 \begin_layout Standard
13558 \begin_layout Standard
13559 \begin_inset VSpace medskip
13562 To color boxes, the command
13569 \begin_inset Index idx
13572 \begin_layout Plain Layout
13580 is used in the following scheme:
13583 \begin_layout Standard
13588 colorbox{color}{box content}
13591 \begin_layout Standard
13592 The box content can also be a box and a
13598 can also be part of another box (see the 2nd and 3rd example).
13599 When the box should contain a formula, an extra formula has to be created,
13600 the same way as for
13610 \begin_layout Plain Layout
13611 This also applies for the command
13625 \begin_layout Standard
13626 One of the following predefined colors can be chosen:
13629 \begin_layout Standard
13663 \begin_layout Standard
13665 \begin_inset Tabular
13666 <lyxtabular version="3" rows="4" columns="2">
13667 <features booktabs="true" tabularvalignment="middle">
13668 <column alignment="center" valignment="top" width="0pt">
13669 <column alignment="center" valignment="top">
13671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13674 \begin_layout Plain Layout
13680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13683 \begin_layout Plain Layout
13691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13694 \begin_layout Plain Layout
13698 \begin_inset Formula $\to$
13708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13711 \begin_layout Plain Layout
13712 \begin_inset Formula $\colorbox{yellow}{A=B}$
13721 <row topspace="1.5mm">
13722 <cell alignment="center" valignment="top" usebox="none">
13725 \begin_layout Plain Layout
13729 \begin_inset Formula $\to$
13737 \begin_inset space \textvisiblespace{}
13745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13748 \begin_layout Plain Layout
13749 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13758 <row topspace="1.5mm" bottomspace="1mm">
13759 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13762 \begin_layout Plain Layout
13766 \begin_inset space \textvisiblespace{}
13772 \begin_inset Formula $\to$
13788 \begin_inset space \textvisiblespace{}
13796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13799 \begin_layout Plain Layout
13800 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13816 \begin_layout Standard
13823 only colors the box but not the characters in the box.
13824 To color all characters, the whole formula is highlighted and the desired
13825 color is chosen in the
13828 \begin_inset space ~
13834 The dialog can be called with the toolbar button
13837 arg "dialog-show character"
13842 Edit\SpecialChar menuseparator
13844 \begin_inset space ~
13847 Style\SpecialChar menuseparator
13851 The formula number then has the same color as the formula.
13852 When the formula number should get another color than the formula characters,
13853 the color must be changed within the formula.
13856 \begin_layout Standard
13860 \begin_layout Standard
13863 \begin_inset Formula
13865 \int A=B\label{eq:red}
13873 \begin_inset Formula
13875 \textcolor{red}{\int A=B}\label{eq:redgreen}
13883 \begin_layout Standard
13885 \begin_inset CommandInset ref
13891 is completely colored red.
13892 \begin_inset Newline newline
13896 \begin_inset CommandInset ref
13898 reference "eq:redgreen"
13902 was first completely colored green to set the color for the formula number.
13903 Subsequently the formula characters were colored red.
13906 \begin_layout Standard
13907 \begin_inset VSpace bigskip
13910 To color the frame different than the rest of the box, the command
13917 \begin_inset Index idx
13920 \begin_layout Plain Layout
13928 is used in the following scheme:
13931 \begin_layout Standard
13936 fcolorbox{frame color}{color}{box content}
13939 \begin_layout Standard
13946 is an extension of the command
13953 The frame width is set, like for
13976 \begin_layout Plain Layout
13988 \begin_inset Formula
13990 \fcolorbox{cyan}{magenta}{A=B}
13999 \begin_layout Plain Layout
14013 \begin_layout Standard
14014 This formula was created with the command
14015 \begin_inset Newline newline
14023 \begin_inset Formula $\to$
14029 \begin_inset Formula $\to$
14039 \begin_layout Standard
14040 \begin_inset VSpace bigskip
14043 To use other colors than the predefined ones, they have to be defined first.
14046 \begin_layout Standard
14047 One can for example define the color
14048 \begin_inset Quotes eld
14056 \begin_inset Quotes erd
14059 with the \SpecialChar LaTeX
14063 \begin_layout Standard
14068 definecolor{darkgreen}{cmyk}{0.5,
14083 \begin_inset Index idx
14086 \begin_layout Plain Layout
14097 \begin_layout Standard
14102 is the color space that denotes the colors
14119 The four comma separated numbers are the portion factor for the corresponding
14120 colors of the color space.
14121 The factors can be in the range of 0
14122 \begin_inset space \thinspace{}
14126 \begin_inset space \thinspace{}
14134 also the color space
14138 can be used for definitions.
14155 , so that there are in this case three portion factors for the corresponding
14157 Furthermore there is the color space
14161 with one portion factor for the gray value.
14164 \begin_layout Standard
14165 As example a framed box with the new defined color
14169 where the characters have been colored
14174 \begin_inset Formula
14176 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14184 \begin_layout Standard
14185 Self-defined colors can also be used for text with the help of the command
14193 \begin_inset Index idx
14196 \begin_layout Plain Layout
14205 \begin_layout Standard
14209 \begin_layout Plain Layout
14213 textcolor{darkgreen}{
14219 \begin_inset Quotes eld
14223 \begin_inset Quotes erd
14230 \begin_layout Plain Layout
14240 \begin_layout Standard
14248 \begin_inset Index idx
14251 \begin_layout Plain Layout
14259 is used in the scheme
14263 textcolor{color}{characters to color}
14268 \begin_layout Subsection
14270 \begin_inset CommandInset label
14272 name "subsec:Paragraph-Boxes"
14277 \begin_inset Index idx
14280 \begin_layout Plain Layout
14281 Boxes ! as paragraph
14289 \begin_layout Standard
14290 A box that can contain several lines and paragraphs, a so-called paragraph
14291 box (parbox), can be created with the menu
14293 Insert\SpecialChar menuseparator
14296 or the toolbar button
14305 \begin_layout Standard
14306 The following example shows a framed parbox in a line:
14309 \begin_layout Standard
14310 \begin_inset VSpace medskip
14314 \begin_inset Box Boxed
14324 height_special "totalheight"
14329 backgroundcolor "none"
14332 \begin_layout Plain Layout
14333 This is a paragraph box.
14335 \begin_inset space \thinspace{}
14338 cm long and can also contain formulas:
14339 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14350 \begin_layout Standard
14351 \begin_inset VSpace medskip
14357 \begin_layout Standard
14358 Such a box is created by right-clicking on the gray box inset.
14359 A dialog pops up showing the box properties.
14373 \begin_inset space \thinspace{}
14378 Vertical Box Alignment
14383 \begin_layout Standard
14384 \begin_inset VSpace medskip
14387 In \SpecialChar LaTeX
14388 a parbox is created with the command
14395 \begin_inset Index idx
14398 \begin_layout Plain Layout
14406 which has the following scheme:
14409 \begin_layout Standard
14414 parbox[position]{width}{box content}
14417 \begin_layout Standard
14432 \begin_inset Quotes eld
14436 \begin_inset Quotes erd
14439 means that the box is aligned within the surrounding text with its last
14446 \begin_inset Quotes eld
14450 \begin_inset Quotes erd
14453 this is done with the first line.
14454 When no position is given, the box will be vertically centered, see section
14462 \begin_inset space ~
14467 manual for examples.
14470 \begin_layout Standard
14471 \begin_inset VSpace bigskip
14474 To frame formulas completely, including the formula number, the formula
14475 must be set into a parbox.
14476 To do this, the command
14490 is inserted in \SpecialChar TeX
14491 mode before the formula.
14499 \begin_inset Index idx
14502 \begin_layout Plain Layout
14510 is hereby the line width set for the document.
14511 Because the frame is outside the parbox, 2
14512 \begin_inset space \thinspace{}
14515 times the frame separation and the frame thickness must be subtracted from
14517 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14526 \begin_layout Plain Layout
14531 is part of every \SpecialChar LaTeX
14532 standard installation.
14538 \begin_inset Index idx
14541 \begin_layout Plain Layout
14547 must be loaded in the \SpecialChar LaTeX
14548 -preamble with the line
14551 \begin_layout Standard
14559 \begin_layout Standard
14560 Behind the formula both boxes are closed by entering
14564 in \SpecialChar TeX
14566 Here is an example:
14570 \begin_layout Plain Layout
14584 \begin_layout Standard
14588 \begin_layout Plain Layout
14606 \begin_inset Formula
14608 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14617 \begin_layout Plain Layout
14628 \begin_layout Plain Layout
14642 \begin_layout Standard
14643 \begin_inset VSpace medskip
14646 As a parbox is used as the argument of
14652 , there is in this case no difference between
14667 \begin_layout Standard
14668 \begin_inset VSpace bigskip
14671 Paragraph boxes are very useful to comment formulas directly.
14678 is used in combination with the command
14692 \begin_inset CommandInset ref
14694 reference "subsec:User-defined-Numbering"
14701 \begin_layout Standard
14702 An example of a formula commented with
14711 \begin_layout Standard
14715 \begin_layout Plain Layout
14728 This is a description.
14729 It is distinctly separated from the formula and multiline.
14733 \begin_layout Plain Layout
14745 \begin_layout Standard
14746 Such a formula must be inserted completely in \SpecialChar TeX
14747 mode because \SpecialChar LyX
14749 support the command
14756 The formula is created with the following command sequence:
14759 \begin_layout Standard
14772 is inserted in \SpecialChar TeX
14777 \begin_layout Plain Layout
14778 When the formula style
14790 can also be replaced by
14797 (formula styles see
14798 \begin_inset CommandInset ref
14800 reference "sec:Formula-Styles"
14809 Then the description follows as normal text and finally
14815 is inserted in \SpecialChar TeX
14829 hereby create a displayed formula.
14832 \begin_layout Standard
14839 can be seen in this example that was
14840 \begin_inset Quotes eld
14844 \begin_inset Quotes erd
14847 using the mathematical textmode:
14848 \begin_inset Formula
14850 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14858 \begin_layout Section
14860 \begin_inset Index idx
14863 \begin_layout Plain Layout
14872 \begin_layout Subsection
14874 \begin_inset CommandInset label
14876 name "subsec:Big-Operators"
14881 \begin_inset Index idx
14884 \begin_layout Plain Layout
14891 \begin_inset Index idx
14894 \begin_layout Plain Layout
14901 \begin_inset Index idx
14904 \begin_layout Plain Layout
14913 \begin_layout Standard
14914 To be able to use all integral operators listed here, the option
14916 Use esint package automatically
14918 must be set in the document settings under
14921 \begin_inset space ~
14929 \begin_layout Standard
14930 \begin_inset space \hfill{}
14934 \begin_inset Tabular
14935 <lyxtabular version="3" rows="11" columns="2">
14936 <features booktabs="true" tabularvalignment="middle">
14937 <column alignment="center" valignment="top" width="0pt">
14938 <column alignment="center" valignment="top" width="0pt">
14940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14943 \begin_layout Plain Layout
14949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14952 \begin_layout Plain Layout
14960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14963 \begin_layout Plain Layout
14967 \begin_inset Index idx
14970 \begin_layout Plain Layout
14983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14986 \begin_layout Plain Layout
14987 \begin_inset Formula $\int$
14997 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15008 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15011 \begin_layout Plain Layout
15012 \begin_inset Formula $\oint$
15022 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15025 \begin_layout Plain Layout
15033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15036 \begin_layout Plain Layout
15037 \begin_inset Formula $\ointctrclockwise$
15047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15050 \begin_layout Plain Layout
15058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15061 \begin_layout Plain Layout
15062 \begin_inset Formula $\ointclockwise$
15072 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15075 \begin_layout Plain Layout
15083 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15086 \begin_layout Plain Layout
15087 \begin_inset Formula $\sqint$
15097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15100 \begin_layout Plain Layout
15108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15111 \begin_layout Plain Layout
15113 \begin_inset Formula $\fint$
15123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15126 \begin_layout Plain Layout
15134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15137 \begin_layout Plain Layout
15139 \begin_inset Formula $\landupint$
15149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15163 \begin_layout Plain Layout
15165 \begin_inset Formula $\landdownint$
15175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Plain Layout
15190 \begin_inset Formula $\bigcap$
15200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15203 \begin_layout Plain Layout
15211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15214 \begin_layout Plain Layout
15215 \begin_inset Formula $\bigcup$
15229 \begin_inset space \hfill{}
15233 \begin_inset Tabular
15234 <lyxtabular version="3" rows="11" columns="2">
15235 <features booktabs="true" tabularvalignment="middle">
15236 <column alignment="center" valignment="top" width="0pt">
15237 <column alignment="center" valignment="top" width="0pt">
15239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15242 \begin_layout Plain Layout
15248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15251 \begin_layout Plain Layout
15259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15262 \begin_layout Plain Layout
15266 \begin_inset Index idx
15269 \begin_layout Plain Layout
15282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15285 \begin_layout Plain Layout
15286 \begin_inset Formula $\sum$
15296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15303 \begin_inset Index idx
15306 \begin_layout Plain Layout
15313 \begin_layout Plain Layout
15332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15335 \begin_layout Plain Layout
15336 \begin_inset Formula $\prod$
15346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15349 \begin_layout Plain Layout
15357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15360 \begin_layout Plain Layout
15361 \begin_inset Formula $\coprod$
15371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15374 \begin_layout Plain Layout
15382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15385 \begin_layout Plain Layout
15386 \begin_inset Formula $\bigodot$
15396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15399 \begin_layout Plain Layout
15407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15410 \begin_layout Plain Layout
15411 \begin_inset Formula $\bigotimes$
15421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15424 \begin_layout Plain Layout
15432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15435 \begin_layout Plain Layout
15436 \begin_inset Formula $\bigoplus$
15446 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15449 \begin_layout Plain Layout
15457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15460 \begin_layout Plain Layout
15461 \begin_inset Formula $\bigwedge$
15471 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15474 \begin_layout Plain Layout
15482 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15485 \begin_layout Plain Layout
15486 \begin_inset Formula $\bigvee$
15496 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15499 \begin_layout Plain Layout
15507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15510 \begin_layout Plain Layout
15511 \begin_inset Formula $\bigsqcup$
15521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15524 \begin_layout Plain Layout
15532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15535 \begin_layout Plain Layout
15536 \begin_inset Formula $\biguplus$
15550 \begin_inset space \hfill{}
15556 \begin_layout Standard
15557 All big operators can also be inserted via the math toolbar button
15560 arg "math-insert \\intop"
15566 \begin_layout Standard
15567 The operators are called big because they are bigger than the sometimes
15568 equal looking binary operators.
15569 All big operators can have limits as described in the next subsection.
15572 \begin_layout Standard
15573 For all integral operators there is a second version available, ending in
15591 These operators are different from
15598 \begin_inset space \space{}
15601 in the style the operator limits are displayed, see
15602 \begin_inset CommandInset ref
15604 reference "subsec:Operator-Limits"
15612 \begin_layout Subsubsection*
15613 Advice for Integrals
15616 \begin_layout Standard
15621 in an integral is an operator, that therefore has to be set upright.
15622 This is done by highlighting the
15626 and using the keyboard shortcut
15636 \begin_layout Plain Layout
15642 \begin_inset CommandInset ref
15644 reference "subsec:Font-Styles"
15654 Finally the smallest space is inserted before the
15658 , as this is usual for operators.
15662 \begin_layout Standard
15664 \begin_inset Formula $\int A(x)dx$
15668 \begin_inset Newline newline
15672 \begin_inset Phantom HPhantom
15675 \begin_layout Plain Layout
15682 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15688 \begin_layout Standard
15689 For multiple integrals there are the following commands:
15690 \begin_inset VSpace medskip
15696 \begin_layout Standard
15697 \begin_inset space \hfill{}
15701 \begin_inset Tabular
15702 <lyxtabular version="3" rows="4" columns="2">
15703 <features booktabs="true" tabularvalignment="middle">
15704 <column alignment="center" valignment="top" width="0pt">
15705 <column alignment="center" valignment="top" width="0pt">
15707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15710 \begin_layout Plain Layout
15716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15719 \begin_layout Plain Layout
15726 <row bottomspace="1mm">
15727 <cell alignment="center" valignment="top" usebox="none">
15730 \begin_layout Plain Layout
15738 <cell alignment="center" valignment="top" usebox="none">
15741 \begin_layout Plain Layout
15742 \begin_inset Formula $\iint$
15751 <row bottomspace="1mm">
15752 <cell alignment="center" valignment="top" usebox="none">
15755 \begin_layout Plain Layout
15763 <cell alignment="center" valignment="top" usebox="none">
15766 \begin_layout Plain Layout
15767 \begin_inset Formula $\oiint$
15776 <row bottomspace="1mm">
15777 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15780 \begin_layout Plain Layout
15788 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15791 \begin_layout Plain Layout
15792 \begin_inset Formula $\sqiint$
15806 \begin_inset space \hfill{}
15810 \begin_inset Tabular
15811 <lyxtabular version="3" rows="4" columns="2">
15812 <features booktabs="true" tabularvalignment="middle">
15813 <column alignment="center" valignment="top" width="0pt">
15814 <column alignment="center" valignment="top" width="0pt">
15816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15819 \begin_layout Plain Layout
15825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15828 \begin_layout Plain Layout
15835 <row bottomspace="1mm">
15836 <cell alignment="center" valignment="top" usebox="none">
15839 \begin_layout Plain Layout
15847 <cell alignment="center" valignment="top" usebox="none">
15850 \begin_layout Plain Layout
15851 \begin_inset Formula $\iiint$
15860 <row bottomspace="1mm">
15861 <cell alignment="center" valignment="top" usebox="none">
15864 \begin_layout Plain Layout
15872 <cell alignment="center" valignment="top" usebox="none">
15875 \begin_layout Plain Layout
15876 \begin_inset Formula $\iiiint$
15885 <row bottomspace="1mm">
15886 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15889 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15900 \begin_layout Plain Layout
15901 \begin_inset Formula $\dotsint$
15915 \begin_inset space \hfill{}
15921 \begin_layout Subsection
15923 \begin_inset CommandInset label
15925 name "subsec:Operator-Limits"
15930 \begin_inset Index idx
15933 \begin_layout Plain Layout
15942 \begin_layout Standard
15943 Limits are created by super- and subscripts:
15946 \begin_layout Standard
15948 \begin_inset Tabular
15949 <lyxtabular version="3" rows="2" columns="2">
15950 <features booktabs="true" tabularvalignment="middle">
15951 <column alignment="center" valignment="top" width="0pt">
15952 <column alignment="center" valignment="top" width="0pt">
15954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15957 \begin_layout Plain Layout
15963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15966 \begin_layout Plain Layout
15974 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15977 \begin_layout Plain Layout
15983 \begin_inset space \textvisiblespace{}
15987 \begin_inset Formula $\to$
15991 \begin_inset Formula $\to$
15999 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16002 \begin_layout Plain Layout
16003 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16019 \begin_layout Standard
16020 Limits of inline formulas are set right beside the operator.
16021 Limits in displayed formulas are set above or below the operator, except
16022 for integral limits.
16025 \begin_layout Standard
16026 To force that the limits are set beside the operator, the cursor is set
16027 directly behind the operator and the limits type is changed with the menu
16030 Edit\SpecialChar menuseparator
16031 Math\SpecialChar menuseparator
16050 \begin_layout Standard
16051 The default limits type is this:
16052 \begin_inset Formula
16054 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16059 This is how it looks when the limits type was changed to
16066 \begin_inset Formula
16068 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16073 For integrals, except those ending with
16089 etc., the limits are by default set beside the operator.
16090 But for multiple integrals the limits are often set below the operator.
16091 In the following example the limits type was therefore set to
16095 and so set below the integrals:
16096 \begin_inset Formula
16098 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16106 \begin_layout Standard
16107 \begin_inset VSpace medskip
16110 To specify conditions for limits, the commands
16117 \begin_inset Index idx
16120 \begin_layout Plain Layout
16135 \begin_inset Index idx
16138 \begin_layout Plain Layout
16147 To create for example this expression
16148 \begin_inset Formula
16150 \sum_{\begin{subarray}{c}
16154 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16162 \begin_layout Standard
16163 the following has to be done:
16164 \begin_inset Newline newline
16176 \begin_inset space \textvisiblespace{}
16182 One is now in a blue box under the summation operator and insert there
16188 \begin_inset space \textvisiblespace{}
16194 The blue box is now within a purple box and now several lines can be written
16196 A new line is created by inserting a line break (
16199 arg "newline-insert newline"
16204 \begin_inset Newline newline
16209 0<k<1000 Ctrl+Return
16210 \begin_inset Newline newline
16215 is typed in, a new box appears below for the new line.
16218 \begin_layout Standard
16219 The alignment of the lines can be changed to left aligned with the
16229 Edit\SpecialChar menuseparator
16233 To get right alignment,
16238 \begin_inset space \textvisiblespace{}
16243 is inserted at the beginning of the line.
16246 \begin_layout Standard
16259 with the difference that the lines are always centered.
16262 \begin_layout Standard
16263 \begin_inset VSpace bigskip
16267 \begin_inset CommandInset ref
16269 reference "eq:substack"
16273 there can be too much space beside an operator, because the characters
16274 following the operator are set beside the limits.
16275 To avoid this the command
16282 \begin_inset Index idx
16285 \begin_layout Plain Layout
16294 To activate it, set in the document settings under
16297 \begin_inset space ~
16307 \begin_inset Index idx
16310 \begin_layout Plain Layout
16311 Packages ! mathtools
16319 \begin_inset space ~
16331 sets the space besides the operator to 0
16332 \begin_inset space \thinspace{}
16336 \begin_inset Newline newline
16340 \begin_inset CommandInset ref
16342 reference "eq:substack"
16346 , one uses the command
16349 \begin_layout Standard
16357 \begin_layout Standard
16358 and inserts the operator with its limits into the braces.
16359 Behind the brace one continues the formula:
16360 \begin_inset Formula
16362 \smashoperator{\sum_{\begin{subarray}{c}
16366 \end{subarray}}^{n}}k^{-2}
16374 \begin_layout Standard
16375 It is possible to set the space of only one side of the operator to 0
16376 \begin_inset space \thinspace{}
16380 To do this write either
16399 stands for the left and
16403 for the right side of the operator.
16404 Here is an example of the possible
16413 \begin_layout Standard
16414 \begin_inset Formula
16416 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}
16424 \begin_layout Standard
16425 \begin_inset VSpace bigskip
16431 \begin_layout Standard
16432 When several consecutive operators have limits the typesetting of the limits
16433 looks often imperfect in the output, see this example:
16434 \begin_inset Formula
16436 \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}
16441 To improve the typesetting set in the document settings under
16444 \begin_inset space ~
16454 \begin_inset Index idx
16457 \begin_layout Plain Layout
16458 Packages ! mathtools
16466 \begin_inset space ~
16472 Then insert into your formula the command
16479 \begin_inset Index idx
16482 \begin_layout Plain Layout
16490 directly before the first operator.
16491 The example will then look like this:
16492 \begin_inset Formula
16494 \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}
16502 \begin_layout Standard
16503 \begin_inset VSpace bigskip
16506 How to use one limit for several operators is described in
16507 \begin_inset CommandInset ref
16509 reference "subsec:Self-defined-Operators"
16516 \begin_layout Subsection
16517 Decoration for Operators
16518 \begin_inset Index idx
16521 \begin_layout Plain Layout
16522 Operators ! Decoration
16530 \begin_layout Standard
16538 \begin_inset Index idx
16541 \begin_layout Plain Layout
16556 \begin_inset Index idx
16559 \begin_layout Plain Layout
16567 characters can be placed above or below an operator, respectively.
16575 \begin_inset Index idx
16578 \begin_layout Plain Layout
16586 characters can be set before and behind a big operator.
16589 \begin_layout Standard
16591 \begin_inset space ~
16603 \begin_layout Itemize
16610 is used to set characters at the corners of the operator
16613 \begin_layout Itemize
16620 is used to set characters before and/or behind the operator (this variant
16621 represents \SpecialChar LaTeX
16631 \begin_layout Itemize
16638 is used to set characters at the left corners and/or behind the operator
16641 \begin_layout Itemize
16648 is used to set characters at the right corners and/or before the operator
16651 \begin_layout Standard
16652 For example the command
16657 \begin_inset space \textvisiblespace{}
16663 \begin_inset space \textvisiblespace{}
16667 \begin_inset Formula $\to$
16671 \begin_inset Formula $\to$
16675 \begin_inset space \textvisiblespace{}
16685 \begin_inset Formula
16687 \sideset{}{'}\sum_{k=1}^{n}
16695 \begin_layout Standard
16696 \begin_inset Note Greyedout
16699 \begin_layout Plain Layout
16706 can only be used to decorate big operators, binary operators are not allowed.
16714 \begin_layout Standard
16727 can also be used to decorate symbols and characters.
16728 For example, the command
16733 \begin_inset space \textvisiblespace{}
16739 \begin_inset space \textvisiblespace{}
16745 \begin_inset Formula $\uparrow$
16753 \begin_inset Formula
16755 \overset{a}{\maltese}
16763 \begin_layout Subsection
16765 \begin_inset CommandInset label
16767 name "subsec:Binary-Operators"
16772 \begin_inset Index idx
16775 \begin_layout Plain Layout
16784 \begin_layout Standard
16785 Binary operators are surrounded by space when there is a character before
16787 \begin_inset VSpace medskip
16793 \begin_layout Standard
16794 \begin_inset Tabular
16795 <lyxtabular version="3" rows="13" columns="2">
16796 <features booktabs="true" tabularvalignment="middle">
16797 <column alignment="center" valignment="top" width="0pt">
16798 <column alignment="center" valignment="top" width="0pt">
16800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16805 \begin_inset Note Note
16808 \begin_layout Plain Layout
16815 is only used as spacer.
16825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16828 \begin_layout Plain Layout
16836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16839 \begin_layout Plain Layout
16845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16848 \begin_layout Plain Layout
16849 \begin_inset Formula $+$
16859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16862 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $-$
16882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16893 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16896 \begin_layout Plain Layout
16897 \begin_inset Formula $\pm$
16907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16910 \begin_layout Plain Layout
16918 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16921 \begin_layout Plain Layout
16922 \begin_inset Formula $\mp$
16932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16935 \begin_layout Plain Layout
16943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16946 \begin_layout Plain Layout
16947 \begin_inset Formula $\cdot$
16957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16960 \begin_layout Plain Layout
16968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16971 \begin_layout Plain Layout
16972 \begin_inset Formula $\times$
16982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16985 \begin_layout Plain Layout
16993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16996 \begin_layout Plain Layout
16997 \begin_inset Formula $\div$
17007 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17010 \begin_layout Plain Layout
17014 \begin_layout Plain Layout
17027 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17042 \begin_layout Plain Layout
17043 \begin_inset Formula $*$
17053 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17067 \begin_layout Plain Layout
17068 \begin_inset Formula $\star$
17078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17081 \begin_layout Plain Layout
17089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17092 \begin_layout Plain Layout
17093 \begin_inset Formula $\circ$
17103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17106 \begin_layout Plain Layout
17114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17117 \begin_layout Plain Layout
17118 \begin_inset Formula $\diamond$
17128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17131 \begin_layout Plain Layout
17139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17142 \begin_layout Plain Layout
17143 \begin_inset Formula $\bullet$
17157 \begin_inset space \hfill{}
17161 \begin_inset Tabular
17162 <lyxtabular version="3" rows="13" columns="2">
17163 <features booktabs="true" tabularvalignment="middle">
17164 <column alignment="center" valignment="top" width="0pt">
17165 <column alignment="center" valignment="top" width="0pt">
17167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17170 \begin_layout Plain Layout
17176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17179 \begin_layout Plain Layout
17187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17190 \begin_layout Plain Layout
17198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17201 \begin_layout Plain Layout
17202 \begin_inset Formula $\nabla$
17212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17215 \begin_layout Plain Layout
17223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17226 \begin_layout Plain Layout
17227 \begin_inset Formula $\bigtriangledown$
17237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17251 \begin_layout Plain Layout
17252 \begin_inset Formula $\bigtriangleup$
17262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17265 \begin_layout Plain Layout
17273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17276 \begin_layout Plain Layout
17277 \begin_inset Formula $\Box$
17287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17290 \begin_layout Plain Layout
17298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17301 \begin_layout Plain Layout
17302 \begin_inset Formula $\cap$
17312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17315 \begin_layout Plain Layout
17323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\cup$
17337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17340 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17352 \begin_inset Formula $\dagger$
17362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17365 \begin_layout Plain Layout
17373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17376 \begin_layout Plain Layout
17377 \begin_inset Formula $\ddagger$
17387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17390 \begin_layout Plain Layout
17398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17401 \begin_layout Plain Layout
17402 \begin_inset Formula $\wr$
17412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17426 \begin_layout Plain Layout
17427 \begin_inset Formula $\bigcirc$
17437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17440 \begin_layout Plain Layout
17448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17451 \begin_layout Plain Layout
17452 \begin_inset Formula $\wedge$
17462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17465 \begin_layout Plain Layout
17473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17476 \begin_layout Plain Layout
17477 \begin_inset Formula $\vee$
17491 \begin_inset space \hfill{}
17495 \begin_inset Tabular
17496 <lyxtabular version="3" rows="13" columns="2">
17497 <features booktabs="true" tabularvalignment="middle">
17498 <column alignment="center" valignment="top" width="0pt">
17499 <column alignment="center" valignment="top" width="0pt">
17501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17504 \begin_layout Plain Layout
17510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17513 \begin_layout Plain Layout
17521 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17524 \begin_layout Plain Layout
17532 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17535 \begin_layout Plain Layout
17536 \begin_inset Formula $\oplus$
17546 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17549 \begin_layout Plain Layout
17557 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17560 \begin_layout Plain Layout
17561 \begin_inset Formula $\ominus$
17571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17574 \begin_layout Plain Layout
17582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17585 \begin_layout Plain Layout
17586 \begin_inset Formula $\otimes$
17596 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17599 \begin_layout Plain Layout
17607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17610 \begin_layout Plain Layout
17611 \begin_inset Formula $\oslash$
17621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17624 \begin_layout Plain Layout
17632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17635 \begin_layout Plain Layout
17636 \begin_inset Formula $\odot$
17646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17649 \begin_layout Plain Layout
17657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17660 \begin_layout Plain Layout
17661 \begin_inset Formula $\amalg$
17671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17674 \begin_layout Plain Layout
17682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17685 \begin_layout Plain Layout
17686 \begin_inset Formula $\uplus$
17696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17699 \begin_layout Plain Layout
17707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17710 \begin_layout Plain Layout
17711 \begin_inset Formula $\setminus$
17721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17724 \begin_layout Plain Layout
17732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17735 \begin_layout Plain Layout
17736 \begin_inset Formula $\sqcap$
17746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17760 \begin_layout Plain Layout
17761 \begin_inset Formula $\sqcup$
17771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17774 \begin_layout Plain Layout
17782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17785 \begin_layout Plain Layout
17786 \begin_inset Formula $\triangleleft$
17796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17799 \begin_layout Plain Layout
17807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17810 \begin_layout Plain Layout
17811 \begin_inset Formula $\triangleright$
17827 \begin_layout Standard
17828 All binary operators can also be inserted via the math toolbar button
17831 arg "math-insert \\pm"
17837 \begin_layout Standard
17838 To typeset the Laplace operator also
17855 \begin_inset Formula $\nabla^{2}$
17858 ) can be used instead of
17867 \begin_layout Standard
17874 Insert\SpecialChar menuseparator
17886 \begin_layout Subsection
17887 Self-defined Operators
17888 \begin_inset CommandInset label
17890 name "subsec:Self-defined-Operators"
17895 \begin_inset Index idx
17898 \begin_layout Plain Layout
17899 Operators ! self-defined
17907 \begin_layout Standard
17908 With the help of the command
17912 DeclareMathOperator
17915 \begin_inset Index idx
17918 \begin_layout Plain Layout
17923 DeclareMathOperator
17928 custom operators can be defined in the \SpecialChar LaTeX
17930 Its command scheme is:
17933 \begin_layout Standard
17938 DeclareMathOperator{new command}{display}
17941 \begin_layout Standard
17942 Display can be characters or symbols that define how the operator looks
17944 To define a big operator a * is set behind the command.
17945 All self-defined big operators can have limits as described in
17946 \begin_inset CommandInset ref
17948 reference "subsec:Operator-Limits"
17955 \begin_layout Standard
17956 For example the \SpecialChar LaTeX
17960 \begin_layout Standard
17965 DeclareMathOperator*{
17972 \begin_layout Standard
17973 defines the command
17979 , that inserts a big operator consisting of the lozenge symbol from
17980 \begin_inset CommandInset ref
17982 reference "subsec:Miscellaneous-Symbols"
17987 \begin_inset Formula
17989 \Lozenge_{n=1}^{\infty}
17994 The command for this formula is:
18005 \begin_inset Formula $\to$
18011 \begin_layout Standard
18012 \begin_inset VSpace bigskip
18015 When self-defined operators are not used several times in the document,
18016 they can also be defined with the commands
18023 \begin_inset Index idx
18026 \begin_layout Plain Layout
18041 \begin_inset Index idx
18044 \begin_layout Plain Layout
18052 , which have the following scheme:
18055 \begin_layout Standard
18069 \begin_layout Standard
18076 defines big operators,
18085 \begin_layout Standard
18093 \begin_inset space \thinspace{}
18097 \begin_inset space \space{}
18100 be used to use one limit for several operators:
18103 \begin_layout Standard
18104 \begin_inset Formula
18106 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18114 \begin_layout Standard
18115 The command for the formula above is:
18116 \begin_inset Newline newline
18132 \begin_inset space \textvisiblespace{}
18138 \begin_inset Formula $\to$
18144 \begin_inset space \textvisiblespace{}
18152 \begin_layout Section
18154 \begin_inset Index idx
18157 \begin_layout Plain Layout
18166 \begin_layout Subsection
18168 \begin_inset CommandInset label
18170 name "subsec:Font-Styles"
18175 \begin_inset Index idx
18178 \begin_layout Plain Layout
18187 \begin_layout Standard
18188 Latin letters in formulas can be set in one of the following font styles:
18191 \begin_layout Standard
18193 \begin_inset Tabular
18194 <lyxtabular version="3" rows="6" columns="3">
18195 <features booktabs="true" tabularvalignment="middle">
18196 <column alignment="center" valignment="top" width="0pt">
18197 <column alignment="center" valignment="top">
18198 <column alignment="center" valignment="top">
18200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18203 \begin_layout Plain Layout
18209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18212 \begin_layout Plain Layout
18218 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18221 \begin_layout Plain Layout
18229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18232 \begin_layout Plain Layout
18238 \begin_inset space \textvisiblespace{}
18248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18251 \begin_layout Plain Layout
18252 \begin_inset Formula $\mathbb{ABC}$
18260 <cell alignment="center" valignment="top" usebox="none">
18263 \begin_layout Plain Layout
18271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18274 \begin_layout Plain Layout
18280 \begin_inset space \textvisiblespace{}
18290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18293 \begin_layout Plain Layout
18294 \begin_inset Formula $\mathbf{AbC}$
18302 <cell alignment="center" valignment="top" usebox="none">
18305 \begin_layout Plain Layout
18318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18321 \begin_layout Plain Layout
18327 \begin_inset space \textvisiblespace{}
18337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18340 \begin_layout Plain Layout
18341 \begin_inset Formula $\boldsymbol{AbC}$
18349 <cell alignment="center" valignment="top" usebox="none">
18352 \begin_layout Plain Layout
18355 arg "font-boldsymbol"
18365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18368 \begin_layout Plain Layout
18374 \begin_inset space \textvisiblespace{}
18384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18387 \begin_layout Plain Layout
18388 \begin_inset Formula $\mathcal{ABC}$
18396 <cell alignment="center" valignment="top" usebox="none">
18399 \begin_layout Plain Layout
18407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18410 \begin_layout Plain Layout
18416 \begin_inset space \textvisiblespace{}
18426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18429 \begin_layout Plain Layout
18430 \begin_inset Formula $\mathfrak{AbC}$
18438 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18441 \begin_layout Plain Layout
18455 \begin_layout Standard
18457 \begin_inset Tabular
18458 <lyxtabular version="3" rows="6" columns="3">
18459 <features booktabs="true" tabularvalignment="middle">
18460 <column alignment="center" valignment="top" width="0pt">
18461 <column alignment="center" valignment="top">
18462 <column alignment="center" valignment="top">
18464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18467 \begin_layout Plain Layout
18473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18476 \begin_layout Plain Layout
18482 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18485 \begin_layout Plain Layout
18493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18496 \begin_layout Plain Layout
18502 \begin_inset space \textvisiblespace{}
18512 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18515 \begin_layout Plain Layout
18516 \begin_inset Formula $\mathit{AbC}$
18524 <cell alignment="center" valignment="top" usebox="none">
18527 \begin_layout Plain Layout
18535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18538 \begin_layout Plain Layout
18544 \begin_inset space \textvisiblespace{}
18554 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18557 \begin_layout Plain Layout
18558 \begin_inset Formula $\mathrm{AbC}$
18566 <cell alignment="center" valignment="top" usebox="none">
18569 \begin_layout Plain Layout
18582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18585 \begin_layout Plain Layout
18591 \begin_inset space \textvisiblespace{}
18601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\mathsf{AbC}$
18613 <cell alignment="center" valignment="top" usebox="none">
18616 \begin_layout Plain Layout
18629 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18632 \begin_layout Plain Layout
18638 \begin_inset space \textvisiblespace{}
18648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18651 \begin_layout Plain Layout
18652 \begin_inset Formula $\mathtt{AbC}$
18660 <cell alignment="center" valignment="top" usebox="none">
18663 \begin_layout Plain Layout
18666 arg "font-typewriter"
18676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18679 \begin_layout Plain Layout
18685 \begin_inset space \textvisiblespace{}
18695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18698 \begin_layout Plain Layout
18699 \begin_inset Formula $\mathscr{ABC}$
18707 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18710 \begin_layout Plain Layout
18724 \begin_layout Standard
18725 \begin_inset Note Greyedout
18728 \begin_layout Plain Layout
18751 can only be used for big letters.
18759 \begin_layout Standard
18760 Predefined is the style
18769 \begin_layout Standard
18770 The style commands work also for letters in mathematical constructs:
18771 \begin_inset Formula
18773 \mathfrak{A=\frac{b}{C}}
18781 \begin_layout Standard
18782 Characters in mathematical text don't appear in a math font style but in
18783 the text font style
18790 That their style can't be set correctly via the text style dialog is a
18791 bug in \SpecialChar LyX
18796 \begin_layout Plain Layout
18797 \begin_inset CommandInset href
18799 name "LyX-bug #4629"
18800 target "https://www.lyx.org/trac/ticket/4629"
18813 \begin_layout Standard
18814 Instead of the style commands the dialog
18816 Edit\SpecialChar menuseparator
18817 Math\SpecialChar menuseparator
18820 or the toolbar button
18823 arg "math-insert \\font"
18829 \begin_layout Subsection
18831 \begin_inset CommandInset label
18833 name "subsec:Bold-Formulas"
18838 \begin_inset Index idx
18841 \begin_layout Plain Layout
18850 \begin_layout Standard
18851 To make a complete formula bold, the command
18857 from the previous subsection cannot be used, because it doesn't work for
18858 small Greek letters.
18859 Furthermore it prints Latin letters always upright, like in the following
18863 \begin_layout Standard
18864 \begin_inset Formula
18866 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18874 \begin_layout Standard
18875 To display the formula correctly, the command
18882 \begin_inset Formula
18884 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18889 It is also possible to set the formula in a
18891 boldmath environment
18894 This environment is created by inserting the command
18901 \begin_inset Index idx
18904 \begin_layout Plain Layout
18912 in \SpecialChar TeX
18914 To end the environment, the command
18921 \begin_inset Index idx
18924 \begin_layout Plain Layout
18932 is inserted in \SpecialChar TeX
18937 \begin_layout Plain Layout
18947 \begin_inset Formula
18949 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18958 \begin_layout Plain Layout
18970 \begin_layout Subsection
18972 \begin_inset Index idx
18975 \begin_layout Plain Layout
18984 \begin_layout Standard
18985 Formulas can be colored like normal text: Highlight a formula or a formula
18991 Here is a formula in magenta:
18992 \begin_inset Formula
18994 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19002 \begin_layout Standard
19003 You can also define your own colors as described in
19004 \begin_inset CommandInset ref
19006 reference "subsec:Colored-Boxes"
19011 They can be used with the \SpecialChar TeX
19019 \begin_inset Index idx
19022 \begin_layout Plain Layout
19033 \begin_layout Standard
19038 textcolor{color}{characters or formula}
19041 \begin_layout Standard
19042 The following example was colored completely dark green and partly red:
19045 \begin_layout Standard
19049 \begin_layout Plain Layout
19053 textcolor{darkgreen}{
19059 \begin_inset Formula
19061 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19070 \begin_layout Plain Layout
19080 \begin_layout Standard
19081 Due to a bug in \SpecialChar LyX
19082 only complete formulas can be colored with self-defined
19087 \begin_layout Plain Layout
19088 \begin_inset CommandInset href
19090 name "LyX-bug #5269"
19091 target "https://www.lyx.org/trac/ticket/5269"
19104 \begin_layout Subsection
19106 \begin_inset CommandInset label
19108 name "subsec:Font-Sizes"
19113 \begin_inset Index idx
19116 \begin_layout Plain Layout
19125 \begin_layout Standard
19126 For characters in formulas there are, analog to characters in text, the
19127 following size commands:
19130 \begin_layout Standard
19174 \begin_inset Newline newline
19196 \begin_layout Standard
19197 The size produced by the commands depends on the document font size, which
19198 corresponds to the command
19205 The other commands produce smaller or larger sizes than
19212 The font size can however not exceed a certain value.
19213 Is for example the document font size 12
19214 \begin_inset space \thinspace{}
19223 switches to the same size as
19233 \begin_layout Standard
19234 A size command is inserted in \SpecialChar TeX
19235 mode before the formula and sets the size
19236 for all following formula and text characters.
19237 To switch back to the initial size, the command
19243 is inserted behind the formula in \SpecialChar TeX
19247 \begin_layout Standard
19248 Within a formula the size can be changed using the following size commands
19249 or the toolbar button
19252 arg "math-insert \\style"
19258 \begin_layout Standard
19261 \begin_inset Tabular
19262 <lyxtabular version="3" rows="5" columns="2">
19263 <features booktabs="true" tabularvalignment="middle">
19264 <column alignment="center" valignment="top" width="0pt">
19265 <column alignment="center" valignment="top">
19267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19270 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19290 \begin_layout Plain Layout
19294 \begin_inset Index idx
19297 \begin_layout Plain Layout
19310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19313 \begin_layout Plain Layout
19314 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19323 <row topspace="1mm">
19324 <cell alignment="center" valignment="top" usebox="none">
19327 \begin_layout Plain Layout
19335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19338 \begin_layout Plain Layout
19339 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19363 \begin_layout Plain Layout
19364 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19377 \begin_layout Plain Layout
19385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19388 \begin_layout Plain Layout
19389 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19405 \begin_layout Standard
19406 After entering these commands, a blue box appears in which the formula parts
19410 \begin_layout Standard
19411 There is a further method to change the font size, that though only works
19412 for symbols or letters in mathematical text.
19413 To use it, one of the above text size commands is inserted in mathematical
19415 All following characters until the end of the mathematical text or until
19416 another size command will have the selected size.
19418 \begin_inset VSpace -2mm
19424 \begin_layout Standard
19428 \begin_layout Plain Layout
19438 \begin_inset Formula
19440 A=\frac{B}{c}\cdot\maltese
19446 \begin_inset Formula
19448 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19457 \begin_layout Plain Layout
19469 \begin_layout Standard
19470 \begin_inset VSpace medskip
19473 Before both formulas the command
19480 The command for the second formula is:
19481 \begin_inset Newline newline
19489 \begin_inset space \textvisiblespace{}
19495 \begin_inset space \textvisiblespace{}
19501 \begin_inset space \textvisiblespace{}
19507 \begin_inset space \textvisiblespace{}
19511 \begin_inset Formula $\to$
19515 \begin_inset Formula $\to$
19519 \begin_inset Newline newline
19523 \begin_inset space \hspace*{}
19534 \begin_inset space \textvisiblespace{}
19540 \begin_inset space \textvisiblespace{}
19546 \begin_inset space \textvisiblespace{}
19552 \begin_layout Standard
19553 If a symbol cannot be displayed in different sizes, it will always be displayed
19554 in the default size.
19557 \begin_layout Section
19559 \begin_inset Index idx
19562 \begin_layout Plain Layout
19571 \begin_layout Standard
19572 Greek letters can also be inserted via the toolbar button
19575 arg "math-insert \\alpha"
19579 All international typesetting norms purport that Greek letters in math
19580 have to be typeset italic/slanted.
19581 In some languages, like French or Russian, they are nevertheless sometimes
19585 \begin_layout Subsection
19587 \begin_inset Index idx
19590 \begin_layout Plain Layout
19591 Greek letters ! small
19599 \begin_layout Standard
19600 \begin_inset space \hfill{}
19604 \begin_inset Tabular
19605 <lyxtabular version="3" rows="11" columns="2">
19606 <features booktabs="true" tabularvalignment="middle">
19607 <column alignment="center" valignment="top" width="0pt">
19608 <column alignment="center" valignment="top" width="0pt">
19610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Plain Layout
19630 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19633 \begin_layout Plain Layout
19641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19644 \begin_layout Plain Layout
19645 \begin_inset Formula $\alpha$
19655 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19658 \begin_layout Plain Layout
19666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19669 \begin_layout Plain Layout
19670 \begin_inset Formula $\beta$
19680 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19683 \begin_layout Plain Layout
19691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19694 \begin_layout Plain Layout
19695 \begin_inset Formula $\gamma$
19705 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19708 \begin_layout Plain Layout
19716 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19719 \begin_layout Plain Layout
19720 \begin_inset Formula $\delta$
19730 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19733 \begin_layout Plain Layout
19741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19744 \begin_layout Plain Layout
19745 \begin_inset Formula $\epsilon$
19755 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19758 \begin_layout Plain Layout
19766 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19769 \begin_layout Plain Layout
19770 \begin_inset Formula $\varepsilon$
19780 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19783 \begin_layout Plain Layout
19791 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19794 \begin_layout Plain Layout
19795 \begin_inset Formula $\zeta$
19805 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19808 \begin_layout Plain Layout
19816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19819 \begin_layout Plain Layout
19820 \begin_inset Formula $\eta$
19830 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19833 \begin_layout Plain Layout
19841 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19844 \begin_layout Plain Layout
19845 \begin_inset Formula $\theta$
19855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19858 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19869 \begin_layout Plain Layout
19870 \begin_inset Formula $\vartheta$
19884 \begin_inset space \hfill{}
19888 \begin_inset Tabular
19889 <lyxtabular version="3" rows="12" columns="2">
19890 <features booktabs="true" tabularvalignment="middle">
19891 <column alignment="center" valignment="top" width="0pt">
19892 <column alignment="center" valignment="top" width="0pt">
19894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19906 \begin_layout Plain Layout
19914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19917 \begin_layout Plain Layout
19925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19928 \begin_layout Plain Layout
19929 \begin_inset Formula $\iota$
19939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19942 \begin_layout Plain Layout
19950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19953 \begin_layout Plain Layout
19954 \begin_inset Formula $\kappa$
19964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19967 \begin_layout Plain Layout
19975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19978 \begin_layout Plain Layout
19979 \begin_inset Formula $\varkappa$
19989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19992 \begin_layout Plain Layout
20000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20003 \begin_layout Plain Layout
20004 \begin_inset Formula $\lambda$
20014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20017 \begin_layout Plain Layout
20025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20028 \begin_layout Plain Layout
20029 \begin_inset Formula $\mu$
20039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20042 \begin_layout Plain Layout
20050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20053 \begin_layout Plain Layout
20054 \begin_inset Formula $\nu$
20064 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20067 \begin_layout Plain Layout
20075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20078 \begin_layout Plain Layout
20079 \begin_inset Formula $\xi$
20089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20092 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $o$
20112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\pi$
20137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\varpi$
20162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\rho$
20191 \begin_inset space \hfill{}
20195 \begin_inset Tabular
20196 <lyxtabular version="3" rows="11" columns="2">
20197 <features booktabs="true" tabularvalignment="middle">
20198 <column alignment="center" valignment="top" width="0pt">
20199 <column alignment="center" valignment="top" width="0pt">
20201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20204 \begin_layout Plain Layout
20210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20213 \begin_layout Plain Layout
20221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20224 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20236 \begin_inset Formula $\varrho$
20246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20260 \begin_layout Plain Layout
20261 \begin_inset Formula $\sigma$
20271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Plain Layout
20286 \begin_inset Formula $\varsigma$
20296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20299 \begin_layout Plain Layout
20307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20310 \begin_layout Plain Layout
20311 \begin_inset Formula $\tau$
20321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20324 \begin_layout Plain Layout
20332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20335 \begin_layout Plain Layout
20336 \begin_inset Formula $\upsilon$
20346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20349 \begin_layout Plain Layout
20357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20360 \begin_layout Plain Layout
20361 \begin_inset Formula $\phi$
20371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20374 \begin_layout Plain Layout
20382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20385 \begin_layout Plain Layout
20386 \begin_inset Formula $\varphi$
20396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20399 \begin_layout Plain Layout
20407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20410 \begin_layout Plain Layout
20411 \begin_inset Formula $\chi$
20421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20424 \begin_layout Plain Layout
20432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20435 \begin_layout Plain Layout
20436 \begin_inset Formula $\psi$
20446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20449 \begin_layout Plain Layout
20457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20460 \begin_layout Plain Layout
20461 \begin_inset Formula $\omega$
20475 \begin_inset space \hfill{}
20481 \begin_layout Standard
20482 \begin_inset VSpace medskip
20488 \begin_layout Standard
20489 How to create special upright Greek letters is explained in
20490 \begin_inset CommandInset ref
20492 reference "subsec:Upright-small-Greek"
20499 \begin_layout Subsection
20501 \begin_inset Index idx
20504 \begin_layout Plain Layout
20505 Greek letters ! big
20513 \begin_layout Standard
20514 \begin_inset space \hfill{}
20518 \begin_inset Tabular
20519 <lyxtabular version="3" rows="7" columns="2">
20520 <features booktabs="true" tabularvalignment="middle">
20521 <column alignment="center" valignment="top" width="0pt">
20522 <column alignment="center" valignment="top" width="0pt">
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Plain Layout
20544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Plain Layout
20559 \begin_inset Formula $\Gamma$
20569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20572 \begin_layout Plain Layout
20580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20583 \begin_layout Plain Layout
20584 \begin_inset Formula $\Delta$
20594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20597 \begin_layout Plain Layout
20605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20608 \begin_layout Plain Layout
20609 \begin_inset Formula $\Theta$
20619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20622 \begin_layout Plain Layout
20630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20633 \begin_layout Plain Layout
20634 \begin_inset Formula $\Lambda$
20644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20658 \begin_layout Plain Layout
20659 \begin_inset Formula $\Xi$
20669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20672 \begin_layout Plain Layout
20680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Plain Layout
20684 \begin_inset Formula $\Pi$
20698 \begin_inset space \hfill{}
20702 \begin_inset Tabular
20703 <lyxtabular version="3" rows="6" columns="2">
20704 <features booktabs="true" tabularvalignment="middle">
20705 <column alignment="center" valignment="top" width="0pt">
20706 <column alignment="center" valignment="top" width="0pt">
20708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20720 \begin_layout Plain Layout
20728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20731 \begin_layout Plain Layout
20739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20742 \begin_layout Plain Layout
20743 \begin_inset Formula $\Sigma$
20753 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20756 \begin_layout Plain Layout
20764 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20767 \begin_layout Plain Layout
20768 \begin_inset Formula $\Upsilon$
20778 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20781 \begin_layout Plain Layout
20789 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20792 \begin_layout Plain Layout
20793 \begin_inset Formula $\Phi$
20803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20806 \begin_layout Plain Layout
20814 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20817 \begin_layout Plain Layout
20818 \begin_inset Formula $\Psi$
20828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20831 \begin_layout Plain Layout
20839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20842 \begin_layout Plain Layout
20843 \begin_inset Formula $\Omega$
20857 \begin_inset space \hfill{}
20863 \begin_layout Standard
20864 \begin_inset VSpace medskip
20867 That the big Greek letters appear upright is caused by a design bug when
20870 To get correct italic big letters, begin every command with
20875 For example the command
20882 \begin_inset Formula $\varGamma$
20886 Another way is to load the package
20894 \begin_layout Plain Layout
20899 is part of the \SpecialChar LaTeX
20905 \begin_inset Index idx
20908 \begin_layout Plain Layout
20913 \begin_layout Plain Layout
20933 \begin_inset Index idx
20936 \begin_layout Plain Layout
20942 with the \SpecialChar LaTeX
20946 \begin_layout Standard
20951 usepackage{fixmath}
20954 \begin_layout Standard
20955 Then all big Greek letters in a document will automatically be typeset italic.
20958 \begin_layout Subsection
20960 \begin_inset Index idx
20963 \begin_layout Plain Layout
20964 Greek letters ! bold
20972 \begin_layout Standard
20973 Greek letters cannot be set with different font styles like Latin letters.
20974 They can only be made bold with the command
20981 \begin_inset Index idx
20984 \begin_layout Plain Layout
20995 \begin_layout Standard
20997 \begin_inset Tabular
20998 <lyxtabular version="3" rows="3" columns="2">
20999 <features booktabs="true" tabularvalignment="middle">
21000 <column alignment="center" valignment="top" width="0pt">
21001 <column alignment="center" valignment="top">
21003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21006 \begin_layout Plain Layout
21012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21015 \begin_layout Plain Layout
21023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21026 \begin_layout Plain Layout
21038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21041 \begin_layout Plain Layout
21042 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21055 \begin_layout Plain Layout
21067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21070 \begin_layout Plain Layout
21071 \begin_inset Formula $\theta\boldsymbol{\theta}$
21087 \begin_layout Section
21092 \begin_layout Plain Layout
21105 \begin_layout Plain Layout
21106 A list with all symbols of most of the \SpecialChar LaTeX
21107 -packages can be found in
21108 \begin_inset CommandInset citation
21124 \begin_layout Plain Layout
21132 \begin_inset Note Note
21135 \begin_layout Plain Layout
21138 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21141 \begin_layout Plain Layout
21144 texorpdfstring is in section
21145 \begin_inset CommandInset ref
21147 reference "subsec:Formulas-in-Section"
21157 \begin_inset Index idx
21160 \begin_layout Plain Layout
21169 \begin_layout Standard
21170 Many of the symbols listed in this section can also be inserted via the
21174 arg "math-insert \\nabla"
21180 arg "math-insert \\digamma"
21186 \begin_layout Subsection
21187 Mathematical Symbols
21188 \begin_inset CommandInset label
21190 name "subsec:Mathematical-Symbols"
21195 \begin_inset Index idx
21198 \begin_layout Plain Layout
21199 Symbols ! mathematical
21207 \begin_layout Standard
21208 \begin_inset Tabular
21209 <lyxtabular version="3" rows="10" columns="2">
21210 <features booktabs="true" tabularvalignment="middle">
21211 <column alignment="center" valignment="top" width="0pt">
21212 <column alignment="center" valignment="top" width="0pt">
21214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21217 \begin_layout Plain Layout
21223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21226 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21237 \begin_layout Plain Layout
21245 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21248 \begin_layout Plain Layout
21249 \begin_inset Formula $\neg$
21259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21262 \begin_layout Plain Layout
21270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21273 \begin_layout Plain Layout
21274 \begin_inset Formula $\Im$
21284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21287 \begin_layout Plain Layout
21295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21298 \begin_layout Plain Layout
21299 \begin_inset Formula $\Re$
21309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21312 \begin_layout Plain Layout
21320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21323 \begin_layout Plain Layout
21324 \begin_inset Formula $\aleph$
21334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21337 \begin_layout Plain Layout
21345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21348 \begin_layout Plain Layout
21349 \begin_inset Formula $\partial$
21359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21362 \begin_layout Plain Layout
21370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21373 \begin_layout Plain Layout
21374 \begin_inset Formula $\infty$
21384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21387 \begin_layout Plain Layout
21395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21398 \begin_layout Plain Layout
21399 \begin_inset Formula $\wp$
21409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21412 \begin_layout Plain Layout
21420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21423 \begin_layout Plain Layout
21424 \begin_inset Formula $\imath$
21434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21437 \begin_layout Plain Layout
21445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21448 \begin_layout Plain Layout
21449 \begin_inset Formula $\jmath$
21463 \begin_inset space \hfill{}
21467 \begin_inset Tabular
21468 <lyxtabular version="3" rows="10" columns="2">
21469 <features booktabs="true" tabularvalignment="middle">
21470 <column alignment="center" valignment="top" width="0pt">
21471 <column alignment="center" valignment="top" width="0pt">
21473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21487 \begin_inset Note Note
21490 \begin_layout Plain Layout
21497 is only used as spacer.
21509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21512 \begin_layout Plain Layout
21520 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21523 \begin_layout Plain Layout
21524 \begin_inset Formula $\forall$
21534 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21537 \begin_layout Plain Layout
21545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21548 \begin_layout Plain Layout
21549 \begin_inset Formula $\exists$
21559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21562 \begin_layout Plain Layout
21570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21573 \begin_layout Plain Layout
21574 \begin_inset Formula $\nexists$
21584 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21587 \begin_layout Plain Layout
21595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21598 \begin_layout Plain Layout
21599 \begin_inset Formula $\emptyset$
21609 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21612 \begin_layout Plain Layout
21620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21623 \begin_layout Plain Layout
21624 \begin_inset Formula $\varnothing$
21634 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21637 \begin_layout Plain Layout
21645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21648 \begin_layout Plain Layout
21649 \begin_inset Formula $\dag$
21659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21662 \begin_layout Plain Layout
21670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21673 \begin_layout Plain Layout
21674 \begin_inset Formula $\ddag$
21684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21687 \begin_layout Plain Layout
21695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21698 \begin_layout Plain Layout
21702 \begin_layout Plain Layout
21712 \begin_inset Formula $\complement$
21719 \begin_layout Plain Layout
21733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21736 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21748 \begin_inset Formula $\Bbbk$
21762 \begin_inset space \hfill{}
21766 \begin_inset Tabular
21767 <lyxtabular version="3" rows="10" columns="2">
21768 <features booktabs="true" tabularvalignment="middle">
21769 <column alignment="center" valignment="top" width="0pt">
21770 <column alignment="center" valignment="top" width="0pt">
21772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21775 \begin_layout Plain Layout
21781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21795 \begin_layout Plain Layout
21803 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21806 \begin_layout Plain Layout
21807 \begin_inset Formula $\prime$
21817 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21820 \begin_layout Plain Layout
21828 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21831 \begin_layout Plain Layout
21832 \begin_inset Formula $\backprime$
21842 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21845 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21856 \begin_layout Plain Layout
21857 \begin_inset Formula $\mho$
21867 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21870 \begin_layout Plain Layout
21878 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21881 \begin_layout Plain Layout
21882 \begin_inset Formula $\triangle$
21892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21895 \begin_layout Plain Layout
21903 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21906 \begin_layout Plain Layout
21907 \begin_inset Formula $\angle$
21917 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21920 \begin_layout Plain Layout
21928 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21931 \begin_layout Plain Layout
21932 \begin_inset Formula $\measuredangle$
21942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21945 \begin_layout Plain Layout
21953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21956 \begin_layout Plain Layout
21957 \begin_inset Formula $\sphericalangle$
21967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21970 \begin_layout Plain Layout
21978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21981 \begin_layout Plain Layout
21982 \begin_inset Formula $\top$
21992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21995 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22007 \begin_inset Formula $\bot$
22023 \begin_layout Subsection
22024 Miscellaneous Symbols
22025 \begin_inset CommandInset label
22027 name "subsec:Miscellaneous-Symbols"
22032 \begin_inset Index idx
22035 \begin_layout Plain Layout
22036 Symbols ! miscellaneous
22044 \begin_layout Standard
22047 \begin_inset Tabular
22048 <lyxtabular version="3" rows="10" columns="2">
22049 <features booktabs="true" tabularvalignment="middle">
22050 <column alignment="center" valignment="top" width="0pt">
22051 <column alignment="center" valignment="top" width="0pt">
22053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Plain Layout
22062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22065 \begin_layout Plain Layout
22073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22076 \begin_layout Plain Layout
22084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22087 \begin_layout Plain Layout
22088 \begin_inset Formula $\flat$
22098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22101 \begin_layout Plain Layout
22109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22112 \begin_layout Plain Layout
22113 \begin_inset Formula $\natural$
22123 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22126 \begin_layout Plain Layout
22134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22137 \begin_layout Plain Layout
22138 \begin_inset Formula $\sharp$
22148 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22151 \begin_layout Plain Layout
22159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22162 \begin_layout Plain Layout
22163 \begin_inset Formula $\surd$
22173 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22176 \begin_layout Plain Layout
22184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22187 \begin_layout Plain Layout
22188 \begin_inset Formula $\checkmark$
22198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22201 \begin_layout Plain Layout
22209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22212 \begin_layout Plain Layout
22213 \begin_inset Formula $\yen$
22223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22226 \begin_layout Plain Layout
22234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22237 \begin_layout Plain Layout
22238 \begin_inset Formula $\pounds$
22248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22251 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22261 \begin_inset Formula $\$$
22271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22284 \begin_inset Formula $§$
22298 \begin_inset space \hfill{}
22302 \begin_inset Tabular
22303 <lyxtabular version="3" rows="10" columns="2">
22304 <features booktabs="true" tabularvalignment="middle">
22305 <column alignment="center" valignment="top" width="0pt">
22306 <column alignment="center" valignment="top">
22308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22320 \begin_layout Plain Layout
22328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22331 \begin_layout Plain Layout
22339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22342 \begin_layout Plain Layout
22343 \begin_inset Formula $\hbar$
22353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22356 \begin_layout Plain Layout
22364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22367 \begin_layout Plain Layout
22368 \begin_inset Formula $\hslash$
22378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22381 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22393 \begin_inset Formula $\clubsuit$
22403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22406 \begin_layout Plain Layout
22414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22417 \begin_layout Plain Layout
22418 \begin_inset Formula $\spadesuit$
22428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22431 \begin_layout Plain Layout
22439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22442 \begin_layout Plain Layout
22443 \begin_inset Formula $\bigstar$
22453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22456 \begin_layout Plain Layout
22464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22467 \begin_layout Plain Layout
22468 \begin_inset Formula $\blacklozenge$
22478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22481 \begin_layout Plain Layout
22489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22492 \begin_layout Plain Layout
22493 \begin_inset Formula $\blacktriangle$
22503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22506 \begin_layout Plain Layout
22514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22517 \begin_layout Plain Layout
22518 \begin_inset Formula $\blacktriangledown$
22528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22542 \begin_layout Plain Layout
22543 \begin_inset Formula $\bullet$
22557 \begin_inset space \hfill{}
22561 \begin_inset Tabular
22562 <lyxtabular version="3" rows="10" columns="2">
22563 <features booktabs="true" tabularvalignment="middle">
22564 <column alignment="center" valignment="top" width="0pt">
22565 <column alignment="center" valignment="top" width="0pt">
22567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22570 \begin_layout Plain Layout
22576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22579 \begin_layout Plain Layout
22587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22590 \begin_layout Plain Layout
22598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22601 \begin_layout Plain Layout
22602 \begin_inset Formula $\diamondsuit$
22612 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22615 \begin_layout Plain Layout
22623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Plain Layout
22627 \begin_inset Formula $\Diamond$
22637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22652 \begin_inset Formula $\heartsuit$
22662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22665 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $\P$
22687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\copyright$
22712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\circledR$
22737 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\maltese$
22762 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\diagup$
22787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\diagdown$
22818 \begin_layout Standard
22819 \begin_inset VSpace medskip
22825 \begin_layout Standard
22826 Some symbols can be displayed in different sizes, see
22827 \begin_inset CommandInset ref
22829 reference "subsec:Font-Sizes"
22836 \begin_layout Subsection
22838 \begin_inset Index idx
22841 \begin_layout Plain Layout
22842 Symbols ! Euro-symbol
22848 \begin_inset Index idx
22851 \begin_layout Plain Layout
22858 \begin_layout Plain Layout
22875 \begin_layout Standard
22876 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22882 \begin_inset Index idx
22885 \begin_layout Plain Layout
22891 must be installed and loaded with the \SpecialChar LaTeX
22895 \begin_layout Standard
22900 usepackage[gennarrow]{eurosym}
22903 \begin_layout Standard
22904 The Euro symbol can now be inserted with the command
22911 \begin_inset Index idx
22914 \begin_layout Plain Layout
22925 \begin_layout Standard
22926 The Euro symbol can directly be inserted with the € key in mathematical
22927 text, without having
22942 can also be inserted in \SpecialChar TeX
22944 The official currency symbol can then be inserted with the command
22951 \begin_inset Index idx
22954 \begin_layout Plain Layout
22962 , that is only available in \SpecialChar TeX
22966 \begin_layout Standard
22970 \begin_layout Plain Layout
22980 \begin_inset Note Note
22983 \begin_layout Plain Layout
22984 The following table will only be displayed when the \SpecialChar LaTeX
22997 \begin_layout Standard
22998 An overview about the different Euro symbols:
23001 \begin_layout Standard
23003 \begin_inset Tabular
23004 <lyxtabular version="3" rows="4" columns="3">
23005 <features booktabs="true" tabularvalignment="middle">
23006 <column alignment="center" valignment="top" width="0pt">
23007 <column alignment="center" valignment="top" width="0pt">
23008 <column alignment="center" valignment="top" width="0pt">
23010 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23013 \begin_layout Plain Layout
23017 \begin_layout Plain Layout
23021 cmidrule[0.08em]{2-3}
23031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23034 \begin_layout Plain Layout
23040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23043 \begin_layout Plain Layout
23051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23054 \begin_layout Plain Layout
23060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23063 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23074 \begin_layout Plain Layout
23075 \begin_inset Formula $\euro$
23085 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23088 \begin_layout Plain Layout
23094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23097 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\mbox{€}$
23117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23130 \begin_layout Plain Layout
23138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23141 \begin_layout Plain Layout
23145 \begin_layout Plain Layout
23165 \begin_inset Note Note
23168 \begin_layout Plain Layout
23175 is used here only for table borders.
23185 manual for details.
23193 \begin_layout Standard
23197 \begin_layout Plain Layout
23207 \begin_inset Note Note
23210 \begin_layout Plain Layout
23211 The following will be displayed when the \SpecialChar LaTeX
23224 \begin_layout Standard
23225 You need to install the \SpecialChar LaTeX
23230 to see the rest of this subsection in the output.
23233 \begin_layout Standard
23237 \begin_layout Plain Layout
23249 \begin_layout Section
23251 \begin_inset CommandInset label
23253 name "sec:Relations"
23258 \begin_inset Index idx
23261 \begin_layout Plain Layout
23268 \begin_inset Index idx
23271 \begin_layout Plain Layout
23276 \begin_layout Plain Layout
23287 \begin_layout Plain Layout
23302 \begin_layout Standard
23303 All following relations can also be inserted via the toolbar button
23306 arg "math-insert \\leq"
23312 \begin_layout Standard
23313 \begin_inset Tabular
23314 <lyxtabular version="3" rows="17" columns="2">
23315 <features booktabs="true" tabularvalignment="middle">
23316 <column alignment="center" valignment="top" width="0pt">
23317 <column alignment="center" valignment="top" width="0pt">
23319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23342 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $<$
23362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23376 \begin_layout Plain Layout
23377 \begin_inset Formula $\le$
23387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23390 \begin_layout Plain Layout
23398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23401 \begin_layout Plain Layout
23402 \begin_inset Formula $\ll$
23412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $\prec$
23437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\preceq$
23462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\subset$
23487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\subseteq$
23512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\sqsubseteq$
23537 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\in$
23562 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\vdash$
23587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23590 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $\smile$
23612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\lhd$
23637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\unlhd$
23662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23665 \begin_layout Plain Layout
23673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23676 \begin_layout Plain Layout
23677 \begin_inset Formula $\gtrless$
23687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23702 \begin_inset Formula $\mid$
23712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23726 \begin_layout Plain Layout
23727 \begin_inset Formula $\nmid$
23741 \begin_inset space \hfill{}
23745 \begin_inset Tabular
23746 <lyxtabular version="3" rows="17" columns="2">
23747 <features booktabs="true" tabularvalignment="middle">
23748 <column alignment="center" valignment="top" width="0pt">
23749 <column alignment="center" valignment="top" width="0pt">
23751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23763 \begin_layout Plain Layout
23771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23774 \begin_layout Plain Layout
23780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23783 \begin_layout Plain Layout
23784 \begin_inset Formula $=$
23794 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23797 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23809 \begin_inset Formula $\not=$
23819 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23822 \begin_layout Plain Layout
23830 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23833 \begin_layout Plain Layout
23834 \begin_inset Formula $\equiv$
23844 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23847 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23859 \begin_inset Formula $\sim$
23869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23872 \begin_layout Plain Layout
23880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23883 \begin_layout Plain Layout
23884 \begin_inset Formula $\simeq$
23894 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23909 \begin_inset Formula $\approx$
23919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23922 \begin_layout Plain Layout
23930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23933 \begin_layout Plain Layout
23934 \begin_inset Formula $\cong$
23944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23959 \begin_inset Formula $\bowtie$
23969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23972 \begin_layout Plain Layout
23980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23983 \begin_layout Plain Layout
23984 \begin_inset Formula $\notin$
23994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24009 \begin_inset Formula $\perp$
24019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24022 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24034 \begin_inset Formula $\propto$
24044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24047 \begin_layout Plain Layout
24055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24058 \begin_layout Plain Layout
24059 \begin_inset Formula $\asymp$
24069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24072 \begin_layout Plain Layout
24080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24083 \begin_layout Plain Layout
24084 \begin_inset Formula $\doteq$
24094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24097 \begin_layout Plain Layout
24105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24108 \begin_layout Plain Layout
24109 \begin_inset Formula $\circeq$
24119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24134 \begin_inset Formula $\models$
24144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24158 \begin_layout Plain Layout
24159 \begin_inset Formula $\widehat{=}$
24173 \begin_inset space \hfill{}
24177 \begin_inset Tabular
24178 <lyxtabular version="3" rows="17" columns="2">
24179 <features booktabs="true" tabularvalignment="middle">
24180 <column alignment="center" valignment="top" width="0pt">
24181 <column alignment="center" valignment="top" width="0pt">
24183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24206 \begin_layout Plain Layout
24212 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24215 \begin_layout Plain Layout
24216 \begin_inset Formula $>$
24226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24229 \begin_layout Plain Layout
24237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24240 \begin_layout Plain Layout
24241 \begin_inset Formula $\ge$
24251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24265 \begin_layout Plain Layout
24266 \begin_inset Formula $\gg$
24276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24279 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24291 \begin_inset Formula $\succ$
24301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24315 \begin_layout Plain Layout
24316 \begin_inset Formula $\succeq$
24326 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24329 \begin_layout Plain Layout
24337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24340 \begin_layout Plain Layout
24341 \begin_inset Formula $\supset$
24351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24354 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24366 \begin_inset Formula $\supseteq$
24376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24379 \begin_layout Plain Layout
24387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24390 \begin_layout Plain Layout
24391 \begin_inset Formula $\sqsupseteq$
24401 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Plain Layout
24416 \begin_inset Formula $\ni$
24426 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24440 \begin_layout Plain Layout
24441 \begin_inset Formula $\dashv$
24451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24454 \begin_layout Plain Layout
24462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24465 \begin_layout Plain Layout
24466 \begin_inset Formula $\frown$
24476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24479 \begin_layout Plain Layout
24487 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24490 \begin_layout Plain Layout
24491 \begin_inset Formula $\rhd$
24501 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24515 \begin_layout Plain Layout
24516 \begin_inset Formula $\unrhd$
24526 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24540 \begin_layout Plain Layout
24541 \begin_inset Formula $\lessgtr$
24551 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24554 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24565 \begin_layout Plain Layout
24566 \begin_inset Formula $\parallel$
24576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24579 \begin_layout Plain Layout
24587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24590 \begin_layout Plain Layout
24591 \begin_inset Formula $\nparallel$
24607 \begin_layout Standard
24608 \begin_inset VSpace medskip
24623 are bigger than the equal looking operators
24638 \begin_layout Standard
24640 supports also many special relations.
24641 Use the toolbar button
24644 arg "math-insert \\leqq"
24647 to see a list of these relations.
24650 \begin_layout Standard
24651 Relations are, in contrary to symbols, always surrounded by space.
24654 \begin_layout Standard
24655 Relations with labels can be created with the command
24662 \begin_inset Index idx
24665 \begin_layout Plain Layout
24676 \begin_layout Standard
24678 \begin_inset Tabular
24679 <lyxtabular version="3" rows="2" columns="2">
24680 <features booktabs="true" tabularvalignment="middle">
24681 <column alignment="center" valignment="top" width="0pt">
24682 <column alignment="center" valignment="top">
24684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24687 \begin_layout Plain Layout
24693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24696 \begin_layout Plain Layout
24703 <row topspace="1.5mm">
24704 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24707 \begin_layout Plain Layout
24711 \begin_inset space \textvisiblespace{}
24719 \begin_inset space \textvisiblespace{}
24723 \begin_inset Formula $\downarrow$
24729 \begin_inset space \textvisiblespace{}
24733 \begin_inset space \textvisiblespace{}
24741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24744 \begin_layout Plain Layout
24745 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24761 \begin_layout Section
24765 \begin_layout Subsection
24766 Predefined Functions
24767 \begin_inset CommandInset label
24769 name "subsec:Predefined-Functions"
24774 \begin_inset Index idx
24777 \begin_layout Plain Layout
24778 Functions ! predefined
24786 \begin_layout Standard
24787 In general, variables are set
24791 in mathematical expressions, but not function names, because
24792 \begin_inset Formula $sin$
24795 could be misunderstood as
24796 \begin_inset Formula $s\cdot i\cdot n$
24800 Therefore there are predefined functions which are additionally a bit separated
24802 They are inserted as commands starting with a backslash before their name.
24805 \begin_layout Standard
24807 \begin_inset Tabular
24808 <lyxtabular version="3" rows="2" columns="2">
24809 <features booktabs="true" tabularvalignment="middle">
24810 <column alignment="center" valignment="top" width="0pt">
24811 <column alignment="center" valignment="top" width="0pt">
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24816 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24825 \begin_layout Plain Layout
24833 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24836 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24845 \begin_layout Plain Layout
24846 \begin_inset Formula $Asin(x)+B$
24860 \begin_inset space \quad{}
24864 \begin_inset Tabular
24865 <lyxtabular version="3" rows="2" columns="2">
24866 <features booktabs="true" tabularvalignment="middle">
24867 <column alignment="center" valignment="top" width="0pt">
24868 <column alignment="center" valignment="top" width="0pt">
24870 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24873 \begin_layout Plain Layout
24879 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24882 \begin_layout Plain Layout
24890 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24893 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24904 \begin_layout Plain Layout
24905 \begin_inset Formula $A\sin(x)+B$
24921 \begin_layout Standard
24922 The following functions are predefined:
24925 \begin_layout Standard
24926 \begin_inset VSpace -2mm
24932 \begin_layout Standard
24934 \begin_inset Tabular
24935 <lyxtabular version="3" rows="9" columns="4">
24936 <features booktabs="true" tabularvalignment="middle">
24937 <column alignment="center" valignment="top" width="0pt">
24938 <column alignment="center" valignment="top" width="0pt">
24939 <column alignment="center" valignment="top" width="0pt">
24940 <column alignment="center" valignment="top" width="0pt">
24942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24963 \begin_layout Plain Layout
24969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24972 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24983 \begin_layout Plain Layout
24991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24994 \begin_layout Plain Layout
25002 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25005 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25016 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25029 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25062 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25075 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25108 \begin_layout Plain Layout
25118 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25121 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25154 \begin_layout Plain Layout
25164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25167 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25200 \begin_layout Plain Layout
25210 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25213 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25246 \begin_layout Plain Layout
25256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25259 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25292 \begin_layout Plain Layout
25302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25305 \begin_layout Plain Layout
25313 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25327 \begin_layout Plain Layout
25335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25338 \begin_layout Plain Layout
25354 \begin_layout Standard
25355 They can also be inserted with the math toolbar button
25358 arg "math-insert \\functions"
25364 \begin_layout Subsection
25365 Self-defined Functions
25366 \begin_inset Index idx
25369 \begin_layout Plain Layout
25370 Functions ! self-defined
25378 \begin_layout Standard
25379 To use a function that is not predefined, like for example the sign function
25380 sgn(x), there are two possibilities:
25383 \begin_layout Itemize
25384 Define the function by inserting the following line to the \SpecialChar LaTeX
25389 \begin_layout Plain Layout
25394 DeclareMathOperator
25397 \begin_inset CommandInset ref
25399 reference "subsec:Self-defined-Operators"
25409 \begin_inset Newline newline
25413 \begin_inset VSpace -3mm
25417 \begin_inset Newline newline
25424 DeclareMathOperator{
25429 \begin_inset Index idx
25432 \begin_layout Plain Layout
25437 DeclareMathOperator
25443 \begin_inset Newline newline
25447 \begin_inset VSpace -2mm
25451 \begin_inset Newline newline
25454 Now the new defined function can be called with the command
25463 \begin_layout Itemize
25464 Write the formula as usual, mark the formula name, in our example the letters
25469 , and change it to mathematical text.
25470 Finally, a space is inserted between prefactor and function.
25473 \begin_layout Standard
25474 The result is the same with both methods as with a predefined function
25478 \begin_layout Plain Layout
25479 In \SpecialChar LyX
25480 self-defined functions are displayed red, predefined ones black.
25488 \begin_layout Standard
25490 \begin_inset Tabular
25491 <lyxtabular version="3" rows="3" columns="2">
25492 <features booktabs="true" tabularvalignment="middle">
25493 <column alignment="center" valignment="top" width="0pt">
25494 <column alignment="center" valignment="top" width="0pt">
25496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25499 \begin_layout Plain Layout
25505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25508 \begin_layout Plain Layout
25516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25519 \begin_layout Plain Layout
25527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25530 \begin_layout Plain Layout
25531 \begin_inset Formula $A\sgn(x)+B$
25541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25548 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25559 \begin_layout Plain Layout
25560 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25576 \begin_layout Standard
25577 The first method is more suitable when the self-defined function should
25578 be used several times.
25581 \begin_layout Subsection
25583 \begin_inset Index idx
25586 \begin_layout Plain Layout
25595 \begin_layout Standard
25596 For limits, in addition to the commands
25603 \begin_inset Index idx
25606 \begin_layout Plain Layout
25626 the following functions are defined:
25629 \begin_layout Standard
25631 \begin_inset Tabular
25632 <lyxtabular version="3" rows="5" columns="2">
25633 <features booktabs="true" tabularvalignment="middle">
25634 <column alignment="center" valignment="top" width="0pt">
25635 <column alignment="center" valignment="top" width="0pt">
25637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25640 \begin_layout Plain Layout
25646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25649 \begin_layout Plain Layout
25657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25671 \begin_layout Plain Layout
25672 \begin_inset Formula $\varliminf$
25681 <row topspace="1.5mm">
25682 <cell alignment="center" valignment="top" usebox="none">
25685 \begin_layout Plain Layout
25693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25696 \begin_layout Plain Layout
25697 \begin_inset Formula $\varlimsup$
25706 <row topspace="1.5mm">
25707 <cell alignment="center" valignment="top" usebox="none">
25710 \begin_layout Plain Layout
25718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25721 \begin_layout Plain Layout
25722 \begin_inset Formula $\varprojlim$
25731 <row topspace="1.5mm" bottomspace="1mm">
25732 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25735 \begin_layout Plain Layout
25743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25746 \begin_layout Plain Layout
25747 \begin_inset Formula $\varinjlim$
25763 \begin_layout Standard
25764 \begin_inset VSpace medskip
25767 The limit is created by inserting a subscript.
25768 It is set right beside the function in an inline formula:
25771 \begin_layout Standard
25773 \begin_inset Tabular
25774 <lyxtabular version="3" rows="2" columns="2">
25775 <features booktabs="true" tabularvalignment="middle">
25776 <column alignment="center" valignment="top" width="0pt">
25777 <column alignment="center" valignment="top" width="0pt">
25779 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25782 \begin_layout Plain Layout
25788 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25791 \begin_layout Plain Layout
25799 <cell alignment="center" valignment="top" usebox="none">
25802 \begin_layout Plain Layout
25808 \begin_inset space \textvisiblespace{}
25812 \begin_inset space \textvisiblespace{}
25820 <cell alignment="center" valignment="top" usebox="none">
25823 \begin_layout Plain Layout
25824 \begin_inset Formula $\lim_{x\to A}x=B$
25840 \begin_layout Standard
25841 In a displayed formula the limit is set below the formula, as usual:
25842 \begin_inset Formula
25852 \begin_layout Standard
25853 \begin_inset VSpace medskip
25859 \begin_layout Standard
25860 How to adjust the typesetting of the limits see
25861 \begin_inset CommandInset ref
25863 reference "subsec:Operator-Limits"
25870 \begin_layout Subsection
25872 \begin_inset Index idx
25875 \begin_layout Plain Layout
25876 Functions ! modulo-
25884 \begin_layout Standard
25885 The modulo-function is special, because it exists in four variants.
25886 The variants in a displayed formula are:
25887 \begin_inset Formula
25889 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25890 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25891 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25892 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25893 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25901 \begin_layout Standard
25902 In an inline formula less space is set before the function names for all
25904 By default the modulo-functions take only the first following character
25906 To use more than one character, one has to put them into \SpecialChar TeX
25908 \begin_inset Formula
25910 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25911 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25912 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25920 \begin_layout Section
25922 \begin_inset Index idx
25925 \begin_layout Plain Layout
25934 \begin_layout Standard
25935 The characters ^ and _ would normally create a superscript and subscript,
25937 To get these characters you have to insert them with a leading
25942 \begin_layout Standard
25945 \begin_inset Tabular
25946 <lyxtabular version="3" rows="3" columns="2">
25947 <features booktabs="true" tabularvalignment="middle">
25948 <column alignment="left" valignment="top" width="0pt">
25949 <column alignment="block" valignment="top">
25951 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25954 \begin_layout Plain Layout
25960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25963 \begin_layout Plain Layout
25971 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25974 \begin_layout Plain Layout
25978 \begin_inset space \textvisiblespace{}
25986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25989 \begin_layout Plain Layout
25990 \begin_inset Formula $\mathcircumflex$
26000 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26003 \begin_layout Plain Layout
26011 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26014 \begin_layout Plain Layout
26015 \begin_inset Formula $\_$
26031 \begin_layout Subsection
26032 Special Characters in Mathematical Text
26035 \begin_layout Standard
26036 The following commands can only be used in mathematical text or in \SpecialChar TeX
26040 \begin_layout Standard
26041 \begin_inset space \hfill{}
26045 \begin_inset Tabular
26046 <lyxtabular version="3" rows="8" columns="2">
26047 <features booktabs="true" tabularvalignment="middle">
26048 <column alignment="left" valignment="top" width="0pt">
26049 <column alignment="block" valignment="top">
26051 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26054 \begin_layout Plain Layout
26060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26063 \begin_layout Plain Layout
26071 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26074 \begin_layout Plain Layout
26082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26085 \begin_layout Plain Layout
26086 \begin_inset Formula $\textrm{œ}$
26096 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26099 \begin_layout Plain Layout
26107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26110 \begin_layout Plain Layout
26111 \begin_inset Formula $\textrm{Œ}$
26121 <cell alignment="left" 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 $\textrm{æ}$
26146 <cell alignment="left" 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 $\textrm{Æ}$
26171 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26174 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26186 \begin_inset Formula $\textrm{å}$
26196 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26199 \begin_layout Plain Layout
26207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26210 \begin_layout Plain Layout
26211 \begin_inset Formula $\textrm{Å}$
26221 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26224 \begin_layout Plain Layout
26232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26235 \begin_layout Plain Layout
26236 \begin_inset Formula $\textrm{ı}$
26250 \begin_inset space \hfill{}
26254 \begin_inset Tabular
26255 <lyxtabular version="3" rows="8" columns="2">
26256 <features booktabs="true" tabularvalignment="middle">
26257 <column alignment="left" valignment="top" width="0pt">
26258 <column alignment="center" valignment="top">
26260 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26263 \begin_layout Plain Layout
26265 \begin_inset Note Note
26268 \begin_layout Plain Layout
26270 \begin_inset space \thinspace{}
26273 mm is used for separation, because otherwise the output will be ¡ and ¿
26284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26287 \begin_layout Plain Layout
26295 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26298 \begin_layout Plain Layout
26306 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26309 \begin_layout Plain Layout
26310 \begin_inset Formula $\textrm{ø}$
26320 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26323 \begin_layout Plain Layout
26331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26334 \begin_layout Plain Layout
26335 \begin_inset Formula $\textrm{Ø}$
26345 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26348 \begin_layout Plain Layout
26356 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26359 \begin_layout Plain Layout
26360 \begin_inset Formula $\textrm{ł}$
26370 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26373 \begin_layout Plain Layout
26381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26384 \begin_layout Plain Layout
26385 \begin_inset Formula $\textrm{Ł}$
26395 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26398 \begin_layout Plain Layout
26400 \begin_inset space \hspace{}
26405 \begin_inset space \textvisiblespace{}
26413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26416 \begin_layout Plain Layout
26417 \begin_inset Formula $\textrm{!`}$
26427 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26430 \begin_layout Plain Layout
26432 \begin_inset space \hspace{}
26437 \begin_inset space \textvisiblespace{}
26445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26448 \begin_layout Plain Layout
26449 \begin_inset Formula $\textrm{?`}$
26459 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26462 \begin_layout Plain Layout
26470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26473 \begin_layout Plain Layout
26474 \begin_inset Formula $\textrm{ȷ}$
26488 \begin_inset space \hfill{}
26494 \begin_layout Standard
26496 \begin_inset Formula $\textrm{Å}$
26500 \begin_inset Formula $\textrm{Ø}$
26503 can also be inserted via the math toolbar button
26506 arg "math-insert \\digamma"
26512 \begin_layout Standard
26513 An exception are the commands
26516 \begin_inset space \hspace{}
26525 \begin_inset space \hspace{}
26531 , because they can be inserted in \SpecialChar LyX
26535 \begin_layout Subsection
26537 \begin_inset CommandInset label
26539 name "subsec:Accents-in-Text"
26544 \begin_inset Index idx
26547 \begin_layout Plain Layout
26556 \begin_layout Standard
26557 With the following commands all letters can be accented.
26558 The commands must be inserted in \SpecialChar TeX
26562 \begin_layout Standard
26563 \begin_inset space \hfill{}
26567 \begin_inset Tabular
26568 <lyxtabular version="3" rows="8" columns="2">
26569 <features booktabs="true" tabularvalignment="middle">
26570 <column alignment="left" valignment="top" width="0pt">
26571 <column alignment="block" valignment="top">
26573 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26576 \begin_layout Plain Layout
26582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26585 \begin_layout Plain Layout
26593 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26596 \begin_layout Plain Layout
26600 \begin_inset Quotes grd
26608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26611 \begin_layout Plain Layout
26615 \begin_layout Plain Layout
26631 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26634 \begin_layout Plain Layout
26642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26645 \begin_layout Plain Layout
26649 \begin_layout Plain Layout
26665 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26668 \begin_layout Plain Layout
26672 \begin_inset space \textvisiblespace{}
26680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26683 \begin_layout Plain Layout
26687 \begin_layout Plain Layout
26703 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26706 \begin_layout Plain Layout
26714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26717 \begin_layout Plain Layout
26721 \begin_layout Plain Layout
26737 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26740 \begin_layout Plain Layout
26744 \begin_inset space \textvisiblespace{}
26752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26755 \begin_layout Plain Layout
26759 \begin_layout Plain Layout
26775 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26778 \begin_layout Plain Layout
26782 \begin_inset space \textvisiblespace{}
26790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26793 \begin_layout Plain Layout
26797 \begin_layout Plain Layout
26813 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26816 \begin_layout Plain Layout
26820 \begin_inset space \textvisiblespace{}
26828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26831 \begin_layout Plain Layout
26835 \begin_layout Plain Layout
26855 \begin_inset space \hfill{}
26859 \begin_inset Tabular
26860 <lyxtabular version="3" rows="8" columns="2">
26861 <features booktabs="true" tabularvalignment="middle">
26862 <column alignment="left" valignment="top" width="0pt">
26863 <column alignment="center" valignment="top">
26865 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26868 \begin_layout Plain Layout
26874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26877 \begin_layout Plain Layout
26885 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26888 \begin_layout Plain Layout
26892 \begin_inset space \textvisiblespace{}
26900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26903 \begin_layout Plain Layout
26907 \begin_layout Plain Layout
26923 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26926 \begin_layout Plain Layout
26934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26937 \begin_layout Plain Layout
26941 \begin_layout Plain Layout
26957 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26960 \begin_layout Plain Layout
26964 \begin_inset Index idx
26967 \begin_layout Plain Layout
26978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26981 \begin_layout Plain Layout
26985 \begin_layout Plain Layout
27001 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27004 \begin_layout Plain Layout
27012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27015 \begin_layout Plain Layout
27019 \begin_layout Plain Layout
27035 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27038 \begin_layout Plain Layout
27042 \begin_inset space \textvisiblespace{}
27050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27053 \begin_layout Plain Layout
27057 \begin_layout Plain Layout
27073 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27076 \begin_layout Plain Layout
27080 \begin_inset space \textvisiblespace{}
27088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27091 \begin_layout Plain Layout
27095 \begin_layout Plain Layout
27111 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27114 \begin_layout Plain Layout
27118 \begin_inset space \textvisiblespace{}
27126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27129 \begin_layout Plain Layout
27133 \begin_layout Plain Layout
27153 \begin_inset space \hfill{}
27159 \begin_layout Standard
27160 \begin_inset VSpace medskip
27169 also two different characters can be accented.
27175 \begin_inset space \textvisiblespace{}
27184 \begin_layout Plain Layout
27196 \begin_layout Standard
27209 can in combination with vowels directly be inserted with the keyboard without
27210 using \SpecialChar TeX
27212 The same applies for the tilde
27216 \begin_layout Plain Layout
27217 This only applies for keyboards where the tilde is defined as accent.
27226 in combination with
27241 \begin_layout Standard
27284 and accents that are inserted directly with the keyboard are also available
27285 in mathematical text.
27286 For the other accents there are special math commands to be used in formulas,
27288 \begin_inset CommandInset ref
27290 reference "subsec:Accents-for-one"
27297 \begin_layout Standard
27298 \begin_inset VSpace bigskip
27301 Furthermore, with the command
27308 \begin_inset Index idx
27311 \begin_layout Plain Layout
27319 all numbers and letters can be set into a circle, quasi accented with a
27320 circle, similar to the copyright symbol.
27323 \begin_layout Standard
27325 \begin_inset Tabular
27326 <lyxtabular version="3" rows="3" columns="2">
27327 <features booktabs="true" tabularvalignment="middle">
27328 <column alignment="center" valignment="top" width="0pt">
27329 <column alignment="center" valignment="top">
27331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27334 \begin_layout Plain Layout
27340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27343 \begin_layout Plain Layout
27351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27354 \begin_layout Plain Layout
27362 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27365 \begin_layout Plain Layout
27369 \begin_layout Plain Layout
27384 <row topspace="1mm">
27385 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27388 \begin_layout Plain Layout
27399 raisebox{-1.5pt}{W}}
27404 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27407 \begin_layout Plain Layout
27411 \begin_layout Plain Layout
27441 \begin_layout Standard
27442 One has to take care that the character fits in the circle.
27453 \begin_layout Plain Layout
27455 \begin_inset CommandInset ref
27457 reference "subsec:Font-Sizes"
27466 specifies thereby the size of the circle.
27477 \begin_layout Plain Layout
27479 \begin_inset CommandInset ref
27481 reference "subsec:Boxes-without-Frame"
27490 the character can be centered.
27493 \begin_layout Subsection
27495 \begin_inset Index idx
27498 \begin_layout Plain Layout
27507 \begin_layout Standard
27508 Old-style figures (also known as old-style numerals) are created with the
27516 \begin_inset Index idx
27519 \begin_layout Plain Layout
27528 The command can be used in formulas and in \SpecialChar TeX
27530 The command scheme is:
27533 \begin_layout Standard
27538 oldstylenums{number}
27541 \begin_layout Standard
27546 oldstylenums{0123456789
27549 \begin_inset Formula $\oldstylenums{0123456789}$
27555 \begin_layout Section
27557 \begin_inset CommandInset label
27559 name "sec:Formula-Styles"
27564 \begin_inset Index idx
27567 \begin_layout Plain Layout
27576 \begin_layout Itemize
27577 There are two different alignment styles:
27581 \begin_layout Description
27582 Centered is the predefined standard.
27585 \begin_layout Description
27586 Indented this can be set using the menu
27588 Document\SpecialChar menuseparator
27594 \begin_inset space ~
27600 \begin_layout Standard
27605 is used, the indentation can be adjusted.
27606 The default value depends on the used document class.
27610 \begin_layout Itemize
27611 And two different numbering styles that can be set in the menu
27613 Document\SpecialChar menuseparator
27619 \begin_inset space ~
27628 \begin_layout Description
27629 Right is in most cases the default.
27632 \begin_layout Description
27637 \begin_layout Standard
27638 The chosen styles are used for all displayed formulas of the document.
27639 When both, centered and indented formulas should be created in a document,
27645 The indented formulas are then set in a flalign environment, see
27646 \begin_inset CommandInset ref
27648 reference "subsec:Flalign-Environment"
27655 \begin_layout Section
27657 \begin_inset CommandInset label
27659 name "sec:Multiline-Formulas"
27664 \begin_inset Index idx
27667 \begin_layout Plain Layout
27668 Formula ! multiline
27676 \begin_layout Subsection
27680 \begin_layout Standard
27681 In \SpecialChar LyX
27682 multiline formulas are created by pressing
27685 arg "newline-insert newline"
27689 This creates either an
27693 that is described in
27694 \begin_inset CommandInset ref
27696 reference "subsec:Standard-align-Environment"
27700 or, when automatically loading the package
27704 is disabled in the document settings, an
27706 eqnarray environment
27708 that is described in
27709 \begin_inset CommandInset ref
27711 reference "subsec:Eqnarray-Environment"
27716 The align environment is recommended because it provides in any case a
27717 typographically correct output.
27720 \begin_layout Standard
27721 There are other multiline formula environments that can be created via the
27724 Insert\SpecialChar menuseparator
27728 These environments are described in the following sections.
27731 \begin_layout Standard
27732 In all multiline formula environments a new line is created by pressing
27736 arg "newline-insert newline"
27740 To add or delete lines, the math toolbar buttons
27743 arg "tabular-feature append-row"
27749 arg "tabular-feature delete-row"
27752 , respectively, or the menu
27754 Edit\SpecialChar menuseparator
27760 \begin_layout Subsubsection
27762 \begin_inset CommandInset label
27764 name "subsec:Line-Separation"
27769 \begin_inset Index idx
27772 \begin_layout Plain Layout
27773 Formula ! multiline ! Line separation
27781 \begin_layout Standard
27782 There is sometimes not enough space in multiline formulas between the lines:
27783 \begin_inset Formula
27785 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}\\
27786 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
27794 \begin_layout Standard
27795 In \SpecialChar LaTeX
27796 additional line space is specified as optional argument of the new line
27798 This is not yet possible in \SpecialChar LyX
27803 \begin_layout Plain Layout
27805 \begin_inset CommandInset href
27807 name "LyX-bug #1505"
27808 target "https://www.lyx.org/trac/ticket/1505"
27818 , therefore the whole formula must be inserted in \SpecialChar TeX
27820 To add in our example space, the command
27828 is inserted at the end of the first line.
27833 \begin_layout Plain Layout
27840 \begin_layout Plain Layout
27842 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27845 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27852 \begin_layout Plain Layout
27856 left(B^{2}+x_{0}^{2}
27864 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27869 \begin_layout Plain Layout
27881 \begin_layout Standard
27882 \begin_inset VSpace bigskip
27885 To set the line separation for all lines in a formula, the length
27892 \begin_inset Index idx
27895 \begin_layout Plain Layout
27905 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27916 \begin_inset space \thinspace{}
27921 \begin_inset space \thinspace{}
27924 mm additional line separation as in the previous example, the command
27927 \begin_layout Standard
27937 \begin_layout Standard
27938 is inserted in \SpecialChar TeX
27939 mode before the formula.
27940 This requires that the \SpecialChar LaTeX
27949 \begin_layout Plain Layout
27954 is part of every \SpecialChar LaTeX
27955 standard installation.
27961 \begin_inset Index idx
27964 \begin_layout Plain Layout
27970 was loaded in \SpecialChar LaTeX
27971 -preamble with the line
27974 \begin_layout Standard
27982 \begin_layout Standard
27987 \begin_layout Plain Layout
27999 \begin_inset Formula
28001 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}\\
28002 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
28010 \begin_layout Standard
28014 \begin_layout Plain Layout
28025 To get back to the predefined distance,
28031 is set to the value 3
28032 \begin_inset space \thinspace{}
28038 \begin_layout Subsubsection
28040 \begin_inset CommandInset label
28042 name "subsec:Column-Separation"
28047 \begin_inset Index idx
28050 \begin_layout Plain Layout
28051 Formula ! multiline ! Column separation
28059 \begin_layout Standard
28060 Multiline formulas form a matrix.
28061 A formula in the eqnarray environment is for example a matrix with three
28063 By changing the column separation in this environment, the space beside
28064 the relation sign can be changed.
28067 \begin_layout Standard
28068 The column separation is specified with the length
28075 \begin_inset Index idx
28078 \begin_layout Plain Layout
28087 \begin_inset Newline newline
28090 column separation = 2
28091 \begin_inset space \thinspace{}
28101 \begin_inset Newline newline
28107 \begin_layout Standard
28117 \begin_layout Standard
28118 inserted in \SpecialChar TeX
28119 mode, sets for all following formulas a column separation of
28121 \begin_inset space \thinspace{}
28125 To get back to the predefined distance,
28132 \begin_inset space \thinspace{}
28138 \begin_layout Standard
28140 \begin_inset space \thinspace{}
28143 cm column separation:
28147 \begin_layout Plain Layout
28159 \begin_inset Formula
28167 A formula with the predefined column separation for matrices of 10
28168 \begin_inset space \thinspace{}
28175 \begin_layout Plain Layout
28187 \begin_inset Formula
28198 \begin_layout Standard
28199 \begin_inset Newpage newpage
28205 \begin_layout Subsubsection
28207 \begin_inset Index idx
28210 \begin_layout Plain Layout
28219 \begin_layout Standard
28220 Long formulas can be typeset using these methods:
28223 \begin_layout Itemize
28224 When one side of the equation is much shorter than the line width, this
28225 one is chosen for the left side and the right side is typeset over two
28227 \begin_inset Formula
28229 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 \\
28230 & & -\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}
28235 The minus sign at the beginning of the second line does normally not appear
28236 as an operator because it is the first character of the line.
28237 Thus it would not be surrounded by space and could not be distinguished
28238 from the fraction bar.
28240 \begin_inset space \thinspace{}
28243 pt space was inserted behind the minus sign with the command
28253 \begin_layout Plain Layout
28261 \begin_inset CommandInset ref
28263 reference "subsec:Variable-Space"
28273 \begin_inset Index idx
28276 \begin_layout Plain Layout
28287 \begin_layout Itemize
28288 When both sides of the equation are too long, the command
28295 \begin_inset Index idx
28298 \begin_layout Plain Layout
28307 It is inserted in the first column of the first line and causes all further
28308 insertions to overwrite the following columns:
28309 \begin_inset Formula
28311 \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 \\
28312 & & -\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 \\
28313 & & =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}
28318 After the insertion of
28324 , the cursor is in a purple box that is a bit shifted to the left from the
28326 In this the formula is inserted.
28327 \begin_inset Newline newline
28330 The content of the further lines is inserted to the second or another formula
28332 The greater the column number where it was inserted, the larger the indentation.
28333 \begin_inset VSpace medskip
28337 \begin_inset Newline newline
28341 \begin_inset Note Greyedout
28344 \begin_layout Plain Layout
28345 Note the following when using
28354 \begin_layout Itemize
28355 The formula doesn't use the full page width.
28357 \begin_inset space \thinspace{}
28361 \begin_inset space \space{}
28365 \begin_inset Formula $-B^{2}$
28368 is added to the first line in the above example, it would have been outside
28370 To better use the width, negative space can be inserted at the beginning
28374 \begin_layout Itemize
28375 Due to a bug in \SpecialChar LyX
28376 the cursor cannot be set with the mouse into the first
28381 \begin_layout Plain Layout
28382 \begin_inset CommandInset href
28384 name "LyX-bug #1429"
28385 target "https://www.lyx.org/trac/ticket/1429"
28395 One can only set the cursor at the beginning of the line and move it with
28404 \begin_layout Itemize
28405 Other methods to set long formulas are offered by the environments described
28407 \begin_inset CommandInset ref
28409 reference "subsec:Multline-Environment"
28414 \begin_inset CommandInset ref
28416 reference "subsec:Multiline-Formula-Parts"
28423 \begin_layout Subsubsection
28424 Multiline Fractions
28425 \begin_inset CommandInset label
28427 name "subsec:Multiline-Fractions"
28432 \begin_inset Index idx
28435 \begin_layout Plain Layout
28436 Fractions ! multiline
28444 \begin_layout Standard
28445 There are cases where the denominator and/or the numerator of a fraction
28446 is so long that the fraction does not fit into one line.
28447 It is then necessary to add a line break within the fraction.
28448 This can be done using the command
28455 \begin_inset Index idx
28458 \begin_layout Plain Layout
28467 To activate it, set in the document settings under
28470 \begin_inset space ~
28480 \begin_inset Index idx
28483 \begin_layout Plain Layout
28484 Packages ! mathtools
28492 \begin_inset space ~
28507 \begin_layout Standard
28512 splitfrac{first line}{second line}
28515 \begin_layout Standard
28516 and is used as denominator and/or numerator:
28519 \begin_layout Standard
28520 \begin_inset Formula
28522 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}
28527 The command for the first numerator above is:
28530 \begin_layout Standard
28535 splitfrac{xy+xy+xy+xy+xy
28536 \begin_inset space \textvisiblespace{}
28544 \begin_layout Subsubsection
28546 \begin_inset CommandInset label
28548 name "subsec:Multiline-Brackets"
28553 \begin_inset Index idx
28556 \begin_layout Plain Layout
28557 Brackets ! for multiline expressions
28565 \begin_layout Standard
28566 For brackets spanning multiple lines the following problem occurs:
28567 \begin_inset Formula
28569 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28570 & & \left.\cdots+B-D\right]
28578 \begin_layout Standard
28579 The closing bracket is smaller than the opening bracket because brackets
28580 with variable size may not span multiple lines.
28583 \begin_layout Standard
28584 To set the bracket size for the second line correctly, the first line is
28592 \begin_inset Index idx
28595 \begin_layout Plain Layout
28603 and the second line with
28611 \begin_layout Plain Layout
28625 \begin_inset CommandInset ref
28627 reference "subsec:Automatic-Bracket-Size"
28639 \begin_inset Index idx
28642 \begin_layout Plain Layout
28665 \begin_inset space \textvisiblespace{}
28675 \begin_inset space \textvisiblespace{}
28685 \begin_inset space \textvisiblespace{}
28691 \begin_inset Formula $\downarrow$
28697 \begin_inset Index idx
28700 \begin_layout Plain Layout
28708 is inserted, because the multiplication operator with its limits is the
28709 largest symbol in the first line and this should be the size for the bracket
28710 in the second line.
28713 \begin_layout Standard
28714 The result is this:
28715 \begin_inset Formula
28717 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28718 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28726 \begin_layout Subsection
28730 \begin_layout Standard
28731 Align environments can be used for every kind of multiline formulas.
28732 They are especially useful to set several formulas side by side.
28735 \begin_layout Standard
28736 Align environments consist of columns.
28737 The odd columns are right aligned, the even ones left aligned.
28738 Every line in an Align environment can be numbered.
28741 \begin_layout Standard
28742 Align environments are created via the menu
28744 Insert\SpecialChar menuseparator
28750 Edit\SpecialChar menuseparator
28751 Math\SpecialChar menuseparator
28752 Change Formula Type
28754 already existing formulas can be converted to Align environments.
28757 \begin_layout Standard
28758 To add or delete columns, the math toolbar buttons
28761 arg "tabular-feature append-column"
28767 arg "tabular-feature delete-column"
28770 , respectively, or the menu
28772 Edit\SpecialChar menuseparator
28778 \begin_layout Subsubsection
28779 Standard align Environment
28780 \begin_inset CommandInset label
28782 name "subsec:Standard-align-Environment"
28787 \begin_inset Index idx
28790 \begin_layout Plain Layout
28791 Formula ! multiline ! align environment
28799 \begin_layout Standard
28800 This Align environment is created by pressing
28803 arg "newline-insert newline"
28806 in a formula or by the menu
28808 Insert\SpecialChar menuseparator
28809 Math\SpecialChar menuseparator
28810 AMS align Environment
28815 \begin_layout Standard
28816 An example for two formulas set side by side, that are created with a four
28817 column align environment:
28818 \begin_inset Formula
28820 A & =\sin(B) & C & =D\\
28821 C & \ne A & B & \ne D
28826 As it can be seen, the formulas in this environment are placed so as if
28835 \begin_layout Plain Layout
28843 \begin_inset CommandInset ref
28845 reference "subsec:Variable-Space"
28856 before the first and after every even column.
28857 When the formula style
28863 \begin_layout Plain Layout
28865 \begin_inset CommandInset ref
28867 reference "sec:Formula-Styles"
28878 is used, the formula is set without the
28884 before the first column.
28887 \begin_layout Subsubsection
28888 Alignat Environment
28889 \begin_inset Index idx
28892 \begin_layout Plain Layout
28893 Formula ! multiline ! alignat environment
28901 \begin_layout Standard
28902 The alignat environment has no predefined column separation.
28903 It can be inserted manually with the spaces that are described
28904 \begin_inset CommandInset ref
28906 reference "subsec:Space"
28913 \begin_layout Standard
28914 The above example in the alignat environment where 1
28915 \begin_inset space \thinspace{}
28918 cm space was inserted at the beginning of the second formula:
28919 \begin_inset Formula
28920 \begin{alignat*}{2}
28921 A & =\sin(B) & \hspace{1cm}C & =D\\
28922 C & \ne A & B & \ne D
28927 Because the column separation can be set separately for every column, this
28928 environment is especially suitable to set three and more formulas side
28932 \begin_layout Subsubsection
28933 Flalign Environment
28934 \begin_inset CommandInset label
28936 name "subsec:Flalign-Environment"
28941 \begin_inset Index idx
28944 \begin_layout Plain Layout
28945 Formula ! multiline ! flalign environment
28953 \begin_layout Standard
28954 In this environment the first two columns are always set as much as possible
28955 to the left and the last two ones to the right.
28957 \begin_inset Formula
28959 A & =1 & B & =2 & C & =3\\
28960 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28968 \begin_layout Standard
28969 By creating a flalign environment with an odd number of columns where an
28970 empty \SpecialChar TeX
28971 brace is inserted to the last column, several formulas in a document
28972 can be set to the left, although the formula style
28977 As example the indented formula
28978 \begin_inset CommandInset ref
28980 reference "eq:VolInt"
28985 \begin_inset Formula
28987 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28992 The first two columns contain the formula.
28993 To indent it as with the formula style
28998 \begin_inset space \thinspace{}
29001 pt space was inserted at the beginning of the first column.
29004 \begin_layout Subsection
29005 Eqnarray Environment
29006 \begin_inset CommandInset label
29008 name "subsec:Eqnarray-Environment"
29013 \begin_inset Index idx
29016 \begin_layout Plain Layout
29017 Formula ! multiline ! eqnarray environment
29025 \begin_layout Standard
29026 When this environment has been created, three blue boxes appear.
29027 The content of the first box is right aligned, the content of the last
29029 The content of the middle box appears centered and a bit smaller, because
29030 it is designed to insert there only relation characters.
29031 \begin_inset Formula
29033 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29043 \begin_layout Subsection
29045 \begin_inset Index idx
29048 \begin_layout Plain Layout
29049 Formula ! multiline ! gather environment
29057 \begin_layout Standard
29058 This environment consists of only one centered column.
29059 Every line can be numbered.
29060 \begin_inset Formula
29071 \begin_layout Subsection
29072 Multline Environment
29073 \begin_inset CommandInset label
29075 name "subsec:Multline-Environment"
29080 \begin_inset Index idx
29083 \begin_layout Plain Layout
29084 Formula ! multiline ! multline environment
29092 \begin_layout Standard
29093 The multline environment consists, like the gather environment, of only
29095 But the first line is left aligned, the last one right aligned.
29096 All other lines are centered.
29097 Therefore this environment is suitable for long formulas.
29099 \begin_inset CommandInset ref
29101 reference "eq:lefteqn"
29105 in the multline environment:
29106 \begin_inset Formula
29108 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}\\
29109 -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}\\
29110 =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}}
29118 \begin_layout Standard
29119 In the output only the last (first) line of a multline environment appears
29120 numbered when the document numbering is right (left).
29124 \begin_layout Plain Layout
29125 numbering styles see
29126 \begin_inset CommandInset ref
29128 reference "sec:Formula-Styles"
29140 \begin_layout Standard
29148 \begin_inset Index idx
29151 \begin_layout Plain Layout
29166 \begin_inset Index idx
29169 \begin_layout Plain Layout
29177 a centered line can be right or left aligned, respectively.
29178 The commands are used as follows:
29181 \begin_layout Standard
29186 shoveright{line content}
29192 shoveleft{line content}
29195 \begin_layout Standard
29196 \begin_inset VSpace medskip
29206 \begin_inset Index idx
29209 \begin_layout Plain Layout
29217 specifies the distance of the first line from the left page margin.
29218 Predefined is the length 0
29219 \begin_inset space \thinspace{}
29225 \begin_layout Standard
29226 As example the above formula where the command
29229 \begin_layout Standard
29239 \begin_layout Standard
29240 was inserted in \SpecialChar TeX
29245 \begin_layout Plain Layout
29257 \begin_inset Formula
29259 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}\\
29260 \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}}\\
29261 =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}}
29270 \begin_layout Plain Layout
29281 The second line was left aligned using
29290 \begin_layout Subsection
29291 Multiline Formula Parts
29292 \begin_inset CommandInset label
29294 name "subsec:Multiline-Formula-Parts"
29299 \begin_inset Index idx
29302 \begin_layout Plain Layout
29303 Formula ! multiline ! formula parts
29311 \begin_layout Standard
29312 To display only parts of a formula with multiple lines, one of the following
29313 environments is used:
29330 They can be inserted via the menu
29332 Insert\SpecialChar menuseparator
29335 or by using the commands described in this section.
29338 \begin_layout Standard
29339 The first three have the same properties as the corresponding multiline
29340 formula environments, but it is possible to set further formula parts beside
29343 \begin_inset Formula
29345 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29346 \Delta E\Delta t & \ge\frac{\hbar}{2}
29348 \right\} \textrm{Uncertainty relations}
29356 \begin_layout Standard
29357 To get this formula, a displayed formula is created where the command
29364 \begin_inset Index idx
29367 \begin_layout Plain Layout
29376 A purple box appears around the blue formula box where now columns and
29377 lines can be added.
29378 Outside the multiline environment other formula parts can be set, like
29382 \begin_layout Standard
29383 The aligned environment is also suitable for long formulas whose lines are
29384 horizontally aligned.
29385 Using aligned in a displayed formula has the advantage that the formula
29386 number is vertically centered behind the lines.
29388 \begin_inset CommandInset ref
29390 reference "eq:shortlong"
29394 in the aligned environment:
29395 \begin_inset Formula
29397 \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}|}\\
29398 & -\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}|}
29407 \begin_layout Standard
29408 To use the environments
29427 \begin_inset Index idx
29430 \begin_layout Plain Layout
29445 \begin_inset Index idx
29448 \begin_layout Plain Layout
29463 \begin_inset Index idx
29466 \begin_layout Plain Layout
29474 are inserted, respectively.
29475 The split environment has the same properties as the aligned environment
29476 but it can only have two columns.
29479 \begin_layout Subsection
29480 Text in multiline Formulas
29481 \begin_inset CommandInset label
29483 name "subsec:Text-in-multiline"
29488 \begin_inset Index idx
29491 \begin_layout Plain Layout
29498 \begin_inset Index idx
29501 \begin_layout Plain Layout
29502 Formula ! multiline ! text
29510 \begin_layout Standard
29511 In the Align environments, and the multline and gather environment, text
29512 can be inserted that will appear in a separate line and doesn't affect
29513 the column alignment.
29514 To do this, the command
29521 \begin_inset Index idx
29524 \begin_layout Plain Layout
29532 is used in the following scheme:
29535 \begin_layout Standard
29543 \begin_layout Standard
29544 The text should not be longer than a line because it cannot be hyphenated.
29545 As \SpecialChar LyX
29546 doesn't yet support
29552 directly, the text is written as mathematical text.
29559 must hereby be at the beginning of a line and appears in the output above
29561 An example where the text was inserted at the beginning of the second line:
29562 \begin_inset Formula
29564 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29565 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29573 \begin_layout Standard
29580 always creates some vertical space between the text and the formula lines.
29581 To avoid this space, set in the document settings under
29584 \begin_inset space ~
29594 \begin_inset Index idx
29597 \begin_layout Plain Layout
29598 Packages ! mathtools
29606 \begin_inset space ~
29612 Then you can use the command
29619 \begin_inset Index idx
29622 \begin_layout Plain Layout
29639 \begin_layout Standard
29640 \begin_inset Formula
29642 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29643 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29651 \begin_layout Section
29653 \begin_inset Index idx
29656 \begin_layout Plain Layout
29663 \begin_inset Index idx
29666 \begin_layout Plain Layout
29667 Formula ! numbering|see
29671 \begin_layout Plain Layout
29682 \begin_layout Plain Layout
29697 \begin_layout Subsection
29701 \begin_layout Standard
29702 Numbered formulas can be created with the menu
29704 Insert\SpecialChar menuseparator
29705 Math\SpecialChar menuseparator
29707 \begin_inset space ~
29715 \begin_inset space ~
29721 Existing formulas can be numbered with the menu
29723 Edit\SpecialChar menuseparator
29724 Math\SpecialChar menuseparator
29726 \begin_inset space ~
29734 arg "math-number-toggle"
29738 The formula number is displayed in \SpecialChar LyX
29739 behind the formula as a number sign
29741 The number sign is replaced in the output by the formula number.
29744 \begin_layout Standard
29745 When numbering is turned on in multiline formulas, all lines will be numbered.
29746 But the numbering can be controlled with the menu
29748 Edit\SpecialChar menuseparator
29749 Math\SpecialChar menuseparator
29751 \begin_inset space ~
29755 \begin_inset space ~
29759 \begin_inset space ~
29767 arg "math-number-line-toggle"
29773 \begin_layout Standard
29774 Except for inline formulas, all formulas can be numbered with two different
29776 \begin_inset CommandInset ref
29778 reference "sec:Formula-Styles"
29785 \begin_layout Subsection
29787 \begin_inset Index idx
29790 \begin_layout Plain Layout
29791 Cross-references ! to formulas
29799 \begin_layout Standard
29800 All labeled formulas can be cross-referenced.
29801 A label is added by the menu
29803 Insert\SpecialChar menuseparator
29806 or the toolbar button
29813 The cursor must hereby be inside a displayed formula.
29814 Alternatively you can right-click on the formula and choose
29819 A dialog pops up displaying the prefix
29824 The label is inserted there behind the prefix.
29825 The predefined prefix means
29826 \begin_inset Quotes eld
29830 \begin_inset Quotes erd
29833 and makes it easier to find labels in large documents because it marks
29834 it as formula label to divide it from e.
29835 \begin_inset space \thinspace{}
29839 \begin_inset space \space{}
29843 To change a label, the menu
29845 Insert\SpecialChar menuseparator
29848 is used again or you right-click on a formula and then on
29855 \begin_layout Standard
29856 The name of the label is displayed in \SpecialChar LyX
29857 within two parentheses behind formula.
29858 A formula with a label is always numbered.
29861 \begin_layout Standard
29862 Cross-references are inserted via the menu
29864 Insert\SpecialChar menuseparator
29867 or with the toolbar button
29870 arg "dialog-show-new-inset ref"
29874 A formula cross-reference appears in the output as formula number.
29875 When in the cross-reference dialog window the format
29879 is chosen, the cross-reference appears in the output as formula number
29881 \begin_inset Newline newline
29884 By right-clicking on a cross-reference in \SpecialChar LyX
29885 , one jumps to the formula that
29889 \begin_layout Standard
29890 Here are as examples cross-references to formulas of the following subsections:
29891 \begin_inset Note Note
29894 \begin_layout Plain Layout
29895 Note the different cross-reference types.
29903 \begin_layout Standard
29905 \begin_inset CommandInset ref
29912 \begin_inset CommandInset ref
29920 \begin_inset CommandInset ref
29926 ) big Latin letters are used for the numbering in contrary to (
29927 \begin_inset CommandInset ref
29936 \begin_layout Standard
29937 \begin_inset VSpace medskip
29940 When the argument of
29948 \begin_layout Plain Layout
29956 \begin_inset CommandInset ref
29958 reference "subsec:User-defined-Numbering"
29969 contains a box like in
29970 \begin_inset CommandInset ref
29972 reference "subsec:Paragraph-Boxes"
29976 , the formula cannot be referenced.
29979 \begin_layout Subsection
29981 \begin_inset Index idx
29984 \begin_layout Plain Layout
29985 Formula numbering ! subnumbering
29993 \begin_layout Standard
29994 Formulas can be numbered as subequations.
29995 To activate this feature, add the module
29999 to the document in the menu
30001 Document\SpecialChar menuseparator
30002 Settings\SpecialChar menuseparator
30006 To insert subequations use the menu
30008 Insert\SpecialChar menuseparator
30009 Custom Insets\SpecialChar menuseparator
30015 \begin_layout Standard
30016 The equations to be subnumbered are put into the
30022 \begin_inset Formula
30030 \begin_inset VSpace -5mm
30034 \begin_inset Flex Subequations
30037 \begin_layout Plain Layout
30038 \begin_inset Formula
30046 \begin_inset Formula
30061 \begin_layout Standard
30062 Every formula in the
30066 inset will be subnumbered with a, b, c, \SpecialChar ldots
30068 For multiline formulas every line will be subnumbered.
30071 \begin_layout Standard
30072 Referencing subequations work like for normal equations:
30073 \begin_inset CommandInset ref
30080 \begin_inset CommandInset ref
30087 If you want to reference the subequations collectively, insert a label
30088 as first thing in the
30094 \begin_inset CommandInset ref
30096 reference "eq:Here-is-an"
30106 \begin_layout Standard
30107 By inserting subequations vertical space is added before it.
30108 To remove this, insert -5
30109 \begin_inset space \thinspace{}
30112 mm vertical space right before the
30117 If the formula style
30123 \begin_layout Plain Layout
30125 \begin_inset CommandInset ref
30127 reference "sec:Formula-Styles"
30139 \begin_inset space \thinspace{}
30145 \begin_layout Standard
30146 To get another subnumber instead of small Latin letters, insert this command
30147 as \SpecialChar TeX
30148 code before the equations in the
30155 \begin_layout Standard
30164 theparentequation -
30169 \begin_layout Standard
30176 creates hereby the parent number and
30182 adds a small Roman number as subnumber.
30183 For more information about the customization of the numbering, see
30184 \begin_inset CommandInset ref
30186 reference "subsec:Numbering-with-Roman"
30193 \begin_layout Standard
30194 Here is an example for a multiline formula where the numbering is customized
30195 and turned off for the second line:
30196 \begin_inset Flex Subequations
30199 \begin_layout Plain Layout
30200 \begin_inset CommandInset label
30202 name "eq:Here-is-an"
30210 \begin_layout Plain Layout
30218 theparentequation -
30226 \begin_inset Formula
30228 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30229 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30230 & = & B^{2}-2BZ+Z^{2}
30243 \begin_layout Subsection
30244 Numbering with Roman Numbers and Letters
30245 \begin_inset CommandInset label
30247 name "subsec:Numbering-with-Roman"
30252 \begin_inset Index idx
30255 \begin_layout Plain Layout
30256 Formula numbering ! with letters
30262 \begin_inset Index idx
30265 \begin_layout Plain Layout
30266 Formula numbering ! with Roman numbers
30274 \begin_layout Standard
30275 Formulas can also be numbered with Roman numbers and Latin letters.
30276 To number for example with small Roman numbers, the command
30279 \begin_layout Standard
30291 \begin_layout Standard
30292 is inserted before the formula in \SpecialChar TeX
30301 \begin_inset Index idx
30304 \begin_layout Plain Layout
30312 redefines the predefined command
30328 \begin_layout Plain Layout
30335 has the same scheme like the command
30341 that is described in
30342 \begin_inset CommandInset ref
30344 reference "subsec:The-Command-newcommand"
30357 is the formula counter.
30364 is used as prefix for a counter, the value of the counter is output as
30366 When a formula is numbered, \SpecialChar LaTeX
30367 sets internally the command
30373 behind the formula.
30379 \begin_inset Index idx
30382 \begin_layout Plain Layout
30392 outputs the counter as small Roman number.
30395 \begin_layout Standard
30396 All formulas behind the command
30406 are now numbered Roman.
30407 To switch to numbering with big Roman numbers, the command is inserted
30421 \begin_inset Index idx
30424 \begin_layout Plain Layout
30436 \begin_inset Quotes eld
30440 \begin_inset Quotes erd
30443 with small Latin letters there is the command
30450 \begin_inset Index idx
30453 \begin_layout Plain Layout
30461 , for big ones there is the command
30468 \begin_inset Index idx
30471 \begin_layout Plain Layout
30484 \begin_layout Standard
30485 \begin_inset Note Greyedout
30488 \begin_layout Plain Layout
30494 \begin_inset space ~
30497 formulas can be numbered with Latin letters in one document.
30505 \begin_layout Standard
30509 \begin_layout Plain Layout
30525 \begin_layout Standard
30526 \begin_inset Formula
30528 A=\textrm{small roman}
30537 \begin_layout Plain Layout
30551 \begin_inset Formula
30553 B=\textrm{big Roman}\label{eq:Rom}
30562 \begin_layout Plain Layout
30576 \begin_inset Formula
30578 C=\textrm{small Latin}
30587 \begin_layout Plain Layout
30601 \begin_inset Formula
30603 D=\textrm{big Latin}\label{eq:Lat}
30611 \begin_layout Standard
30612 To switch back to the default numbering, insert the command:
30615 \begin_layout Standard
30625 \begin_inset Index idx
30628 \begin_layout Plain Layout
30639 \begin_layout Standard
30643 \begin_layout Plain Layout
30657 \begin_inset Formula
30667 \begin_layout Standard
30668 \begin_inset VSpace medskip
30671 As you see, formulas are numbered serially independent from the numbering
30673 When then numbering should start with
30674 \begin_inset Quotes eld
30678 \begin_inset Quotes erd
30681 when the style is changed, new equation counters have to be defined.
30682 A description about this can be found in the file
30683 \begin_inset CommandInset href
30685 name "Formula-numbering.lyx"
30686 target "run:Formula-numbering.lyx"
30694 \begin_layout Subsection
30695 User-defined Numbering
30696 \begin_inset CommandInset label
30698 name "subsec:User-defined-Numbering"
30703 \begin_inset Index idx
30706 \begin_layout Plain Layout
30707 Formula numbering ! user-defined
30715 \begin_layout Standard
30716 \begin_inset Note Greyedout
30719 \begin_layout Plain Layout
30724 If the document language is a right-to-left language such as Arabic, you
30725 must add this to the to the \SpecialChar LaTeX
30726 -preamble to be able to use the commands described
30728 \begin_inset Newline newline
30736 \begin_inset Newline newline
30740 \begin_inset Phantom HPhantom
30743 \begin_layout Plain Layout
30746 \begin_inset space ~
30772 \begin_layout Standard
30773 \begin_inset Index idx
30776 \begin_layout Plain Layout
30777 Formula numbering ! self-defined delimiters
30782 With the standard numbering parentheses are set around the formula number.
30783 To replace the parentheses for example by vertical bars, the following
30784 line is added to the \SpecialChar LaTeX
30788 \begin_layout Standard
30794 \begin_inset Newline newline
30798 \begin_inset Phantom HPhantom
30801 \begin_layout Plain Layout
30804 \begin_inset space ~
30818 maketag@@@{|#1|}} }
30821 \begin_inset Note Note
30824 \begin_layout Plain Layout
30825 This macro is already declared in the \SpecialChar LaTeX
30826 -preamble for testing.
30827 To activate it, remove the percent signs at the beginning.
30835 \begin_layout Standard
30836 To use other characters, the vertical bars besides the
30840 are replaced by one ore more characters.
30841 To get only the formula number the vertical bars are omitted.
30844 \begin_layout Standard
30845 \begin_inset VSpace bigskip
30848 When there should be an expression of your choice instead of the consecutive
30849 formula number in parentheses behind the formula, the command
30856 \begin_inset Index idx
30859 \begin_layout Plain Layout
30868 \begin_inset Formula
30870 A+B=C\tag{something}\label{eq:tag}
30875 In this example the command
30880 \begin_inset space \textvisiblespace{}
30885 was inserted in the formula.
30888 \begin_layout Standard
30894 \begin_inset space \textvisiblespace{}
30899 is inserted instead, the star prevents the parentheses around the expression:
30900 \begin_inset Formula
30902 A+B=C\tag*{something}
30910 \begin_layout Standard
30911 \begin_inset VSpace bigskip
30914 To restart the formula numbering with new document parts or sections, the
30915 following command is used:
30918 \begin_layout Standard
30923 @addtoreset{equation}{part}
30926 \begin_inset Index idx
30929 \begin_layout Plain Layout
30934 \begin_layout Plain Layout
30945 \begin_layout Plain Layout
30958 \begin_layout Plain Layout
30969 \begin_layout Plain Layout
30982 \begin_inset Newline newline
30986 \begin_inset Newline newline
30993 @addtoreset{equation}{section}
30996 \begin_layout Standard
30997 To be able to use these commands in \SpecialChar TeX
30999 \begin_inset Quotes eld
31003 \begin_inset Quotes erd
31006 character has to be made
31007 \begin_inset Quotes eld
31011 \begin_inset Quotes erd
31014 for \SpecialChar LaTeX
31029 So the command sequence in \SpecialChar TeX
31033 \begin_layout Standard
31039 \begin_inset Newline newline
31044 @addtoreset{equation}{section}
31045 \begin_inset Newline newline
31053 \begin_layout Standard
31054 In the \SpecialChar LaTeX
31067 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31071 \begin_layout Standard
31086 \begin_layout Plain Layout
31091 is part of the \SpecialChar LaTeX
31097 \begin_inset Index idx
31100 \begin_layout Plain Layout
31101 Packages ! carlisle
31106 that is part of every \SpecialChar LaTeX
31107 standard installation.
31113 \begin_inset Index idx
31116 \begin_layout Plain Layout
31117 Packages ! remreset
31122 has to be loaded in the \SpecialChar LaTeX
31123 -preamble with the line
31126 \begin_layout Standard
31131 usepackage{remreset}
31134 \begin_layout Standard
31142 \begin_inset Index idx
31145 \begin_layout Plain Layout
31150 \begin_layout Plain Layout
31161 \begin_layout Plain Layout
31174 \begin_layout Plain Layout
31185 \begin_layout Plain Layout
31197 can be used with the same scheme as
31206 \begin_layout Standard
31207 \begin_inset VSpace bigskip
31210 Sometimes formulas should be numbered in the following form:
31213 \begin_layout Standard
31216 (section number.formula number)
31219 \begin_layout Standard
31220 The formula number should start with every section with
31221 \begin_inset Quotes eld
31225 \begin_inset Quotes erd
31231 \begin_layout Standard
31232 For this case there is the command
31239 \begin_inset Index idx
31242 \begin_layout Plain Layout
31250 , which is used with the following scheme:
31253 \begin_layout Standard
31258 numberwithin{counter}{sectioning}
31261 \begin_layout Standard
31262 Counter denotes what kind of numbering is affected, sectioning denotes what
31263 number is before the dot.
31266 \begin_layout Standard
31267 Thus in our case the following \SpecialChar LaTeX
31268 preamble or \SpecialChar TeX
31272 \begin_layout Standard
31277 numberwithin{equation}{section}
31280 \begin_layout Standard
31281 This is the result:
31285 \begin_layout Plain Layout
31289 numberwithin{equation}{section}
31295 \begin_inset Formula
31305 \begin_layout Standard
31307 \begin_inset space \thinspace{}
31311 \begin_inset space \space{}
31314 tables so that the number of the part is the sectioning,
31315 \begin_inset Newline newline
31322 numberwithin{table}{part}
31327 \begin_layout Standard
31328 To go back to the standard numbering or to prevent this kind of numbering
31329 when it is defined by the document class, the following command is inserted
31330 as \SpecialChar TeX
31331 code or to the \SpecialChar LaTeX
31335 \begin_layout Standard
31345 \begin_inset Index idx
31348 \begin_layout Plain Layout
31362 \begin_layout Plain Layout
31378 \begin_inset Newline newline
31386 \begin_inset Newline newline
31398 \begin_layout Standard
31405 uses internally the command
31411 , described above, that also needs to be reverted.
31415 \begin_layout Plain Layout
31422 \begin_layout Plain Layout
31426 @removefromreset{equation}{section}
31429 \begin_layout Plain Layout
31441 \begin_layout Section
31442 Chemical Symbols and Equations
31443 \begin_inset CommandInset label
31445 name "subsec:Chemical-Symbols-and"
31450 \begin_inset Index idx
31453 \begin_layout Plain Layout
31454 Chemical characters ! Symbols
31460 \begin_inset Index idx
31463 \begin_layout Plain Layout
31470 \begin_inset Index idx
31473 \begin_layout Plain Layout
31482 \begin_layout Standard
31483 An example text from chemistry:
31486 \begin_layout Quote
31488 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31491 -ion reacts with two
31492 \begin_inset Formula $\mathrm{Na^{+}}$
31495 -ions to sodium sulfate
31496 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31500 The chemical equation for this is:
31501 \begin_inset Formula
31503 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31511 \begin_layout Standard
31512 This chemical equation can directly be created as formula.
31513 To avoid that the symbols appear italic, everything is highlighted and
31514 changed by the shortcut
31520 to the upright font style.
31524 \begin_layout Plain Layout
31530 \begin_inset CommandInset ref
31532 reference "subsec:Font-Styles"
31544 \begin_layout Standard
31545 A more convenient way to typeset chemical formulas is to use the command
31553 \begin_inset Index idx
31556 \begin_layout Plain Layout
31564 that is available when the \SpecialChar LaTeX
31570 \begin_inset Index idx
31573 \begin_layout Plain Layout
31586 to a formula a new blue box appears where chemical formulas can be inserted
31587 in an intuitive way.
31590 \begin_layout Standard
31592 \begin_inset Tabular
31593 <lyxtabular version="3" rows="10" columns="2">
31594 <features booktabs="true" tabularvalignment="middle">
31595 <column alignment="center" valignment="top" width="0pt">
31596 <column alignment="center" valignment="top">
31598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31601 \begin_layout Plain Layout
31607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31610 \begin_layout Plain Layout
31618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31621 \begin_layout Plain Layout
31625 \begin_inset space \textvisiblespace{}
31633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31636 \begin_layout Plain Layout
31637 \begin_inset Formula $\ce{H2CO3}$
31646 <row topspace="1.5mm">
31647 <cell alignment="center" valignment="top" usebox="none">
31650 \begin_layout Plain Layout
31654 \begin_inset space \textvisiblespace{}
31662 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31665 \begin_layout Plain Layout
31666 \begin_inset Formula $\ce{SO4^{2-}}$
31675 <row topspace="1.5mm">
31676 <cell alignment="center" valignment="top" usebox="none">
31679 \begin_layout Plain Layout
31683 \begin_inset space \textvisiblespace{}
31691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31694 \begin_layout Plain Layout
31695 \begin_inset Formula $\ce{(NH4)2S}$
31704 <row topspace="1.5mm">
31705 <cell alignment="center" valignment="top" usebox="none">
31708 \begin_layout Plain Layout
31712 \begin_inset space \textvisiblespace{}
31720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31723 \begin_layout Plain Layout
31724 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31733 <row topspace="1.5mm">
31734 <cell alignment="center" valignment="top" usebox="none">
31737 \begin_layout Plain Layout
31741 \begin_inset space \textvisiblespace{}
31747 \begin_inset space \textvisiblespace{}
31753 \begin_inset space \textvisiblespace{}
31761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31764 \begin_layout Plain Layout
31765 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31774 <row topspace="1.5mm">
31775 <cell alignment="center" valignment="top" usebox="none">
31778 \begin_layout Plain Layout
31782 \begin_inset space \textvisiblespace{}
31786 \begin_inset Formula $\downarrow$
31790 \begin_inset Formula $\to$
31798 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31801 \begin_layout Plain Layout
31802 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31812 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31815 \begin_layout Plain Layout
31819 \begin_inset space \textvisiblespace{}
31825 \begin_inset space \textvisiblespace{}
31831 \begin_inset space \textvisiblespace{}
31839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31842 \begin_layout Plain Layout
31843 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31856 \begin_layout Plain Layout
31860 \begin_inset space \textvisiblespace{}
31864 \begin_inset space \textvisiblespace{}
31868 \begin_inset space \textvisiblespace{}
31872 \begin_inset space \textvisiblespace{}
31876 \begin_inset space \textvisiblespace{}
31884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31887 \begin_layout Plain Layout
31888 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31897 <row topspace="1.5mm">
31898 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31901 \begin_layout Plain Layout
31905 \begin_inset space \textvisiblespace{}
31909 \begin_inset space \textvisiblespace{}
31913 \begin_inset space \textvisiblespace{}
31917 \begin_inset space \textvisiblespace{}
31925 \begin_inset space \textvisiblespace{}
31933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31936 \begin_layout Plain Layout
31937 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31953 \begin_layout Standard
31954 \begin_inset Note Greyedout
31957 \begin_layout Plain Layout
31962 It is not possible in \SpecialChar LyX
31963 to use the character ^ to get an up-arrow as described
31969 One instead uses a negative thin space followed by the command
31976 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31987 \begin_layout Standard
31994 the command for equation
31995 \begin_inset space ~
31999 \begin_inset CommandInset ref
32001 reference "eq:chem-reaction"
32006 \begin_inset Newline newline
32014 \begin_inset space \textvisiblespace{}
32018 \begin_inset space \textvisiblespace{}
32022 \begin_inset space \textvisiblespace{}
32026 \begin_inset space \textvisiblespace{}
32030 \begin_inset space \textvisiblespace{}
32034 \begin_inset space \textvisiblespace{}
32040 \begin_layout Standard
32041 To create multiline chemical equations first a multiline formula is created
32043 \begin_inset CommandInset ref
32045 reference "sec:Multiline-Formulas"
32050 Afterwards the command
32056 is used in every small blue box of the formula.
32058 \begin_inset CommandInset ref
32060 reference "eq:TEOS-reaction-1"
32065 \begin_inset CommandInset ref
32067 reference "eq:TEOS-reaction-2"
32071 are an example of a multi-stage chemical reaction where every equation
32072 has its own number.
32073 \begin_inset Formula
32075 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32076 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32084 \begin_layout Standard
32095 package provides the command
32102 \begin_inset Index idx
32105 \begin_layout Plain Layout
32113 that has to be used for special cases.
32114 For more information about
32120 and more examples have a look at the documentation of
32125 \begin_inset CommandInset citation
32135 \begin_layout Section
32139 \begin_layout Standard
32141 supports two types of commutative diagrams:
32149 that are explained in the following.
32152 \begin_layout Subsection
32154 \begin_inset Index idx
32157 \begin_layout Plain Layout
32166 \begin_layout Standard
32167 Diagrams of this type visualize relations by vertical and horizontal lines
32169 \begin_inset Formula
32171 \begin{CD}A@>>>B@>>>C\\
32182 \begin_layout Standard
32183 To get them, the command
32188 \begin_inset Index idx
32191 \begin_layout Plain Layout
32201 is inserted to a formula.
32202 A blue box appears with two dashed lines where further commands can be
32207 arg "newline-insert newline"
32210 a new line is created.
32211 Horizontal relations are inserted in odd, vertical in even formula lines.
32214 \begin_layout Standard
32215 To create the relations there are the following commands:
32218 \begin_layout Itemize
32223 creates a left arrow,
32234 \begin_layout Itemize
32239 creates an up arrow,
32247 a vertical equal sign
32250 \begin_layout Itemize
32256 is a placeholder for non-existent relations
32259 \begin_layout Standard
32260 All arrows can be labeled as follows:
32263 \begin_layout Itemize
32264 If text inserted between the first and second < or >, resp., it is placed
32266 When it is inserted between the second and third one, it appears under
32270 \begin_layout Itemize
32271 When text for vertical arrows is inserted between the first and second A
32272 or V, resp., it is placed left beside the arrow.
32273 When it is inserted between the second and third one, it appears right
32275 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32279 \begin_layout Standard
32280 As example a diagram with all possible relations:
32283 \begin_layout Standard
32284 \begin_inset Formula
32286 \begin{CD}A@>j>>B@>>k>C@=F\\
32297 \begin_layout Standard
32298 The command for this is:
32299 \begin_inset Newline newline
32307 \begin_inset space \textvisiblespace{}
32310 A@>j>>B@>>k>C@=F Ctrl+Return
32311 \begin_inset Newline newline
32315 \begin_inset Phantom HPhantom
32318 \begin_layout Plain Layout
32324 \begin_inset space \textvisiblespace{}
32337 \begin_inset Formula $\to$
32343 \begin_inset Newline newline
32347 \begin_inset Phantom HPhantom
32350 \begin_layout Plain Layout
32356 \begin_inset space \textvisiblespace{}
32367 \begin_layout Subsection
32369 \begin_inset Index idx
32372 \begin_layout Plain Layout
32373 Diagrams ! xymatrix
32381 \begin_layout Standard
32382 To be able to use xymatrices, the \SpecialChar LaTeX
32388 A xymatrix is created by inserting the command
32395 Then you are able to add new matrix columns and rows like for normal matrices,
32397 \begin_inset CommandInset ref
32399 reference "sec:Matrices"
32406 \begin_layout Standard
32407 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32409 All possibilities to create commutative diagrams and decorations are explained
32414 that you find in the menu
32416 Help\SpecialChar menuseparator
32418 \begin_inset space ~
32426 \begin_layout Subsection
32432 \begin_inset Index idx
32435 \begin_layout Plain Layout
32444 \begin_layout Standard
32449 -diagrams, the \SpecialChar LaTeX
32459 -diagram is created by inserting the command
32466 Then you are able to add new matrix columns and rows like for normal matrices,
32468 \begin_inset CommandInset ref
32470 reference "sec:Matrices"
32477 \begin_layout Standard
32478 Examples how to create
32482 diagrams in \SpecialChar LyX
32485 Feynman-diagram manual
32487 that you find in the menu
32489 Help\SpecialChar menuseparator
32491 \begin_inset space ~
32499 \begin_layout Section
32500 User-defined Commands
32501 \begin_inset Index idx
32504 \begin_layout Plain Layout
32505 User-defined commands
32513 \begin_layout Standard
32514 \begin_inset Note Greyedout
32517 \begin_layout Plain Layout
32522 The names of user-defined commands and macros may only consist of Latin
32531 \begin_layout Subsection
32535 \begin_inset CommandInset label
32537 name "subsec:The-Command-newcommand"
32542 \begin_inset Index idx
32545 \begin_layout Plain Layout
32546 User-defined commands !
32554 \begin_inset Index idx
32557 \begin_layout Plain Layout
32568 \begin_layout Standard
32569 Many \SpecialChar LaTeX
32570 -commands are too long to be used frequently.
32571 But it is possible to define with the command
32577 new shorter commands.
32580 \begin_layout Standard
32581 The command scheme of
32590 \begin_layout Standard
32595 newcommand{new command name}[number of arguments][optional
32600 \begin_inset Newline newline
32604 \begin_inset Phantom HPhantom
32607 \begin_layout Plain Layout
32617 {command definition}
32620 \begin_layout Standard
32621 \begin_inset Note Greyedout
32624 \begin_layout Plain Layout
32629 Assure that the name of the new command is not already used in your document
32630 or by \SpecialChar LaTeX
32631 -packages that you use.
32632 When you for example define the command
32644 , you get an error message because
32650 is already defined as command for
32651 \begin_inset Quotes eld
32655 \begin_inset Formula $\le$
32659 \begin_inset Quotes erd
32670 \begin_layout Standard
32671 The number of arguments is an integer in the range 0
32672 \begin_inset space \thinspace{}
32676 \begin_inset space \thinspace{}
32679 9 and specifies how many arguments the new command should have.
32680 With the optional value a value for an optional argument can be predefined.
32681 When this is done, the
32689 rgument of the new command is automatically an optional one.
32692 \begin_layout Standard
32693 Here are some examples:
32696 \begin_layout Itemize
32697 To define the command
32709 , the \SpecialChar LaTeX
32711 \begin_inset VSpace medskip
32715 \begin_inset Newline newline
32729 \begin_layout Itemize
32730 To define the command
32742 , the argument (that should be underlined) must be taken into account.
32743 For this the preamble line is:
32744 \begin_inset VSpace medskip
32748 \begin_inset Newline newline
32762 \begin_inset VSpace medskip
32766 \begin_inset Newline newline
32773 acts as argument placeholder, the
32777 behind it denotes that it is the placeholder for the first argument.
32780 \begin_layout Itemize
32788 \begin_inset space \thinspace{}
32792 \begin_inset space \space{}
32802 \begin_inset VSpace medskip
32806 \begin_inset Newline newline
32817 framebox#1#2{$#3$}}
32820 \begin_inset VSpace medskip
32824 \begin_inset Newline newline
32827 The two Dollar signs creates the extra formula needed for
32834 \begin_inset CommandInset ref
32836 reference "subsec:Boxes-with-Frame"
32843 \begin_layout Itemize
32844 To create a new command for
32850 where the color for the box need not be specified, the argument for the
32851 color is defined optional:
32852 \begin_inset VSpace medskip
32856 \begin_inset Newline newline
32867 fcolorbox{#2}{#1}{$#3$}}
32870 \begin_inset VSpace medskip
32874 \begin_inset Newline newline
32877 When the color is not specified when using
32883 , the predefined color
32890 \begin_layout Standard
32891 A test of the new defined commands:
32894 \begin_layout Standard
32896 \begin_inset Tabular
32897 <lyxtabular version="3" rows="6" columns="2">
32898 <features booktabs="true" tabularvalignment="middle">
32899 <column alignment="center" valignment="top" width="0pt">
32900 <column alignment="center" valignment="top">
32902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32905 \begin_layout Plain Layout
32911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32914 \begin_layout Plain Layout
32922 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32925 \begin_layout Plain Layout
32929 \begin_inset space \textvisiblespace{}
32937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32940 \begin_layout Plain Layout
32941 \begin_inset Formula $A\gr B$
32951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32954 \begin_layout Plain Layout
32962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32965 \begin_layout Plain Layout
32966 \begin_inset Formula $\us{ABcd}$
32975 <row topspace="1mm">
32976 <cell alignment="center" valignment="top" usebox="none">
32979 \begin_layout Plain Layout
32983 \begin_inset Formula $\to$
32989 \begin_inset Formula $\to$
32997 \begin_inset space \textvisiblespace{}
33005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33008 \begin_layout Plain Layout
33009 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33018 <row topspace="1.5mm">
33019 <cell alignment="center" valignment="top" usebox="none">
33022 \begin_layout Plain Layout
33026 \begin_inset Formula $\to$
33034 \begin_inset space \textvisiblespace{}
33042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33045 \begin_layout Plain Layout
33046 \begin_inset Formula $\cb{red}{\int A=B}$
33055 <row topspace="1.5mm" bottomspace="1mm">
33056 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33059 \begin_layout Plain Layout
33065 \begin_inset Formula $\to$
33073 \begin_inset space \textvisiblespace{}
33081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33084 \begin_layout Plain Layout
33085 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33101 \begin_layout Subsection
33103 \begin_inset Index idx
33106 \begin_layout Plain Layout
33107 User-defined commands! Math macros
33113 \begin_inset Index idx
33116 \begin_layout Plain Layout
33125 \begin_layout Standard
33126 User-defined commands are especially convenient for complex expressions.
33127 When you are for example dealing with a document that has quadratic equations,
33128 the same solution type occurs several times.
33129 The general form of a quadratic equation is
33130 \begin_inset Formula
33132 0=\lambda^{2}+p\lambda+q
33137 The general form of the solution is
33138 \begin_inset Formula
33140 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33148 \begin_layout Standard
33149 To define a command for the solution formula where only the three parameters
33151 \begin_inset Formula $\lambda$
33155 \begin_inset Formula $p$
33159 \begin_inset Formula $q$
33162 need to be specified and the index of
33163 \begin_inset Formula $\lambda$
33166 can be given optionally, the \SpecialChar LaTeX
33168 \begin_inset Newline newline
33184 \begin_inset Newline newline
33188 \begin_inset Phantom HPhantom
33191 \begin_layout Plain Layout
33205 frac{#3^{2}}{4}-#4}}
33208 \begin_layout Standard
33209 To create with this the solution formula, the command
33210 \begin_inset Newline newline
33220 \begin_inset Formula $\to$
33226 \begin_inset Formula $\to$
33233 is inserted to a formula
33238 \begin_layout Standard
33239 The definition of the new command is unintuitive because one has to know
33240 the schemes of all used \SpecialChar LaTeX
33242 \begin_inset space \thinspace{}
33246 \begin_inset space \space{}
33249 that a fraction is inserted in \SpecialChar LaTeX
33254 frac{numerator}{denominator}
33257 Furthermore one can easily forget a brace in the definition and cannot
33258 see in \SpecialChar LyX
33259 what the new command is doing.
33260 To avoid these problems \SpecialChar LyX
33261 offers the possibility to use math macros instead
33271 \begin_layout Standard
33272 A math macro is created by using the menu
33274 Insert\SpecialChar menuseparator
33275 Math\SpecialChar menuseparator
33278 or the toolbar button
33281 arg "math-macro newmacroname_newcommand"
33285 The math macro toolbar appears together with the following box where the
33287 \begin_inset Newline newline
33291 \begin_inset space \hspace*{\fill}
33295 \begin_inset Graphics
33296 filename clipart/macrobox.png
33302 \begin_inset space \hspace*{\fill}
33306 \begin_inset Newline newline
33310 \begin_inset FormulaMacro
33311 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33316 newmacroname is the default name of the macro that should be changed to
33317 something sensible.
33318 The wanted formula is inserted in the first blue box.
33319 An argument placeholder is inserted with the command
33326 \begin_inset space \thinspace{}
33330 \begin_inset space \space{}
33339 or by using the macro toolbar button
33342 arg "math-macro-add-param"
33346 Argument placeholders are displayed red.
33348 \begin_inset space ~
33351 arguments are possible.
33352 Optional arguments are created with the toolbar button
33355 arg "math-macro-add-optional-param"
33359 The first non-optional argument can be transformed to an optional one with
33363 arg "math-macro-make-optional"
33367 In the second blue box the appearance of the macro in \SpecialChar LyX
33369 Normally you want to see it as it is defined, so the box is kept empty.
33370 But when you have created a macro that needs lot of space on the screen,
33371 you can insert in the box for example
33372 \begin_inset Newline newline
33402 \begin_inset Newline newline
33407 For the macro only the arguments with the macro name in front of them will
33408 then be displayed in \SpecialChar LyX
33409 , leading to a better overview.
33410 The formula appears in the output as defined in the first box.
33411 \begin_inset Newline newline
33414 The appearance of macros in formulas can furthermore be changed for single
33415 macros by setting the cursor in the macro and using the menu
33417 View\SpecialChar menuseparator
33419 \begin_inset space ~
33423 \begin_inset space ~
33431 \begin_layout Standard
33432 To use a macro, the macro name is inserted as command to a formula, in our
33440 Our macro looks in \SpecialChar LyX
33442 \begin_inset Newline newline
33446 \begin_inset space \hspace*{\fill}
33450 \begin_inset Graphics
33451 filename clipart/macrouse.png
33457 \begin_inset space \hspace*{\fill}
33461 \begin_inset Newline newline
33464 Here is our macro example with the arguments
33465 \begin_inset Formula $x$
33469 \begin_inset Formula $\ln(x)$
33473 \begin_inset Formula $B$
33479 \begin_layout Standard
33480 \begin_inset Formula
33490 \begin_layout Standard
33494 Tools\SpecialChar menuseparator
33495 Preferences\SpecialChar menuseparator
33496 Editing\SpecialChar menuseparator
33499 different styles to edit macros.
33500 To find the style that suits you the most, choose a style and set the cursor
33501 in a macro formula to see the difference.
33504 \begin_layout Standard
33505 A math macro is transformed internally to a
33511 command when exporting the document.
33518 command is not placed in the \SpecialChar LaTeX
33519 -preamble, therefore macros can only be used
33520 in formulas that are in the document below the macro definition box.
33523 \begin_layout Standard
33524 Math macros can also be directly created from a
33531 When writing for example the command
33534 \begin_inset Newline newline
33543 xleftarrow[#2]{#1}}
33544 \begin_inset Newline newline
33549 in \SpecialChar LyX
33550 as normal text, highlighting it completely and using then the shortcut
33555 , the command will be transformed to a math macro.
33556 Using this method you need to be careful that the
33562 command is typed correctly, otherwise you get a faulty macro leading to
33567 \begin_layout Standard
33568 Math macros currently have the problem that further formulas in macro definition
33569 s are handled wrongly.
33570 Therefore the example
33577 \begin_inset CommandInset ref
33579 reference "subsec:The-Command-newcommand"
33583 cannot be created as macro.
33586 \begin_layout Standard
33587 When the cursor is in a macro definition box, you will see the macro toolbar
33588 in \SpecialChar LyX
33592 \begin_layout Standard
33593 \begin_inset VSpace defskip
33599 \begin_layout Standard
33600 \begin_inset Graphics
33601 filename clipart/MacroToolbar.png
33606 \begin_inset Index idx
33609 \begin_layout Plain Layout
33618 \begin_layout Standard
33619 \begin_inset VSpace defskip
33625 \begin_layout Standard
33626 The macro toolbar contains from left to right the following buttons:
33629 \begin_layout Standard
33630 \begin_inset VSpace defskip
33636 \begin_layout Standard
33637 \begin_inset Tabular
33638 <lyxtabular version="3" rows="9" columns="2">
33639 <features islongtable="true" longtabularalignment="center">
33640 <column alignment="left" valignment="top">
33641 <column alignment="left" valignment="top" width="85col%">
33642 <row interlinespace="2.5mm">
33643 <cell alignment="center" valignment="top" usebox="none">
33646 \begin_layout Plain Layout
33649 arg "math-macro-remove-param"
33657 <cell alignment="center" valignment="top" usebox="none">
33660 \begin_layout Plain Layout
33663 Edit\SpecialChar menuseparator
33664 Math\SpecialChar menuseparator
33666 \begin_inset space ~
33669 Definition\SpecialChar menuseparator
33670 Remove Last Argument
33676 <row interlinespace="2.5mm">
33677 <cell alignment="center" valignment="top" usebox="none">
33680 \begin_layout Plain Layout
33683 arg "math-macro-add-param"
33691 <cell alignment="center" valignment="top" usebox="none">
33694 \begin_layout Plain Layout
33697 Edit\SpecialChar menuseparator
33698 Math\SpecialChar menuseparator
33700 \begin_inset space ~
33703 Definition\SpecialChar menuseparator
33710 <row interlinespace="2.5mm">
33711 <cell alignment="center" valignment="top" usebox="none">
33714 \begin_layout Plain Layout
33717 arg "math-macro-make-optional"
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33731 Edit\SpecialChar menuseparator
33732 Math\SpecialChar menuseparator
33734 \begin_inset space ~
33737 Definition\SpecialChar menuseparator
33738 Transform First Non-Optional to
33739 \begin_inset Newline newline
33743 \begin_inset Phantom HPhantom
33746 \begin_layout Plain Layout
33749 Edit\SpecialChar menuseparator
33750 Math\SpecialChar menuseparator
33752 \begin_inset space ~
33755 Definition\SpecialChar menuseparator
33767 <row interlinespace="2.5mm">
33768 <cell alignment="center" valignment="top" usebox="none">
33771 \begin_layout Plain Layout
33774 arg "math-macro-make-nonoptional"
33782 <cell alignment="center" valignment="top" usebox="none">
33785 \begin_layout Plain Layout
33788 Edit\SpecialChar menuseparator
33789 Math\SpecialChar menuseparator
33791 \begin_inset space ~
33794 Definition\SpecialChar menuseparator
33795 Transform Last Optional to
33796 \begin_inset Newline newline
33800 \begin_inset Phantom HPhantom
33803 \begin_layout Plain Layout
33806 Edit\SpecialChar menuseparator
33807 Math\SpecialChar menuseparator
33809 \begin_inset space ~
33812 Definition\SpecialChar menuseparator
33818 Non-Optional Argument
33824 <row interlinespace="2.5mm">
33825 <cell alignment="center" valignment="top" usebox="none">
33828 \begin_layout Plain Layout
33831 arg "math-macro-remove-optional-param"
33839 <cell alignment="center" valignment="top" usebox="none">
33842 \begin_layout Plain Layout
33845 Edit\SpecialChar menuseparator
33846 Math\SpecialChar menuseparator
33848 \begin_inset space ~
33851 Definition\SpecialChar menuseparator
33852 Remove Optional Argument
33858 <row interlinespace="2.5mm">
33859 <cell alignment="center" valignment="top" usebox="none">
33862 \begin_layout Plain Layout
33865 arg "math-macro-add-optional-param"
33873 <cell alignment="center" valignment="top" usebox="none">
33876 \begin_layout Plain Layout
33879 Edit\SpecialChar menuseparator
33880 Math\SpecialChar menuseparator
33882 \begin_inset space ~
33885 Definition\SpecialChar menuseparator
33886 Insert Optional Argument
33892 <row interlinespace="2.5mm">
33893 <cell alignment="center" valignment="top" usebox="none">
33896 \begin_layout Plain Layout
33899 arg "math-macro-remove-greedy-param"
33907 <cell alignment="center" valignment="top" usebox="none">
33910 \begin_layout Plain Layout
33913 Edit\SpecialChar menuseparator
33914 Math\SpecialChar menuseparator
33916 \begin_inset space ~
33919 Definition\SpecialChar menuseparator
33920 Remove Last Argument
33921 \begin_inset Newline newline
33925 \begin_inset Phantom HPhantom
33928 \begin_layout Plain Layout
33931 Edit\SpecialChar menuseparator
33932 Math\SpecialChar menuseparator
33934 \begin_inset space ~
33937 Definition\SpecialChar menuseparator
33943 Spitting Out To The Right
33949 <row interlinespace="2.5mm">
33950 <cell alignment="center" valignment="top" usebox="none">
33953 \begin_layout Plain Layout
33956 arg "math-macro-append-greedy-param"
33964 <cell alignment="center" valignment="top" usebox="none">
33967 \begin_layout Plain Layout
33970 Edit\SpecialChar menuseparator
33971 Math\SpecialChar menuseparator
33973 \begin_inset space ~
33976 Definition\SpecialChar menuseparator
33978 \begin_inset Newline newline
33982 \begin_inset Phantom HPhantom
33985 \begin_layout Plain Layout
33988 Edit\SpecialChar menuseparator
33989 Math\SpecialChar menuseparator
33991 \begin_inset space ~
33994 Definition\SpecialChar menuseparator
34000 Eating From The Right
34006 <row interlinespace="2.5mm">
34007 <cell alignment="center" valignment="top" usebox="none">
34010 \begin_layout Plain Layout
34013 arg "math-macro-add-greedy-optional-param"
34021 <cell alignment="center" valignment="top" usebox="none">
34024 \begin_layout Plain Layout
34027 Edit\SpecialChar menuseparator
34028 Math\SpecialChar menuseparator
34030 \begin_inset space ~
34033 Definition\SpecialChar menuseparator
34034 Append Optional Argument
34035 \begin_inset Newline newline
34039 \begin_inset Phantom HPhantom
34042 \begin_layout Plain Layout
34045 Edit\SpecialChar menuseparator
34046 Math\SpecialChar menuseparator
34048 \begin_inset space ~
34051 Definition\SpecialChar menuseparator
34057 Eating From The Right
34070 \begin_layout Section
34071 Computer Algebra Systems
34074 \begin_layout Standard
34076 offers the exchange between mathematical expressions written in \SpecialChar LyX
34078 editor and external applications or user defined scripts.
34079 Currently supported applications are
34096 Note that the set of supported mathematical constructs is limited only
34097 to very simple cases.
34100 \begin_layout Subsection
34104 \begin_layout Standard
34105 Write some expression in a formula, go to the
34107 Edit\SpecialChar menuseparator
34108 Math\SpecialChar menuseparator
34109 Use Computer Algebra System
34111 menu and choose the application you have installed on the computer.
34112 After that the result of computation should show on the right side of the
34113 expression together with the
34114 \begin_inset Quotes eld
34118 \begin_inset Quotes erd
34124 \begin_layout Standard
34125 Here are few simple examples (with results from
34129 ) to show what kind of computations can be performed:
34132 \begin_layout Itemize
34133 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34139 \begin_layout Itemize
34140 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34146 \begin_layout Itemize
34147 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34153 \begin_layout Itemize
34154 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34158 \begin_inset Newline newline
34162 \begin_inset Note Greyedout
34165 \begin_layout Plain Layout
34170 One needs to use proper delimiter insets
34171 \begin_inset Formula $\left(\right)$
34174 instead of simple '(' ')' characters.
34182 \begin_layout Itemize
34183 \begin_inset Formula $\det\left[\begin{array}{ccc}
34187 \end{array}\right]=-56$
34193 \begin_layout Itemize
34194 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34200 \begin_layout Itemize
34201 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34207 \begin_layout Itemize
34208 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34214 \begin_layout Subsection
34218 \begin_layout Standard
34219 Currently there is no keyboard shortcut for calling the algebra applications.
34220 One can easily bind a shortcut to the
34234 \begin_inset space \thinspace{}
34238 \begin_inset space \space{}
34245 key inside the math editor.
34250 one would use this shortcut definition command:
34253 \begin_layout Standard
34256 command-alternatives paragraph-break;math-extern maxima
34259 \begin_layout Section
34261 \begin_inset Index idx
34264 \begin_layout Plain Layout
34273 \begin_layout Subsection
34275 \begin_inset Index idx
34278 \begin_layout Plain Layout
34287 \begin_layout Standard
34288 Negative numbers often look ugly in formulas because the minus sign before
34289 the number is set with the same length as the minus operator sign.
34290 When writing the negative number in normal text, the minus sign appears
34294 \begin_layout Standard
34295 Thus, the problem disappears when converting the minus sign to mathematical
34299 \begin_layout Standard
34300 An example to visualize the problem:
34303 \begin_layout Standard
34305 \begin_inset Tabular
34306 <lyxtabular version="3" rows="3" columns="2">
34307 <features booktabs="true" tabularvalignment="middle">
34308 <column alignment="right" valignment="top" width="0pt">
34309 <column alignment="left" valignment="top">
34311 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34314 \begin_layout Plain Layout
34320 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34323 \begin_layout Plain Layout
34331 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34334 \begin_layout Plain Layout
34340 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34343 \begin_layout Plain Layout
34344 \begin_inset Formula $x=-2$
34354 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34357 \begin_layout Plain Layout
34363 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34366 \begin_layout Plain Layout
34367 \begin_inset Formula $x=\textrm{-}2$
34383 \begin_layout Subsection
34384 Comma as decimal Separator
34385 \begin_inset Index idx
34388 \begin_layout Plain Layout
34397 \begin_layout Standard
34398 In \SpecialChar LaTeX
34399 a comma inside a formula is used, according to the English convention,
34400 as number group separator.
34401 So there will be space added behind all commas in formulas.
34404 \begin_layout Standard
34405 To avoid this, the comma is highlighted and changed to mathematical text
34415 \begin_layout Standard
34416 To use all formula commas in the document as decimal separator, the file
34425 \begin_layout Plain Layout
34430 is part of the \SpecialChar LaTeX
34436 \begin_inset Index idx
34439 \begin_layout Plain Layout
34444 \begin_layout Plain Layout
34464 \begin_inset Index idx
34467 \begin_layout Plain Layout
34473 is loaded with the \SpecialChar LaTeX
34477 \begin_layout Standard
34485 \begin_layout Subsection
34487 \begin_inset CommandInset label
34489 name "subsec:Physical-Vectors"
34494 \begin_inset Index idx
34497 \begin_layout Plain Layout
34506 \begin_layout Standard
34507 Predefined vectors are offered by the \SpecialChar LaTeX
34513 \begin_inset Index idx
34516 \begin_layout Plain Layout
34522 that is loaded with the \SpecialChar LaTeX
34526 \begin_layout Standard
34534 \begin_layout Standard
34538 \begin_layout Plain Layout
34548 \begin_inset Note Note
34551 \begin_layout Plain Layout
34552 The following table will only be displayed when the \SpecialChar LaTeX
34565 \begin_layout Standard
34566 The following commands are defined:
34569 \begin_layout Standard
34571 \begin_inset Tabular
34572 <lyxtabular version="3" rows="4" columns="2">
34573 <features booktabs="true" tabularvalignment="middle">
34574 <column alignment="center" valignment="top" width="0pt">
34575 <column alignment="center" valignment="top">
34577 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34580 \begin_layout Plain Layout
34586 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34589 \begin_layout Plain Layout
34597 <cell alignment="center" valignment="top" usebox="none">
34600 \begin_layout Plain Layout
34610 <cell alignment="center" valignment="top" usebox="none">
34613 \begin_layout Plain Layout
34614 \begin_inset Formula $\Bra{\psi}$
34624 <cell alignment="center" valignment="top" usebox="none">
34627 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" usebox="none">
34640 \begin_layout Plain Layout
34641 \begin_inset Formula $\Ket{\psi}$
34651 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34654 \begin_layout Plain Layout
34666 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34669 \begin_layout Plain Layout
34670 \begin_inset Formula $\Braket{\psi|\phi}$
34686 \begin_layout Standard
34693 assures that all vertical bars are set in the size of the surrounding brackets:
34694 \begin_inset Formula
34696 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34705 \begin_layout Plain Layout
34715 \begin_inset Note Note
34718 \begin_layout Plain Layout
34719 The following will be displayed when the \SpecialChar LaTeX
34732 \begin_layout Standard
34733 You need to install the \SpecialChar LaTeX
34738 to see the rest of this subsection in the output.
34741 \begin_layout Standard
34745 \begin_layout Plain Layout
34757 \begin_layout Standard
34764 can also be achieved using the command
34770 , that is described in
34771 \begin_inset CommandInset ref
34773 reference "subsec:Automatic-Bracket-Size"
34780 \begin_layout Subsection
34781 Self-defined Fractions
34782 \begin_inset CommandInset label
34784 name "subsec:Self-defined-Fractions"
34789 \begin_inset Index idx
34792 \begin_layout Plain Layout
34793 Fractions ! self-defined
34801 \begin_layout Standard
34802 To define custom commands for fractions, the command
34809 \begin_inset Index idx
34812 \begin_layout Plain Layout
34819 \begin_layout Plain Layout
34833 is used in the following scheme:
34836 \begin_layout Standard
34849 bracket}{fraction bar thickness}{style}
34850 \begin_inset Newline newline
34854 \begin_inset Phantom HPhantom
34857 \begin_layout Plain Layout
34867 {numerator}{denominator}
34870 \begin_layout Standard
34871 The style is a number in the range of 0
34872 \begin_inset space \thinspace{}
34876 \begin_inset space \thinspace{}
34882 \begin_layout Standard
34884 \begin_inset Tabular
34885 <lyxtabular version="3" rows="5" columns="2">
34886 <features booktabs="true" tabularvalignment="middle">
34887 <column alignment="center" valignment="top" width="0pt">
34888 <column alignment="center" valignment="top">
34890 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34893 \begin_layout Plain Layout
34899 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34902 \begin_layout Plain Layout
34910 <cell alignment="center" valignment="top" usebox="none">
34913 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" usebox="none">
34922 \begin_layout Plain Layout
34923 display style formula
34930 <cell alignment="center" valignment="top" usebox="none">
34933 \begin_layout Plain Layout
34939 <cell alignment="center" valignment="top" usebox="none">
34942 \begin_layout Plain Layout
34950 <cell alignment="center" valignment="top" usebox="none">
34953 \begin_layout Plain Layout
34959 <cell alignment="center" valignment="top" usebox="none">
34962 \begin_layout Plain Layout
34970 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34973 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34982 \begin_layout Plain Layout
34996 \begin_layout Standard
34997 When no style is given, the size is adjusted to the surrounding environment
34998 like for the command
35007 \begin_layout Standard
35008 When no fraction bar thickness is given, the predefined value of 0.4
35009 \begin_inset space \thinspace{}
35015 \begin_layout Standard
35016 \begin_inset VSpace medskip
35019 For example, the commands
35032 \begin_inset CommandInset ref
35034 reference "subsec:Fractions"
35038 are defined with the commands
35041 \begin_layout Standard
35050 genfrac{}{}{}{0}{#1}{#2}}
35053 \begin_layout Standard
35057 \begin_layout Standard
35066 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35069 \begin_layout Standard
35070 \begin_inset VSpace medskip
35073 To define a fraction where the fraction bar thickness can be given as optional
35074 argument, the following line is inserted to the \SpecialChar LaTeX
35078 \begin_layout Standard
35087 genfrac{}{}{#1}{}{#2}{#3}}
35090 \begin_layout Standard
35092 \begin_inset Formula
35094 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35095 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35100 As one can see, the distance of the numerator and the denominator to the
35101 fraction bar is round about three times the bar thickness.
35104 \begin_layout Subsection
35106 \begin_inset Index idx
35109 \begin_layout Plain Layout
35118 \begin_layout Standard
35119 There are four ways to cancel formulas or parts of formulas:
35122 \begin_layout Standard
35126 \begin_layout Plain Layout
35136 \begin_inset Note Note
35139 \begin_layout Plain Layout
35140 The following table will only be displayed when the \SpecialChar LaTeX
35153 \begin_layout Standard
35155 \begin_inset Tabular
35156 <lyxtabular version="3" rows="5" columns="2">
35157 <features booktabs="true" tabularvalignment="middle">
35158 <column alignment="center" valignment="top" width="0pt">
35159 <column alignment="center" valignment="top">
35161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35164 \begin_layout Plain Layout
35170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35173 \begin_layout Plain Layout
35181 <cell alignment="center" valignment="top" usebox="none">
35184 \begin_layout Plain Layout
35188 \begin_inset space \textvisiblespace{}
35194 \begin_inset space \textvisiblespace{}
35202 <cell alignment="center" valignment="top" usebox="none">
35205 \begin_layout Plain Layout
35206 \begin_inset Formula $\cancel{\int A=B}$
35215 <row topspace="1.5mm">
35216 <cell alignment="center" valignment="top" usebox="none">
35219 \begin_layout Plain Layout
35223 \begin_inset space \textvisiblespace{}
35229 \begin_inset space \textvisiblespace{}
35237 <cell alignment="center" valignment="top" usebox="none">
35240 \begin_layout Plain Layout
35241 \begin_inset Formula $\bcancel{\int A=B}$
35250 <row topspace="1.5mm">
35251 <cell alignment="center" valignment="top" usebox="none">
35254 \begin_layout Plain Layout
35258 \begin_inset space \textvisiblespace{}
35264 \begin_inset space \textvisiblespace{}
35272 <cell alignment="center" valignment="top" usebox="none">
35275 \begin_layout Plain Layout
35276 \begin_inset Formula $\xcancel{\int A=B}$
35286 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35289 \begin_layout Plain Layout
35293 \begin_inset space \textvisiblespace{}
35299 \begin_inset space \textvisiblespace{}
35303 \begin_inset Formula $\to$
35311 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35314 \begin_layout Plain Layout
35315 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35331 \begin_layout Standard
35338 is especially suitable to visualize the reduction of fractions within formulas:
35339 \begin_inset Formula
35341 \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}}}
35349 \begin_layout Standard
35350 To change the size of
35357 \begin_inset Quotes eld
35361 \begin_inset Quotes erd
35364 value one can add the \SpecialChar LaTeX
35368 \begin_layout Standard
35373 PassOptionsToPackage{option}{cancel}
35376 \begin_layout Standard
35385 which leads to the same size as for the canceled value, or
35389 which makes is it a bit smaller than normal.
35392 \begin_layout Standard
35393 To color the cancellation bar one adds this command as \SpecialChar TeX
35397 \begin_layout Standard
35409 \begin_layout Standard
35414 can be replaced by a color of your choice.
35417 \begin_layout Standard
35421 \begin_layout Plain Layout
35437 \begin_layout Standard
35438 \begin_inset Formula
35440 \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}}}
35448 \begin_layout Standard
35452 \begin_layout Plain Layout
35466 \begin_inset Note Note
35469 \begin_layout Plain Layout
35478 \begin_layout Standard
35479 For further customizations, see the documentation of the package
35484 \begin_inset CommandInset citation
35492 \begin_inset Index idx
35495 \begin_layout Plain Layout
35504 \begin_layout Standard
35508 \begin_layout Plain Layout
35518 \begin_inset Note Note
35521 \begin_layout Plain Layout
35522 The following will be displayed when the \SpecialChar LaTeX
35535 \begin_layout Standard
35536 You need to install the \SpecialChar LaTeX
35541 to see the rest of this subsection in the output.
35544 \begin_layout Standard
35548 \begin_layout Plain Layout
35560 \begin_layout Subsection
35561 Formulas in Section Headings
35562 \begin_inset CommandInset label
35564 name "subsec:Formulas-in-Section"
35569 \begin_inset Index idx
35572 \begin_layout Plain Layout
35573 Formula ! in section headings
35581 \begin_layout Standard
35582 When formulas are used in section headings, the following has to be taken
35586 \begin_layout Standard
35587 \begin_inset Note Greyedout
35590 \begin_layout Plain Layout
35596 \begin_inset Index idx
35599 \begin_layout Plain Layout
35600 Packages ! hyperref
35605 support is enabled in the document settings dialog under
35608 \begin_inset space ~
35613 , PDF-bookmarks are created for every section heading in the table of contents.
35614 If a section heading contains formulas, they are incorrectly displayed
35615 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35624 \begin_layout Standard
35625 Both problems can be solved by inserting at the end of the section heading
35626 a short title with the menu
35628 Insert\SpecialChar menuseparator
35630 \begin_inset space ~
35636 Short titles are used as alternative for multiline section headings to
35637 keep the table of contents clearly arranged.
35638 Only the short title appears in the table of contents and therefore also
35639 in the PDF-bookmark.
35642 \begin_layout Standard
35643 When formulas should be used in the table of contents but
35647 is used, one can use the following command in \SpecialChar TeX
35651 \begin_layout Standard
35656 texorpdfstring{part}{alternative}
35657 \begin_inset Index idx
35660 \begin_layout Plain Layout
35671 \begin_layout Standard
35672 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35673 This can be characters, formulas, footnotes, but also cross-references.
35674 The alternative is used instead of the part for the bookmark.
35677 \begin_layout Standard
35678 Here are two example headings:
35679 \begin_inset VSpace -3mm
35686 \begin_layout Plain Layout
35698 \begin_layout Subsubsection
35699 Heading without formula in table of contents
35700 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35704 \begin_inset Argument 1
35707 \begin_layout Plain Layout
35708 Heading without formula in table of contents
35716 \begin_layout Subsubsection
35717 Heading with formula in table of contents
35721 \begin_layout Plain Layout
35731 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35738 \begin_layout Plain Layout
35748 \begin_layout Standard
35752 \begin_layout Plain Layout
35761 In the first heading a short title was used, in the second one
35770 \begin_layout Standard
35771 To get the same formatting as for the other headings, the complete heading
35780 \begin_layout Plain Layout
35782 \begin_inset CommandInset ref
35784 reference "subsec:Bold-Formulas"
35796 \begin_layout Subsection
35797 Formulas in multi-column Text
35798 \begin_inset Index idx
35801 \begin_layout Plain Layout
35802 Formula ! in multi-column text
35810 \begin_layout Standard
35811 Formulas in multi-column text are often too wide to fit into a column and
35812 thus need to be set over the whole page width.
35813 This is done by using the \SpecialChar LaTeX
35822 \begin_layout Plain Layout
35827 is part of every \SpecialChar LaTeX
35828 standard installation.
35834 \begin_inset Index idx
35837 \begin_layout Plain Layout
35838 Packages ! multicol
35843 , that is loaded with the \SpecialChar LaTeX
35847 \begin_layout Standard
35852 usepackage{multicol}
35855 \begin_layout Standard
35856 \begin_inset Note Greyedout
35859 \begin_layout Plain Layout
35860 Note that in this case the setting
35863 \begin_inset space ~
35870 Document\SpecialChar menuseparator
35876 \begin_inset space ~
35896 \begin_layout Standard
35897 Before the multi-column text the command
35900 \begin_layout Standard
35905 begin{multicols}{column number}
35908 \begin_layout Standard
35909 is written in \SpecialChar TeX
35911 The column number is a number in the range of 2
35912 \begin_inset space \thinspace{}
35916 \begin_inset space \thinspace{}
35920 Before the formula the multi-column text is ended by inserting the command
35923 \begin_layout Standard
35931 \begin_layout Standard
35932 in \SpecialChar TeX
35936 \begin_layout Standard
35937 Due to the command some space is automatically added before the formula.
35939 \begin_inset space \thinspace{}
35942 mm vertical space is inserted before the formula.
35943 When the formula style
35949 \begin_layout Plain Layout
35951 \begin_inset CommandInset ref
35953 reference "sec:Formula-Styles"
35965 \begin_inset space \thinspace{}
35968 mm space is inserted instead.
35971 \begin_layout Standard
35972 As example a multi-column text with a displayed formula:
35975 \begin_layout Standard
35981 \begin_layout Plain Layout
35985 begin{multicols}{2}
35990 Das Spektrum wird fouriertransformiert.
35991 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35992 , Lösungsmittel) zu trennen.
35993 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35994 nun das Aussehen des Ausgangssignals.
35995 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35996 über alle Phasen integrieren muss.
35998 \begin_inset Formula $S$
36001 unser normiertes Ausgangssignal und
36002 \begin_inset Formula $P$
36005 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36009 \begin_layout Plain Layout
36019 \begin_inset VSpace -6mm
36023 \begin_inset Formula
36025 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36034 \begin_layout Plain Layout
36038 begin{multicols}{2}
36044 \begin_inset Formula $S_{0}$
36047 das Signal ohne Gradient ist und die Normierungsbedingung
36048 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36052 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36054 \begin_inset Formula $\nicefrac{\pi}{2}$
36058 \begin_inset space \thinspace{}
36061 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36062 das Signal zusätzlich abschwächt.
36063 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36065 \begin_inset Formula $T_{2}$
36071 \begin_layout Standard
36077 \begin_layout Plain Layout
36089 \begin_layout Subsection
36090 Formulas with Description of Variables
36091 \begin_inset Index idx
36094 \begin_layout Plain Layout
36095 Formula ! with description of variables
36103 \begin_layout Standard
36104 To describe variables within a formula, like in formula
36105 \begin_inset CommandInset ref
36107 reference "eq:within"
36116 \begin_inset Formula $n$
36120 \begin_inset space ~
36123 matrix is used with left aligned columns for the
36124 \begin_inset Formula $n$
36131 \begin_layout Plain Layout
36133 \begin_inset CommandInset ref
36135 reference "sec:Matrices"
36144 To set the description in a smaller size, before the matrix e.
36145 \begin_inset space \thinspace{}
36149 \begin_inset space \space{}
36162 \begin_layout Plain Layout
36164 \begin_inset CommandInset ref
36166 reference "subsec:Font-Sizes"
36178 \begin_layout Standard
36179 When the formula style
36185 \begin_layout Plain Layout
36187 \begin_inset CommandInset ref
36189 reference "sec:Formula-Styles"
36210 \begin_layout Plain Layout
36217 only works in formulas with the style
36222 \begin_inset CommandInset ref
36224 reference "subsec:Variable-Space"
36233 is inserted before and after the matrix to have the same separation of
36234 the matrix from the equation and the side margin.
36237 \begin_layout Standard
36238 When the formula style
36242 is used, the method described in
36243 \begin_inset CommandInset ref
36245 reference "subsec:Flalign-Environment"
36249 is used to indent formulas.
36251 \begin_inset CommandInset ref
36253 reference "eq:within"
36257 consists of five columns where in the first two columns contain the equation,
36258 the third the matrix and the last one an empty \SpecialChar TeX
36260 \begin_inset Formula
36262 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36263 \rho & \textrm{density}\\
36264 V & \textrm{volume}\\
36265 g & \textrm{gravitational acceleration}
36266 \end{array} & & {}\label{eq:within}
36274 \begin_layout Subsection
36275 Upright small Greek Letters
36276 \begin_inset CommandInset label
36278 name "subsec:Upright-small-Greek"
36283 \begin_inset Index idx
36286 \begin_layout Plain Layout
36287 Greek letters ! upright
36295 \begin_layout Standard
36296 Most of the math fonts only provide italic small Greek letters.
36297 But for symbols of elementary particles like pions and neutrinos, upright
36298 Greek letters are needed.
36307 \begin_layout Plain Layout
36312 is part of the \SpecialChar LaTeX
36318 \begin_inset Index idx
36321 \begin_layout Plain Layout
36326 \begin_layout Plain Layout
36346 \begin_inset Index idx
36349 \begin_layout Plain Layout
36355 that is loaded with the \SpecialChar LaTeX
36359 \begin_layout Standard
36364 usepackage{upgreek}
36367 \begin_layout Standard
36373 \begin_layout Plain Layout
36383 \begin_inset Note Note
36386 \begin_layout Plain Layout
36387 The following table will only be displayed when the \SpecialChar LaTeX
36397 They are created when the command for a small Greek letter is started with
36403 For example the command
36410 \begin_inset Formula $\uptau$
36416 \begin_layout Standard
36417 With these commands reactions of elementary particles can be typeset:
36418 \begin_inset Formula
36420 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36428 \begin_layout Standard
36429 The upright letters are more bold and wider than the italic ones.
36430 They should therefore not be used for units like
36431 \begin_inset Quotes eld
36435 \begin_inset Quotes erd
36441 \begin_layout Standard
36445 \begin_layout Plain Layout
36455 \begin_inset Note Note
36458 \begin_layout Plain Layout
36459 The following will be displayed when the \SpecialChar LaTeX
36472 \begin_layout Standard
36473 You need to install the \SpecialChar LaTeX
36478 to see the rest of this subsection in the output.
36481 \begin_layout Standard
36485 \begin_layout Plain Layout
36497 \begin_layout Subsection
36498 Text Characters in Formulas
36499 \begin_inset Index idx
36502 \begin_layout Plain Layout
36511 \begin_layout Standard
36512 In some cases you might want to insert text characters directly into formulas.
36513 When for example the centered dot · is often used in formulas like
36514 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36517 , one would have to insert the command
36527 \begin_layout Plain Layout
36529 \begin_inset CommandInset ref
36531 reference "subsec:Binary-Operators"
36540 all the time, because this character is defined in all encodings as text
36542 But the encoding can be changed by this \SpecialChar LaTeX
36546 \begin_layout Standard
36551 Declare Inputtext{183}{
36561 f\SpecialChar ligaturebreak
36565 \begin_layout Standard
36566 The character encoding (menu
36568 Document\SpecialChar menuseparator
36569 Settings\SpecialChar menuseparator
36572 ) specifies what character appears when a keyboard key is pressed.
36573 When the key for the character '·' is pressed, internally the command
36580 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36582 With the changed encoding the right command is chosen automatically, depending
36583 on if the character was inserted into a formula or not.
36586 \begin_layout Standard
36587 The encoding of several characters is saved in definition files.
36588 For example the encoding
36592 is defined in the file
36596 which is in the installation folder of \SpecialChar LaTeX
36598 Encodings should only be changed via the \SpecialChar LaTeX
36599 -preamble and not in the definition
36601 Otherwise documents could not be edited by other \SpecialChar LyX
36602 users working on other
36606 \begin_layout Standard
36607 \begin_inset VSpace medskip
36610 Besides the centered dot, in this document the degree sign ° is defined
36611 with the following \SpecialChar LaTeX
36612 -preamble line so that it can be directly inserted into
36616 \begin_layout Standard
36621 DeclareInputtext{176}{
36631 f\SpecialChar ligaturebreak
36635 \begin_layout Subsection
36637 -comments in formulas
36638 \begin_inset Index idx
36641 \begin_layout Plain Layout
36651 \begin_layout Standard
36652 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36654 code of your file with the menu
36656 Insert\SpecialChar menuseparator
36657 Note\SpecialChar menuseparator
36661 This is not possible in a formula but you can insert \SpecialChar LaTeX
36666 \begin_layout Standard
36674 \begin_layout Standard
36675 This creates a box in which you can write your comment.
36676 Due to a bug in \SpecialChar LyX
36681 \begin_layout Plain Layout
36682 \begin_inset CommandInset href
36684 name "LyX-bug #9002"
36685 target "https://www.lyx.org/trac/ticket/9002"
36695 you cannot write normal text inside the comment, even when you use mathematical
36696 text, you will see its \SpecialChar LaTeX
36697 -commands in the \SpecialChar LaTeX
36699 \begin_inset Newline newline
36702 This a formula with a \SpecialChar LaTeX
36704 \begin_inset Formula
36706 A=B%\text{This is the comment}
36714 \begin_layout Standard
36715 \begin_inset Newpage newpage
36721 \begin_layout Section
36724 \begin_inset Index idx
36727 \begin_layout Plain Layout
36736 \begin_layout Standard
36737 This section is a summary of the most important typographic rules, listed
36742 \begin_layout Plain Layout
36743 This collection was partly taken from the German semi-official dictionary
36745 \begin_inset Quotes eld
36749 \begin_inset Quotes erd
36753 \begin_inset CommandInset citation
36760 that lists some of the ISO rules.
36761 More rules are listed in
36762 \begin_inset CommandInset citation
36777 \begin_layout Itemize
36786 \begin_layout Plain Layout
36787 done with font styles, see
36788 \begin_inset CommandInset ref
36790 reference "subsec:Font-Styles"
36799 , no matter if they appear in italic text: 30
36800 \begin_inset space \thinspace{}
36804 \begin_inset Newline newline
36807 Between the value and the unit is the smallest space, see
36808 \begin_inset CommandInset ref
36810 reference "subsec:Predefined-Space"
36815 \begin_inset Newline newline
36818 This convention is automatically fulfilled when the command
36825 When it is entered to a formula, two boxes appear.
36826 In the first one the value is inserted, in the second one the unit, and
36828 \begin_inset Formula $\unit[30]{km/h}$
36832 \begin_inset space \thinspace{}
36842 is not a real \SpecialChar LaTeX
36843 command but the command
36849 , therefore you cannot use it in \SpecialChar TeX
36853 \begin_layout Itemize
36854 Percent and perthousand signs are set like physical units:
36855 \begin_inset Newline newline
36859 \begin_inset space \thinspace{}
36865 \begin_layout Itemize
36866 The degree sign follows directly on the value: 15°, but not when it is used
36868 \begin_inset space \thinspace{}
36874 \begin_layout Itemize
36875 In numbers with more than four digits the smallest space is inserted before
36876 every third digit to group them:
36886 \begin_inset space \thinspace{}
36890 \begin_inset space \thinspace{}
36896 \begin_layout Itemize
36897 For dimensions like 120×90×40
36898 \begin_inset space \thinspace{}
36901 cm the multiplication sign
36902 \begin_inset Quotes eld
36906 \begin_inset Quotes erd
36910 It is available either via the command
36918 Insert\SpecialChar menuseparator
36919 Special Character\SpecialChar menuseparator
36925 \begin_layout Itemize
36926 Functions with names consisting of several letters are set upright to avoid
36928 \begin_inset CommandInset ref
36930 reference "subsec:Predefined-Functions"
36937 \begin_layout Itemize
36938 Indices consisting of several letters, are set upright:
36939 \begin_inset Formula $E_{\mathrm{kin}}$
36943 \begin_inset Newline newline
36946 Components of matrices are set italic:
36947 \begin_inset Formula $\hat{H}_{kl}$
36953 \begin_layout Itemize
36954 The differentiation/integration operator 'd', the Euler's number 'e' and
36955 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36959 \begin_layout Itemize
36960 The character that denotes a
36964 transformation is inserted either by the command
36969 \begin_inset space \textvisiblespace{}
36976 Insert\SpecialChar menuseparator
36977 Special Character\SpecialChar menuseparator
36978 Symbols\SpecialChar menuseparator
36980 \begin_inset space ~
36986 \begin_inset Formula $\mathscr{F}$
36992 \begin_layout Standard
36993 \begin_inset Newpage newpage
36999 \begin_layout Section
37001 \begin_inset Index idx
37004 \begin_layout Plain Layout
37013 \begin_layout Standard
37014 Some characters and symbols can be created with several commands.
37015 Here is a list of the synonym commands:
37018 \begin_layout Standard
37019 \begin_inset VSpace bigskip
37023 \begin_inset space \hfill{}
37027 \begin_inset Tabular
37028 <lyxtabular version="3" rows="12" columns="2">
37029 <features booktabs="true" tabularvalignment="middle">
37030 <column alignment="center" valignment="top" width="0pt">
37031 <column alignment="center" valignment="top" width="0pt">
37033 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37036 \begin_layout Plain Layout
37042 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37045 \begin_layout Plain Layout
37053 <cell alignment="center" valignment="top" usebox="none">
37056 \begin_layout Plain Layout
37064 <cell alignment="center" valignment="top" usebox="none">
37067 \begin_layout Plain Layout
37075 <cell alignment="center" valignment="top" usebox="none">
37078 \begin_layout Plain Layout
37086 <cell alignment="center" valignment="top" usebox="none">
37089 \begin_layout Plain Layout
37099 <cell alignment="center" valignment="top" usebox="none">
37102 \begin_layout Plain Layout
37110 <cell alignment="center" valignment="top" usebox="none">
37113 \begin_layout Plain Layout
37123 <cell alignment="center" valignment="top" usebox="none">
37126 \begin_layout Plain Layout
37134 <cell alignment="center" valignment="top" usebox="none">
37137 \begin_layout Plain Layout
37145 <cell alignment="center" valignment="top" usebox="none">
37148 \begin_layout Plain Layout
37156 <cell alignment="center" valignment="top" usebox="none">
37159 \begin_layout Plain Layout
37167 <cell alignment="center" valignment="top" usebox="none">
37170 \begin_layout Plain Layout
37178 <cell alignment="center" valignment="top" usebox="none">
37181 \begin_layout Plain Layout
37191 <cell alignment="center" valignment="top" usebox="none">
37194 \begin_layout Plain Layout
37202 <cell alignment="center" valignment="top" usebox="none">
37205 \begin_layout Plain Layout
37215 <cell alignment="center" valignment="top" usebox="none">
37218 \begin_layout Plain Layout
37226 <cell alignment="center" valignment="top" usebox="none">
37229 \begin_layout Plain Layout
37239 <cell alignment="center" valignment="top" usebox="none">
37242 \begin_layout Plain Layout
37250 <cell alignment="center" valignment="top" usebox="none">
37253 \begin_layout Plain Layout
37263 <cell alignment="center" valignment="top" usebox="none">
37266 \begin_layout Plain Layout
37274 <cell alignment="center" valignment="top" usebox="none">
37277 \begin_layout Plain Layout
37285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37288 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37299 \begin_layout Plain Layout
37311 \begin_inset space \hfill{}
37315 \begin_inset Tabular
37316 <lyxtabular version="3" rows="12" columns="2">
37317 <features booktabs="true" tabularvalignment="middle">
37318 <column alignment="center" valignment="top" width="0pt">
37319 <column alignment="center" valignment="top" width="0pt">
37321 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37324 \begin_layout Plain Layout
37330 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37333 \begin_layout Plain Layout
37341 <cell alignment="center" valignment="top" usebox="none">
37344 \begin_layout Plain Layout
37352 <cell alignment="center" valignment="top" usebox="none">
37355 \begin_layout Plain Layout
37367 <cell alignment="center" valignment="top" usebox="none">
37370 \begin_layout Plain Layout
37378 <cell alignment="center" valignment="top" usebox="none">
37381 \begin_layout Plain Layout
37391 <cell alignment="center" valignment="top" usebox="none">
37394 \begin_layout Plain Layout
37402 <cell alignment="center" valignment="top" usebox="none">
37405 \begin_layout Plain Layout
37415 <cell alignment="center" valignment="top" usebox="none">
37418 \begin_layout Plain Layout
37426 <cell alignment="center" valignment="top" usebox="none">
37429 \begin_layout Plain Layout
37437 <cell alignment="center" valignment="top" usebox="none">
37440 \begin_layout Plain Layout
37448 <cell alignment="center" valignment="top" usebox="none">
37451 \begin_layout Plain Layout
37459 <cell alignment="center" valignment="top" usebox="none">
37462 \begin_layout Plain Layout
37470 <cell alignment="center" valignment="top" usebox="none">
37473 \begin_layout Plain Layout
37483 <cell alignment="center" valignment="top" usebox="none">
37486 \begin_layout Plain Layout
37494 <cell alignment="center" valignment="top" usebox="none">
37497 \begin_layout Plain Layout
37507 <cell alignment="center" valignment="top" usebox="none">
37510 \begin_layout Plain Layout
37518 <cell alignment="center" valignment="top" usebox="none">
37521 \begin_layout Plain Layout
37531 <cell alignment="center" valignment="top" usebox="none">
37534 \begin_layout Plain Layout
37542 <cell alignment="center" valignment="top" usebox="none">
37545 \begin_layout Plain Layout
37555 <cell alignment="center" valignment="top" usebox="none">
37558 \begin_layout Plain Layout
37566 <cell alignment="center" valignment="top" usebox="none">
37569 \begin_layout Plain Layout
37579 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37582 \begin_layout Plain Layout
37590 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37593 \begin_layout Plain Layout
37607 \begin_inset space \hfill{}
37611 \begin_inset CommandInset href
37614 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37622 \begin_layout Standard
37623 \begin_inset Newpage newpage
37629 \begin_layout Bibliography
37630 \begin_inset CommandInset bibitem
37631 LatexCommand bibitem
37645 The \SpecialChar LaTeX
37649 Addison Wesley, 2004
37652 \begin_layout Bibliography
37653 \begin_inset CommandInset bibitem
37654 LatexCommand bibitem
37661 \begin_inset CommandInset href
37664 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37669 of \SpecialChar LaTeX
37673 \begin_layout Bibliography
37674 \begin_inset CommandInset bibitem
37675 LatexCommand bibitem
37682 \begin_inset CommandInset href
37685 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
37694 \begin_layout Plain Layout
37703 -\SpecialChar LaTeX
37707 \begin_layout Bibliography
37708 \begin_inset CommandInset bibitem
37709 LatexCommand bibitem
37716 \begin_inset CommandInset href
37719 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37724 of all symbols available with \SpecialChar LaTeX
37728 \begin_layout Bibliography
37729 \begin_inset CommandInset bibitem
37730 LatexCommand bibitem
37737 \begin_inset CommandInset href
37739 name "Documentation"
37740 target "https://www.ctan.org/tex-archive/macros/latex/contrib/cancel/cancel.pdf"
37745 of the \SpecialChar LaTeX
37751 \begin_inset Index idx
37754 \begin_layout Plain Layout
37763 \begin_layout Bibliography
37764 \begin_inset CommandInset bibitem
37765 LatexCommand bibitem
37772 \begin_inset CommandInset href
37774 name "Documentation"
37775 target "https://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/doc/manual.pdf"
37780 of the \SpecialChar LaTeX
37786 \begin_inset Index idx
37789 \begin_layout Plain Layout
37790 Packages ! hyperref
37798 \begin_layout Bibliography
37799 \begin_inset CommandInset bibitem
37800 LatexCommand bibitem
37807 \begin_inset CommandInset href
37809 name "Documentation"
37810 target "https://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37815 of the \SpecialChar LaTeX
37821 \begin_inset Index idx
37824 \begin_layout Plain Layout
37833 \begin_layout Bibliography
37834 \begin_inset CommandInset bibitem
37835 LatexCommand bibitem
37844 \begin_inset space ~
37851 \begin_inset space ~
37854 Auflage, Dudenverlag, 2000
37857 \begin_layout Bibliography
37858 \begin_inset CommandInset bibitem
37859 LatexCommand bibitem
37866 \begin_inset CommandInset href
37869 target "https://www.nist.gov/physical-measurement-laboratory/special-publication-811"
37874 for reviewing manuscripts
37877 \begin_layout Standard
37878 \begin_inset CommandInset index_print
37879 LatexCommand printindex