1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
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32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
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
124 \IfFileExists{cancel.sty}
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
141 \maintain_unincluded_children false
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
151 \use_non_tex_fonts false
154 \font_sf_scale 100 100
155 \font_tt_scale 100 100
157 \use_dash_ligatures false
159 \default_output_format pdf2
161 \bibtex_command default
162 \index_command default
166 \pdf_title "LyX's Math Manual"
167 \pdf_author "LyX Team, Uwe Stöhr"
168 \pdf_subject "LyX-documentation about math"
169 \pdf_keywords "LyX, Mathed"
171 \pdf_bookmarksnumbered true
172 \pdf_bookmarksopen true
173 \pdf_bookmarksopenlevel 1
174 \pdf_breaklinks false
178 \pdf_pdfusetitle false
179 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
182 \use_package amsmath 2
183 \use_package amssymb 2
184 \use_package cancel 1
186 \use_package mathdots 1
187 \use_package mathtools 2
188 \use_package mhchem 1
189 \use_package stackrel 1
190 \use_package stmaryrd 1
191 \use_package undertilde 0
193 \cite_engine_type default
197 \paperorientation portrait
202 \notefontcolor #0000ff
209 \paragraph_separation skip
212 \math_numbering_side default
213 \quotes_style english
217 \paperpagestyle plain
221 \tracking_changes false
222 \output_changes false
225 \html_be_strict false
232 's detailed Math manual
236 by the \SpecialChar LyX
241 \begin_layout Plain Layout
243 If you have comments or error corrections, please send them to the \SpecialChar LyX
248 \begin_inset CommandInset href
250 name "lyx-docs@lists.lyx.org"
251 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
263 \begin_inset Note Note
266 \begin_layout Plain Layout
273 \begin_inset Newline newline
277 \begin_inset Newline newline
285 \begin_layout Standard
286 \begin_inset CommandInset toc
287 LatexCommand tableofcontents
294 \begin_layout Standard
295 \begin_inset Note Note
298 \begin_layout Plain Layout
299 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
302 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
309 If they are not installed the document can be exported anyway but the sections
310 where the packages are required will not appear in the output.
315 ; if it is not installed, this file cannot be exported.
318 \begin_layout Plain Layout
319 The latest PDF-version of this document can be found here:
320 \begin_inset Newline newline
325 https://wiki.lyx.org/LyX/Manuals#Math
333 \begin_layout Standard
334 \begin_inset Newpage newpage
340 \begin_layout Section
344 \begin_layout Standard
345 This document explains \SpecialChar LyX
346 's math features and is furthermore a collection
347 of \SpecialChar LaTeX
348 -commands used for mathematical characters and constructs.
349 The explanations are designed for the usage of commands.
350 It is therefore required that you have read the section
361 \begin_layout Standard
362 Most of the characters and many constructs explained in this manual are
363 also accessible via the menu
367 \SpecialChar menuseparator
383 But everybody who has to write lots of formulas will notice that it is
384 much faster to use commands instead of the math toolbar.
385 Therefore this manual is focused on commands but also mentions the correspondin
386 g toolbar buttons when available.
389 \begin_layout Standard
390 If not specially mentioned the commands are only available within formulas.
391 To be able to use all commands explained in this document, the option
395 must be checked in the document settings (menu
397 Document\SpecialChar menuseparator
398 Settings\SpecialChar menuseparator
409 \begin_layout Plain Layout
412 Use AMS math package automatically
418 \begin_layout Plain Layout
427 -math when math constructs are found that are supported by \SpecialChar LyX
436 \begin_layout Standard
437 This document doesn't list all
441 \begin_layout Plain Layout
454 \begin_layout Plain Layout
459 \begin_layout Plain Layout
468 -math commands is in the file
471 \begin_inset CommandInset href
474 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
481 , which is part of every \SpecialChar LaTeX
482 standard installation.
487 for lucidity reasons.
490 \begin_layout Section
494 \begin_layout Standard
495 To create an inline formula
496 \begin_inset Index idx
499 \begin_layout Plain Layout
505 that is embedded into a text line, use one of the shortcuts
511 or the toolbar button
518 \begin_inset Newline newline
521 To create a display style formula
522 \begin_inset Index idx
525 \begin_layout Plain Layout
526 Formula ! display style
531 which will appear bigger, has a different format, and will be in a separate
532 paragraph, use one of these shortcuts:
541 \begin_layout Standard
542 To change a display style formula to an inline formula, set the cursor into
543 the formula and use one of the shortcuts
551 Edit\SpecialChar menuseparator
552 Math\SpecialChar menuseparator
556 The same way is used to change an inline formula to a display style formula.
559 \begin_layout Standard
560 To display parts of an inline formula in the size of a display style formula,
568 \begin_inset Index idx
571 \begin_layout Plain Layout
580 Then a new blue box appears in which the desired formula part is inserted.
583 \begin_layout Standard
584 Only inline formulas are allowed inside tables.
587 \begin_layout Standard
592 can be turned on in the menu
594 View\SpecialChar menuseparator
598 When you click there on
599 \begin_inset Quotes eld
603 \begin_inset Quotes erd
606 the toolbar will be shown permanently at the bottom; this state is visualized
611 menu with a checkmark.
612 When you click in this state again on
613 \begin_inset Quotes eld
617 \begin_inset Quotes erd
628 is only shown when the cursor is within a formula; this state is visualized
629 by the renaming of the menu entry from
630 \begin_inset Quotes eld
634 \begin_inset Quotes erd
638 \begin_inset Quotes eld
646 \begin_inset Quotes erd
652 \begin_layout Standard
655 \begin_inset Index idx
658 \begin_layout Plain Layout
665 is invoked by pressing the toolbar button
673 Insert\SpecialChar menuseparator
685 \begin_layout Standard
686 To change the \SpecialChar LaTeX
688 \begin_inset Index idx
691 \begin_layout Plain Layout
700 Document\SpecialChar menuseparator
701 Settings\SpecialChar menuseparator
711 \begin_layout Standard
712 To edit matrices, case differentiations and multiline formulas subsequently,
715 Edit\SpecialChar menuseparator
720 Edit\SpecialChar menuseparator
722 \begin_inset space \thinspace{}
726 \begin_inset space \thinspace{}
736 When lines and columns are swapped via the menu, the column or line where
737 the cursor is in is exchanged with the column to the right or the line
739 Is the cursor in the last column or row, the exchange is done with the
740 column to the left or the line above.
743 \begin_layout Standard
744 To write text in formulas
748 \begin_layout Plain Layout
749 For multiline formulas the command
756 \begin_inset CommandInset ref
758 reference "subsec:Text-in-multiline"
772 \begin_inset Index idx
775 \begin_layout Plain Layout
782 \begin_inset Index idx
785 \begin_layout Plain Layout
792 This mode is invoked with the shortcut
798 or by the insertion of the command
805 \begin_inset Index idx
808 \begin_layout Plain Layout
817 The text appears black in \SpecialChar LyX
818 and can therefore be distinguished from the
819 other formula parts which appear blue.
820 In the output mathematical text is set upright, in contrary to other formula
824 \begin_layout Subsection*
828 \begin_layout Standard
829 Most of the \SpecialChar LaTeX
830 -commands for math constructs have the following scheme:
833 \begin_layout Standard
849 \begin_layout Standard
850 A command always starts with a backslash
851 \begin_inset Quotes gld
861 \begin_inset Quotes grd
865 To omit optional arguments, also omit the associated brackets.
866 The braces around the required arguments are named in this document as
869 \begin_inset Index idx
872 \begin_layout Plain Layout
880 If you add in a formula a left brace to a command name, \SpecialChar LyX
882 creates a \SpecialChar TeX
884 In all other cases \SpecialChar TeX
885 braces are created in formulas with the command
893 braces appear red in \SpecialChar LyX
894 , in contrary to normal braces which appear blue.
896 mode no command is needed to get \SpecialChar TeX
899 braces don't appear in the output.
902 \begin_layout Standard
903 When commands without arguments, like commands for symbols are entered in
905 mode, a space character must
909 be behind the command to end it.
910 This space doesn't appear in the output.
911 When the space should appear in the output, the space must be followed
912 by a protected space in normal text.
915 \begin_layout Standard
916 A protected space is inserted with
919 arg "command-alternatives space-insert protected ; math-space"
925 \begin_layout Subsection*
926 \begin_inset Newpage newpage
932 \begin_layout Itemize
934 \begin_inset space \textvisiblespace{}
937 denotes a space character to be input.
940 \begin_layout Itemize
942 \begin_inset Formula $\to$
945 denotes the usage of the corresponding arrow key on the keyboard.
950 key can often be used instead of
951 \begin_inset Formula $\to$
955 \begin_inset Formula $\downarrow$
963 \begin_inset Formula $\leftarrow$
967 \begin_inset Formula $\uparrow$
973 \begin_layout Subsection*
977 \begin_layout Standard
979 \begin_inset Float table
985 \begin_layout Plain Layout
987 \begin_inset Caption Standard
989 \begin_layout Plain Layout
990 \begin_inset CommandInset label
992 name "tab:Available-units"
1004 \begin_layout Plain Layout
1006 \begin_inset Tabular
1007 <lyxtabular version="3" rows="13" columns="2">
1008 <features booktabs="true" tabularvalignment="middle">
1009 <column alignment="center" valignment="top">
1010 <column alignment="center" valignment="top" width="0pt">
1012 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1015 \begin_layout Plain Layout
1021 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1024 \begin_layout Plain Layout
1032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1035 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1044 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1055 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1064 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1075 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1084 \begin_layout Plain Layout
1086 \begin_inset space \thinspace{}
1090 \begin_inset space \thinspace{}
1100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1103 \begin_layout Plain Layout
1109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1112 \begin_layout Plain Layout
1114 \begin_inset space \thinspace{}
1118 \begin_inset space \thinspace{}
1128 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1131 \begin_layout Plain Layout
1137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1140 \begin_layout Plain Layout
1142 \begin_inset space \thinspace{}
1146 \begin_inset space \thinspace{}
1156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1159 \begin_layout Plain Layout
1165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1168 \begin_layout Plain Layout
1170 \begin_inset space \thinspace{}
1174 \begin_inset space \thinspace{}
1184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1187 \begin_layout Plain Layout
1193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1196 \begin_layout Plain Layout
1198 \begin_inset space \thinspace{}
1202 \begin_inset space \thinspace{}
1212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1215 \begin_layout Plain Layout
1221 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1224 \begin_layout Plain Layout
1226 \begin_inset space \thinspace{}
1230 \begin_inset Formula $\approx$
1234 \begin_inset space \thinspace{}
1244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1247 \begin_layout Plain Layout
1253 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1256 \begin_layout Plain Layout
1258 \begin_inset space \thinspace{}
1262 \begin_inset space \thinspace{}
1272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1275 \begin_layout Plain Layout
1281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1284 \begin_layout Plain Layout
1288 \begin_inset Quotes eld
1294 \begin_inset Quotes erd
1304 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1307 \begin_layout Plain Layout
1313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1316 \begin_layout Plain Layout
1318 \begin_inset Quotes eld
1326 \begin_inset Quotes erd
1336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1339 \begin_layout Plain Layout
1345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1348 \begin_layout Plain Layout
1350 \begin_inset space \thinspace{}
1354 \begin_inset Formula $\nicefrac{1}{18}$
1358 \begin_inset space \thinspace{}
1379 \begin_layout Standard
1380 \begin_inset Newpage newpage
1386 \begin_layout Section
1390 \begin_layout Subsection
1392 \begin_inset Index idx
1395 \begin_layout Plain Layout
1402 \begin_inset Index idx
1405 \begin_layout Plain Layout
1412 \begin_inset Index idx
1415 \begin_layout Plain Layout
1420 \begin_layout Plain Layout
1431 \begin_layout Plain Layout
1444 \begin_inset Index idx
1447 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1463 \begin_layout Plain Layout
1478 \begin_layout Standard
1479 Indices are created with an underscore
1480 \begin_inset Quotes eld
1484 \begin_inset Quotes erd
1487 or via the math toolbar button
1490 arg "math-subscript"
1493 , exponents with a caret
1494 \begin_inset Quotes eld
1498 \begin_inset Quotes erd
1501 or via the math toolbar button
1504 arg "math-superscript"
1510 \begin_layout Standard
1512 \begin_inset Tabular
1513 <lyxtabular version="3" rows="4" columns="2">
1514 <features booktabs="true" tabularvalignment="middle">
1515 <column alignment="center" valignment="top" width="0pt">
1516 <column alignment="center" valignment="top" width="0pt">
1518 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1521 \begin_layout Plain Layout
1527 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1530 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" usebox="none">
1541 \begin_layout Plain Layout
1547 <cell alignment="center" valignment="top" usebox="none">
1550 \begin_layout Plain Layout
1551 \begin_inset Formula $B_{V}$
1560 <row topspace="1.5mm">
1561 <cell alignment="center" valignment="top" usebox="none">
1564 \begin_layout Plain Layout
1570 <cell alignment="center" valignment="top" usebox="none">
1573 \begin_layout Plain Layout
1574 \begin_inset Formula $B^{V}$
1583 <row topspace="1.5mm">
1584 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1587 \begin_layout Plain Layout
1589 \begin_inset space \textvisiblespace{}
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $B^{A}$
1617 \begin_layout Standard
1618 As the caret is in some languages an accent, vowels will be accentuated
1619 in this case and not set as exponents
1623 \begin_layout Plain Layout
1624 Depending on the used keyboard settings this can also happen for characters
1631 To get exponents in this case, press
1635 after the caret as in the last example.
1638 \begin_layout Subsection
1640 \begin_inset CommandInset label
1642 name "subsec:Fractions"
1647 \begin_inset Index idx
1650 \begin_layout Plain Layout
1659 \begin_layout Standard
1660 Fractions are generated with the command
1667 \begin_inset Index idx
1670 \begin_layout Plain Layout
1678 or via the math toolbar button
1681 arg "math-insert \\frac"
1685 The font size is adjusted automatically, depending on whether the fraction
1686 is in an inline or display style formula.
1687 With the math toolbar button
1690 arg "math-insert \\frac-square"
1693 you can select different fraction types.
1696 \begin_layout Standard
1704 \begin_inset Index idx
1707 \begin_layout Plain Layout
1715 a fraction can be created that always has the size of a display style formula.
1723 \begin_inset Index idx
1726 \begin_layout Plain Layout
1734 the fraction appears always with the size of an inline formula.
1738 \begin_layout Standard
1739 A line with the fraction
1740 \begin_inset Formula $\frac{1}{2}$
1743 that was created with the command
1752 \begin_layout Standard
1753 A line with the fraction
1754 \begin_inset Formula $\dfrac{1}{2}$
1757 that was created with the command
1766 \begin_layout Standard
1768 \begin_inset Tabular
1769 <lyxtabular version="3" rows="4" columns="2">
1770 <features booktabs="true" tabularvalignment="middle">
1771 <column alignment="center" valignment="top" width="0pt">
1772 <column alignment="center" valignment="top" width="0pt">
1774 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1777 \begin_layout Plain Layout
1783 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1786 \begin_layout Plain Layout
1793 <row topspace="1.5mm">
1794 <cell alignment="center" valignment="top" usebox="none">
1797 \begin_layout Plain Layout
1801 \begin_inset space \textvisiblespace{}
1805 \begin_inset Formula $\downarrow$
1813 <cell alignment="center" valignment="top" usebox="none">
1816 \begin_layout Plain Layout
1817 \begin_inset Formula $\frac{A}{B}$
1826 <row topspace="2mm">
1827 <cell alignment="center" valignment="top" usebox="none">
1830 \begin_layout Plain Layout
1834 \begin_inset space \textvisiblespace{}
1838 \begin_inset Formula $\downarrow$
1846 <cell alignment="center" valignment="top" usebox="none">
1849 \begin_layout Plain Layout
1850 \begin_inset Formula $\dfrac{A}{B}$
1859 <row topspace="2mm" bottomspace="1mm">
1860 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1863 \begin_layout Plain Layout
1867 \begin_inset space \textvisiblespace{}
1873 \begin_inset space \textvisiblespace{}
1877 \begin_inset Formula $\downarrow$
1881 \begin_inset Formula $\downarrow\downarrow$
1889 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1892 \begin_layout Plain Layout
1893 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1909 \begin_layout Standard
1910 \begin_inset VSpace bigskip
1914 \begin_inset Newpage newpage
1917 For nested fractions the command
1924 \begin_inset Index idx
1927 \begin_layout Plain Layout
1937 \begin_inset VSpace -3mm
1943 \begin_layout Standard
1944 \begin_inset Formula
1946 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1947 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1955 \begin_layout Standard
1956 The command for the example above is:
1959 \begin_layout Standard
1965 \begin_inset space \textvisiblespace{}
1969 \begin_inset Formula $\downarrow$
1975 \begin_inset space \textvisiblespace{}
1981 \begin_inset space \textvisiblespace{}
1985 \begin_inset Formula $\downarrow$
1989 \begin_inset Formula $\downarrow$
1995 \begin_layout Standard
1996 \begin_inset VSpace medskip
2002 \begin_layout Standard
2009 sets the fraction always in the size of a displayed formula, also when
2010 it is part of another fraction.
2013 \begin_layout Standard
2014 It is possible to specify the alignment of the numerator.
2021 is used to left align it, the command
2034 centers the numerator.
2035 These fractions demonstrate the different alignments:
2038 \begin_layout Standard
2041 \begin_inset Formula
2043 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2051 \begin_layout Standard
2052 \begin_inset Note Greyedout
2055 \begin_layout Plain Layout
2072 are no real \SpecialChar LaTeX
2073 commands but represent the command
2077 cfrac[alignment]{numerator}{denominator}
2080 Therefore you cannot use them in \SpecialChar TeX
2089 \begin_layout Standard
2090 \begin_inset VSpace medskip
2093 It is often advantageous to combine
2106 \begin_inset Formula
2108 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2116 \begin_layout Standard
2117 For inline fractions with a sloped fraction stroke you can use the command
2125 \begin_inset Index idx
2128 \begin_layout Plain Layout
2137 \begin_inset Formula $\nicefrac{5}{31}$
2147 \begin_inset Index idx
2150 \begin_layout Plain Layout
2159 \begin_inset Formula $\unitfrac{5}{31}$
2162 There is furthermore the command
2168 that offers to write a fraction in combination with a number:
2169 \begin_inset Formula $\unitfrac[2]{1}{3}$
2175 \begin_layout Standard
2176 \begin_inset Note Greyedout
2179 \begin_layout Plain Layout
2190 is not a real \SpecialChar LaTeX
2191 command but the command
2192 \begin_inset Newline newline
2199 unitfrac[number]{numerator}{denominator}
2202 Therefore you cannot use it in \SpecialChar TeX
2211 \begin_layout Standard
2212 How to define own fractions where the fraction stroke can be changed, is
2214 \begin_inset CommandInset ref
2216 reference "subsec:Self-defined-Fractions"
2223 \begin_layout Standard
2224 Multiline fractions are explained in
2225 \begin_inset CommandInset ref
2227 reference "subsec:Multiline-Fractions"
2234 \begin_layout Subsection
2236 \begin_inset Index idx
2239 \begin_layout Plain Layout
2248 \begin_layout Standard
2249 Square roots are created with
2256 \begin_inset Index idx
2259 \begin_layout Plain Layout
2267 or the math toolbar button
2270 arg "math-insert \\sqrt"
2273 , all other roots with the command
2280 \begin_inset Index idx
2283 \begin_layout Plain Layout
2291 or with the math toolbar button
2294 arg "math-insert \\root"
2300 \begin_layout Standard
2302 \begin_inset Tabular
2303 <lyxtabular version="3" rows="3" columns="2">
2304 <features booktabs="true" tabularvalignment="middle">
2305 <column alignment="center" valignment="top" width="0pt">
2306 <column alignment="center" valignment="top" width="0pt">
2308 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2311 \begin_layout Plain Layout
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2327 <row topspace="1mm">
2328 <cell alignment="center" valignment="top" usebox="none">
2331 \begin_layout Plain Layout
2335 \begin_inset space \textvisiblespace{}
2343 <cell alignment="center" valignment="top" usebox="none">
2346 \begin_layout Plain Layout
2347 \begin_inset Formula $\sqrt{A-B}$
2356 <row topspace="1mm">
2357 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2360 \begin_layout Plain Layout
2364 \begin_inset space \textvisiblespace{}
2368 \begin_inset Formula $\downarrow$
2376 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2379 \begin_layout Plain Layout
2380 \begin_inset Formula $\sqrt[3]{A-B}$
2396 \begin_layout Standard
2397 A square root can also be created with
2403 when the root index field is left empty.
2406 \begin_layout Standard
2407 With certain indices the distance to the root is too small, like in this
2409 \begin_inset Formula $\sqrt[\beta]{B}$
2413 \begin_inset Newline newline
2417 \begin_inset Formula $\beta$
2421 To avoid this, the commands
2428 \begin_inset Index idx
2431 \begin_layout Plain Layout
2446 \begin_inset Index idx
2449 \begin_layout Plain Layout
2457 are used with the following scheme:
2460 \begin_layout Standard
2474 \begin_layout Standard
2475 Distance is the number of Big Points (unit bp;
2476 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2479 ), that the index should be moved to the left or top, resp..
2480 The commands are written to the index.
2481 This way the command
2482 \begin_inset Newline newline
2492 \begin_inset Formula $\to$
2498 \begin_inset Formula $\to$
2504 \begin_inset space \textvisiblespace{}
2508 \begin_inset Formula $\to$
2512 \begin_inset Newline newline
2517 produces a correct typeset formula:
2518 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2524 \begin_layout Subsection
2525 Binomial Coefficients
2526 \begin_inset Index idx
2529 \begin_layout Plain Layout
2530 Binomial coefficients
2538 \begin_layout Standard
2539 Binomial coefficients are inserted with the command
2546 \begin_inset Index idx
2549 \begin_layout Plain Layout
2557 or with the submenu of the math toolbar button
2560 arg "math-insert \\frac-square"
2576 there are the commands
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2601 \begin_inset Index idx
2604 \begin_layout Plain Layout
2613 For other brackets around binomial coeficients there are the commands
2620 \begin_inset Index idx
2623 \begin_layout Plain Layout
2638 \begin_inset Index idx
2641 \begin_layout Plain Layout
2652 \begin_layout Standard
2654 \begin_inset Tabular
2655 <lyxtabular version="3" rows="6" columns="2">
2656 <features booktabs="true" tabularvalignment="middle">
2657 <column alignment="center" valignment="top" width="0pt">
2658 <column alignment="center" valignment="top" width="0pt">
2660 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2663 \begin_layout Plain Layout
2669 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2672 \begin_layout Plain Layout
2679 <row topspace="1mm">
2680 <cell alignment="center" valignment="top" usebox="none">
2683 \begin_layout Plain Layout
2687 \begin_inset space \textvisiblespace{}
2691 \begin_inset Formula $\downarrow$
2699 <cell alignment="center" valignment="top" usebox="none">
2702 \begin_layout Plain Layout
2703 \begin_inset Formula $\binom{A}{B}$
2712 <row topspace="2mm">
2713 <cell alignment="center" valignment="top" usebox="none">
2716 \begin_layout Plain Layout
2720 \begin_inset space \textvisiblespace{}
2724 \begin_inset Formula $\downarrow$
2732 <cell alignment="center" valignment="top" usebox="none">
2735 \begin_layout Plain Layout
2736 \begin_inset Formula $\dbinom{A}{B}$
2745 <row topspace="2mm" bottomspace="0.5mm">
2746 <cell alignment="center" valignment="top" usebox="none">
2749 \begin_layout Plain Layout
2753 \begin_inset space \textvisiblespace{}
2757 \begin_inset Formula $\downarrow$
2765 <cell alignment="center" valignment="top" usebox="none">
2768 \begin_layout Plain Layout
2769 \begin_inset Formula $\tbinom{A}{B}$
2778 <row topspace="1mm">
2779 <cell alignment="center" valignment="top" topline="true" usebox="none">
2782 \begin_layout Plain Layout
2786 \begin_inset space \textvisiblespace{}
2790 \begin_inset Formula $\downarrow$
2798 <cell alignment="center" valignment="top" topline="true" usebox="none">
2801 \begin_layout Plain Layout
2802 \begin_inset Formula ${A \brack B}$
2811 <row topspace="2mm" bottomspace="0.5mm">
2812 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2815 \begin_layout Plain Layout
2819 \begin_inset space \textvisiblespace{}
2823 \begin_inset Formula $\downarrow$
2831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2834 \begin_layout Plain Layout
2835 \begin_inset Formula ${A \brace B}$
2851 \begin_layout Subsection
2852 Case Differentiations
2853 \begin_inset Index idx
2856 \begin_layout Plain Layout
2857 Case differentiations
2865 \begin_layout Standard
2867 \begin_inset Tabular
2868 <lyxtabular version="3" rows="3" columns="2">
2869 <features booktabs="true" tabularvalignment="middle">
2870 <column alignment="center" valignment="top" width="0pt">
2871 <column alignment="center" valignment="top" width="0pt">
2873 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2876 \begin_layout Plain Layout
2882 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2885 \begin_layout Plain Layout
2893 <cell alignment="center" valignment="top" usebox="none">
2896 \begin_layout Plain Layout
2900 \begin_inset space \textvisiblespace{}
2904 \begin_inset Formula $\to$
2908 \begin_inset Index idx
2911 \begin_layout Plain Layout
2924 <cell alignment="center" valignment="top" usebox="none">
2927 \begin_layout Plain Layout
2928 \begin_inset Formula $\begin{cases}
2938 <row topspace="1.5mm">
2939 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2942 \begin_layout Plain Layout
2946 \begin_inset space \textvisiblespace{}
2952 arg "newline-insert newline"
2960 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2963 \begin_layout Plain Layout
2964 \begin_inset Formula $\begin{cases}
2965 A & \textrm{for }x>0\\
2966 B & \textrm{for }x=0
2983 \begin_layout Standard
2990 or pressing the math toolbar button
2993 arg "math-insert \\cases"
2996 you can create new lines with the shortcut
2999 arg "newline-insert newline"
3002 or the table toolbar button
3005 arg "tabular-feature append-row"
3011 \begin_layout Standard
3018 is also available via the menu
3020 Insert\SpecialChar menuseparator
3021 Math\SpecialChar menuseparator
3027 \begin_layout Subsection
3029 \begin_inset Index idx
3032 \begin_layout Plain Layout
3041 \begin_layout Standard
3049 \begin_inset Index idx
3052 \begin_layout Plain Layout
3060 every character can be displayed canceled.
3061 The characters are quasi accentuated by a slash.
3064 \begin_layout Standard
3066 \begin_inset Tabular
3067 <lyxtabular version="3" rows="4" columns="2">
3068 <features booktabs="true" tabularvalignment="middle">
3069 <column alignment="center" valignment="top" width="0pt">
3070 <column alignment="center" valignment="top" width="0pt">
3072 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3075 \begin_layout Plain Layout
3081 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3084 \begin_layout Plain Layout
3092 <cell alignment="center" valignment="top" usebox="none">
3095 \begin_layout Plain Layout
3103 <cell alignment="center" valignment="top" usebox="none">
3106 \begin_layout Plain Layout
3107 \begin_inset Formula $\not=$
3117 <cell alignment="center" valignment="top" usebox="none">
3120 \begin_layout Plain Layout
3130 <cell alignment="center" valignment="top" usebox="none">
3133 \begin_layout Plain Layout
3134 \begin_inset Formula $\not\le$
3144 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3147 \begin_layout Plain Layout
3157 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3160 \begin_layout Plain Layout
3161 \begin_inset Formula $\not\parallel$
3177 \begin_layout Standard
3178 The last example shows that not all negations look good.
3179 Therefore there are special commands for some negations (see
3180 \begin_inset CommandInset ref
3182 reference "subsec:Mathematical-Symbols"
3187 \begin_inset CommandInset ref
3189 reference "sec:Relations"
3196 \begin_layout Subsection
3198 \begin_inset CommandInset label
3200 name "subsec:Placeholders"
3205 \begin_inset Index idx
3208 \begin_layout Plain Layout
3215 \begin_inset Index idx
3218 \begin_layout Plain Layout
3219 Chemical characters ! Isotopes
3225 \begin_inset Index idx
3228 \begin_layout Plain Layout
3233 \begin_layout Plain Layout
3244 \begin_layout Plain Layout
3259 \begin_layout Standard
3261 \begin_inset space \thinspace{}
3265 \begin_inset space \space{}
3272 \begin_layout Plain Layout
3273 Typesetting isotopes and chemical symbols is described in
3274 \begin_inset CommandInset ref
3276 reference "subsec:Chemical-Symbols-and"
3285 the following problem occurs:
3288 \begin_layout Standard
3290 \begin_inset Tabular
3291 <lyxtabular version="3" rows="2" columns="2">
3292 <features booktabs="true" tabularvalignment="middle">
3293 <column alignment="center" valignment="top" width="0pt">
3294 <column alignment="center" valignment="top" width="0pt">
3296 <cell alignment="center" valignment="top" usebox="none">
3299 \begin_layout Plain Layout
3300 Indices created with sub- and superscripts:
3305 <cell alignment="center" valignment="top" usebox="none">
3308 \begin_layout Plain Layout
3309 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3318 <row topspace="1.5mm">
3319 <cell alignment="center" valignment="top" usebox="none">
3322 \begin_layout Plain Layout
3328 <cell alignment="center" valignment="top" usebox="none">
3331 \begin_layout Plain Layout
3332 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3348 \begin_layout Standard
3349 The shorter index is by default placed below or above the first character
3350 of the longer index.
3351 To avoid this there is the command
3358 \begin_inset Index idx
3361 \begin_layout Plain Layout
3369 or the math toolbar button
3370 \begin_inset space \thinspace{}
3377 \begin_layout Plain Layout
3378 can be found in the submenu of the toolbar button
3381 arg "math-insert \\space"
3395 that creates one or more phantom characters.
3402 a small blue box appears that is superposed with two red arrows.
3403 The arrows indicate that the complete width and height of the box content
3404 will be created as placeholder.
3405 Phantom characters are accordingly placeholders with the size of the characters.
3408 \begin_layout Standard
3410 \begin_inset Tabular
3411 <lyxtabular version="3" rows="4" columns="2">
3412 <features booktabs="true" tabularvalignment="middle">
3413 <column alignment="center" valignment="top" width="0pt">
3414 <column alignment="center" valignment="top" width="0pt">
3416 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3419 \begin_layout Plain Layout
3425 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3428 \begin_layout Plain Layout
3435 <row topspace="1.5mm">
3436 <cell alignment="center" valignment="top" usebox="none">
3439 \begin_layout Plain Layout
3441 \begin_inset space \textvisiblespace{}
3447 \begin_inset space \textvisiblespace{}
3451 \begin_inset Formula $\to$
3455 \begin_inset space \textvisiblespace{}
3463 <cell alignment="center" valignment="top" usebox="none">
3466 \begin_layout Plain Layout
3467 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3476 <row topspace="1.5mm" bottomspace="0.5mm">
3477 <cell alignment="center" valignment="top" usebox="none">
3480 \begin_layout Plain Layout
3482 \begin_inset space \textvisiblespace{}
3488 \begin_inset space \textvisiblespace{}
3492 \begin_inset Formula $\to$
3496 \begin_inset space \textvisiblespace{}
3504 <cell alignment="center" valignment="top" usebox="none">
3507 \begin_layout Plain Layout
3508 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3517 <row topspace="1.5mm" bottomspace="0.5mm">
3518 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3521 \begin_layout Plain Layout
3525 \begin_inset space \textvisiblespace{}
3531 \begin_inset space \textvisiblespace{}
3535 \begin_inset Formula $\to$
3539 \begin_inset space \textvisiblespace{}
3547 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3550 \begin_layout Plain Layout
3551 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3567 \begin_layout Standard
3568 Furthermore there are the commands
3575 \begin_inset Index idx
3578 \begin_layout Plain Layout
3599 \begin_inset Index idx
3602 \begin_layout Plain Layout
3623 creates only space for the maximal height of the characters in the box
3624 but not for its width.
3631 creates only space for the width of the box content.
3632 Therefore the boxes of both commands have only one red arrow.
3635 \begin_layout Standard
3636 For example the command
3641 \begin_inset space \textvisiblespace{}
3648 creates space for the height of the integral sign,
3652 \begin_layout Plain Layout
3659 creates an integral sign, see
3660 \begin_inset CommandInset ref
3662 reference "subsec:Big-Operators"
3671 because this is the larger character.
3672 An example application is in
3673 \begin_inset CommandInset ref
3675 reference "subsec:Multiline-Brackets"
3682 \begin_layout Standard
3683 Placeholders can also be used for text when they are inserted via the menu
3686 Insert\SpecialChar menuseparator
3687 Formatting\SpecialChar menuseparator
3693 \begin_layout Standard
3695 \begin_inset Newline newline
3699 \begin_inset Phantom Phantom
3702 \begin_layout Plain Layout
3711 \begin_layout Subsection
3713 \begin_inset Index idx
3716 \begin_layout Plain Layout
3723 \begin_inset Index idx
3726 \begin_layout Plain Layout
3727 Formula ! underlined
3735 \begin_layout Standard
3737 \begin_inset Tabular
3738 <lyxtabular version="3" rows="4" columns="2">
3739 <features booktabs="true" tabularvalignment="middle">
3740 <column alignment="center" valignment="top" width="0pt">
3741 <column alignment="center" valignment="top" width="0pt">
3743 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3746 \begin_layout Plain Layout
3752 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3755 \begin_layout Plain Layout
3762 <row topspace="2mm">
3763 <cell alignment="center" valignment="top" usebox="none">
3766 \begin_layout Plain Layout
3770 \begin_inset space \textvisiblespace{}
3774 \begin_inset Index idx
3777 \begin_layout Plain Layout
3790 <cell alignment="center" valignment="top" usebox="none">
3793 \begin_layout Plain Layout
3794 \begin_inset Formula $\overline{A+B}$
3803 <row bottomspace="1mm">
3804 <cell alignment="center" valignment="top" usebox="none">
3807 \begin_layout Plain Layout
3811 \begin_inset space \textvisiblespace{}
3815 \begin_inset Index idx
3818 \begin_layout Plain Layout
3831 <cell alignment="center" valignment="top" usebox="none">
3834 \begin_layout Plain Layout
3835 \begin_inset Formula $\underline{A+B}$
3844 <row topspace="2mm" bottomspace="1mm">
3845 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3848 \begin_layout Plain Layout
3852 \begin_inset space \textvisiblespace{}
3858 \begin_inset space \textvisiblespace{}
3866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3869 \begin_layout Plain Layout
3870 \begin_inset Formula $\overline{\underline{A+B}}$
3886 \begin_layout Standard
3887 In the last example it doesn't matter if first
3902 \begin_layout Standard
3903 To double underline use
3912 \begin_layout Standard
3913 It is possible to place up to 6 lines above or below characters.
3916 \begin_layout Standard
3917 \begin_inset VSpace bigskip
3920 Custom lines can be created using the command
3927 \begin_inset Index idx
3930 \begin_layout Plain Layout
3938 which has the following scheme:
3941 \begin_layout Standard
3946 rule[vertical offset]{length}{thickness}
3949 \begin_layout Standard
3950 The optional vertical offset shifts the line upwards (or downwards, when
3951 the value is negative).
3953 \begin_inset CommandInset ref
3955 reference "tab:Available-units"
3959 can be used for the values.
3960 Here are two example lines created with the commands
3961 \begin_inset Newline newline
3968 rule[-2ex]{3cm}{2pt}
3979 \begin_layout Standard
3981 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3987 \begin_layout Standard
3994 can also be used for text when a line is inserted via the menu
3996 Insert\SpecialChar menuseparator
3997 Formatting\SpecialChar menuseparator
3999 \begin_inset space ~
4007 \begin_layout Standard
4009 \begin_inset CommandInset line
4020 \begin_layout Subsection
4022 \begin_inset CommandInset label
4024 name "subsec:Ellipses"
4029 \begin_inset Index idx
4032 \begin_layout Plain Layout
4041 \begin_layout Standard
4042 There are different types of ellipses available.
4046 \begin_layout Plain Layout
4047 In the math toolbar in the submenu of the button
4050 arg "math-insert \\ldots"
4058 For listings dots at the baseline are used (
4065 \begin_inset Index idx
4068 \begin_layout Plain Layout
4076 ), while for operations dots are needed that are on the same height as the
4084 \begin_inset Index idx
4087 \begin_layout Plain Layout
4096 When using the command
4103 \begin_inset Index idx
4106 \begin_layout Plain Layout
4114 , \SpecialChar LaTeX
4115 decides on the basis of the next character what type is used.
4118 \begin_layout Standard
4120 \begin_inset Tabular
4121 <lyxtabular version="3" rows="9" columns="2">
4122 <features booktabs="true" tabularvalignment="middle">
4123 <column alignment="center" valignment="top" width="0pt">
4124 <column alignment="center" valignment="top" width="0pt">
4126 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4129 \begin_layout Plain Layout
4135 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4138 \begin_layout Plain Layout
4146 <cell alignment="center" valignment="top" usebox="none">
4149 \begin_layout Plain Layout
4151 \begin_inset space \textvisiblespace{}
4157 \begin_inset space \textvisiblespace{}
4165 <cell alignment="center" valignment="top" usebox="none">
4168 \begin_layout Plain Layout
4169 \begin_inset Formula $A_{1},\dots,A_{n}$
4179 <cell alignment="center" valignment="top" usebox="none">
4182 \begin_layout Plain Layout
4184 \begin_inset space \textvisiblespace{}
4190 \begin_inset space \textvisiblespace{}
4198 <cell alignment="center" valignment="top" usebox="none">
4201 \begin_layout Plain Layout
4202 \begin_inset Formula $A_{1}+\dots+A_{n}$
4212 <cell alignment="center" valignment="top" usebox="none">
4215 \begin_layout Plain Layout
4217 \begin_inset space \textvisiblespace{}
4223 \begin_inset space \textvisiblespace{}
4231 <cell alignment="center" valignment="top" usebox="none">
4234 \begin_layout Plain Layout
4235 \begin_inset Formula $A_{1},\ldots,A_{n}$
4245 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4248 \begin_layout Plain Layout
4250 \begin_inset space \textvisiblespace{}
4256 \begin_inset space \textvisiblespace{}
4264 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4267 \begin_layout Plain Layout
4268 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4278 <cell alignment="center" valignment="top" usebox="none">
4281 \begin_layout Plain Layout
4289 <cell alignment="center" valignment="top" usebox="none">
4292 \begin_layout Plain Layout
4293 \begin_inset Formula $\vdots$
4303 <cell alignment="center" valignment="top" usebox="none">
4306 \begin_layout Plain Layout
4314 <cell alignment="center" valignment="top" usebox="none">
4317 \begin_layout Plain Layout
4318 \begin_inset Formula $\ddots$
4328 <cell alignment="center" valignment="top" usebox="none">
4331 \begin_layout Plain Layout
4339 <cell alignment="center" valignment="top" usebox="none">
4342 \begin_layout Plain Layout
4343 \begin_inset Formula $\iddots$
4353 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4356 \begin_layout Plain Layout
4358 \begin_inset space \thinspace{}
4361 matrix with the different dots
4366 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4369 \begin_layout Plain Layout
4370 \begin_inset Formula $\begin{array}{ccc}
4371 A_{11} & \cdots & A_{1m}\\
4372 \vdots & \ddots & \vdots\\
4373 A_{n1} & \cdots & A_{nm}
4390 \begin_layout Standard
4391 The ellipses available in menu
4393 Insert\SpecialChar menuseparator
4395 \begin_inset space ~
4409 \begin_layout Standard
4410 \begin_inset VSpace medskip
4419 , one of the options
4421 Use mathdots package (automatically)
4423 must be set in the document settings under
4426 \begin_inset space ~
4432 \begin_inset Newline newline
4437 Use mathdots package
4439 will improve the appearance of all dots in the documents if their font
4440 style or size is not the default.
4443 \begin_layout Standard
4444 \begin_inset VSpace medskip
4447 Specially for matrices there are ellipses that span over several columns.
4448 They are created with the command
4455 \begin_inset Index idx
4458 \begin_layout Plain Layout
4466 , that has the following scheme:
4469 \begin_layout Standard
4474 hdotsfor[distance]{number of columns}
4477 \begin_layout Standard
4478 The number of columns specifies how many columns should be spanned.
4479 Distance is a factor for the distance between the dots.
4482 \begin_layout Standard
4483 In the following matrix the command
4489 was inserted in the first box of the second line, to get an ellipsis with
4490 a dot distance twice as long as with the command
4497 \begin_inset Formula
4499 \left(\begin{array}{cccc}
4508 Note that the matrix fields that should be spanned must be empty, otherwise
4509 you get \SpecialChar LaTeX
4513 \begin_layout Standard
4514 \begin_inset VSpace bigskip
4517 Furthermore you can fill with the command
4524 \begin_inset Index idx
4527 \begin_layout Plain Layout
4535 the rest of a line with dots.
4536 The effect of these commands is the same as with
4543 \begin_inset CommandInset ref
4545 reference "subsec:Variable-Space"
4552 \begin_layout Standard
4553 For example the command
4558 \begin_inset space \textvisiblespace{}
4566 \begin_layout Standard
4567 \begin_inset Formula $A\dotfill B$
4573 \begin_layout Standard
4580 there is for a line the command
4587 \begin_inset Index idx
4590 \begin_layout Plain Layout
4601 \begin_layout Standard
4602 \begin_inset Formula $A\hrulefill B$
4608 \begin_layout Standard
4609 To use the commands for text, they have to be inserted in \SpecialChar TeX
4613 \begin_layout Section
4615 \begin_inset CommandInset label
4622 \begin_inset Index idx
4625 \begin_layout Plain Layout
4634 \begin_layout Standard
4635 Matrices can be inserted via the math toolbar button
4638 arg "dialog-show mathmatrix"
4643 Insert\SpecialChar menuseparator
4644 Math\SpecialChar menuseparator
4648 In the matrix dialog you can specify the number of columns and rows, the
4649 alignment and the decoration.
4650 The vertical alignment is only of importance for matrices in inline formulas:
4653 \begin_layout Standard
4654 The first matrix is top
4655 \begin_inset Formula $\begin{array}[t]{cccc}
4663 \begin_inset Formula $\begin{array}{cccc}
4670 and the third bottom
4671 \begin_inset Formula $\begin{array}[b]{cccc}
4681 \begin_layout Standard
4682 The horizontal alignment specifies how the column entries should be aligned.
4683 It is set by entering a letter for every column.
4688 denotes left aligned,
4697 To create for example a 4
4702 \begin_inset space ~
4705 matrix where the first column is left aligned, the second and third are
4706 centered and the last one is right aligned, one enters for the horizontal
4712 Normally in a matrix all columns are centered, therefore the default for
4720 \begin_layout Standard
4721 Horizontal alignment:
4724 \begin_layout Standard
4730 \begin_inset Formula $\begin{array}{lll}
4742 \begin_inset Formula $\begin{array}{ccc}
4754 \begin_inset Formula $\begin{array}{rrr}
4764 \begin_layout Standard
4765 To add or delete rows and columns subsequently, the math toolbar buttons
4769 arg "tabular-feature append-row"
4775 arg "tabular-feature delete-row"
4779 \begin_inset space \thinspace{}
4784 Edit\SpecialChar menuseparator
4788 New rows can also be created with
4791 arg "newline-insert newline"
4797 \begin_layout Standard
4798 \begin_inset VSpace bigskip
4805 adds parentheses in the selected style around the matrix.
4806 Alternatively, parentheses can can either be created with the commands
4814 \begin_inset Index idx
4817 \begin_layout Plain Layout
4832 \begin_inset Index idx
4835 \begin_layout Plain Layout
4846 \begin_inset space ~
4852 \begin_inset CommandInset ref
4854 reference "subsec:Automatic-Bracket-Size"
4858 , or by using the following commands:
4859 \begin_inset VSpace medskip
4865 \begin_layout Standard
4866 \begin_inset space \hfill{}
4870 \begin_inset Tabular
4871 <lyxtabular version="3" rows="4" columns="2">
4872 <features booktabs="true" tabularvalignment="middle">
4873 <column alignment="center" valignment="top" width="0pt">
4874 <column alignment="center" valignment="top">
4876 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4879 \begin_layout Plain Layout
4885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4888 \begin_layout Plain Layout
4895 <row topspace="1.5mm">
4896 <cell alignment="center" valignment="top" usebox="none">
4899 \begin_layout Plain Layout
4903 \begin_inset space \textvisiblespace{}
4911 \begin_inset space \thinspace{}
4919 <cell alignment="center" valignment="top" usebox="none">
4922 \begin_layout Plain Layout
4923 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4924 0 & \textrm{-}\mathrm{i}\\
4926 \end{array}\end{bmatrix}$
4935 <row topspace="1.5mm" bottomspace="0.5mm">
4936 <cell alignment="center" valignment="top" usebox="none">
4939 \begin_layout Plain Layout
4943 \begin_inset space \textvisiblespace{}
4951 \begin_inset space \thinspace{}
4959 <cell alignment="center" valignment="top" usebox="none">
4962 \begin_layout Plain Layout
4963 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4964 0 & \textrm{-}\mathrm{i}\\
4966 \end{array}\end{Bmatrix}$
4976 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4979 \begin_layout Plain Layout
4983 \begin_inset space \textvisiblespace{}
4991 \begin_inset space \thinspace{}
4999 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5002 \begin_layout Plain Layout
5003 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5004 0 & \textrm{-}\mathrm{i}\\
5006 \end{array}\end{pmatrix}$
5020 \begin_inset space \hfill{}
5024 \begin_inset Tabular
5025 <lyxtabular version="3" rows="4" columns="2">
5026 <features booktabs="true" tabularvalignment="middle">
5027 <column alignment="center" valignment="top" width="0pt">
5028 <column alignment="center" valignment="top">
5030 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5033 \begin_layout Plain Layout
5039 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5042 \begin_layout Plain Layout
5049 <row topspace="1.5mm">
5050 <cell alignment="center" valignment="top" usebox="none">
5053 \begin_layout Plain Layout
5057 \begin_inset space \textvisiblespace{}
5065 \begin_inset space \thinspace{}
5073 <cell alignment="center" valignment="top" usebox="none">
5076 \begin_layout Plain Layout
5077 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5078 0 & \textrm{-}\mathrm{i}\\
5080 \end{array}\end{vmatrix}$
5089 <row topspace="1.5mm" bottomspace="0.5mm">
5090 <cell alignment="center" valignment="top" usebox="none">
5093 \begin_layout Plain Layout
5097 \begin_inset space \textvisiblespace{}
5105 \begin_inset space \thinspace{}
5113 <cell alignment="center" valignment="top" usebox="none">
5116 \begin_layout Plain Layout
5117 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5118 0 & \textrm{-}\mathrm{i}\\
5120 \end{array}\end{Vmatrix}$
5130 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5133 \begin_layout Plain Layout
5137 \begin_inset space \textvisiblespace{}
5145 \begin_inset space \thinspace{}
5153 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5156 \begin_layout Plain Layout
5157 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5158 0 & \textrm{-}\mathrm{i}\\
5160 \end{array}\end{matrix}$
5174 \begin_inset space \hfill{}
5180 \begin_layout Standard
5181 \begin_inset VSpace medskip
5185 \begin_inset space \thinspace{}
5189 \begin_inset space \space{}
5198 is inserted, a blue box appears between two vertical lines where the matrix
5200 \begin_inset Newline newline
5203 Note that decorated matrices ignore the vertical alignment.
5206 \begin_layout Standard
5207 \begin_inset VSpace bigskip
5210 As all multiline formulas are matrices, the length
5217 \begin_inset Index idx
5220 \begin_layout Plain Layout
5228 that is described in
5229 \begin_inset CommandInset ref
5231 reference "subsec:Column-Separation"
5235 can also be used to change the column separation of matrices.
5238 \begin_layout Standard
5239 To change the row separation, the command
5246 \begin_inset Index idx
5249 \begin_layout Plain Layout
5258 It is used as follows:
5261 \begin_layout Standard
5268 arraystretch}{stretch factor}
5269 \begin_inset Index idx
5272 \begin_layout Plain Layout
5283 \begin_layout Standard
5290 assigns the stretch factor to the predefined command
5298 \begin_inset space \thinspace{}
5302 \begin_inset space \space{}
5305 the row separation, use the factor 2.
5306 This is then used for all following matrices.
5307 To go back to the original separation, assign the factor 1 to
5316 \begin_layout Standard
5317 To set matrices into a text line, the command
5324 \begin_inset Index idx
5327 \begin_layout Plain Layout
5336 When it is inserted a blue box with two dashed lines appears.
5337 In this box the matrix is inserted.
5340 \begin_layout Standard
5342 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5344 \end{smallmatrix}\right)$
5350 \begin_layout Section
5351 Brackets and Delimiters
5352 \begin_inset Index idx
5355 \begin_layout Plain Layout
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5374 \begin_layout Subsection
5375 Vertical Brackets and Delimiters
5376 \begin_inset Index idx
5379 \begin_layout Plain Layout
5388 \begin_layout Standard
5389 \begin_inset space \hfill{}
5393 \begin_inset Tabular
5394 <lyxtabular version="3" rows="9" columns="2">
5395 <features booktabs="true" tabularvalignment="middle">
5396 <column alignment="center" valignment="top" width="0pt">
5397 <column alignment="center" valignment="top" width="0pt">
5399 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5402 \begin_layout Plain Layout
5408 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5411 \begin_layout Plain Layout
5419 <cell alignment="center" valignment="top" usebox="none">
5422 \begin_layout Plain Layout
5428 <cell alignment="center" valignment="top" usebox="none">
5431 \begin_layout Plain Layout
5432 \begin_inset Formula $($
5442 <cell alignment="center" valignment="top" usebox="none">
5445 \begin_layout Plain Layout
5451 <cell alignment="center" valignment="top" usebox="none">
5454 \begin_layout Plain Layout
5455 \begin_inset Formula $\{$
5465 <cell alignment="center" valignment="top" usebox="none">
5468 \begin_layout Plain Layout
5474 <cell alignment="center" valignment="top" usebox="none">
5477 \begin_layout Plain Layout
5478 \begin_inset Formula $[$
5488 <cell alignment="center" valignment="top" usebox="none">
5491 \begin_layout Plain Layout
5499 <cell alignment="center" valignment="top" usebox="none">
5502 \begin_layout Plain Layout
5503 \begin_inset Formula $\langle$
5513 <cell alignment="center" valignment="top" usebox="none">
5516 \begin_layout Plain Layout
5524 <cell alignment="center" valignment="top" usebox="none">
5527 \begin_layout Plain Layout
5528 \begin_inset Formula $\lceil$
5538 <cell alignment="center" valignment="top" usebox="none">
5541 \begin_layout Plain Layout
5549 <cell alignment="center" valignment="top" usebox="none">
5552 \begin_layout Plain Layout
5553 \begin_inset Formula $\lfloor$
5563 <cell alignment="center" valignment="top" usebox="none">
5566 \begin_layout Plain Layout
5572 <cell alignment="center" valignment="top" usebox="none">
5575 \begin_layout Plain Layout
5576 \begin_inset Formula $/$
5586 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5589 \begin_layout Plain Layout
5595 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5598 \begin_layout Plain Layout
5599 \begin_inset Formula $|$
5613 \begin_inset space \hfill{}
5617 \begin_inset Tabular
5618 <lyxtabular version="3" rows="9" columns="2">
5619 <features booktabs="true" tabularvalignment="middle">
5620 <column alignment="center" valignment="top" width="0pt">
5621 <column alignment="center" valignment="top" width="0pt">
5623 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5626 \begin_layout Plain Layout
5632 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5635 \begin_layout Plain Layout
5643 <cell alignment="center" valignment="top" usebox="none">
5646 \begin_layout Plain Layout
5652 <cell alignment="center" valignment="top" usebox="none">
5655 \begin_layout Plain Layout
5656 \begin_inset Formula $)$
5666 <cell alignment="center" valignment="top" usebox="none">
5669 \begin_layout Plain Layout
5675 <cell alignment="center" valignment="top" usebox="none">
5678 \begin_layout Plain Layout
5679 \begin_inset Formula $\}$
5689 <cell alignment="center" valignment="top" usebox="none">
5692 \begin_layout Plain Layout
5698 <cell alignment="center" valignment="top" usebox="none">
5701 \begin_layout Plain Layout
5702 \begin_inset Formula $]$
5712 <cell alignment="center" valignment="top" usebox="none">
5715 \begin_layout Plain Layout
5723 <cell alignment="center" valignment="top" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $\rangle$
5737 <cell alignment="center" valignment="top" usebox="none">
5740 \begin_layout Plain Layout
5748 <cell alignment="center" valignment="top" usebox="none">
5751 \begin_layout Plain Layout
5752 \begin_inset Formula $\rceil$
5762 <cell alignment="center" valignment="top" usebox="none">
5765 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" usebox="none">
5776 \begin_layout Plain Layout
5777 \begin_inset Formula $\rfloor$
5787 <cell alignment="center" valignment="top" usebox="none">
5790 \begin_layout Plain Layout
5800 <cell alignment="center" valignment="top" usebox="none">
5803 \begin_layout Plain Layout
5804 \begin_inset Formula $\backslash$
5814 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5817 \begin_layout Plain Layout
5825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5828 \begin_layout Plain Layout
5829 \begin_inset Formula $\|$
5843 \begin_inset space \hfill{}
5849 \begin_layout Standard
5852 \begin_inset Note Greyedout
5855 \begin_layout Plain Layout
5868 \begin_inset Index idx
5871 \begin_layout Plain Layout
5879 must be used for the backslash, because the command
5887 produces a line break there.
5895 \begin_layout Standard
5896 For all characters listed above the size can be adjusted with the commands
5897 described in the following two subsections.
5898 When using these commands, the characters < and > can directly be used
5899 instead of the commands
5914 \begin_layout Subsubsection
5916 \begin_inset CommandInset label
5918 name "subsec:Manual-Bracket-Size"
5923 \begin_inset Index idx
5926 \begin_layout Plain Layout
5927 Bracket size ! manual
5935 \begin_layout Standard
5936 The bracket size can be specified manually by the \SpecialChar LaTeX
5944 \begin_inset Index idx
5947 \begin_layout Plain Layout
5980 denotes the smallest and
5986 the largest bracket size.
5989 \begin_layout Standard
5990 These commands are used to emphasize levels of brackets:
5993 \begin_layout Standard
5995 \begin_inset Tabular
5996 <lyxtabular version="3" rows="2" columns="2">
5997 <features booktabs="true" tabularvalignment="middle">
5998 <column alignment="center" valignment="top" width="0pt">
5999 <column alignment="center" valignment="top" width="0pt">
6001 <cell alignment="center" valignment="top" usebox="none">
6004 \begin_layout Plain Layout
6005 all brackets in the same size:
6010 <cell alignment="center" valignment="top" usebox="none">
6013 \begin_layout Plain Layout
6014 \begin_inset Formula $((A+B)(A-B))^{C}$
6023 <row topspace="2mm">
6024 <cell alignment="center" valignment="top" usebox="none">
6027 \begin_layout Plain Layout
6033 <cell alignment="center" valignment="top" usebox="none">
6036 \begin_layout Plain Layout
6037 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6053 \begin_layout Standard
6054 For the second formula the command
6061 \begin_inset space \textvisiblespace{}
6069 \begin_layout Standard
6070 Here is an overview about all bracket sizes:
6073 \begin_layout Standard
6090 \begin_inset space \textvisiblespace{}
6098 \begin_inset space \textvisiblespace{}
6102 \begin_inset space \textvisiblespace{}
6112 \begin_layout Standard
6114 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6120 \begin_layout Standard
6127 -commands there is the variant
6134 \begin_inset Index idx
6137 \begin_layout Plain Layout
6145 that adds a bit more space between the bracket and its content, and the
6159 \begin_inset Index idx
6162 \begin_layout Plain Layout
6172 , that don't add additional space.
6177 at the end of the command
6183 is for a left bracket; for a right bracket this will be replaced by an
6189 A left or right bracket can each be an opening or closing bracket.
6192 \begin_layout Standard
6193 In the following table is a comparison of the variants:
6196 \begin_layout Standard
6198 \begin_inset Tabular
6199 <lyxtabular version="3" rows="5" columns="2">
6200 <features booktabs="true" tabularvalignment="middle">
6201 <column alignment="center" valignment="top" width="0pt">
6202 <column alignment="center" valignment="middle">
6204 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6207 \begin_layout Plain Layout
6213 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6216 \begin_layout Plain Layout
6223 <row topspace="2mm">
6224 <cell alignment="center" valignment="top" usebox="none">
6227 \begin_layout Plain Layout
6237 \begin_inset space \textvisiblespace{}
6247 <cell alignment="center" valignment="top" usebox="none">
6250 \begin_layout Plain Layout
6251 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6260 <row topspace="2mm">
6261 <cell alignment="center" valignment="top" usebox="none">
6264 \begin_layout Plain Layout
6274 \begin_inset space \textvisiblespace{}
6284 <cell alignment="center" valignment="top" usebox="none">
6287 \begin_layout Plain Layout
6288 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6297 <row topspace="2mm" bottomspace="0.5mm">
6298 <cell alignment="center" valignment="top" usebox="none">
6301 \begin_layout Plain Layout
6311 \begin_inset space \textvisiblespace{}
6321 <cell alignment="center" valignment="top" usebox="none">
6324 \begin_layout Plain Layout
6325 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6334 <row topspace="1.5mm" bottomspace="0.5mm">
6335 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6338 \begin_layout Plain Layout
6350 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6353 \begin_layout Plain Layout
6354 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6370 \begin_layout Subsubsection
6371 Automatic Bracket Size
6372 \begin_inset CommandInset label
6374 name "subsec:Automatic-Bracket-Size"
6379 \begin_inset Index idx
6382 \begin_layout Plain Layout
6383 Bracket size ! automatic
6391 \begin_layout Standard
6392 Brackets with variable size can be inserted with the commands
6399 \begin_inset Index idx
6402 \begin_layout Plain Layout
6417 \begin_inset Index idx
6420 \begin_layout Plain Layout
6428 or via the math toolbar button
6431 arg "dialog-show mathdelimiter"
6447 the wanted bracket must be inserted.
6448 The bracket size will then automatically be calculated for the output.
6451 \begin_layout Standard
6453 normal bracket: The command
6460 \begin_inset space \textvisiblespace{}
6464 \begin_inset Formula $\downarrow$
6468 \begin_inset space \textvisiblespace{}
6474 \begin_inset Formula
6484 \begin_layout Standard
6486 multiline bracket: The command
6495 \begin_inset space \textvisiblespace{}
6499 \begin_inset Formula $\downarrow$
6503 \begin_inset space \textvisiblespace{}
6511 \begin_inset Formula
6513 \ln\left(\frac{A}{C}\right)
6521 \begin_layout Standard
6537 \begin_inset space ~
6543 This has the advantage that you can see in \SpecialChar LyX
6544 immediately the real bracket
6545 size and that the matching right bracket will be created too.
6546 \begin_inset Newline newline
6549 The command for the last example would then be:
6560 \begin_inset space \textvisiblespace{}
6564 \begin_inset Formula $\downarrow$
6570 \begin_layout Standard
6571 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6572 For example the command
6579 \begin_inset space \textvisiblespace{}
6583 \begin_inset Formula $\downarrow$
6587 \begin_inset space \textvisiblespace{}
6597 \begin_inset Formula
6599 \left.\frac{A}{B}\right\}
6618 will be converted by \SpecialChar LyX
6619 to brackets in the right size when the document is
6620 reloaded and an omitted bracket will appear as dashed line.
6623 \begin_layout Standard
6624 \begin_inset VSpace bigskip
6627 Because all popular \SpecialChar LaTeX
6628 distributions use e\SpecialChar TeX
6629 , an extension to \SpecialChar LaTeX
6638 \begin_inset Index idx
6641 \begin_layout Plain Layout
6649 is additionally available for all brackets and limits.
6650 With this command the height of the following character is adapted to the
6651 one of the surrounding brackets, what is e.
6652 \begin_inset space \thinspace{}
6656 \begin_inset space \space{}
6659 needed for physical vectors:
6660 \begin_inset Formula
6662 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6667 For physical vectors there is a special \SpecialChar LaTeX
6668 -package, described in
6669 \begin_inset CommandInset ref
6671 reference "subsec:Physical-Vectors"
6678 \begin_layout Subsection
6680 \begin_inset Index idx
6683 \begin_layout Plain Layout
6684 Brackets ! horizontal
6692 \begin_layout Standard
6694 \begin_inset Tabular
6695 <lyxtabular version="3" rows="4" columns="2">
6696 <features booktabs="true" tabularvalignment="middle">
6697 <column alignment="center" valignment="top" width="0pt">
6698 <column alignment="center" valignment="top" width="0pt">
6700 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6703 \begin_layout Plain Layout
6709 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6712 \begin_layout Plain Layout
6720 <cell alignment="center" valignment="top" usebox="none">
6723 \begin_layout Plain Layout
6727 \begin_inset space \textvisiblespace{}
6731 \begin_inset space \textvisiblespace{}
6735 \begin_inset Index idx
6738 \begin_layout Plain Layout
6751 <cell alignment="center" valignment="top" usebox="none">
6754 \begin_layout Plain Layout
6755 \begin_inset Formula $\overbrace{A+B}^{3}$
6764 <row topspace="2mm">
6765 <cell alignment="center" valignment="top" usebox="none">
6768 \begin_layout Plain Layout
6772 \begin_inset space \textvisiblespace{}
6776 \begin_inset space \textvisiblespace{}
6780 \begin_inset Index idx
6783 \begin_layout Plain Layout
6796 <cell alignment="center" valignment="top" usebox="none">
6799 \begin_layout Plain Layout
6800 \begin_inset Formula $\underbrace{A+B}_{5}$
6810 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6813 \begin_layout Plain Layout
6817 \begin_inset space \textvisiblespace{}
6823 \begin_inset space \textvisiblespace{}
6827 \begin_inset space \textvisiblespace{}
6831 \begin_inset space \textvisiblespace{}
6835 \begin_inset space \textvisiblespace{}
6839 \begin_inset space \textvisiblespace{}
6843 \begin_inset space \textvisiblespace{}
6851 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6854 \begin_layout Plain Layout
6855 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6871 \begin_layout Standard
6872 In the last example it doesn't matter if
6884 is inserted at first.
6887 \begin_layout Standard
6888 \begin_inset VSpace medskip
6894 \begin_layout Standard
6895 If you set in the document settings under
6898 \begin_inset space ~
6908 \begin_inset Index idx
6911 \begin_layout Plain Layout
6912 Packages ! mathtools
6920 \begin_inset space ~
6925 , you have access to square backets:
6928 \begin_layout Standard
6930 \begin_inset Tabular
6931 <lyxtabular version="3" rows="4" columns="2">
6932 <features booktabs="true" tabularvalignment="middle">
6933 <column alignment="center" valignment="top" width="0pt">
6934 <column alignment="center" valignment="top" width="0pt">
6936 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6939 \begin_layout Plain Layout
6945 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6948 \begin_layout Plain Layout
6956 <cell alignment="center" valignment="top" usebox="none">
6959 \begin_layout Plain Layout
6987 \begin_inset space \textvisiblespace{}
6991 \begin_inset Index idx
6994 \begin_layout Plain Layout
7007 <cell alignment="center" valignment="top" usebox="none">
7010 \begin_layout Plain Layout
7011 \begin_inset Formula $\overbracket{A+B}^{3}$
7020 <row topspace="2mm">
7021 <cell alignment="center" valignment="top" usebox="none">
7024 \begin_layout Plain Layout
7052 \begin_inset space \textvisiblespace{}
7056 \begin_inset Index idx
7059 \begin_layout Plain Layout
7084 <cell alignment="center" valignment="top" usebox="none">
7087 \begin_layout Plain Layout
7088 \begin_inset Formula $\underbracket{A+B}_{5}$
7098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7101 \begin_layout Plain Layout
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset space \textvisiblespace{}
7115 \begin_inset space \textvisiblespace{}
7119 \begin_inset space \textvisiblespace{}
7123 \begin_inset space \textvisiblespace{}
7131 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7134 \begin_layout Plain Layout
7135 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7151 \begin_layout Standard
7164 you can change the thickness of the bracket's stroke by specifying the
7165 desired thickness in square brackets behind the command:
7168 \begin_layout Standard
7170 \begin_inset Tabular
7171 <lyxtabular version="3" rows="3" columns="2">
7172 <features booktabs="true" tabularvalignment="middle">
7173 <column alignment="center" valignment="top" width="0pt">
7174 <column alignment="center" valignment="top" width="0pt">
7176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7179 \begin_layout Plain Layout
7185 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7188 \begin_layout Plain Layout
7196 <cell alignment="center" valignment="top" usebox="none">
7199 \begin_layout Plain Layout
7229 \begin_inset space \textvisiblespace{}
7237 <cell alignment="center" valignment="top" usebox="none">
7240 \begin_layout Plain Layout
7241 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7250 <row topspace="2mm">
7251 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7254 \begin_layout Plain Layout
7284 \begin_inset space \textvisiblespace{}
7292 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7295 \begin_layout Plain Layout
7296 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7312 \begin_layout Standard
7313 \begin_inset VSpace bigskip
7316 When brackets should overlap each other, multiline formulas, as described
7318 \begin_inset CommandInset ref
7320 reference "sec:Multiline-Formulas"
7325 \begin_inset Formula
7327 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7328 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7333 In the first row the formula is inserted together with the first brace.
7334 It is hereby important that the space command
7338 \begin_layout Plain Layout
7339 Space commands are explained in
7340 \begin_inset CommandInset ref
7342 reference "subsec:Predefined-Space"
7357 is inserted before the first
7358 \begin_inset Formula $d$
7361 , because the brace that ends behind the
7362 \begin_inset Formula $q$
7365 prevents that the following
7366 \begin_inset Quotes eld
7370 \begin_inset Quotes erd
7373 is surrounded by space.
7377 \begin_layout Plain Layout
7378 because a bracket is not handled as a character, see
7379 \begin_inset CommandInset ref
7381 reference "subsec:Binary-Operators"
7390 In the second row the second brace is inserted.
7391 As it should begin before the
7392 \begin_inset Formula $b$
7407 \begin_layout Plain Layout
7415 \begin_inset CommandInset ref
7417 reference "subsec:Placeholders"
7426 This space is needed because the
7427 \begin_inset Quotes eld
7431 \begin_inset Quotes erd
7434 is also surrounded by space in the formula.
7435 The brace is placed under the command
7444 \begin_layout Standard
7445 It gets more complicated when brackets overlap each other above and under
7446 the formula, like in the following example:
7450 \begin_layout Plain Layout
7462 \begin_inset Formula
7464 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7465 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7474 \begin_layout Plain Layout
7485 The first formula row is the same as the second row of the previous example,
7486 with the difference that the brace is above.
7487 The second row contains the formula together with the second brace.
7488 To avoid that there is space between the upper brace in the first row and
7489 the formula, the row spacing needs to be reduced.
7490 This is not easily possible due to a bug in \SpecialChar LyX
7495 \begin_layout Plain Layout
7496 \begin_inset CommandInset href
7498 name "LyX-bug #1505"
7499 target "https://www.lyx.org/trac/ticket/1505"
7509 As a solution for the problem, the global formula row separation
7516 \begin_inset Index idx
7519 \begin_layout Plain Layout
7527 must be changed to -6
7528 \begin_inset space \thinspace{}
7531 pt before the formula with the command
7547 is set back after the formula to the standard value of 3
7548 \begin_inset space \thinspace{}
7551 pt using the same command.
7552 More about the row separation in formulas is explained in
7553 \begin_inset CommandInset ref
7555 reference "subsec:Line-Separation"
7562 \begin_layout Section
7564 \begin_inset Index idx
7567 \begin_layout Plain Layout
7576 \begin_layout Standard
7577 Arrows can be inserted via the math toolbar button
7580 arg "math-insert \\leftarrow"
7583 or the commands listed in the following subsections.
7586 \begin_layout Subsection
7588 \begin_inset Index idx
7591 \begin_layout Plain Layout
7600 \begin_layout Standard
7601 \begin_inset space \hfill{}
7605 \begin_inset Tabular
7606 <lyxtabular version="3" rows="8" columns="2">
7607 <features booktabs="true" tabularvalignment="middle">
7608 <column alignment="center" valignment="top" width="0pt">
7609 <column alignment="center" valignment="top" width="0pt">
7611 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7614 \begin_layout Plain Layout
7620 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7623 \begin_layout Plain Layout
7631 <cell alignment="center" valignment="top" usebox="none">
7634 \begin_layout Plain Layout
7642 <cell alignment="center" valignment="top" usebox="none">
7645 \begin_layout Plain Layout
7646 \begin_inset Formula $\gets$
7656 <cell alignment="center" valignment="top" usebox="none">
7659 \begin_layout Plain Layout
7667 <cell alignment="center" valignment="top" usebox="none">
7670 \begin_layout Plain Layout
7671 \begin_inset Formula $\Leftarrow$
7681 <cell alignment="center" valignment="top" usebox="none">
7684 \begin_layout Plain Layout
7692 <cell alignment="center" valignment="top" usebox="none">
7695 \begin_layout Plain Layout
7696 \begin_inset Formula $\longleftarrow$
7706 <cell alignment="center" valignment="top" usebox="none">
7709 \begin_layout Plain Layout
7717 <cell alignment="center" valignment="top" usebox="none">
7720 \begin_layout Plain Layout
7721 \begin_inset Formula $\Longleftarrow$
7731 <cell alignment="center" valignment="top" usebox="none">
7734 \begin_layout Plain Layout
7742 <cell alignment="center" valignment="top" usebox="none">
7745 \begin_layout Plain Layout
7746 \begin_inset Formula $\leftharpoonup$
7756 <cell alignment="center" valignment="top" usebox="none">
7759 \begin_layout Plain Layout
7767 <cell alignment="center" valignment="top" usebox="none">
7770 \begin_layout Plain Layout
7771 \begin_inset Formula $\leftharpoondown$
7781 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7784 \begin_layout Plain Layout
7792 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7795 \begin_layout Plain Layout
7796 \begin_inset Formula $\hookleftarrow$
7810 \begin_inset space \hfill{}
7814 \begin_inset Tabular
7815 <lyxtabular version="3" rows="8" columns="2">
7816 <features booktabs="true" tabularvalignment="middle">
7817 <column alignment="center" valignment="top" width="0pt">
7818 <column alignment="center" valignment="top" width="0pt">
7820 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7823 \begin_layout Plain Layout
7829 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7832 \begin_layout Plain Layout
7840 <cell alignment="center" valignment="top" usebox="none">
7843 \begin_layout Plain Layout
7851 <cell alignment="center" valignment="top" usebox="none">
7854 \begin_layout Plain Layout
7855 \begin_inset Formula $\to$
7865 <cell alignment="center" valignment="top" usebox="none">
7868 \begin_layout Plain Layout
7876 <cell alignment="center" valignment="top" usebox="none">
7879 \begin_layout Plain Layout
7880 \begin_inset Formula $\Rightarrow$
7890 <cell alignment="center" valignment="top" usebox="none">
7893 \begin_layout Plain Layout
7901 <cell alignment="center" valignment="top" usebox="none">
7904 \begin_layout Plain Layout
7905 \begin_inset Formula $\longrightarrow$
7915 <cell alignment="center" valignment="top" usebox="none">
7918 \begin_layout Plain Layout
7926 <cell alignment="center" valignment="top" usebox="none">
7929 \begin_layout Plain Layout
7930 \begin_inset Formula $\Longrightarrow$
7940 <cell alignment="center" valignment="top" usebox="none">
7943 \begin_layout Plain Layout
7951 <cell alignment="center" valignment="top" usebox="none">
7954 \begin_layout Plain Layout
7955 \begin_inset Formula $\rightharpoonup$
7965 <cell alignment="center" valignment="top" usebox="none">
7968 \begin_layout Plain Layout
7976 <cell alignment="center" valignment="top" usebox="none">
7979 \begin_layout Plain Layout
7980 \begin_inset Formula $\rightharpoondown$
7990 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7993 \begin_layout Plain Layout
8001 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8004 \begin_layout Plain Layout
8005 \begin_inset Formula $\hookrightarrow$
8019 \begin_inset space \hfill{}
8025 \begin_layout Standard
8026 \begin_inset space \hfill{}
8030 \begin_inset Tabular
8031 <lyxtabular version="3" rows="6" columns="2">
8032 <features booktabs="true" tabularvalignment="middle">
8033 <column alignment="center" valignment="top" width="0pt">
8034 <column alignment="center" valignment="top" width="0pt">
8036 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8039 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8048 \begin_layout Plain Layout
8056 <cell alignment="center" valignment="top" usebox="none">
8059 \begin_layout Plain Layout
8067 <cell alignment="center" valignment="top" usebox="none">
8070 \begin_layout Plain Layout
8071 \begin_inset Formula $\leftrightarrow$
8081 <cell alignment="center" valignment="top" usebox="none">
8084 \begin_layout Plain Layout
8092 <cell alignment="center" valignment="top" usebox="none">
8095 \begin_layout Plain Layout
8096 \begin_inset Formula $\Leftrightarrow$
8106 <cell alignment="center" valignment="top" usebox="none">
8109 \begin_layout Plain Layout
8117 <cell alignment="center" valignment="top" usebox="none">
8120 \begin_layout Plain Layout
8121 \begin_inset Formula $\longleftrightarrow$
8131 <cell alignment="center" valignment="top" usebox="none">
8134 \begin_layout Plain Layout
8142 <cell alignment="center" valignment="top" usebox="none">
8145 \begin_layout Plain Layout
8146 \begin_inset Formula $\Longleftrightarrow$
8156 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8159 \begin_layout Plain Layout
8167 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8170 \begin_layout Plain Layout
8171 \begin_inset Formula $\rightleftharpoons$
8185 \begin_inset space \hspace{}
8190 \begin_inset space \hfill{}
8194 \begin_inset Tabular
8195 <lyxtabular version="3" rows="5" columns="2">
8196 <features booktabs="true" tabularvalignment="middle">
8197 <column alignment="center" valignment="top" width="0pt">
8198 <column alignment="center" valignment="top" width="0pt">
8200 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8203 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8212 \begin_layout Plain Layout
8220 <cell alignment="center" valignment="top" usebox="none">
8223 \begin_layout Plain Layout
8231 <cell alignment="center" valignment="top" usebox="none">
8234 \begin_layout Plain Layout
8235 \begin_inset Formula $\mapsto$
8245 <cell alignment="center" valignment="top" usebox="none">
8248 \begin_layout Plain Layout
8256 <cell alignment="center" valignment="top" usebox="none">
8259 \begin_layout Plain Layout
8260 \begin_inset Formula $\longmapsto$
8270 <cell alignment="center" valignment="top" usebox="none">
8273 \begin_layout Plain Layout
8281 <cell alignment="center" valignment="top" usebox="none">
8284 \begin_layout Plain Layout
8285 \begin_inset Formula $\leadsto$
8295 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8298 \begin_layout Plain Layout
8306 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8309 \begin_layout Plain Layout
8310 \begin_inset Formula $\dasharrow$
8324 \begin_inset space \hfill{}
8330 \begin_layout Standard
8331 \begin_inset VSpace medskip
8334 Arrows used as accents like e.
8335 \begin_inset space \thinspace{}
8339 \begin_inset space \space{}
8342 vector arrows are listed in
8343 \begin_inset CommandInset ref
8345 reference "sec:Accents"
8352 \begin_layout Standard
8353 \begin_inset VSpace bigskip
8356 Furthermore there are the labeled arrows
8357 \begin_inset Index idx
8360 \begin_layout Plain Layout
8373 \begin_inset Index idx
8376 \begin_layout Plain Layout
8391 \begin_inset Index idx
8394 \begin_layout Plain Layout
8401 \begin_layout Plain Layout
8416 When inserting one of these commands in a formula, an arrow with two blue
8417 boxes appear where the label can be inserted.
8418 The length of the arrow adapts to the label width.
8421 \begin_layout Standard
8423 \begin_inset Tabular
8424 <lyxtabular version="3" rows="3" columns="2">
8425 <features booktabs="true" tabularvalignment="middle">
8426 <column alignment="center" valignment="top" width="0pt">
8427 <column alignment="center" valignment="top" width="0pt">
8429 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8432 \begin_layout Plain Layout
8438 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8441 \begin_layout Plain Layout
8449 <cell alignment="center" valignment="top" usebox="none">
8452 \begin_layout Plain Layout
8456 \begin_inset space \textvisiblespace{}
8460 \begin_inset Formula $\downarrow$
8464 \begin_inset Formula $\to$
8472 <cell alignment="center" valignment="top" usebox="none">
8475 \begin_layout Plain Layout
8476 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8485 <row topspace="2mm">
8486 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8489 \begin_layout Plain Layout
8493 \begin_inset space \textvisiblespace{}
8497 \begin_inset Formula $\downarrow$
8501 \begin_inset Formula $\to$
8509 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8512 \begin_layout Plain Layout
8513 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8529 \begin_layout Standard
8530 \begin_inset VSpace medskip
8536 \begin_layout Standard
8537 If you set in the document settings under
8540 \begin_inset space ~
8550 \begin_inset Index idx
8553 \begin_layout Plain Layout
8554 Packages ! mathtools
8562 \begin_inset space ~
8567 , you have access to the following labeled arrows:
8570 \begin_layout Standard
8571 \begin_inset Newpage newpage
8577 \begin_layout Standard
8579 \begin_inset space \hspace*{\fill}
8583 \begin_inset Tabular
8584 <lyxtabular version="3" rows="7" columns="2">
8585 <features booktabs="true" tabularvalignment="middle">
8586 <column alignment="center" valignment="top" width="0pt">
8587 <column alignment="center" valignment="top" width="0pt">
8589 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8592 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" usebox="none">
8612 \begin_layout Plain Layout
8632 <cell alignment="center" valignment="top" usebox="none">
8635 \begin_layout Plain Layout
8636 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8645 <row topspace="2mm">
8646 <cell alignment="center" valignment="top" usebox="none">
8649 \begin_layout Plain Layout
8669 <cell alignment="center" valignment="top" usebox="none">
8672 \begin_layout Plain Layout
8673 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8682 <row topspace="2mm">
8683 <cell alignment="center" valignment="top" usebox="none">
8686 \begin_layout Plain Layout
8706 <cell alignment="center" valignment="top" usebox="none">
8709 \begin_layout Plain Layout
8710 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8719 <row topspace="2mm">
8720 <cell alignment="center" valignment="top" usebox="none">
8723 \begin_layout Plain Layout
8743 <cell alignment="center" valignment="top" usebox="none">
8746 \begin_layout Plain Layout
8747 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8756 <row topspace="2mm">
8757 <cell alignment="center" valignment="top" usebox="none">
8760 \begin_layout Plain Layout
8780 <cell alignment="center" valignment="top" usebox="none">
8783 \begin_layout Plain Layout
8784 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8793 <row topspace="2mm">
8794 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8797 \begin_layout Plain Layout
8817 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8820 \begin_layout Plain Layout
8821 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8835 \begin_inset space \hspace*{\fill}
8839 \begin_inset Tabular
8840 <lyxtabular version="3" rows="7" columns="2">
8841 <features booktabs="true" tabularvalignment="middle">
8842 <column alignment="center" valignment="top" width="0pt">
8843 <column alignment="center" valignment="top" width="0pt">
8845 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8848 \begin_layout Plain Layout
8854 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8857 \begin_layout Plain Layout
8865 <cell alignment="center" valignment="top" usebox="none">
8868 \begin_layout Plain Layout
8888 <cell alignment="center" valignment="top" usebox="none">
8891 \begin_layout Plain Layout
8892 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8901 <row topspace="2mm">
8902 <cell alignment="center" valignment="top" usebox="none">
8905 \begin_layout Plain Layout
8925 <cell alignment="center" valignment="top" usebox="none">
8928 \begin_layout Plain Layout
8929 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8938 <row topspace="2mm">
8939 <cell alignment="center" valignment="top" usebox="none">
8942 \begin_layout Plain Layout
8962 <cell alignment="center" valignment="top" usebox="none">
8965 \begin_layout Plain Layout
8966 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8975 <row topspace="2mm">
8976 <cell alignment="center" valignment="top" usebox="none">
8979 \begin_layout Plain Layout
8999 <cell alignment="center" valignment="top" usebox="none">
9002 \begin_layout Plain Layout
9003 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9012 <row topspace="2mm">
9013 <cell alignment="center" valignment="top" usebox="none">
9016 \begin_layout Plain Layout
9036 <cell alignment="center" valignment="top" usebox="none">
9039 \begin_layout Plain Layout
9040 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9049 <row topspace="2mm">
9050 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9053 \begin_layout Plain Layout
9073 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9076 \begin_layout Plain Layout
9077 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9091 \begin_inset space \hspace*{\fill}
9097 \begin_layout Standard
9098 The command scheme is for all these arrows:
9101 \begin_layout Standard
9103 \begin_inset Tabular
9104 <lyxtabular version="3" rows="2" columns="2">
9105 <features booktabs="true" tabularvalignment="middle">
9106 <column alignment="center" valignment="top" width="0pt">
9107 <column alignment="center" valignment="top" width="0pt">
9109 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9112 \begin_layout Plain Layout
9118 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9121 \begin_layout Plain Layout
9128 <row bottomspace="0.5mm">
9129 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9132 \begin_layout Plain Layout
9135 xleftrightarrow[x=a]
9138 \begin_inset Formula $\to$
9146 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9149 \begin_layout Plain Layout
9150 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9166 \begin_layout Subsection
9167 Vertical and diagonal Arrows
9168 \begin_inset Index idx
9171 \begin_layout Plain Layout
9178 \begin_inset Index idx
9181 \begin_layout Plain Layout
9190 \begin_layout Standard
9191 \begin_inset space \hfill{}
9195 \begin_inset Tabular
9196 <lyxtabular version="3" rows="7" columns="2">
9197 <features booktabs="true" tabularvalignment="middle">
9198 <column alignment="center" valignment="top" width="0pt">
9199 <column alignment="center" valignment="top" width="0pt">
9201 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9204 \begin_layout Plain Layout
9210 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9213 \begin_layout Plain Layout
9221 <cell alignment="center" valignment="top" usebox="none">
9224 \begin_layout Plain Layout
9232 <cell alignment="center" valignment="top" usebox="none">
9235 \begin_layout Plain Layout
9236 \begin_inset Formula $\uparrow$
9246 <cell alignment="center" valignment="top" usebox="none">
9249 \begin_layout Plain Layout
9257 <cell alignment="center" valignment="top" usebox="none">
9260 \begin_layout Plain Layout
9261 \begin_inset Formula $\Uparrow$
9271 <cell alignment="center" valignment="top" usebox="none">
9274 \begin_layout Plain Layout
9282 <cell alignment="center" valignment="top" usebox="none">
9285 \begin_layout Plain Layout
9286 \begin_inset Formula $\updownarrow$
9296 <cell alignment="center" valignment="top" usebox="none">
9299 \begin_layout Plain Layout
9307 <cell alignment="center" valignment="top" usebox="none">
9310 \begin_layout Plain Layout
9311 \begin_inset Formula $\Updownarrow$
9321 <cell alignment="center" valignment="top" usebox="none">
9324 \begin_layout Plain Layout
9332 <cell alignment="center" valignment="top" usebox="none">
9335 \begin_layout Plain Layout
9336 \begin_inset Formula $\Downarrow$
9346 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9349 \begin_layout Plain Layout
9357 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9360 \begin_layout Plain Layout
9361 \begin_inset Formula $\downarrow$
9375 \begin_inset space \hfill{}
9379 \begin_inset Tabular
9380 <lyxtabular version="3" rows="5" columns="2">
9381 <features booktabs="true" tabularvalignment="middle">
9382 <column alignment="center" valignment="top" width="0pt">
9383 <column alignment="center" valignment="top" width="0pt">
9385 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9388 \begin_layout Plain Layout
9394 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9397 \begin_layout Plain Layout
9405 <cell alignment="center" valignment="top" usebox="none">
9408 \begin_layout Plain Layout
9416 <cell alignment="center" valignment="top" usebox="none">
9419 \begin_layout Plain Layout
9420 \begin_inset Formula $\nearrow$
9430 <cell alignment="center" valignment="top" usebox="none">
9433 \begin_layout Plain Layout
9441 <cell alignment="center" valignment="top" usebox="none">
9444 \begin_layout Plain Layout
9445 \begin_inset Formula $\searrow$
9455 <cell alignment="center" valignment="top" usebox="none">
9458 \begin_layout Plain Layout
9466 <cell alignment="center" valignment="top" usebox="none">
9469 \begin_layout Plain Layout
9470 \begin_inset Formula $\swarrow$
9480 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9483 \begin_layout Plain Layout
9491 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9494 \begin_layout Plain Layout
9495 \begin_inset Formula $\nwarrow$
9509 \begin_inset space \hfill{}
9515 \begin_layout Standard
9516 \begin_inset VSpace medskip
9519 Vertical arrows can be used also as delimiters together with the commands
9521 \begin_inset CommandInset ref
9523 reference "subsec:Manual-Bracket-Size"
9528 \begin_inset CommandInset ref
9530 reference "subsec:Automatic-Bracket-Size"
9537 \begin_layout Section
9539 \begin_inset CommandInset label
9546 \begin_inset Index idx
9549 \begin_layout Plain Layout
9558 \begin_layout Standard
9559 Accents can be inserted via the math toolbar button
9562 arg "math-insert \\hat"
9565 or the commands listed in the following subsections.
9568 \begin_layout Subsection
9569 Accents for one Character
9573 \begin_layout Plain Layout
9586 \begin_layout Plain Layout
9588 \begin_inset CommandInset ref
9590 reference "subsec:Accents-in-Text"
9603 \begin_layout Plain Layout
9611 \begin_inset Note Note
9614 \begin_layout Plain Layout
9621 is used to avoid that the footnote appears in the PDF-bookmark.
9624 \begin_layout Plain Layout
9632 \begin_inset CommandInset ref
9634 reference "subsec:Formulas-in-Section"
9644 \begin_inset CommandInset label
9646 name "subsec:Accents-for-one"
9651 \begin_inset Index idx
9654 \begin_layout Plain Layout
9655 Accents ! for one character
9663 \begin_layout Standard
9664 \begin_inset space \hfill{}
9668 \begin_inset Tabular
9669 <lyxtabular version="3" rows="8" columns="2">
9670 <features booktabs="true" tabularvalignment="middle">
9671 <column alignment="center" valignment="top" width="0pt">
9672 <column alignment="center" valignment="top" width="0pt">
9674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9677 \begin_layout Plain Layout
9683 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9686 \begin_layout Plain Layout
9693 <row topspace="1.5mm">
9694 <cell alignment="center" valignment="top" usebox="none">
9697 \begin_layout Plain Layout
9701 \begin_inset space \textvisiblespace{}
9709 <cell alignment="center" valignment="top" usebox="none">
9712 \begin_layout Plain Layout
9713 \begin_inset Formula $\dot{A}$
9722 <row topspace="1.5mm">
9723 <cell alignment="center" valignment="top" usebox="none">
9726 \begin_layout Plain Layout
9730 \begin_inset space \textvisiblespace{}
9738 <cell alignment="center" valignment="top" usebox="none">
9741 \begin_layout Plain Layout
9742 \begin_inset Formula $\ddot{A}$
9751 <row topspace="1.5mm">
9752 <cell alignment="center" valignment="top" usebox="none">
9755 \begin_layout Plain Layout
9759 \begin_inset space \textvisiblespace{}
9767 <cell alignment="center" valignment="top" usebox="none">
9770 \begin_layout Plain Layout
9771 \begin_inset Formula $\dddot{A}$
9780 <row topspace="1.5mm">
9781 <cell alignment="center" valignment="top" usebox="none">
9784 \begin_layout Plain Layout
9788 \begin_inset space \textvisiblespace{}
9796 <cell alignment="center" valignment="top" usebox="none">
9799 \begin_layout Plain Layout
9800 \begin_inset Formula $\ddddot{A}$
9809 <row topspace="1.5mm">
9810 <cell alignment="center" valignment="top" usebox="none">
9813 \begin_layout Plain Layout
9817 \begin_inset space \textvisiblespace{}
9821 \begin_inset Index idx
9824 \begin_layout Plain Layout
9835 <cell alignment="center" valignment="top" usebox="none">
9838 \begin_layout Plain Layout
9839 \begin_inset Formula $\vec{A}$
9848 <row topspace="1.5mm">
9849 <cell alignment="center" valignment="top" usebox="none">
9852 \begin_layout Plain Layout
9856 \begin_inset space \textvisiblespace{}
9864 <cell alignment="center" valignment="top" usebox="none">
9867 \begin_layout Plain Layout
9868 \begin_inset Formula $\bar{A}$
9877 <row topspace="1.5mm">
9878 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9881 \begin_layout Plain Layout
9885 \begin_inset space \textvisiblespace{}
9893 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9896 \begin_layout Plain Layout
9897 \begin_inset Formula $\mathring{A}$
9911 \begin_inset space \hfill{}
9915 \begin_inset Tabular
9916 <lyxtabular version="3" rows="7" columns="2">
9917 <features booktabs="true" tabularvalignment="middle">
9918 <column alignment="center" valignment="top" width="0pt">
9919 <column alignment="center" valignment="top" width="0pt">
9921 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9924 \begin_layout Plain Layout
9930 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9933 \begin_layout Plain Layout
9940 <row topspace="1.5mm">
9941 <cell alignment="center" valignment="top" usebox="none">
9944 \begin_layout Plain Layout
9948 \begin_inset space \textvisiblespace{}
9956 <cell alignment="center" valignment="top" usebox="none">
9959 \begin_layout Plain Layout
9960 \begin_inset Formula $\tilde{A}$
9969 <row topspace="1.5mm">
9970 <cell alignment="center" valignment="top" usebox="none">
9973 \begin_layout Plain Layout
9977 \begin_inset space \textvisiblespace{}
9985 <cell alignment="center" valignment="top" usebox="none">
9988 \begin_layout Plain Layout
9989 \begin_inset Formula $\hat{A}$
9998 <row topspace="1.5mm">
9999 <cell alignment="center" valignment="top" usebox="none">
10002 \begin_layout Plain Layout
10006 \begin_inset space \textvisiblespace{}
10014 <cell alignment="center" valignment="top" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\check{A}$
10027 <row topspace="1.5mm">
10028 <cell alignment="center" valignment="top" usebox="none">
10031 \begin_layout Plain Layout
10035 \begin_inset space \textvisiblespace{}
10043 <cell alignment="center" valignment="top" usebox="none">
10046 \begin_layout Plain Layout
10047 \begin_inset Formula $\acute{A}$
10056 <row topspace="1.5mm">
10057 <cell alignment="center" valignment="top" usebox="none">
10060 \begin_layout Plain Layout
10064 \begin_inset space \textvisiblespace{}
10072 <cell alignment="center" valignment="top" usebox="none">
10075 \begin_layout Plain Layout
10076 \begin_inset Formula $\grave{A}$
10085 <row topspace="1.5mm">
10086 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10089 \begin_layout Plain Layout
10093 \begin_inset space \textvisiblespace{}
10101 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10104 \begin_layout Plain Layout
10105 \begin_inset Formula $\breve{A}$
10119 \begin_inset space \hfill{}
10125 \begin_layout Standard
10126 \begin_inset VSpace bigskip
10132 \begin_layout Standard
10133 You can directly insert accents like é to formulas.
10135 will transform them to the corresponding accent command.
10137 \begin_inset Index idx
10140 \begin_layout Plain Layout
10146 it is better to insert a quotation mark before the vowel.
10147 These two characters are then treated by \SpecialChar LaTeX
10152 character when the formula part with the umlaut is marked as German.
10160 \begin_inset Quotes eld
10164 \begin_inset Quotes erd
10167 umlauts are created as demonstrated in the following example:
10170 \begin_layout Standard
10171 \begin_inset VSpace -2mm
10177 \begin_layout Standard
10179 \begin_inset Tabular
10180 <lyxtabular version="3" rows="3" columns="2">
10181 <features booktabs="true" tabularvalignment="middle">
10182 <column alignment="center" valignment="top" width="0pt">
10183 <column alignment="center" valignment="top">
10185 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10188 \begin_layout Plain Layout
10194 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10197 \begin_layout Plain Layout
10205 <cell alignment="center" valignment="top" usebox="none">
10208 \begin_layout Plain Layout
10209 \begin_inset Quotes grd
10217 <cell alignment="center" valignment="top" usebox="none">
10220 \begin_layout Plain Layout
10221 \begin_inset space \hspace{}
10228 \begin_inset Formula $"i$
10237 <row topspace="1.5mm">
10238 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10241 \begin_layout Plain Layout
10245 \begin_inset space \textvisiblespace{}
10253 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10256 \begin_layout Plain Layout
10257 \begin_inset Formula $\ddot{i}$
10273 \begin_layout Standard
10274 Another advantage to
10280 is that umlauts can directly be converted to mathematical text because
10281 the accent commands above are
10287 in mathematical text
10290 To convert an accented character to mathematical text, only the character
10291 under the accent may be converted.
10292 This applies also for all other conversions, e.
10293 \begin_inset space \thinspace{}
10297 \begin_inset space \space{}
10303 \begin_layout Standard
10304 In mathematical text, umlauts and other accented characters can directly
10308 \begin_layout Standard
10309 \begin_inset VSpace bigskip
10315 \begin_layout Standard
10317 also supports a tilde under the character if the \SpecialChar LaTeX
10323 \begin_inset Index idx
10326 \begin_layout Plain Layout
10327 Packages ! undertilde
10332 is installed on your system:
10335 \begin_layout Standard
10339 \begin_layout Plain Layout
10349 \begin_inset Note Note
10352 \begin_layout Plain Layout
10353 The following table will only be displayed when the \SpecialChar LaTeX
10366 \begin_layout Standard
10369 \begin_inset Tabular
10370 <lyxtabular version="3" rows="2" columns="2">
10371 <features booktabs="true" tabularvalignment="middle">
10372 <column alignment="center" valignment="top" width="0pt">
10373 <column alignment="center" valignment="top" width="0pt">
10375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10378 \begin_layout Plain Layout
10384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10387 \begin_layout Plain Layout
10395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10398 \begin_layout Plain Layout
10402 \begin_inset space \textvisiblespace{}
10410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10413 \begin_layout Plain Layout
10414 \begin_inset Formula $\utilde{A}$
10430 \begin_layout Standard
10434 \begin_layout Plain Layout
10444 \begin_inset Note Note
10447 \begin_layout Plain Layout
10448 The following will be displayed when the \SpecialChar LaTeX
10461 \begin_layout Standard
10462 You need to install the \SpecialChar LaTeX
10467 to see the rest of this subsection in the output.
10470 \begin_layout Standard
10474 \begin_layout Plain Layout
10486 \begin_layout Standard
10487 \begin_inset Newpage newpage
10493 \begin_layout Subsection
10494 Accents for several Characters
10495 \begin_inset Index idx
10498 \begin_layout Plain Layout
10499 Accents ! for several characters
10507 \begin_layout Standard
10508 \begin_inset space \hfill{}
10512 \begin_inset Tabular
10513 <lyxtabular version="3" rows="5" columns="2">
10514 <features booktabs="true" tabularvalignment="middle">
10515 <column alignment="center" valignment="top" width="0pt">
10516 <column alignment="center" valignment="top" width="0pt">
10518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10521 \begin_layout Plain Layout
10527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10530 \begin_layout Plain Layout
10537 <row topspace="1.5mm">
10538 <cell alignment="center" valignment="top" usebox="none">
10541 \begin_layout Plain Layout
10545 \begin_inset space \textvisiblespace{}
10553 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10556 \begin_layout Plain Layout
10557 \begin_inset Formula $\overleftarrow{A=B}$
10566 <row topspace="1.5mm">
10567 <cell alignment="center" valignment="top" usebox="none">
10570 \begin_layout Plain Layout
10574 \begin_inset space \textvisiblespace{}
10582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10585 \begin_layout Plain Layout
10586 \begin_inset Formula $\underleftarrow{A=B}$
10595 <row topspace="1.5mm">
10596 <cell alignment="center" valignment="top" usebox="none">
10599 \begin_layout Plain Layout
10603 \begin_inset space \textvisiblespace{}
10611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10614 \begin_layout Plain Layout
10615 \begin_inset Formula $\overleftrightarrow{A=B}$
10624 <row topspace="1.5mm" bottomspace="1mm">
10625 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10628 \begin_layout Plain Layout
10631 underleftrightarrow
10632 \begin_inset space \textvisiblespace{}
10640 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10643 \begin_layout Plain Layout
10644 \begin_inset Formula $\underleftrightarrow{A=B}$
10658 \begin_inset space \hfill{}
10662 \begin_inset Tabular
10663 <lyxtabular version="3" rows="5" columns="2">
10664 <features booktabs="true" tabularvalignment="middle">
10665 <column alignment="center" valignment="top" width="0pt">
10666 <column alignment="center" valignment="top" width="0pt">
10668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10671 \begin_layout Plain Layout
10677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10680 \begin_layout Plain Layout
10687 <row topspace="1.5mm">
10688 <cell alignment="center" valignment="top" usebox="none">
10691 \begin_layout Plain Layout
10695 \begin_inset space \textvisiblespace{}
10703 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10706 \begin_layout Plain Layout
10707 \begin_inset Formula $\overrightarrow{A=B}$
10716 <row topspace="1.5mm">
10717 <cell alignment="center" valignment="top" usebox="none">
10720 \begin_layout Plain Layout
10724 \begin_inset space \textvisiblespace{}
10732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10735 \begin_layout Plain Layout
10736 \begin_inset Formula $\underrightarrow{A=B}$
10745 <row topspace="1.5mm">
10746 <cell alignment="center" valignment="top" usebox="none">
10749 \begin_layout Plain Layout
10753 \begin_inset space \textvisiblespace{}
10761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10764 \begin_layout Plain Layout
10765 \begin_inset Formula $\widetilde{A=B}$
10774 <row topspace="1.5mm" bottomspace="1mm">
10775 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10778 \begin_layout Plain Layout
10782 \begin_inset space \textvisiblespace{}
10790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10793 \begin_layout Plain Layout
10794 \begin_inset Formula $\widehat{A=B}$
10808 \begin_inset space \hfill{}
10814 \begin_layout Standard
10815 \begin_inset VSpace medskip
10818 With these commands as many characters as you like can be accented.
10831 will only be set in the output with a length of three characters, as shown
10832 in the following example:
10833 \begin_inset Formula
10835 \widetilde{A+B=C-D}
10843 \begin_layout Standard
10851 \begin_inset Index idx
10854 \begin_layout Plain Layout
10869 \begin_inset Index idx
10872 \begin_layout Plain Layout
10880 described in the previous subsection it is also possible to accent several
10887 \begin_inset space \textvisiblespace{}
10891 \begin_inset Formula $\downarrow$
10897 \begin_inset Formula
10899 \underset{***}{A=B}
10907 \begin_layout Section
10909 \begin_inset CommandInset label
10911 name "subsec:Space"
10916 \begin_inset Index idx
10919 \begin_layout Plain Layout
10928 \begin_layout Subsection
10930 \begin_inset CommandInset label
10932 name "subsec:Predefined-Space"
10937 \begin_inset Index idx
10940 \begin_layout Plain Layout
10941 Space ! horizontal ! predefined
10949 \begin_layout Standard
10950 Sometimes it is necessary to insert horizontal space into a formula.
10951 This is done by inserting a protected space (shortcut
10954 arg "command-alternatives space-insert protected ; math-space"
10959 \begin_inset Quotes eld
10965 \begin_inset space \textvisiblespace{}
10971 \begin_inset Quotes erd
10974 appears and by pressing
10978 several times one can select one of eight different space sizes.
10979 The spaces can also be inserted using the math toolbar button
10982 arg "math-insert \\space"
10985 or special commands.
10986 Independent from the inserted command, one can select the size again by
10994 \begin_layout Standard
10997 \begin_inset Tabular
10998 <lyxtabular version="3" rows="6" columns="3">
10999 <features booktabs="true" tabularvalignment="middle">
11000 <column alignment="center" valignment="top">
11001 <column alignment="center" valignment="top" width="15col%">
11002 <column alignment="center" valignment="top">
11004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11007 \begin_layout Plain Layout
11013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11016 \begin_layout Plain Layout
11026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11029 \begin_layout Plain Layout
11037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11040 \begin_layout Plain Layout
11048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11051 \begin_layout Plain Layout
11057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11060 \begin_layout Plain Layout
11061 \begin_inset Formula $A\,B$
11071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11074 \begin_layout Plain Layout
11082 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11085 \begin_layout Plain Layout
11091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11094 \begin_layout Plain Layout
11095 \begin_inset Formula $A\:B$
11105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11108 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11128 \begin_layout Plain Layout
11129 \begin_inset Formula $A\;B$
11139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11142 \begin_layout Plain Layout
11150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11153 \begin_layout Plain Layout
11159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11162 \begin_layout Plain Layout
11163 \begin_inset Formula $A\quad B$
11173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11176 \begin_layout Plain Layout
11184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11196 \begin_layout Plain Layout
11197 \begin_inset Formula $A\qquad B$
11211 \begin_inset space \hfill{}
11215 \begin_inset Tabular
11216 <lyxtabular version="3" rows="6" columns="3">
11217 <features booktabs="true" tabularvalignment="middle">
11218 <column alignment="center" valignment="top">
11219 <column alignment="center" valignment="top" width="15col%">
11220 <column alignment="center" valignment="top">
11222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11225 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11234 \begin_layout Plain Layout
11244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11247 \begin_layout Plain Layout
11255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11258 \begin_layout Plain Layout
11266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11269 \begin_layout Plain Layout
11275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11278 \begin_layout Plain Layout
11279 \begin_inset Formula $A\hfill B$
11289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11292 \begin_layout Plain Layout
11300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11303 \begin_layout Plain Layout
11309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11312 \begin_layout Plain Layout
11313 \begin_inset Formula $A\hspace*{1em}B$
11323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11326 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11337 \begin_layout Plain Layout
11343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11346 \begin_layout Plain Layout
11347 \begin_inset Formula $A\hspace{1em}B$
11357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11360 \begin_layout Plain Layout
11364 \begin_inset space \textvisiblespace{}
11372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11375 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11384 \begin_layout Plain Layout
11385 \begin_inset Formula $A\ B$
11395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11398 \begin_layout Plain Layout
11406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11409 \begin_layout Plain Layout
11415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11418 \begin_layout Plain Layout
11419 \begin_inset Formula $A\!B$
11435 \begin_layout Standard
11437 \begin_inset space ~
11441 \begin_inset space \thinspace{}
11445 \begin_inset space \thinspace{}
11448 7 are variable spaces which are explained in
11449 \begin_inset CommandInset ref
11451 reference "subsec:Variable-Space"
11457 \begin_inset space ~
11460 9 seems to produce no space.
11461 It is displayed red in \SpecialChar LyX
11462 contrary to the other sizes, because it is a negative
11464 There are two more negative spaces:
11467 \begin_layout Standard
11469 \begin_inset Tabular
11470 <lyxtabular version="3" rows="3" columns="3">
11471 <features booktabs="true" tabularvalignment="middle">
11472 <column alignment="center" valignment="middle" width="6.8cm">
11473 <column alignment="center" valignment="top" width="0pt">
11474 <column alignment="center" valignment="top" width="0pt">
11476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11479 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11488 \begin_layout Plain Layout
11496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11499 \begin_layout Plain Layout
11509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11512 \begin_layout Plain Layout
11517 keystrokes after inserting the protected space
11522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11525 \begin_layout Plain Layout
11531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11534 \begin_layout Plain Layout
11542 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11545 \begin_layout Plain Layout
11551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11554 \begin_layout Plain Layout
11555 \begin_inset Formula $A\negmedspace B$
11563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11566 \begin_layout Plain Layout
11567 \begin_inset Formula $A\negthickspace B$
11583 \begin_layout Standard
11584 Negative spaces can lead to characters overlapping each other.
11585 Thus they can be used to enforce ligatures, which are e.
11586 \begin_inset space \thinspace{}
11590 \begin_inset space \space{}
11593 useful for summation operators:
11596 \begin_layout Standard
11598 \begin_inset Tabular
11599 <lyxtabular version="3" rows="3" columns="2">
11600 <features booktabs="true" tabularvalignment="middle">
11601 <column alignment="center" valignment="top" width="0pt">
11602 <column alignment="center" valignment="top">
11604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11607 \begin_layout Plain Layout
11613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11616 \begin_layout Plain Layout
11624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11627 \begin_layout Plain Layout
11633 \begin_inset space \textvisiblespace{}
11641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11644 \begin_layout Plain Layout
11645 \begin_inset Formula $\sum\sum f_{kl}$
11655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11658 \begin_layout Plain Layout
11666 \begin_inset space \textvisiblespace{}
11674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11677 \begin_layout Plain Layout
11678 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11694 \begin_layout Standard
11696 \begin_inset VSpace medskip
11702 \begin_layout Standard
11704 Relations like for example equal signs, are always surrounded by space.
11705 To suppress this, the equal sign is placed into a \SpecialChar TeX
11707 The following example demonstrates this:
11710 \begin_layout Standard
11712 \begin_inset Tabular
11713 <lyxtabular version="3" rows="2" columns="2">
11714 <features tabularvalignment="middle">
11715 <column alignment="center" valignment="top" width="0pt">
11716 <column alignment="center" valignment="top" width="0pt">
11718 <cell alignment="center" valignment="top" usebox="none">
11721 \begin_layout Plain Layout
11727 <cell alignment="center" valignment="top" usebox="none">
11730 \begin_layout Plain Layout
11731 \begin_inset Formula $A=B$
11741 <cell alignment="center" valignment="top" usebox="none">
11744 \begin_layout Plain Layout
11745 equation without space
11750 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11753 \begin_layout Plain Layout
11754 \begin_inset Formula $A{=}B$
11770 \begin_layout Standard
11772 The command for the last formula is:
11777 \begin_inset Formula $\to$
11783 \begin_layout Standard
11784 \begin_inset VSpace bigskip
11790 \begin_layout Standard
11791 Spaces are needed for physical units, because the space between the value
11792 and the unit is the smallest one and not a normal space.
11793 For units in text, the smallest space is inserted via the menu
11795 Insert\SpecialChar menuseparator
11796 Formatting\SpecialChar menuseparator
11798 \begin_inset space ~
11806 arg "space-insert thin"
11812 \begin_layout Standard
11813 An example to visualize the difference:
11816 \begin_layout Standard
11817 \begin_inset Tabular
11818 <lyxtabular version="3" rows="2" columns="2">
11819 <features tabularvalignment="middle">
11820 <column alignment="left" valignment="top">
11821 <column alignment="left" valignment="top">
11823 <cell alignment="center" valignment="top" usebox="none">
11826 \begin_layout Plain Layout
11828 \begin_inset Formula $\cdot$
11836 <cell alignment="center" valignment="top" usebox="none">
11839 \begin_layout Plain Layout
11840 space between value and unit
11847 <cell alignment="center" valignment="top" usebox="none">
11850 \begin_layout Plain Layout
11852 \begin_inset space \thinspace{}
11856 \begin_inset Formula $\cdot$
11864 <cell alignment="center" valignment="top" usebox="none">
11867 \begin_layout Plain Layout
11868 smallest space between value and unit
11881 \begin_layout Subsection
11886 \begin_layout Plain Layout
11899 \begin_layout Plain Layout
11900 for vertical space in formulas see
11901 \begin_inset CommandInset ref
11903 reference "subsec:Line-Separation"
11916 \begin_layout Plain Layout
11924 \begin_inset Note Note
11927 \begin_layout Plain Layout
11930 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11933 \begin_layout Plain Layout
11936 texorpdfstring is in section
11937 \begin_inset CommandInset ref
11939 reference "subsec:Formulas-in-Section"
11949 \begin_inset CommandInset label
11951 name "subsec:Variable-Space"
11956 \begin_inset Index idx
11959 \begin_layout Plain Layout
11960 Space ! horizontal ! variable
11968 \begin_layout Standard
11969 Space with a defined length can be inserted with the command
11976 \begin_inset Index idx
11979 \begin_layout Plain Layout
11989 \begin_inset Quotes eld
11995 \begin_inset space \textvisiblespace{}
12001 \begin_inset Quotes erd
12005 The length can be specified by left-clicking on the
12006 \begin_inset Quotes eld
12012 \begin_inset space \textvisiblespace{}
12018 \begin_inset Quotes erd
12022 The length may also be negative.
12023 When a space would be the first character in a line it would be omitted.
12024 To force its output use the command
12036 or left-click on the
12037 \begin_inset Quotes eld
12043 \begin_inset space \textvisiblespace{}
12049 \begin_inset Quotes erd
12052 and check the option
12057 \begin_inset Newline newline
12060 To insert as much space as is available, the command
12067 \begin_inset Index idx
12070 \begin_layout Plain Layout
12081 \begin_layout Standard
12083 \begin_inset Tabular
12084 <lyxtabular version="3" rows="4" columns="2">
12085 <features booktabs="true" tabularvalignment="middle">
12086 <column alignment="center" valignment="top" width="0pt">
12087 <column alignment="center" valignment="top">
12089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12092 \begin_layout Plain Layout
12100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12103 \begin_layout Plain Layout
12111 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12114 \begin_layout Plain Layout
12118 \begin_inset space \textvisiblespace{}
12124 \begin_inset space \thinspace{}
12132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12135 \begin_layout Plain Layout
12136 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12149 \begin_layout Plain Layout
12153 \begin_inset space \textvisiblespace{}
12159 \begin_inset space \thinspace{}
12167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12170 \begin_layout Plain Layout
12171 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12184 \begin_layout Plain Layout
12188 \begin_inset space \textvisiblespace{}
12196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12199 \begin_layout Plain Layout
12200 \begin_inset Formula $A=A\hfill B=B$
12216 \begin_layout Standard
12217 In the last example the available space is given by the longest column entry
12219 In an inline formula the space depends on the length of the line in which
12227 Thus, when the line uses the full width, no space will be created.
12234 only has an effect on displayed formulas when the formula style
12239 (Formula styles are explained in
12240 \begin_inset CommandInset ref
12242 reference "sec:Formula-Styles"
12249 \begin_layout Standard
12256 , there are the commands
12268 that fill the space with a pattern, see
12269 \begin_inset CommandInset ref
12271 reference "subsec:Ellipses"
12278 \begin_layout Standard
12279 For text, variable space can be inserted via the menu
12281 Insert\SpecialChar menuseparator
12282 Formatting\SpecialChar menuseparator
12284 \begin_inset space ~
12292 \begin_layout Standard
12293 This is a line with
12294 \begin_inset space \hspace{}
12299 \begin_inset space \thinspace{}
12305 \begin_layout Standard
12306 This is a line with
12307 \begin_inset space \hfill{}
12313 \begin_layout Subsection
12314 Space besides inline Formulas
12315 \begin_inset Index idx
12318 \begin_layout Plain Layout
12319 Space ! besides inline formulas
12327 \begin_layout Standard
12328 The space that surrounds inline formulas can be adjusted with the length
12336 \begin_inset Index idx
12339 \begin_layout Plain Layout
12348 The value of a length is set with the command
12355 \begin_inset Index idx
12358 \begin_layout Plain Layout
12366 which has the following scheme:
12369 \begin_layout Standard
12374 setlength{length name}{value}
12377 \begin_layout Standard
12385 \begin_inset space \thinspace{}
12391 \begin_layout Standard
12401 \begin_layout Standard
12402 is inserted in \SpecialChar TeX
12405 \begin_inset space \thinspace{}
12408 mm space will now be set around all inline formulas:
12412 \begin_layout Plain Layout
12426 \begin_layout Standard
12427 This is a line with an inline formula
12428 \begin_inset Formula $A=B$
12432 \begin_inset space \thinspace{}
12435 mm surrounding space.
12439 \begin_layout Plain Layout
12453 \begin_layout Standard
12454 To return to the predefined value,
12460 is set to the value 0
12461 \begin_inset space \thinspace{}
12467 \begin_layout Standard
12468 \begin_inset Newpage newpage
12474 \begin_layout Section
12476 \begin_inset Index idx
12479 \begin_layout Plain Layout
12486 \begin_inset Index idx
12489 \begin_layout Plain Layout
12494 \begin_layout Plain Layout
12505 \begin_layout Plain Layout
12520 \begin_layout Standard
12521 Boxes for text are described in chapter
12528 \begin_inset space ~
12536 \begin_layout Subsection
12538 \begin_inset CommandInset label
12540 name "subsec:Boxes-with-Frame"
12545 \begin_inset Index idx
12548 \begin_layout Plain Layout
12557 \begin_layout Standard
12558 It is possible to frame a formula or part of one with the commands
12565 \begin_inset Index idx
12568 \begin_layout Plain Layout
12583 \begin_inset Index idx
12586 \begin_layout Plain Layout
12597 \begin_layout Standard
12598 When one of these commands is inserted in a formula, a blue box appears
12599 within a frame to enter formula parts.
12606 an additional formula has to be created by
12610 within this box, because the box content will otherwise be treated as mathemati
12618 is used, a new formula is automatically created inside the frame.
12621 \begin_layout Standard
12628 is not suitable to frame displayed formulas because the formula will always
12629 be set in the size of the text.
12636 is in contrary not suitable to frame inline formulas, because the formula
12637 will always be set in the size of a displayed formula.
12640 \begin_layout Standard
12654 \begin_inset Index idx
12657 \begin_layout Plain Layout
12665 where additionally the frame width and the alignment can be specified.
12672 is used in the following scheme:
12675 \begin_layout Standard
12680 framebox[frame width][position]{box content}
12683 \begin_layout Standard
12684 The position can either be
12701 right aligns the formula in the box.
12702 When no position is given, the formula will be centered.
12703 \begin_inset Newline newline
12706 If no width is given, also no position can be given.
12707 In this case the frame width is adjusted to the box content like for
12716 \begin_layout Standard
12723 is inserted, a box appears containing three blue boxes.
12724 The first two boxes are surrounded by brackets and denote the two optional
12726 The third box is for formula parts like for
12735 \begin_layout Standard
12737 \begin_inset Tabular
12738 <lyxtabular version="3" rows="5" columns="2">
12739 <features booktabs="true" tabularvalignment="middle">
12740 <column alignment="center" valignment="top" width="0pt">
12741 <column alignment="center" valignment="top">
12743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12746 \begin_layout Plain Layout
12752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12755 \begin_layout Plain Layout
12762 <row topspace="1.5mm">
12763 <cell alignment="center" valignment="top" usebox="none">
12766 \begin_layout Plain Layout
12770 \begin_inset space \textvisiblespace{}
12780 \begin_inset space \textvisiblespace{}
12788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12791 \begin_layout Plain Layout
12792 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12801 <row topspace="1.5mm">
12802 <cell alignment="center" valignment="top" usebox="none">
12805 \begin_layout Plain Layout
12809 \begin_inset space \textvisiblespace{}
12815 \begin_inset space \textvisiblespace{}
12823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12826 \begin_layout Plain Layout
12827 \begin_inset Formula $\boxed{\int A=B}$
12836 <row topspace="1.5mm">
12837 <cell alignment="center" valignment="top" usebox="none">
12840 \begin_layout Plain Layout
12844 \begin_inset space \textvisiblespace{}
12852 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12855 \begin_layout Plain Layout
12856 \begin_inset Formula $A+\fbox{B}$
12865 <row topspace="1.5mm" bottomspace="1mm">
12866 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12869 \begin_layout Plain Layout
12873 \begin_inset space \textvisiblespace{}
12877 \begin_inset Formula $\to$
12881 \begin_inset Formula $\to$
12891 \begin_inset space \textvisiblespace{}
12895 \begin_inset Formula $\downarrow$
12903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12906 \begin_layout Plain Layout
12907 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12923 \begin_layout Standard
12924 The frame thickness can also be adjusted.
12925 To do this the following commands have to be inserted in \SpecialChar TeX
12930 \begin_layout Standard
12940 \begin_inset Quotes eld
12944 \begin_inset Quotes erd
12958 \begin_inset Quotes eld
12962 \begin_inset Quotes erd
12968 \begin_layout Standard
12969 \begin_inset Quotes eld
12973 \begin_inset Quotes erd
12976 specifies the minimal distance between the frame and the first character
12978 An example for this is the following framed formula:
12982 \begin_layout Plain Layout
12994 \begin_inset Formula
13001 Before this formula the commands
13004 \begin_layout Standard
13026 \begin_layout Standard
13027 were inserted in \SpecialChar TeX
13029 The given values are used for all following boxes.
13032 \begin_layout Standard
13033 To return to the standard frame size, the command
13036 \begin_layout Standard
13061 \begin_layout Plain Layout
13075 \begin_layout Standard
13076 is inserted in \SpecialChar TeX
13077 mode before the next formula.
13080 \begin_layout Subsection
13081 Boxes without Frame
13082 \begin_inset CommandInset label
13084 name "subsec:Boxes-without-Frame"
13089 \begin_inset Index idx
13092 \begin_layout Plain Layout
13093 Boxes ! without frame
13101 \begin_layout Standard
13102 For boxes without a frame there are the following box commands:
13109 \begin_inset Index idx
13112 \begin_layout Plain Layout
13127 \begin_inset Index idx
13130 \begin_layout Plain Layout
13145 \begin_inset Index idx
13148 \begin_layout Plain Layout
13159 \begin_layout Standard
13166 a box can be super- or subscripted.
13167 But in contrary to normal super- and subscripting, the characters in the
13168 box keep their font size.
13175 is used in the following scheme:
13178 \begin_layout Standard
13183 raisebox{height}{box content}
13186 \begin_layout Standard
13187 When the box should contain a formula, an extra formula is needed like for
13198 \begin_inset Note Greyedout
13201 \begin_layout Plain Layout
13212 this extra formula is created by pressing
13216 twice instead of once because \SpecialChar LyX
13217 doesn't yet support
13231 \begin_layout Standard
13233 \begin_inset Tabular
13234 <lyxtabular version="3" rows="4" columns="2">
13235 <features booktabs="true" tabularvalignment="middle">
13236 <column alignment="center" valignment="top" width="0pt">
13237 <column alignment="center" valignment="top">
13239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13242 \begin_layout Plain Layout
13248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13251 \begin_layout Plain Layout
13259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13262 \begin_layout Plain Layout
13266 \begin_inset Formula $\to$
13272 \begin_inset Formula $\to$
13280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13283 \begin_layout Plain Layout
13284 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13297 \begin_layout Plain Layout
13301 \begin_inset Formula $\to$
13307 \begin_inset Formula $\to$
13315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13318 \begin_layout Plain Layout
13319 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13332 \begin_layout Plain Layout
13336 \begin_inset Formula $\to$
13352 \begin_inset space \textvisiblespace{}
13360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13363 \begin_layout Plain Layout
13364 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13380 \begin_layout Standard
13405 , with the difference that there is no frame.
13408 \begin_layout Subsection
13410 \begin_inset CommandInset label
13412 name "subsec:Colored-Boxes"
13417 \begin_inset Index idx
13420 \begin_layout Plain Layout
13429 \begin_layout Standard
13430 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13439 \begin_layout Plain Layout
13440 The \SpecialChar LaTeX
13445 is part of every \SpecialChar LaTeX
13446 standard installation.
13452 \begin_inset Index idx
13455 \begin_layout Plain Layout
13461 has to be loaded in the \SpecialChar LaTeX
13462 -preamble with the line
13466 \begin_layout Plain Layout
13467 When text is colored somewhere in the document with a predefined color,
13469 loads the \SpecialChar LaTeX
13475 Thus it is possible that the package is loaded twice, but this does not
13482 \begin_inset Note Note
13485 \begin_layout Plain Layout
13486 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13495 \begin_layout Standard
13503 \begin_layout Standard
13504 \begin_inset VSpace medskip
13507 To color boxes, the command
13514 \begin_inset Index idx
13517 \begin_layout Plain Layout
13525 is used in the following scheme:
13528 \begin_layout Standard
13533 colorbox{color}{box content}
13536 \begin_layout Standard
13537 The box content can also be a box and a
13543 can also be part of another box (see the 2nd and 3rd example).
13544 When the box should contain a formula, an extra formula has to be created,
13545 the same way as for
13555 \begin_layout Plain Layout
13556 This also applies for the command
13570 \begin_layout Standard
13571 One of the following predefined colors can be chosen:
13574 \begin_layout Standard
13608 \begin_layout Standard
13610 \begin_inset Tabular
13611 <lyxtabular version="3" rows="4" columns="2">
13612 <features booktabs="true" tabularvalignment="middle">
13613 <column alignment="center" valignment="top" width="0pt">
13614 <column alignment="center" valignment="top">
13616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13619 \begin_layout Plain Layout
13625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13628 \begin_layout Plain Layout
13636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13639 \begin_layout Plain Layout
13643 \begin_inset Formula $\to$
13653 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13656 \begin_layout Plain Layout
13657 \begin_inset Formula $\colorbox{yellow}{A=B}$
13666 <row topspace="1.5mm">
13667 <cell alignment="center" valignment="top" usebox="none">
13670 \begin_layout Plain Layout
13674 \begin_inset Formula $\to$
13682 \begin_inset space \textvisiblespace{}
13690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13693 \begin_layout Plain Layout
13694 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13703 <row topspace="1.5mm" bottomspace="1mm">
13704 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13707 \begin_layout Plain Layout
13711 \begin_inset space \textvisiblespace{}
13717 \begin_inset Formula $\to$
13733 \begin_inset space \textvisiblespace{}
13741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13744 \begin_layout Plain Layout
13745 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13761 \begin_layout Standard
13768 only colors the box but not the characters in the box.
13769 To color all characters, the whole formula is highlighted and the desired
13770 color is chosen in the
13773 \begin_inset space ~
13779 The dialog can be called with the toolbar button
13782 arg "dialog-show character"
13787 Edit\SpecialChar menuseparator
13789 \begin_inset space ~
13792 Style\SpecialChar menuseparator
13796 The formula number then has the same color as the formula.
13797 When the formula number should get another color than the formula characters,
13798 the color must be changed within the formula.
13801 \begin_layout Standard
13805 \begin_layout Standard
13808 \begin_inset Formula
13810 \int A=B\label{eq:red}
13818 \begin_inset Formula
13820 \textcolor{red}{\int A=B}\label{eq:redgreen}
13828 \begin_layout Standard
13830 \begin_inset CommandInset ref
13836 is completely colored red.
13837 \begin_inset Newline newline
13841 \begin_inset CommandInset ref
13843 reference "eq:redgreen"
13847 was first completely colored green to set the color for the formula number.
13848 Subsequently the formula characters were colored red.
13851 \begin_layout Standard
13852 \begin_inset VSpace bigskip
13855 To color the frame different than the rest of the box, the command
13862 \begin_inset Index idx
13865 \begin_layout Plain Layout
13873 is used in the following scheme:
13876 \begin_layout Standard
13881 fcolorbox{frame color}{color}{box content}
13884 \begin_layout Standard
13891 is an extension of the command
13898 The frame width is set, like for
13921 \begin_layout Plain Layout
13933 \begin_inset Formula
13935 \fcolorbox{cyan}{magenta}{A=B}
13944 \begin_layout Plain Layout
13958 \begin_layout Standard
13959 This formula was created with the command
13960 \begin_inset Newline newline
13968 \begin_inset Formula $\to$
13974 \begin_inset Formula $\to$
13984 \begin_layout Standard
13985 \begin_inset VSpace bigskip
13988 To use other colors than the predefined ones, they have to be defined first.
13991 \begin_layout Standard
13992 One can for example define the color
13993 \begin_inset Quotes eld
14001 \begin_inset Quotes erd
14004 with the \SpecialChar LaTeX
14008 \begin_layout Standard
14013 definecolor{darkgreen}{cmyk}{0.5,
14028 \begin_inset Index idx
14031 \begin_layout Plain Layout
14042 \begin_layout Standard
14047 is the color space that denotes the colors
14064 The four comma separated numbers are the portion factor for the corresponding
14065 colors of the color space.
14066 The factors can be in the range of 0
14067 \begin_inset space \thinspace{}
14071 \begin_inset space \thinspace{}
14079 also the color space
14083 can be used for definitions.
14100 , so that there are in this case three portion factors for the corresponding
14102 Furthermore there is the color space
14106 with one portion factor for the gray value.
14109 \begin_layout Standard
14110 As example a framed box with the new defined color
14114 where the characters have been colored
14119 \begin_inset Formula
14121 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14129 \begin_layout Standard
14130 Self-defined colors can also be used for text with the help of the command
14138 \begin_inset Index idx
14141 \begin_layout Plain Layout
14150 \begin_layout Standard
14154 \begin_layout Plain Layout
14158 textcolor{darkgreen}{
14164 \begin_inset Quotes eld
14168 \begin_inset Quotes erd
14175 \begin_layout Plain Layout
14185 \begin_layout Standard
14193 \begin_inset Index idx
14196 \begin_layout Plain Layout
14204 is used in the scheme
14208 textcolor{color}{characters to color}
14213 \begin_layout Subsection
14215 \begin_inset CommandInset label
14217 name "subsec:Paragraph-Boxes"
14222 \begin_inset Index idx
14225 \begin_layout Plain Layout
14226 Boxes ! as paragraph
14234 \begin_layout Standard
14235 A box that can contain several lines and paragraphs, a so-called paragraph
14236 box (parbox), can be created with the menu
14238 Insert\SpecialChar menuseparator
14241 or the toolbar button
14250 \begin_layout Standard
14251 The following example shows a framed parbox in a line:
14254 \begin_layout Standard
14255 \begin_inset VSpace medskip
14259 \begin_inset Box Boxed
14269 height_special "totalheight"
14274 backgroundcolor "none"
14277 \begin_layout Plain Layout
14278 This is a paragraph box.
14280 \begin_inset space \thinspace{}
14283 cm long and can also contain formulas:
14284 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14295 \begin_layout Standard
14296 \begin_inset VSpace medskip
14302 \begin_layout Standard
14303 Such a box is created by right-clicking on the gray box inset.
14304 A dialog pops up showing the box properties.
14318 \begin_inset space \thinspace{}
14323 Vertical Box Alignment
14328 \begin_layout Standard
14329 \begin_inset VSpace medskip
14332 In \SpecialChar LaTeX
14333 a parbox is created with the command
14340 \begin_inset Index idx
14343 \begin_layout Plain Layout
14351 which has the following scheme:
14354 \begin_layout Standard
14359 parbox[position]{width}{box content}
14362 \begin_layout Standard
14377 \begin_inset Quotes eld
14381 \begin_inset Quotes erd
14384 means that the box is aligned within the surrounding text with its last
14391 \begin_inset Quotes eld
14395 \begin_inset Quotes erd
14398 this is done with the first line.
14399 When no position is given, the box will be vertically centered, see section
14407 \begin_inset space ~
14412 manual for examples.
14415 \begin_layout Standard
14416 \begin_inset VSpace bigskip
14419 To frame formulas completely, including the formula number, the formula
14420 must be set into a parbox.
14421 To do this, the command
14435 is inserted in \SpecialChar TeX
14436 mode before the formula.
14444 \begin_inset Index idx
14447 \begin_layout Plain Layout
14455 is hereby the line width set for the document.
14456 Because the frame is outside the parbox, 2
14457 \begin_inset space \thinspace{}
14460 times the frame separation and the frame thickness must be subtracted from
14462 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14471 \begin_layout Plain Layout
14476 is part of every \SpecialChar LaTeX
14477 standard installation.
14483 \begin_inset Index idx
14486 \begin_layout Plain Layout
14492 must be loaded in the \SpecialChar LaTeX
14493 -preamble with the line
14496 \begin_layout Standard
14504 \begin_layout Standard
14505 Behind the formula both boxes are closed by entering
14509 in \SpecialChar TeX
14511 Here is an example:
14515 \begin_layout Plain Layout
14529 \begin_layout Standard
14533 \begin_layout Plain Layout
14551 \begin_inset Formula
14553 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14562 \begin_layout Plain Layout
14573 \begin_layout Plain Layout
14587 \begin_layout Standard
14588 \begin_inset VSpace medskip
14591 As a parbox is used as the argument of
14597 , there is in this case no difference between
14612 \begin_layout Standard
14613 \begin_inset VSpace bigskip
14616 Paragraph boxes are very useful to comment formulas directly.
14623 is used in combination with the command
14637 \begin_inset CommandInset ref
14639 reference "subsec:User-defined-Numbering"
14646 \begin_layout Standard
14647 An example of a formula commented with
14656 \begin_layout Standard
14660 \begin_layout Plain Layout
14673 This is a description.
14674 It is distinctly separated from the formula and multiline.
14678 \begin_layout Plain Layout
14690 \begin_layout Standard
14691 Such a formula must be inserted completely in \SpecialChar TeX
14692 mode because \SpecialChar LyX
14694 support the command
14701 The formula is created with the following command sequence:
14704 \begin_layout Standard
14717 is inserted in \SpecialChar TeX
14722 \begin_layout Plain Layout
14723 When the formula style
14735 can also be replaced by
14742 (formula styles see
14743 \begin_inset CommandInset ref
14745 reference "sec:Formula-Styles"
14754 Then the description follows as normal text and finally
14760 is inserted in \SpecialChar TeX
14774 hereby create a displayed formula.
14777 \begin_layout Standard
14784 can be seen in this example that was
14785 \begin_inset Quotes eld
14789 \begin_inset Quotes erd
14792 using the mathematical textmode:
14793 \begin_inset Formula
14795 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14803 \begin_layout Section
14805 \begin_inset Index idx
14808 \begin_layout Plain Layout
14817 \begin_layout Subsection
14819 \begin_inset CommandInset label
14821 name "subsec:Big-Operators"
14826 \begin_inset Index idx
14829 \begin_layout Plain Layout
14836 \begin_inset Index idx
14839 \begin_layout Plain Layout
14846 \begin_inset Index idx
14849 \begin_layout Plain Layout
14858 \begin_layout Standard
14859 To be able to use all integral operators listed here, the option
14861 Use esint package automatically
14863 must be set in the document settings under
14866 \begin_inset space ~
14874 \begin_layout Standard
14875 \begin_inset space \hfill{}
14879 \begin_inset Tabular
14880 <lyxtabular version="3" rows="11" columns="2">
14881 <features booktabs="true" tabularvalignment="middle">
14882 <column alignment="center" valignment="top" width="0pt">
14883 <column alignment="center" valignment="top" width="0pt">
14885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14888 \begin_layout Plain Layout
14894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14908 \begin_layout Plain Layout
14912 \begin_inset Index idx
14915 \begin_layout Plain Layout
14928 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14931 \begin_layout Plain Layout
14932 \begin_inset Formula $\int$
14942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14945 \begin_layout Plain Layout
14953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14956 \begin_layout Plain Layout
14957 \begin_inset Formula $\oint$
14967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14970 \begin_layout Plain Layout
14978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14981 \begin_layout Plain Layout
14982 \begin_inset Formula $\ointctrclockwise$
14992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
15003 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15006 \begin_layout Plain Layout
15007 \begin_inset Formula $\ointclockwise$
15017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15031 \begin_layout Plain Layout
15032 \begin_inset Formula $\sqint$
15042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15045 \begin_layout Plain Layout
15053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15056 \begin_layout Plain Layout
15058 \begin_inset Formula $\fint$
15068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15071 \begin_layout Plain Layout
15079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15082 \begin_layout Plain Layout
15084 \begin_inset Formula $\landupint$
15094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15097 \begin_layout Plain Layout
15105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15108 \begin_layout Plain Layout
15110 \begin_inset Formula $\landdownint$
15120 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15123 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\bigcap$
15145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\bigcup$
15174 \begin_inset space \hfill{}
15178 \begin_inset Tabular
15179 <lyxtabular version="3" rows="11" columns="2">
15180 <features booktabs="true" tabularvalignment="middle">
15181 <column alignment="center" valignment="top" width="0pt">
15182 <column alignment="center" valignment="top" width="0pt">
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15196 \begin_layout Plain Layout
15204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15207 \begin_layout Plain Layout
15211 \begin_inset Index idx
15214 \begin_layout Plain Layout
15227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15230 \begin_layout Plain Layout
15231 \begin_inset Formula $\sum$
15241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15244 \begin_layout Plain Layout
15248 \begin_inset Index idx
15251 \begin_layout Plain Layout
15258 \begin_layout Plain Layout
15277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15280 \begin_layout Plain Layout
15281 \begin_inset Formula $\prod$
15291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15294 \begin_layout Plain Layout
15302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15305 \begin_layout Plain Layout
15306 \begin_inset Formula $\coprod$
15316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15330 \begin_layout Plain Layout
15331 \begin_inset Formula $\bigodot$
15341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15344 \begin_layout Plain Layout
15352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15355 \begin_layout Plain Layout
15356 \begin_inset Formula $\bigotimes$
15366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15369 \begin_layout Plain Layout
15377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15380 \begin_layout Plain Layout
15381 \begin_inset Formula $\bigoplus$
15391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15394 \begin_layout Plain Layout
15402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15405 \begin_layout Plain Layout
15406 \begin_inset Formula $\bigwedge$
15416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15419 \begin_layout Plain Layout
15427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15430 \begin_layout Plain Layout
15431 \begin_inset Formula $\bigvee$
15441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15444 \begin_layout Plain Layout
15452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15455 \begin_layout Plain Layout
15456 \begin_inset Formula $\bigsqcup$
15466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15469 \begin_layout Plain Layout
15477 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15480 \begin_layout Plain Layout
15481 \begin_inset Formula $\biguplus$
15495 \begin_inset space \hfill{}
15501 \begin_layout Standard
15502 All big operators can also be inserted via the math toolbar button
15505 arg "math-insert \\intop"
15511 \begin_layout Standard
15512 The operators are called big because they are bigger than the sometimes
15513 equal looking binary operators.
15514 All big operators can have limits as described in the next subsection.
15517 \begin_layout Standard
15518 For all integral operators there is a second version available, ending in
15536 These operators are different from
15543 \begin_inset space \space{}
15546 in the style the operator limits are displayed, see
15547 \begin_inset CommandInset ref
15549 reference "subsec:Operator-Limits"
15557 \begin_layout Subsubsection*
15558 Advice for Integrals
15561 \begin_layout Standard
15566 in an integral is an operator, that therefore has to be set upright.
15567 This is done by highlighting the
15571 and using the keyboard shortcut
15581 \begin_layout Plain Layout
15587 \begin_inset CommandInset ref
15589 reference "subsec:Font-Styles"
15599 Finally the smallest space is inserted before the
15603 , as this is usual for operators.
15607 \begin_layout Standard
15609 \begin_inset Formula $\int A(x)dx$
15613 \begin_inset Newline newline
15617 \begin_inset Phantom HPhantom
15620 \begin_layout Plain Layout
15627 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15633 \begin_layout Standard
15634 For multiple integrals there are the following commands:
15635 \begin_inset VSpace medskip
15641 \begin_layout Standard
15642 \begin_inset space \hfill{}
15646 \begin_inset Tabular
15647 <lyxtabular version="3" rows="4" columns="2">
15648 <features booktabs="true" tabularvalignment="middle">
15649 <column alignment="center" valignment="top" width="0pt">
15650 <column alignment="center" valignment="top" width="0pt">
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15655 \begin_layout Plain Layout
15661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15664 \begin_layout Plain Layout
15671 <row bottomspace="1mm">
15672 <cell alignment="center" valignment="top" usebox="none">
15675 \begin_layout Plain Layout
15683 <cell alignment="center" valignment="top" usebox="none">
15686 \begin_layout Plain Layout
15687 \begin_inset Formula $\iint$
15696 <row bottomspace="1mm">
15697 <cell alignment="center" valignment="top" usebox="none">
15700 \begin_layout Plain Layout
15708 <cell alignment="center" valignment="top" usebox="none">
15711 \begin_layout Plain Layout
15712 \begin_inset Formula $\oiint$
15721 <row bottomspace="1mm">
15722 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15725 \begin_layout Plain Layout
15733 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15736 \begin_layout Plain Layout
15737 \begin_inset Formula $\sqiint$
15751 \begin_inset space \hfill{}
15755 \begin_inset Tabular
15756 <lyxtabular version="3" rows="4" columns="2">
15757 <features booktabs="true" tabularvalignment="middle">
15758 <column alignment="center" valignment="top" width="0pt">
15759 <column alignment="center" valignment="top" width="0pt">
15761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15764 \begin_layout Plain Layout
15770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15773 \begin_layout Plain Layout
15780 <row bottomspace="1mm">
15781 <cell alignment="center" valignment="top" usebox="none">
15784 \begin_layout Plain Layout
15792 <cell alignment="center" valignment="top" usebox="none">
15795 \begin_layout Plain Layout
15796 \begin_inset Formula $\iiint$
15805 <row bottomspace="1mm">
15806 <cell alignment="center" valignment="top" usebox="none">
15809 \begin_layout Plain Layout
15817 <cell alignment="center" valignment="top" usebox="none">
15820 \begin_layout Plain Layout
15821 \begin_inset Formula $\iiiint$
15830 <row bottomspace="1mm">
15831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15834 \begin_layout Plain Layout
15842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15845 \begin_layout Plain Layout
15846 \begin_inset Formula $\dotsint$
15860 \begin_inset space \hfill{}
15866 \begin_layout Subsection
15868 \begin_inset CommandInset label
15870 name "subsec:Operator-Limits"
15875 \begin_inset Index idx
15878 \begin_layout Plain Layout
15887 \begin_layout Standard
15888 Limits are created by super- and subscripts:
15891 \begin_layout Standard
15893 \begin_inset Tabular
15894 <lyxtabular version="3" rows="2" columns="2">
15895 <features booktabs="true" tabularvalignment="middle">
15896 <column alignment="center" valignment="top" width="0pt">
15897 <column alignment="center" valignment="top" width="0pt">
15899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15902 \begin_layout Plain Layout
15908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15911 \begin_layout Plain Layout
15919 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15922 \begin_layout Plain Layout
15928 \begin_inset space \textvisiblespace{}
15932 \begin_inset Formula $\to$
15936 \begin_inset Formula $\to$
15944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15947 \begin_layout Plain Layout
15948 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15964 \begin_layout Standard
15965 Limits of inline formulas are set right beside the operator.
15966 Limits in displayed formulas are set above or below the operator, except
15967 for integral limits.
15970 \begin_layout Standard
15971 To force that the limits are set beside the operator, the cursor is set
15972 directly behind the operator and the limits type is changed with the menu
15975 Edit\SpecialChar menuseparator
15976 Math\SpecialChar menuseparator
15995 \begin_layout Standard
15996 The default limits type is this:
15997 \begin_inset Formula
15999 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16004 This is how it looks when the limits type was changed to
16011 \begin_inset Formula
16013 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16018 For integrals, except those ending with
16034 etc., the limits are by default set beside the operator.
16035 But for multiple integrals the limits are often set below the operator.
16036 In the following example the limits type was therefore set to
16040 and so set below the integrals:
16041 \begin_inset Formula
16043 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16051 \begin_layout Standard
16052 \begin_inset VSpace medskip
16055 To specify conditions for limits, the commands
16062 \begin_inset Index idx
16065 \begin_layout Plain Layout
16080 \begin_inset Index idx
16083 \begin_layout Plain Layout
16092 To create for example this expression
16093 \begin_inset Formula
16095 \sum_{\begin{subarray}{c}
16099 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16107 \begin_layout Standard
16108 the following has to be done:
16109 \begin_inset Newline newline
16121 \begin_inset space \textvisiblespace{}
16127 One is now in a blue box under the summation operator and insert there
16133 \begin_inset space \textvisiblespace{}
16139 The blue box is now within a purple box and now several lines can be written
16141 A new line is created by inserting a line break (
16144 arg "newline-insert newline"
16149 \begin_inset Newline newline
16154 0<k<1000 Ctrl+Return
16155 \begin_inset Newline newline
16160 is typed in, a new box appears below for the new line.
16163 \begin_layout Standard
16164 The alignment of the lines can be changed to left aligned with the
16174 Edit\SpecialChar menuseparator
16178 To get right alignment,
16183 \begin_inset space \textvisiblespace{}
16188 is inserted at the beginning of the line.
16191 \begin_layout Standard
16204 with the difference that the lines are always centered.
16207 \begin_layout Standard
16208 \begin_inset VSpace bigskip
16212 \begin_inset CommandInset ref
16214 reference "eq:substack"
16218 there can be too much space beside an operator, because the characters
16219 following the operator are set beside the limits.
16220 To avoid this the command
16227 \begin_inset Index idx
16230 \begin_layout Plain Layout
16239 To activate it, set in the document settings under
16242 \begin_inset space ~
16252 \begin_inset Index idx
16255 \begin_layout Plain Layout
16256 Packages ! mathtools
16264 \begin_inset space ~
16276 sets the space besides the operator to 0
16277 \begin_inset space \thinspace{}
16281 \begin_inset Newline newline
16285 \begin_inset CommandInset ref
16287 reference "eq:substack"
16291 , one uses the command
16294 \begin_layout Standard
16302 \begin_layout Standard
16303 and inserts the operator with its limits into the braces.
16304 Behind the brace one continues the formula:
16305 \begin_inset Formula
16307 \smashoperator{\sum_{\begin{subarray}{c}
16311 \end{subarray}}^{n}}k^{-2}
16319 \begin_layout Standard
16320 It is possible to set the space of only one side of the operator to 0
16321 \begin_inset space \thinspace{}
16325 To do this write either
16344 stands for the left and
16348 for the right side of the operator.
16349 Here is an example of the possible
16358 \begin_layout Standard
16359 \begin_inset Formula
16361 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}
16369 \begin_layout Standard
16370 \begin_inset VSpace bigskip
16376 \begin_layout Standard
16377 When several consecutive operators have limits the typesetting of the limits
16378 looks often imperfect in the output, see this example:
16379 \begin_inset Formula
16381 \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}
16386 To improve the typesetting set in the document settings under
16389 \begin_inset space ~
16399 \begin_inset Index idx
16402 \begin_layout Plain Layout
16403 Packages ! mathtools
16411 \begin_inset space ~
16417 Then insert into your formula the command
16424 \begin_inset Index idx
16427 \begin_layout Plain Layout
16435 directly before the first operator.
16436 The example will then look like this:
16437 \begin_inset Formula
16439 \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}
16447 \begin_layout Standard
16448 \begin_inset VSpace bigskip
16451 How to use one limit for several operators is described in
16452 \begin_inset CommandInset ref
16454 reference "subsec:Self-defined-Operators"
16461 \begin_layout Subsection
16462 Decoration for Operators
16463 \begin_inset Index idx
16466 \begin_layout Plain Layout
16467 Operators ! Decoration
16475 \begin_layout Standard
16483 \begin_inset Index idx
16486 \begin_layout Plain Layout
16501 \begin_inset Index idx
16504 \begin_layout Plain Layout
16512 characters can be placed above or below an operator, respectively.
16520 \begin_inset Index idx
16523 \begin_layout Plain Layout
16531 characters can be set before and behind a big operator.
16534 \begin_layout Standard
16536 \begin_inset space ~
16548 \begin_layout Itemize
16555 is used to set characters at the corners of the operator
16558 \begin_layout Itemize
16565 is used to set characters before and/or behind the operator (this variant
16566 represents \SpecialChar LaTeX
16576 \begin_layout Itemize
16583 is used to set characters at the left corners and/or behind the operator
16586 \begin_layout Itemize
16593 is used to set characters at the right corners and/or before the operator
16596 \begin_layout Standard
16597 For example the command
16602 \begin_inset space \textvisiblespace{}
16608 \begin_inset space \textvisiblespace{}
16612 \begin_inset Formula $\to$
16616 \begin_inset Formula $\to$
16620 \begin_inset space \textvisiblespace{}
16630 \begin_inset Formula
16632 \sideset{}{'}\sum_{k=1}^{n}
16640 \begin_layout Standard
16641 \begin_inset Note Greyedout
16644 \begin_layout Plain Layout
16651 can only be used to decorate big operators, binary operators are not allowed.
16659 \begin_layout Standard
16672 can also be used to decorate symbols and characters.
16673 For example, the command
16678 \begin_inset space \textvisiblespace{}
16684 \begin_inset space \textvisiblespace{}
16690 \begin_inset Formula $\uparrow$
16698 \begin_inset Formula
16700 \overset{a}{\maltese}
16708 \begin_layout Subsection
16710 \begin_inset CommandInset label
16712 name "subsec:Binary-Operators"
16717 \begin_inset Index idx
16720 \begin_layout Plain Layout
16729 \begin_layout Standard
16730 Binary operators are surrounded by space when there is a character before
16732 \begin_inset VSpace medskip
16738 \begin_layout Standard
16739 \begin_inset Tabular
16740 <lyxtabular version="3" rows="13" columns="2">
16741 <features booktabs="true" tabularvalignment="middle">
16742 <column alignment="center" valignment="top" width="0pt">
16743 <column alignment="center" valignment="top" width="0pt">
16745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16748 \begin_layout Plain Layout
16750 \begin_inset Note Note
16753 \begin_layout Plain Layout
16760 is only used as spacer.
16770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16784 \begin_layout Plain Layout
16790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16793 \begin_layout Plain Layout
16794 \begin_inset Formula $+$
16804 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16807 \begin_layout Plain Layout
16813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16816 \begin_layout Plain Layout
16817 \begin_inset Formula $-$
16827 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16830 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16842 \begin_inset Formula $\pm$
16852 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16855 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16867 \begin_inset Formula $\mp$
16877 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Plain Layout
16892 \begin_inset Formula $\cdot$
16902 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $\times$
16927 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Plain Layout
16942 \begin_inset Formula $\div$
16952 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16959 \begin_layout Plain Layout
16972 \begin_layout Plain Layout
16984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16987 \begin_layout Plain Layout
16988 \begin_inset Formula $*$
16998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17001 \begin_layout Plain Layout
17009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17012 \begin_layout Plain Layout
17013 \begin_inset Formula $\star$
17023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17026 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17037 \begin_layout Plain Layout
17038 \begin_inset Formula $\circ$
17048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17051 \begin_layout Plain Layout
17059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17062 \begin_layout Plain Layout
17063 \begin_inset Formula $\diamond$
17073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17076 \begin_layout Plain Layout
17084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17087 \begin_layout Plain Layout
17088 \begin_inset Formula $\bullet$
17102 \begin_inset space \hfill{}
17106 \begin_inset Tabular
17107 <lyxtabular version="3" rows="13" columns="2">
17108 <features booktabs="true" tabularvalignment="middle">
17109 <column alignment="center" valignment="top" width="0pt">
17110 <column alignment="center" valignment="top" width="0pt">
17112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17115 \begin_layout Plain Layout
17121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17124 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\nabla$
17157 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17171 \begin_layout Plain Layout
17172 \begin_inset Formula $\bigtriangledown$
17182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17185 \begin_layout Plain Layout
17193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17196 \begin_layout Plain Layout
17197 \begin_inset Formula $\bigtriangleup$
17207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17210 \begin_layout Plain Layout
17218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17221 \begin_layout Plain Layout
17222 \begin_inset Formula $\Box$
17232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17235 \begin_layout Plain Layout
17243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17246 \begin_layout Plain Layout
17247 \begin_inset Formula $\cap$
17257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17260 \begin_layout Plain Layout
17268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17271 \begin_layout Plain Layout
17272 \begin_inset Formula $\cup$
17282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17285 \begin_layout Plain Layout
17293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17296 \begin_layout Plain Layout
17297 \begin_inset Formula $\dagger$
17307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17310 \begin_layout Plain Layout
17318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17321 \begin_layout Plain Layout
17322 \begin_inset Formula $\ddagger$
17332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17335 \begin_layout Plain Layout
17343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17346 \begin_layout Plain Layout
17347 \begin_inset Formula $\wr$
17357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17360 \begin_layout Plain Layout
17368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17371 \begin_layout Plain Layout
17372 \begin_inset Formula $\bigcirc$
17382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17385 \begin_layout Plain Layout
17393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17396 \begin_layout Plain Layout
17397 \begin_inset Formula $\wedge$
17407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17410 \begin_layout Plain Layout
17418 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17421 \begin_layout Plain Layout
17422 \begin_inset Formula $\vee$
17436 \begin_inset space \hfill{}
17440 \begin_inset Tabular
17441 <lyxtabular version="3" rows="13" columns="2">
17442 <features booktabs="true" tabularvalignment="middle">
17443 <column alignment="center" valignment="top" width="0pt">
17444 <column alignment="center" valignment="top" width="0pt">
17446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17449 \begin_layout Plain Layout
17455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17458 \begin_layout Plain Layout
17466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17469 \begin_layout Plain Layout
17477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17480 \begin_layout Plain Layout
17481 \begin_inset Formula $\oplus$
17491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17494 \begin_layout Plain Layout
17502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17505 \begin_layout Plain Layout
17506 \begin_inset Formula $\ominus$
17516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17519 \begin_layout Plain Layout
17527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17530 \begin_layout Plain Layout
17531 \begin_inset Formula $\otimes$
17541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17544 \begin_layout Plain Layout
17552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17555 \begin_layout Plain Layout
17556 \begin_inset Formula $\oslash$
17566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17569 \begin_layout Plain Layout
17577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17580 \begin_layout Plain Layout
17581 \begin_inset Formula $\odot$
17591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17594 \begin_layout Plain Layout
17602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17605 \begin_layout Plain Layout
17606 \begin_inset Formula $\amalg$
17616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17619 \begin_layout Plain Layout
17627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17630 \begin_layout Plain Layout
17631 \begin_inset Formula $\uplus$
17641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17644 \begin_layout Plain Layout
17652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17655 \begin_layout Plain Layout
17656 \begin_inset Formula $\setminus$
17666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17669 \begin_layout Plain Layout
17677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17680 \begin_layout Plain Layout
17681 \begin_inset Formula $\sqcap$
17691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17694 \begin_layout Plain Layout
17702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17705 \begin_layout Plain Layout
17706 \begin_inset Formula $\sqcup$
17716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17719 \begin_layout Plain Layout
17727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17730 \begin_layout Plain Layout
17731 \begin_inset Formula $\triangleleft$
17741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17744 \begin_layout Plain Layout
17752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17755 \begin_layout Plain Layout
17756 \begin_inset Formula $\triangleright$
17772 \begin_layout Standard
17773 All binary operators can also be inserted via the math toolbar button
17776 arg "math-insert \\pm"
17782 \begin_layout Standard
17783 To typeset the Laplace operator also
17800 \begin_inset Formula $\nabla^{2}$
17803 ) can be used instead of
17812 \begin_layout Standard
17819 Insert\SpecialChar menuseparator
17831 \begin_layout Subsection
17832 Self-defined Operators
17833 \begin_inset CommandInset label
17835 name "subsec:Self-defined-Operators"
17840 \begin_inset Index idx
17843 \begin_layout Plain Layout
17844 Operators ! self-defined
17852 \begin_layout Standard
17853 With the help of the command
17857 DeclareMathOperator
17860 \begin_inset Index idx
17863 \begin_layout Plain Layout
17868 DeclareMathOperator
17873 custom operators can be defined in the \SpecialChar LaTeX
17875 Its command scheme is:
17878 \begin_layout Standard
17883 DeclareMathOperator{new command}{display}
17886 \begin_layout Standard
17887 Display can be characters or symbols that define how the operator looks
17889 To define a big operator a * is set behind the command.
17890 All self-defined big operators can have limits as described in
17891 \begin_inset CommandInset ref
17893 reference "subsec:Operator-Limits"
17900 \begin_layout Standard
17901 For example the \SpecialChar LaTeX
17905 \begin_layout Standard
17910 DeclareMathOperator*{
17917 \begin_layout Standard
17918 defines the command
17924 , that inserts a big operator consisting of the lozenge symbol from
17925 \begin_inset CommandInset ref
17927 reference "subsec:Miscellaneous-Symbols"
17932 \begin_inset Formula
17934 \Lozenge_{n=1}^{\infty}
17939 The command for this formula is:
17950 \begin_inset Formula $\to$
17956 \begin_layout Standard
17957 \begin_inset VSpace bigskip
17960 When self-defined operators are not used several times in the document,
17961 they can also be defined with the commands
17968 \begin_inset Index idx
17971 \begin_layout Plain Layout
17986 \begin_inset Index idx
17989 \begin_layout Plain Layout
17997 , which have the following scheme:
18000 \begin_layout Standard
18014 \begin_layout Standard
18021 defines big operators,
18030 \begin_layout Standard
18038 \begin_inset space \thinspace{}
18042 \begin_inset space \space{}
18045 be used to use one limit for several operators:
18048 \begin_layout Standard
18049 \begin_inset Formula
18051 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18059 \begin_layout Standard
18060 The command for the formula above is:
18061 \begin_inset Newline newline
18077 \begin_inset space \textvisiblespace{}
18083 \begin_inset Formula $\to$
18089 \begin_inset space \textvisiblespace{}
18097 \begin_layout Section
18099 \begin_inset Index idx
18102 \begin_layout Plain Layout
18111 \begin_layout Subsection
18113 \begin_inset CommandInset label
18115 name "subsec:Font-Styles"
18120 \begin_inset Index idx
18123 \begin_layout Plain Layout
18132 \begin_layout Standard
18133 Latin letters in formulas can be set in one of the following font styles:
18136 \begin_layout Standard
18138 \begin_inset Tabular
18139 <lyxtabular version="3" rows="6" columns="3">
18140 <features booktabs="true" tabularvalignment="middle">
18141 <column alignment="center" valignment="top" width="0pt">
18142 <column alignment="center" valignment="top">
18143 <column alignment="center" valignment="top">
18145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18148 \begin_layout Plain Layout
18154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18157 \begin_layout Plain Layout
18163 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18166 \begin_layout Plain Layout
18174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18177 \begin_layout Plain Layout
18183 \begin_inset space \textvisiblespace{}
18193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18196 \begin_layout Plain Layout
18197 \begin_inset Formula $\mathbb{ABC}$
18205 <cell alignment="center" valignment="top" usebox="none">
18208 \begin_layout Plain Layout
18216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18219 \begin_layout Plain Layout
18225 \begin_inset space \textvisiblespace{}
18235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18238 \begin_layout Plain Layout
18239 \begin_inset Formula $\mathbf{AbC}$
18247 <cell alignment="center" valignment="top" usebox="none">
18250 \begin_layout Plain Layout
18263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18272 \begin_inset space \textvisiblespace{}
18282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18285 \begin_layout Plain Layout
18286 \begin_inset Formula $\boldsymbol{AbC}$
18294 <cell alignment="center" valignment="top" usebox="none">
18297 \begin_layout Plain Layout
18300 arg "font-boldsymbol"
18310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18313 \begin_layout Plain Layout
18319 \begin_inset space \textvisiblespace{}
18329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18332 \begin_layout Plain Layout
18333 \begin_inset Formula $\mathcal{ABC}$
18341 <cell alignment="center" valignment="top" usebox="none">
18344 \begin_layout Plain Layout
18352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18355 \begin_layout Plain Layout
18361 \begin_inset space \textvisiblespace{}
18371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18374 \begin_layout Plain Layout
18375 \begin_inset Formula $\mathfrak{AbC}$
18383 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18386 \begin_layout Plain Layout
18400 \begin_layout Standard
18402 \begin_inset Tabular
18403 <lyxtabular version="3" rows="6" columns="3">
18404 <features booktabs="true" tabularvalignment="middle">
18405 <column alignment="center" valignment="top" width="0pt">
18406 <column alignment="center" valignment="top">
18407 <column alignment="center" valignment="top">
18409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18412 \begin_layout Plain Layout
18418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18421 \begin_layout Plain Layout
18427 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18430 \begin_layout Plain Layout
18438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18441 \begin_layout Plain Layout
18447 \begin_inset space \textvisiblespace{}
18457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18460 \begin_layout Plain Layout
18461 \begin_inset Formula $\mathit{AbC}$
18469 <cell alignment="center" valignment="top" usebox="none">
18472 \begin_layout Plain Layout
18480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18483 \begin_layout Plain Layout
18489 \begin_inset space \textvisiblespace{}
18499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18502 \begin_layout Plain Layout
18503 \begin_inset Formula $\mathrm{AbC}$
18511 <cell alignment="center" valignment="top" usebox="none">
18514 \begin_layout Plain Layout
18527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18530 \begin_layout Plain Layout
18536 \begin_inset space \textvisiblespace{}
18546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18549 \begin_layout Plain Layout
18550 \begin_inset Formula $\mathsf{AbC}$
18558 <cell alignment="center" valignment="top" usebox="none">
18561 \begin_layout Plain Layout
18574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18577 \begin_layout Plain Layout
18583 \begin_inset space \textvisiblespace{}
18593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18596 \begin_layout Plain Layout
18597 \begin_inset Formula $\mathtt{AbC}$
18605 <cell alignment="center" valignment="top" usebox="none">
18608 \begin_layout Plain Layout
18611 arg "font-typewriter"
18621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18624 \begin_layout Plain Layout
18630 \begin_inset space \textvisiblespace{}
18640 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18643 \begin_layout Plain Layout
18644 \begin_inset Formula $\mathscr{ABC}$
18652 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18655 \begin_layout Plain Layout
18669 \begin_layout Standard
18670 \begin_inset Note Greyedout
18673 \begin_layout Plain Layout
18696 can only be used for big letters.
18704 \begin_layout Standard
18705 Predefined is the style
18714 \begin_layout Standard
18715 The style commands work also for letters in mathematical constructs:
18716 \begin_inset Formula
18718 \mathfrak{A=\frac{b}{C}}
18726 \begin_layout Standard
18727 Characters in mathematical text don't appear in a math font style but in
18728 the text font style
18735 That their style can't be set correctly via the text style dialog is a
18736 bug in \SpecialChar LyX
18741 \begin_layout Plain Layout
18742 \begin_inset CommandInset href
18744 name "LyX-bug #4629"
18745 target "https://www.lyx.org/trac/ticket/4629"
18758 \begin_layout Standard
18759 Instead of the style commands the dialog
18761 Edit\SpecialChar menuseparator
18762 Math\SpecialChar menuseparator
18765 or the toolbar button
18768 arg "math-insert \\font"
18774 \begin_layout Subsection
18776 \begin_inset CommandInset label
18778 name "subsec:Bold-Formulas"
18783 \begin_inset Index idx
18786 \begin_layout Plain Layout
18795 \begin_layout Standard
18796 To make a complete formula bold, the command
18802 from the previous subsection cannot be used, because it doesn't work for
18803 small Greek letters.
18804 Furthermore it prints Latin letters always upright, like in the following
18808 \begin_layout Standard
18809 \begin_inset Formula
18811 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18819 \begin_layout Standard
18820 To display the formula correctly, the command
18827 \begin_inset Formula
18829 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18834 It is also possible to set the formula in a
18836 boldmath environment
18839 This environment is created by inserting the command
18846 \begin_inset Index idx
18849 \begin_layout Plain Layout
18857 in \SpecialChar TeX
18859 To end the environment, the command
18866 \begin_inset Index idx
18869 \begin_layout Plain Layout
18877 is inserted in \SpecialChar TeX
18882 \begin_layout Plain Layout
18892 \begin_inset Formula
18894 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18903 \begin_layout Plain Layout
18915 \begin_layout Subsection
18917 \begin_inset Index idx
18920 \begin_layout Plain Layout
18929 \begin_layout Standard
18930 Formulas can be colored like normal text: Highlight a formula or a formula
18936 Here is a formula in magenta:
18937 \begin_inset Formula
18939 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18947 \begin_layout Standard
18948 You can also define your own colors as described in
18949 \begin_inset CommandInset ref
18951 reference "subsec:Colored-Boxes"
18956 They can be used with the \SpecialChar TeX
18964 \begin_inset Index idx
18967 \begin_layout Plain Layout
18978 \begin_layout Standard
18983 textcolor{color}{characters or formula}
18986 \begin_layout Standard
18987 The following example was colored completely dark green and partly red:
18990 \begin_layout Standard
18994 \begin_layout Plain Layout
18998 textcolor{darkgreen}{
19004 \begin_inset Formula
19006 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19015 \begin_layout Plain Layout
19025 \begin_layout Standard
19026 Due to a bug in \SpecialChar LyX
19027 only complete formulas can be colored with self-defined
19032 \begin_layout Plain Layout
19033 \begin_inset CommandInset href
19035 name "LyX-bug #5269"
19036 target "https://www.lyx.org/trac/ticket/5269"
19049 \begin_layout Subsection
19051 \begin_inset CommandInset label
19053 name "subsec:Font-Sizes"
19058 \begin_inset Index idx
19061 \begin_layout Plain Layout
19070 \begin_layout Standard
19071 For characters in formulas there are, analog to characters in text, the
19072 following size commands:
19075 \begin_layout Standard
19119 \begin_inset Newline newline
19141 \begin_layout Standard
19142 The size produced by the commands depends on the document font size, which
19143 corresponds to the command
19150 The other commands produce smaller or larger sizes than
19157 The font size can however not exceed a certain value.
19158 Is for example the document font size 12
19159 \begin_inset space \thinspace{}
19168 switches to the same size as
19178 \begin_layout Standard
19179 A size command is inserted in \SpecialChar TeX
19180 mode before the formula and sets the size
19181 for all following formula and text characters.
19182 To switch back to the initial size, the command
19188 is inserted behind the formula in \SpecialChar TeX
19192 \begin_layout Standard
19193 Within a formula the size can be changed using the following size commands
19194 or the toolbar button
19197 arg "math-insert \\style"
19203 \begin_layout Standard
19206 \begin_inset Tabular
19207 <lyxtabular version="3" rows="5" columns="2">
19208 <features booktabs="true" tabularvalignment="middle">
19209 <column alignment="center" valignment="top" width="0pt">
19210 <column alignment="center" valignment="top">
19212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19215 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19235 \begin_layout Plain Layout
19239 \begin_inset Index idx
19242 \begin_layout Plain Layout
19255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19258 \begin_layout Plain Layout
19259 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19268 <row topspace="1mm">
19269 <cell alignment="center" valignment="top" usebox="none">
19272 \begin_layout Plain Layout
19280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19283 \begin_layout Plain Layout
19284 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19297 \begin_layout Plain Layout
19305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19308 \begin_layout Plain Layout
19309 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19322 \begin_layout Plain Layout
19330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19333 \begin_layout Plain Layout
19334 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19350 \begin_layout Standard
19351 After entering these commands, a blue box appears in which the formula parts
19355 \begin_layout Standard
19356 There is a further method to change the font size, that though only works
19357 for symbols or letters in mathematical text.
19358 To use it, one of the above text size commands is inserted in mathematical
19360 All following characters until the end of the mathematical text or until
19361 another size command will have the selected size.
19363 \begin_inset VSpace -2mm
19369 \begin_layout Standard
19373 \begin_layout Plain Layout
19383 \begin_inset Formula
19385 A=\frac{B}{c}\cdot\maltese
19391 \begin_inset Formula
19393 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19402 \begin_layout Plain Layout
19414 \begin_layout Standard
19415 \begin_inset VSpace medskip
19418 Before both formulas the command
19425 The command for the second formula is:
19426 \begin_inset Newline newline
19434 \begin_inset space \textvisiblespace{}
19440 \begin_inset space \textvisiblespace{}
19446 \begin_inset space \textvisiblespace{}
19452 \begin_inset space \textvisiblespace{}
19456 \begin_inset Formula $\to$
19460 \begin_inset Formula $\to$
19464 \begin_inset Newline newline
19468 \begin_inset space \hspace*{}
19479 \begin_inset space \textvisiblespace{}
19485 \begin_inset space \textvisiblespace{}
19491 \begin_inset space \textvisiblespace{}
19497 \begin_layout Standard
19498 If a symbol cannot be displayed in different sizes, it will always be displayed
19499 in the default size.
19502 \begin_layout Section
19504 \begin_inset Index idx
19507 \begin_layout Plain Layout
19516 \begin_layout Standard
19517 Greek letters can also be inserted via the toolbar button
19520 arg "math-insert \\alpha"
19524 All international typesetting norms purport that Greek letters in math
19525 have to be typeset italic/slanted.
19526 In some languages, like French or Russian, they are nevertheless sometimes
19530 \begin_layout Subsection
19532 \begin_inset Index idx
19535 \begin_layout Plain Layout
19536 Greek letters ! small
19544 \begin_layout Standard
19545 \begin_inset space \hfill{}
19549 \begin_inset Tabular
19550 <lyxtabular version="3" rows="11" columns="2">
19551 <features booktabs="true" tabularvalignment="middle">
19552 <column alignment="center" valignment="top" width="0pt">
19553 <column alignment="center" valignment="top" width="0pt">
19555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19558 \begin_layout Plain Layout
19564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19567 \begin_layout Plain Layout
19575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19578 \begin_layout Plain Layout
19586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19589 \begin_layout Plain Layout
19590 \begin_inset Formula $\alpha$
19600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19603 \begin_layout Plain Layout
19611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19614 \begin_layout Plain Layout
19615 \begin_inset Formula $\beta$
19625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19628 \begin_layout Plain Layout
19636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Plain Layout
19640 \begin_inset Formula $\gamma$
19650 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19664 \begin_layout Plain Layout
19665 \begin_inset Formula $\delta$
19675 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19678 \begin_layout Plain Layout
19686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19689 \begin_layout Plain Layout
19690 \begin_inset Formula $\epsilon$
19700 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19703 \begin_layout Plain Layout
19711 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19714 \begin_layout Plain Layout
19715 \begin_inset Formula $\varepsilon$
19725 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19728 \begin_layout Plain Layout
19736 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19739 \begin_layout Plain Layout
19740 \begin_inset Formula $\zeta$
19750 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19753 \begin_layout Plain Layout
19761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19764 \begin_layout Plain Layout
19765 \begin_inset Formula $\eta$
19775 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19778 \begin_layout Plain Layout
19786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19789 \begin_layout Plain Layout
19790 \begin_inset Formula $\theta$
19800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19803 \begin_layout Plain Layout
19811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19814 \begin_layout Plain Layout
19815 \begin_inset Formula $\vartheta$
19829 \begin_inset space \hfill{}
19833 \begin_inset Tabular
19834 <lyxtabular version="3" rows="12" columns="2">
19835 <features booktabs="true" tabularvalignment="middle">
19836 <column alignment="center" valignment="top" width="0pt">
19837 <column alignment="center" valignment="top" width="0pt">
19839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19842 \begin_layout Plain Layout
19848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19851 \begin_layout Plain Layout
19859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19862 \begin_layout Plain Layout
19870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19873 \begin_layout Plain Layout
19874 \begin_inset Formula $\iota$
19884 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19887 \begin_layout Plain Layout
19895 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19898 \begin_layout Plain Layout
19899 \begin_inset Formula $\kappa$
19909 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19912 \begin_layout Plain Layout
19920 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19923 \begin_layout Plain Layout
19924 \begin_inset Formula $\varkappa$
19934 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19937 \begin_layout Plain Layout
19945 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19948 \begin_layout Plain Layout
19949 \begin_inset Formula $\lambda$
19959 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19962 \begin_layout Plain Layout
19970 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19973 \begin_layout Plain Layout
19974 \begin_inset Formula $\mu$
19984 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19987 \begin_layout Plain Layout
19995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19998 \begin_layout Plain Layout
19999 \begin_inset Formula $\nu$
20009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20012 \begin_layout Plain Layout
20020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20023 \begin_layout Plain Layout
20024 \begin_inset Formula $\xi$
20034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20037 \begin_layout Plain Layout
20043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20046 \begin_layout Plain Layout
20047 \begin_inset Formula $o$
20057 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20060 \begin_layout Plain Layout
20068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20071 \begin_layout Plain Layout
20072 \begin_inset Formula $\pi$
20082 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20085 \begin_layout Plain Layout
20093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20096 \begin_layout Plain Layout
20097 \begin_inset Formula $\varpi$
20107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20110 \begin_layout Plain Layout
20118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20121 \begin_layout Plain Layout
20122 \begin_inset Formula $\rho$
20136 \begin_inset space \hfill{}
20140 \begin_inset Tabular
20141 <lyxtabular version="3" rows="11" columns="2">
20142 <features booktabs="true" tabularvalignment="middle">
20143 <column alignment="center" valignment="top" width="0pt">
20144 <column alignment="center" valignment="top" width="0pt">
20146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20149 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20158 \begin_layout Plain Layout
20166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20169 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20180 \begin_layout Plain Layout
20181 \begin_inset Formula $\varrho$
20191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20194 \begin_layout Plain Layout
20202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20205 \begin_layout Plain Layout
20206 \begin_inset Formula $\sigma$
20216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20219 \begin_layout Plain Layout
20227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20230 \begin_layout Plain Layout
20231 \begin_inset Formula $\varsigma$
20241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20244 \begin_layout Plain Layout
20252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20255 \begin_layout Plain Layout
20256 \begin_inset Formula $\tau$
20266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20269 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20281 \begin_inset Formula $\upsilon$
20291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20294 \begin_layout Plain Layout
20302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20305 \begin_layout Plain Layout
20306 \begin_inset Formula $\phi$
20316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20319 \begin_layout Plain Layout
20327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20330 \begin_layout Plain Layout
20331 \begin_inset Formula $\varphi$
20341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20344 \begin_layout Plain Layout
20352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20355 \begin_layout Plain Layout
20356 \begin_inset Formula $\chi$
20366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20369 \begin_layout Plain Layout
20377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20380 \begin_layout Plain Layout
20381 \begin_inset Formula $\psi$
20391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20394 \begin_layout Plain Layout
20402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20405 \begin_layout Plain Layout
20406 \begin_inset Formula $\omega$
20420 \begin_inset space \hfill{}
20426 \begin_layout Standard
20427 \begin_inset VSpace medskip
20433 \begin_layout Standard
20434 How to create special upright Greek letters is explained in
20435 \begin_inset CommandInset ref
20437 reference "subsec:Upright-small-Greek"
20444 \begin_layout Subsection
20446 \begin_inset Index idx
20449 \begin_layout Plain Layout
20450 Greek letters ! big
20458 \begin_layout Standard
20459 \begin_inset space \hfill{}
20463 \begin_inset Tabular
20464 <lyxtabular version="3" rows="7" columns="2">
20465 <features booktabs="true" tabularvalignment="middle">
20466 <column alignment="center" valignment="top" width="0pt">
20467 <column alignment="center" valignment="top" width="0pt">
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20481 \begin_layout Plain Layout
20489 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20492 \begin_layout Plain Layout
20500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20503 \begin_layout Plain Layout
20504 \begin_inset Formula $\Gamma$
20514 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20517 \begin_layout Plain Layout
20525 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20528 \begin_layout Plain Layout
20529 \begin_inset Formula $\Delta$
20539 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20542 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Plain Layout
20554 \begin_inset Formula $\Theta$
20564 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20567 \begin_layout Plain Layout
20575 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20578 \begin_layout Plain Layout
20579 \begin_inset Formula $\Lambda$
20589 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20592 \begin_layout Plain Layout
20600 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Plain Layout
20604 \begin_inset Formula $\Xi$
20614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20617 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Plain Layout
20629 \begin_inset Formula $\Pi$
20643 \begin_inset space \hfill{}
20647 \begin_inset Tabular
20648 <lyxtabular version="3" rows="6" columns="2">
20649 <features booktabs="true" tabularvalignment="middle">
20650 <column alignment="center" valignment="top" width="0pt">
20651 <column alignment="center" valignment="top" width="0pt">
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20656 \begin_layout Plain Layout
20662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20665 \begin_layout Plain Layout
20673 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20676 \begin_layout Plain Layout
20684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20687 \begin_layout Plain Layout
20688 \begin_inset Formula $\Sigma$
20698 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20701 \begin_layout Plain Layout
20709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Plain Layout
20713 \begin_inset Formula $\Upsilon$
20723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20726 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20738 \begin_inset Formula $\Phi$
20748 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20751 \begin_layout Plain Layout
20759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20762 \begin_layout Plain Layout
20763 \begin_inset Formula $\Psi$
20773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20776 \begin_layout Plain Layout
20784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20787 \begin_layout Plain Layout
20788 \begin_inset Formula $\Omega$
20802 \begin_inset space \hfill{}
20808 \begin_layout Standard
20809 \begin_inset VSpace medskip
20812 That the big Greek letters appear upright is caused by a design bug when
20815 To get correct italic big letters, begin every command with
20820 For example the command
20827 \begin_inset Formula $\varGamma$
20831 Another way is to load the package
20839 \begin_layout Plain Layout
20844 is part of the \SpecialChar LaTeX
20850 \begin_inset Index idx
20853 \begin_layout Plain Layout
20858 \begin_layout Plain Layout
20878 \begin_inset Index idx
20881 \begin_layout Plain Layout
20887 with the \SpecialChar LaTeX
20891 \begin_layout Standard
20896 usepackage{fixmath}
20899 \begin_layout Standard
20900 Then all big Greek letters in a document will automatically be typeset italic.
20903 \begin_layout Subsection
20905 \begin_inset Index idx
20908 \begin_layout Plain Layout
20909 Greek letters ! bold
20917 \begin_layout Standard
20918 Greek letters cannot be set with different font styles like Latin letters.
20919 They can only be made bold with the command
20926 \begin_inset Index idx
20929 \begin_layout Plain Layout
20940 \begin_layout Standard
20942 \begin_inset Tabular
20943 <lyxtabular version="3" rows="3" columns="2">
20944 <features booktabs="true" tabularvalignment="middle">
20945 <column alignment="center" valignment="top" width="0pt">
20946 <column alignment="center" valignment="top">
20948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20951 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20960 \begin_layout Plain Layout
20968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20971 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21000 \begin_layout Plain Layout
21012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21015 \begin_layout Plain Layout
21016 \begin_inset Formula $\theta\boldsymbol{\theta}$
21032 \begin_layout Section
21037 \begin_layout Plain Layout
21050 \begin_layout Plain Layout
21051 A list with all symbols of most of the \SpecialChar LaTeX
21052 -packages can be found in
21053 \begin_inset CommandInset citation
21069 \begin_layout Plain Layout
21077 \begin_inset Note Note
21080 \begin_layout Plain Layout
21083 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21086 \begin_layout Plain Layout
21089 texorpdfstring is in section
21090 \begin_inset CommandInset ref
21092 reference "subsec:Formulas-in-Section"
21102 \begin_inset Index idx
21105 \begin_layout Plain Layout
21114 \begin_layout Standard
21115 Many of the symbols listed in this section can also be inserted via the
21119 arg "math-insert \\nabla"
21125 arg "math-insert \\digamma"
21131 \begin_layout Subsection
21132 Mathematical Symbols
21133 \begin_inset CommandInset label
21135 name "subsec:Mathematical-Symbols"
21140 \begin_inset Index idx
21143 \begin_layout Plain Layout
21144 Symbols ! mathematical
21152 \begin_layout Standard
21153 \begin_inset Tabular
21154 <lyxtabular version="3" rows="10" columns="2">
21155 <features booktabs="true" tabularvalignment="middle">
21156 <column alignment="center" valignment="top" width="0pt">
21157 <column alignment="center" valignment="top" width="0pt">
21159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21182 \begin_layout Plain Layout
21190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21193 \begin_layout Plain Layout
21194 \begin_inset Formula $\neg$
21204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21207 \begin_layout Plain Layout
21215 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21218 \begin_layout Plain Layout
21219 \begin_inset Formula $\Im$
21229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21232 \begin_layout Plain Layout
21240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21243 \begin_layout Plain Layout
21244 \begin_inset Formula $\Re$
21254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21257 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\aleph$
21279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\partial$
21304 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\infty$
21329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\wp$
21354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\imath$
21379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\jmath$
21408 \begin_inset space \hfill{}
21412 \begin_inset Tabular
21413 <lyxtabular version="3" rows="10" columns="2">
21414 <features booktabs="true" tabularvalignment="middle">
21415 <column alignment="center" valignment="top" width="0pt">
21416 <column alignment="center" valignment="top" width="0pt">
21418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21421 \begin_layout Plain Layout
21427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Plain Layout
21432 \begin_inset Note Note
21435 \begin_layout Plain Layout
21442 is only used as spacer.
21454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21457 \begin_layout Plain Layout
21465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21468 \begin_layout Plain Layout
21469 \begin_inset Formula $\forall$
21479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21482 \begin_layout Plain Layout
21490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21493 \begin_layout Plain Layout
21494 \begin_inset Formula $\exists$
21504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21507 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21519 \begin_inset Formula $\nexists$
21529 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21543 \begin_layout Plain Layout
21544 \begin_inset Formula $\emptyset$
21554 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21557 \begin_layout Plain Layout
21565 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21568 \begin_layout Plain Layout
21569 \begin_inset Formula $\varnothing$
21579 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21582 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21593 \begin_layout Plain Layout
21594 \begin_inset Formula $\dag$
21604 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21615 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21618 \begin_layout Plain Layout
21619 \begin_inset Formula $\ddag$
21629 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21647 \begin_layout Plain Layout
21657 \begin_inset Formula $\complement$
21664 \begin_layout Plain Layout
21678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21681 \begin_layout Plain Layout
21689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21692 \begin_layout Plain Layout
21693 \begin_inset Formula $\Bbbk$
21707 \begin_inset space \hfill{}
21711 \begin_inset Tabular
21712 <lyxtabular version="3" rows="10" columns="2">
21713 <features booktabs="true" tabularvalignment="middle">
21714 <column alignment="center" valignment="top" width="0pt">
21715 <column alignment="center" valignment="top" width="0pt">
21717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21720 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21752 \begin_inset Formula $\prime$
21762 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\backprime$
21787 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21802 \begin_inset Formula $\mho$
21812 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21815 \begin_layout Plain Layout
21823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21826 \begin_layout Plain Layout
21827 \begin_inset Formula $\triangle$
21837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Plain Layout
21852 \begin_inset Formula $\angle$
21862 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21865 \begin_layout Plain Layout
21873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21876 \begin_layout Plain Layout
21877 \begin_inset Formula $\measuredangle$
21887 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21890 \begin_layout Plain Layout
21898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21901 \begin_layout Plain Layout
21902 \begin_inset Formula $\sphericalangle$
21912 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21915 \begin_layout Plain Layout
21923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21926 \begin_layout Plain Layout
21927 \begin_inset Formula $\top$
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21940 \begin_layout Plain Layout
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21951 \begin_layout Plain Layout
21952 \begin_inset Formula $\bot$
21968 \begin_layout Subsection
21969 Miscellaneous Symbols
21970 \begin_inset CommandInset label
21972 name "subsec:Miscellaneous-Symbols"
21977 \begin_inset Index idx
21980 \begin_layout Plain Layout
21981 Symbols ! miscellaneous
21989 \begin_layout Standard
21992 \begin_inset Tabular
21993 <lyxtabular version="3" rows="10" columns="2">
21994 <features booktabs="true" tabularvalignment="middle">
21995 <column alignment="center" valignment="top" width="0pt">
21996 <column alignment="center" valignment="top" width="0pt">
21998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22001 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22021 \begin_layout Plain Layout
22029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22032 \begin_layout Plain Layout
22033 \begin_inset Formula $\flat$
22043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22046 \begin_layout Plain Layout
22054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22057 \begin_layout Plain Layout
22058 \begin_inset Formula $\natural$
22068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22071 \begin_layout Plain Layout
22079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22082 \begin_layout Plain Layout
22083 \begin_inset Formula $\sharp$
22093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Plain Layout
22104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22107 \begin_layout Plain Layout
22108 \begin_inset Formula $\surd$
22118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22121 \begin_layout Plain Layout
22129 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22132 \begin_layout Plain Layout
22133 \begin_inset Formula $\checkmark$
22143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22146 \begin_layout Plain Layout
22154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22157 \begin_layout Plain Layout
22158 \begin_inset Formula $\yen$
22168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22171 \begin_layout Plain Layout
22179 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22182 \begin_layout Plain Layout
22183 \begin_inset Formula $\pounds$
22193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22196 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22206 \begin_inset Formula $\$$
22216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22219 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula $§$
22243 \begin_inset space \hfill{}
22247 \begin_inset Tabular
22248 <lyxtabular version="3" rows="10" columns="2">
22249 <features booktabs="true" tabularvalignment="middle">
22250 <column alignment="center" valignment="top" width="0pt">
22251 <column alignment="center" valignment="top">
22253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22256 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22276 \begin_layout Plain Layout
22284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22287 \begin_layout Plain Layout
22288 \begin_inset Formula $\hbar$
22298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22301 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22312 \begin_layout Plain Layout
22313 \begin_inset Formula $\hslash$
22323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22326 \begin_layout Plain Layout
22334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22337 \begin_layout Plain Layout
22338 \begin_inset Formula $\clubsuit$
22348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22351 \begin_layout Plain Layout
22359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22362 \begin_layout Plain Layout
22363 \begin_inset Formula $\spadesuit$
22373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22376 \begin_layout Plain Layout
22384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22387 \begin_layout Plain Layout
22388 \begin_inset Formula $\bigstar$
22398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22401 \begin_layout Plain Layout
22409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22412 \begin_layout Plain Layout
22413 \begin_inset Formula $\blacklozenge$
22423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22426 \begin_layout Plain Layout
22434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22437 \begin_layout Plain Layout
22438 \begin_inset Formula $\blacktriangle$
22448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22451 \begin_layout Plain Layout
22459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22462 \begin_layout Plain Layout
22463 \begin_inset Formula $\blacktriangledown$
22473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22476 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $\bullet$
22502 \begin_inset space \hfill{}
22506 \begin_inset Tabular
22507 <lyxtabular version="3" rows="10" columns="2">
22508 <features booktabs="true" tabularvalignment="middle">
22509 <column alignment="center" valignment="top" width="0pt">
22510 <column alignment="center" valignment="top" width="0pt">
22512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22515 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22524 \begin_layout Plain Layout
22532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\diamondsuit$
22557 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\Diamond$
22582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Plain Layout
22597 \begin_inset Formula $\heartsuit$
22607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22610 \begin_layout Plain Layout
22618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22621 \begin_layout Plain Layout
22622 \begin_inset Formula $\P$
22632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22635 \begin_layout Plain Layout
22643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22646 \begin_layout Plain Layout
22647 \begin_inset Formula $\copyright$
22657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22660 \begin_layout Plain Layout
22668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22671 \begin_layout Plain Layout
22672 \begin_inset Formula $\circledR$
22682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22685 \begin_layout Plain Layout
22693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22696 \begin_layout Plain Layout
22697 \begin_inset Formula $\maltese$
22707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22710 \begin_layout Plain Layout
22718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22721 \begin_layout Plain Layout
22722 \begin_inset Formula $\diagup$
22732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22735 \begin_layout Plain Layout
22743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22746 \begin_layout Plain Layout
22747 \begin_inset Formula $\diagdown$
22763 \begin_layout Standard
22764 \begin_inset VSpace medskip
22770 \begin_layout Standard
22771 Some symbols can be displayed in different sizes, see
22772 \begin_inset CommandInset ref
22774 reference "subsec:Font-Sizes"
22781 \begin_layout Subsection
22783 \begin_inset Index idx
22786 \begin_layout Plain Layout
22787 Symbols ! Euro-symbol
22793 \begin_inset Index idx
22796 \begin_layout Plain Layout
22803 \begin_layout Plain Layout
22820 \begin_layout Standard
22821 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22827 \begin_inset Index idx
22830 \begin_layout Plain Layout
22836 must be installed and loaded with the \SpecialChar LaTeX
22840 \begin_layout Standard
22845 usepackage[gennarrow]{eurosym}
22848 \begin_layout Standard
22849 The Euro symbol can now be inserted with the command
22856 \begin_inset Index idx
22859 \begin_layout Plain Layout
22870 \begin_layout Standard
22871 The Euro symbol can directly be inserted with the € key in mathematical
22872 text, without having
22887 can also be inserted in \SpecialChar TeX
22889 The official currency symbol can then be inserted with the command
22896 \begin_inset Index idx
22899 \begin_layout Plain Layout
22907 , that is only available in \SpecialChar TeX
22911 \begin_layout Standard
22915 \begin_layout Plain Layout
22925 \begin_inset Note Note
22928 \begin_layout Plain Layout
22929 The following table will only be displayed when the \SpecialChar LaTeX
22942 \begin_layout Standard
22943 An overview about the different Euro symbols:
22946 \begin_layout Standard
22948 \begin_inset Tabular
22949 <lyxtabular version="3" rows="4" columns="3">
22950 <features booktabs="true" tabularvalignment="middle">
22951 <column alignment="center" valignment="top" width="0pt">
22952 <column alignment="center" valignment="top" width="0pt">
22953 <column alignment="center" valignment="top" width="0pt">
22955 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22958 \begin_layout Plain Layout
22962 \begin_layout Plain Layout
22966 cmidrule[0.08em]{2-3}
22976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23020 \begin_inset Formula $\euro$
23030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23042 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\mbox{€}$
23062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23075 \begin_layout Plain Layout
23083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23086 \begin_layout Plain Layout
23090 \begin_layout Plain Layout
23110 \begin_inset Note Note
23113 \begin_layout Plain Layout
23120 is used here only for table borders.
23130 manual for details.
23138 \begin_layout Standard
23142 \begin_layout Plain Layout
23152 \begin_inset Note Note
23155 \begin_layout Plain Layout
23156 The following will be displayed when the \SpecialChar LaTeX
23169 \begin_layout Standard
23170 You need to install the \SpecialChar LaTeX
23175 to see the rest of this subsection in the output.
23178 \begin_layout Standard
23182 \begin_layout Plain Layout
23194 \begin_layout Section
23196 \begin_inset CommandInset label
23198 name "sec:Relations"
23203 \begin_inset Index idx
23206 \begin_layout Plain Layout
23213 \begin_inset Index idx
23216 \begin_layout Plain Layout
23221 \begin_layout Plain Layout
23232 \begin_layout Plain Layout
23247 \begin_layout Standard
23248 All following relations can also be inserted via the toolbar button
23251 arg "math-insert \\leq"
23257 \begin_layout Standard
23258 \begin_inset Tabular
23259 <lyxtabular version="3" rows="17" columns="2">
23260 <features booktabs="true" tabularvalignment="middle">
23261 <column alignment="center" valignment="top" width="0pt">
23262 <column alignment="center" valignment="top" width="0pt">
23264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23267 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23287 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23297 \begin_inset Formula $<$
23307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23310 \begin_layout Plain Layout
23318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23321 \begin_layout Plain Layout
23322 \begin_inset Formula $\le$
23332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23335 \begin_layout Plain Layout
23343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23346 \begin_layout Plain Layout
23347 \begin_inset Formula $\ll$
23357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23360 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23371 \begin_layout Plain Layout
23372 \begin_inset Formula $\prec$
23382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23385 \begin_layout Plain Layout
23393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23396 \begin_layout Plain Layout
23397 \begin_inset Formula $\preceq$
23407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23410 \begin_layout Plain Layout
23418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23421 \begin_layout Plain Layout
23422 \begin_inset Formula $\subset$
23432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23435 \begin_layout Plain Layout
23443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23446 \begin_layout Plain Layout
23447 \begin_inset Formula $\subseteq$
23457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23460 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $\sqsubseteq$
23482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\in$
23507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\vdash$
23532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\smile$
23557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\lhd$
23582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\unlhd$
23607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23610 \begin_layout Plain Layout
23618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23621 \begin_layout Plain Layout
23622 \begin_inset Formula $\gtrless$
23632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23635 \begin_layout Plain Layout
23643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23646 \begin_layout Plain Layout
23647 \begin_inset Formula $\mid$
23657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23660 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23671 \begin_layout Plain Layout
23672 \begin_inset Formula $\nmid$
23686 \begin_inset space \hfill{}
23690 \begin_inset Tabular
23691 <lyxtabular version="3" rows="17" columns="2">
23692 <features booktabs="true" tabularvalignment="middle">
23693 <column alignment="center" valignment="top" width="0pt">
23694 <column alignment="center" valignment="top" width="0pt">
23696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23699 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23729 \begin_inset Formula $=$
23739 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23753 \begin_layout Plain Layout
23754 \begin_inset Formula $\not=$
23764 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23767 \begin_layout Plain Layout
23775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23778 \begin_layout Plain Layout
23779 \begin_inset Formula $\equiv$
23789 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23792 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23803 \begin_layout Plain Layout
23804 \begin_inset Formula $\sim$
23814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23817 \begin_layout Plain Layout
23825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23828 \begin_layout Plain Layout
23829 \begin_inset Formula $\simeq$
23839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23842 \begin_layout Plain Layout
23850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23853 \begin_layout Plain Layout
23854 \begin_inset Formula $\approx$
23864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23867 \begin_layout Plain Layout
23875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23878 \begin_layout Plain Layout
23879 \begin_inset Formula $\cong$
23889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $\bowtie$
23914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\notin$
23939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\perp$
23964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\propto$
23989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
24000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24003 \begin_layout Plain Layout
24004 \begin_inset Formula $\asymp$
24014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\doteq$
24039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $\circeq$
24064 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24067 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24079 \begin_inset Formula $\models$
24089 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24092 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24103 \begin_layout Plain Layout
24104 \begin_inset Formula $\widehat{=}$
24118 \begin_inset space \hfill{}
24122 \begin_inset Tabular
24123 <lyxtabular version="3" rows="17" columns="2">
24124 <features booktabs="true" tabularvalignment="middle">
24125 <column alignment="center" valignment="top" width="0pt">
24126 <column alignment="center" valignment="top" width="0pt">
24128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24131 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24160 \begin_layout Plain Layout
24161 \begin_inset Formula $>$
24171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24174 \begin_layout Plain Layout
24182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24185 \begin_layout Plain Layout
24186 \begin_inset Formula $\ge$
24196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24199 \begin_layout Plain Layout
24207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24210 \begin_layout Plain Layout
24211 \begin_inset Formula $\gg$
24221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24224 \begin_layout Plain Layout
24232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24235 \begin_layout Plain Layout
24236 \begin_inset Formula $\succ$
24246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24249 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24260 \begin_layout Plain Layout
24261 \begin_inset Formula $\succeq$
24271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24274 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24285 \begin_layout Plain Layout
24286 \begin_inset Formula $\supset$
24296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24299 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24310 \begin_layout Plain Layout
24311 \begin_inset Formula $\supseteq$
24321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24324 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24335 \begin_layout Plain Layout
24336 \begin_inset Formula $\sqsupseteq$
24346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24360 \begin_layout Plain Layout
24361 \begin_inset Formula $\ni$
24371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24385 \begin_layout Plain Layout
24386 \begin_inset Formula $\dashv$
24396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Plain Layout
24411 \begin_inset Formula $\frown$
24421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24424 \begin_layout Plain Layout
24432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24435 \begin_layout Plain Layout
24436 \begin_inset Formula $\rhd$
24446 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24461 \begin_inset Formula $\unrhd$
24471 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24485 \begin_layout Plain Layout
24486 \begin_inset Formula $\lessgtr$
24496 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24499 \begin_layout Plain Layout
24507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24510 \begin_layout Plain Layout
24511 \begin_inset Formula $\parallel$
24521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24524 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24535 \begin_layout Plain Layout
24536 \begin_inset Formula $\nparallel$
24552 \begin_layout Standard
24553 \begin_inset VSpace medskip
24568 are bigger than the equal looking operators
24583 \begin_layout Standard
24585 supports also many special relations.
24586 Use the toolbar button
24589 arg "math-insert \\leqq"
24592 to see a list of these relations.
24595 \begin_layout Standard
24596 Relations are, in contrary to symbols, always surrounded by space.
24599 \begin_layout Standard
24600 Relations with labels can be created with the command
24607 \begin_inset Index idx
24610 \begin_layout Plain Layout
24621 \begin_layout Standard
24623 \begin_inset Tabular
24624 <lyxtabular version="3" rows="2" columns="2">
24625 <features booktabs="true" tabularvalignment="middle">
24626 <column alignment="center" valignment="top" width="0pt">
24627 <column alignment="center" valignment="top">
24629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24632 \begin_layout Plain Layout
24638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24641 \begin_layout Plain Layout
24648 <row topspace="1.5mm">
24649 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24652 \begin_layout Plain Layout
24656 \begin_inset space \textvisiblespace{}
24664 \begin_inset space \textvisiblespace{}
24668 \begin_inset Formula $\downarrow$
24674 \begin_inset space \textvisiblespace{}
24678 \begin_inset space \textvisiblespace{}
24686 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24689 \begin_layout Plain Layout
24690 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24706 \begin_layout Section
24710 \begin_layout Subsection
24711 Predefined Functions
24712 \begin_inset CommandInset label
24714 name "subsec:Predefined-Functions"
24719 \begin_inset Index idx
24722 \begin_layout Plain Layout
24723 Functions ! predefined
24731 \begin_layout Standard
24732 In general, variables are set
24736 in mathematical expressions, but not function names, because
24737 \begin_inset Formula $sin$
24740 could be misunderstood as
24741 \begin_inset Formula $s\cdot i\cdot n$
24745 Therefore there are predefined functions which are additionally a bit separated
24747 They are inserted as commands starting with a backslash before their name.
24750 \begin_layout Standard
24752 \begin_inset Tabular
24753 <lyxtabular version="3" rows="2" columns="2">
24754 <features booktabs="true" tabularvalignment="middle">
24755 <column alignment="center" valignment="top" width="0pt">
24756 <column alignment="center" valignment="top" width="0pt">
24758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24761 \begin_layout Plain Layout
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24770 \begin_layout Plain Layout
24778 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24781 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24791 \begin_inset Formula $Asin(x)+B$
24805 \begin_inset space \quad{}
24809 \begin_inset Tabular
24810 <lyxtabular version="3" rows="2" columns="2">
24811 <features booktabs="true" tabularvalignment="middle">
24812 <column alignment="center" valignment="top" width="0pt">
24813 <column alignment="center" valignment="top" width="0pt">
24815 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24818 \begin_layout Plain Layout
24824 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24827 \begin_layout Plain Layout
24835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24838 \begin_layout Plain Layout
24846 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24849 \begin_layout Plain Layout
24850 \begin_inset Formula $A\sin(x)+B$
24866 \begin_layout Standard
24867 The following functions are predefined:
24870 \begin_layout Standard
24871 \begin_inset VSpace -2mm
24877 \begin_layout Standard
24879 \begin_inset Tabular
24880 <lyxtabular version="3" rows="9" columns="4">
24881 <features booktabs="true" tabularvalignment="middle">
24882 <column alignment="center" valignment="top" width="0pt">
24883 <column alignment="center" valignment="top" width="0pt">
24884 <column alignment="center" valignment="top" width="0pt">
24885 <column alignment="center" valignment="top" width="0pt">
24887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24890 \begin_layout Plain Layout
24896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24899 \begin_layout Plain Layout
24905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24908 \begin_layout Plain Layout
24914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24917 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24928 \begin_layout Plain Layout
24936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24939 \begin_layout Plain Layout
24947 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24950 \begin_layout Plain Layout
24958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24961 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24985 \begin_layout Plain Layout
24993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24996 \begin_layout Plain Layout
25004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25007 \begin_layout Plain Layout
25017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25020 \begin_layout Plain Layout
25028 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25031 \begin_layout Plain Layout
25039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25042 \begin_layout Plain Layout
25050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25053 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25074 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25077 \begin_layout Plain Layout
25085 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25088 \begin_layout Plain Layout
25096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25099 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25112 \begin_layout Plain Layout
25120 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25123 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25134 \begin_layout Plain Layout
25142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25145 \begin_layout Plain Layout
25155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25180 \begin_layout Plain Layout
25188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25191 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25226 \begin_layout Plain Layout
25234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25237 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25283 \begin_layout Plain Layout
25299 \begin_layout Standard
25300 They can also be inserted with the math toolbar button
25303 arg "math-insert \\functions"
25309 \begin_layout Subsection
25310 Self-defined Functions
25311 \begin_inset Index idx
25314 \begin_layout Plain Layout
25315 Functions ! self-defined
25323 \begin_layout Standard
25324 To use a function that is not predefined, like for example the sign function
25325 sgn(x), there are two possibilities:
25328 \begin_layout Itemize
25329 Define the function by inserting the following line to the \SpecialChar LaTeX
25334 \begin_layout Plain Layout
25339 DeclareMathOperator
25342 \begin_inset CommandInset ref
25344 reference "subsec:Self-defined-Operators"
25354 \begin_inset Newline newline
25358 \begin_inset VSpace -3mm
25362 \begin_inset Newline newline
25369 DeclareMathOperator{
25374 \begin_inset Index idx
25377 \begin_layout Plain Layout
25382 DeclareMathOperator
25388 \begin_inset Newline newline
25392 \begin_inset VSpace -2mm
25396 \begin_inset Newline newline
25399 Now the new defined function can be called with the command
25408 \begin_layout Itemize
25409 Write the formula as usual, mark the formula name, in our example the letters
25414 , and change it to mathematical text.
25415 Finally, a space is inserted between prefactor and function.
25418 \begin_layout Standard
25419 The result is the same with both methods as with a predefined function
25423 \begin_layout Plain Layout
25424 In \SpecialChar LyX
25425 self-defined functions are displayed red, predefined ones black.
25433 \begin_layout Standard
25435 \begin_inset Tabular
25436 <lyxtabular version="3" rows="3" columns="2">
25437 <features booktabs="true" tabularvalignment="middle">
25438 <column alignment="center" valignment="top" width="0pt">
25439 <column alignment="center" valignment="top" width="0pt">
25441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25444 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25464 \begin_layout Plain Layout
25472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25475 \begin_layout Plain Layout
25476 \begin_inset Formula $A\sgn(x)+B$
25486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25489 \begin_layout Plain Layout
25493 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25505 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25521 \begin_layout Standard
25522 The first method is more suitable when the self-defined function should
25523 be used several times.
25526 \begin_layout Subsection
25528 \begin_inset Index idx
25531 \begin_layout Plain Layout
25540 \begin_layout Standard
25541 For limits, in addition to the commands
25548 \begin_inset Index idx
25551 \begin_layout Plain Layout
25571 the following functions are defined:
25574 \begin_layout Standard
25576 \begin_inset Tabular
25577 <lyxtabular version="3" rows="5" columns="2">
25578 <features booktabs="true" tabularvalignment="middle">
25579 <column alignment="center" valignment="top" width="0pt">
25580 <column alignment="center" valignment="top" width="0pt">
25582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25585 \begin_layout Plain Layout
25591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25594 \begin_layout Plain Layout
25602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25605 \begin_layout Plain Layout
25613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25616 \begin_layout Plain Layout
25617 \begin_inset Formula $\varliminf$
25626 <row topspace="1.5mm">
25627 <cell alignment="center" valignment="top" usebox="none">
25630 \begin_layout Plain Layout
25638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25641 \begin_layout Plain Layout
25642 \begin_inset Formula $\varlimsup$
25651 <row topspace="1.5mm">
25652 <cell alignment="center" valignment="top" usebox="none">
25655 \begin_layout Plain Layout
25663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25666 \begin_layout Plain Layout
25667 \begin_inset Formula $\varprojlim$
25676 <row topspace="1.5mm" bottomspace="1mm">
25677 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25680 \begin_layout Plain Layout
25688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25691 \begin_layout Plain Layout
25692 \begin_inset Formula $\varinjlim$
25708 \begin_layout Standard
25709 \begin_inset VSpace medskip
25712 The limit is created by inserting a subscript.
25713 It is set right beside the function in an inline formula:
25716 \begin_layout Standard
25718 \begin_inset Tabular
25719 <lyxtabular version="3" rows="2" columns="2">
25720 <features booktabs="true" tabularvalignment="middle">
25721 <column alignment="center" valignment="top" width="0pt">
25722 <column alignment="center" valignment="top" width="0pt">
25724 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25727 \begin_layout Plain Layout
25733 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25736 \begin_layout Plain Layout
25744 <cell alignment="center" valignment="top" usebox="none">
25747 \begin_layout Plain Layout
25753 \begin_inset space \textvisiblespace{}
25757 \begin_inset space \textvisiblespace{}
25765 <cell alignment="center" valignment="top" usebox="none">
25768 \begin_layout Plain Layout
25769 \begin_inset Formula $\lim_{x\to A}x=B$
25785 \begin_layout Standard
25786 In a displayed formula the limit is set below the formula, as usual:
25787 \begin_inset Formula
25797 \begin_layout Standard
25798 \begin_inset VSpace medskip
25804 \begin_layout Standard
25805 How to adjust the typesetting of the limits see
25806 \begin_inset CommandInset ref
25808 reference "subsec:Operator-Limits"
25815 \begin_layout Subsection
25817 \begin_inset Index idx
25820 \begin_layout Plain Layout
25821 Functions ! modulo-
25829 \begin_layout Standard
25830 The modulo-function is special, because it exists in four variants.
25831 The variants in a displayed formula are:
25832 \begin_inset Formula
25834 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25835 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25836 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25837 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25838 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25846 \begin_layout Standard
25847 In an inline formula less space is set before the function names for all
25849 By default the modulo-functions take only the first following character
25851 To use more than one character, one has to put them into \SpecialChar TeX
25853 \begin_inset Formula
25855 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25856 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25857 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25865 \begin_layout Section
25867 \begin_inset Index idx
25870 \begin_layout Plain Layout
25879 \begin_layout Standard
25880 The characters ^ and _ would normally create a superscript and subscript,
25882 To get these characters you have to insert them with a leading
25887 \begin_layout Standard
25890 \begin_inset Tabular
25891 <lyxtabular version="3" rows="3" columns="2">
25892 <features booktabs="true" tabularvalignment="middle">
25893 <column alignment="left" valignment="top" width="0pt">
25894 <column alignment="block" valignment="top">
25896 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25899 \begin_layout Plain Layout
25905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25908 \begin_layout Plain Layout
25916 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25919 \begin_layout Plain Layout
25923 \begin_inset space \textvisiblespace{}
25931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25934 \begin_layout Plain Layout
25935 \begin_inset Formula $\mathcircumflex$
25945 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25948 \begin_layout Plain Layout
25956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25959 \begin_layout Plain Layout
25960 \begin_inset Formula $\_$
25976 \begin_layout Subsection
25977 Special Characters in Mathematical Text
25980 \begin_layout Standard
25981 The following commands can only be used in mathematical text or in \SpecialChar TeX
25985 \begin_layout Standard
25986 \begin_inset space \hfill{}
25990 \begin_inset Tabular
25991 <lyxtabular version="3" rows="8" columns="2">
25992 <features booktabs="true" tabularvalignment="middle">
25993 <column alignment="left" valignment="top" width="0pt">
25994 <column alignment="block" valignment="top">
25996 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25999 \begin_layout Plain Layout
26005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26008 \begin_layout Plain Layout
26016 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26019 \begin_layout Plain Layout
26027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26030 \begin_layout Plain Layout
26031 \begin_inset Formula $\textrm{œ}$
26041 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26044 \begin_layout Plain Layout
26052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26055 \begin_layout Plain Layout
26056 \begin_inset Formula $\textrm{Œ}$
26066 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26080 \begin_layout Plain Layout
26081 \begin_inset Formula $\textrm{æ}$
26091 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26094 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26105 \begin_layout Plain Layout
26106 \begin_inset Formula $\textrm{Æ}$
26116 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26119 \begin_layout Plain Layout
26127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26130 \begin_layout Plain Layout
26131 \begin_inset Formula $\textrm{å}$
26141 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26144 \begin_layout Plain Layout
26152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26155 \begin_layout Plain Layout
26156 \begin_inset Formula $\textrm{Å}$
26166 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26169 \begin_layout Plain Layout
26177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26180 \begin_layout Plain Layout
26181 \begin_inset Formula $\textrm{ı}$
26195 \begin_inset space \hfill{}
26199 \begin_inset Tabular
26200 <lyxtabular version="3" rows="8" columns="2">
26201 <features booktabs="true" tabularvalignment="middle">
26202 <column alignment="left" valignment="top" width="0pt">
26203 <column alignment="center" valignment="top">
26205 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26210 \begin_inset Note Note
26213 \begin_layout Plain Layout
26215 \begin_inset space \thinspace{}
26218 mm is used for separation, because otherwise the output will be ¡ and ¿
26229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26232 \begin_layout Plain Layout
26240 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26254 \begin_layout Plain Layout
26255 \begin_inset Formula $\textrm{ø}$
26265 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26268 \begin_layout Plain Layout
26276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26279 \begin_layout Plain Layout
26280 \begin_inset Formula $\textrm{Ø}$
26290 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26293 \begin_layout Plain Layout
26301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26304 \begin_layout Plain Layout
26305 \begin_inset Formula $\textrm{ł}$
26315 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26318 \begin_layout Plain Layout
26326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26329 \begin_layout Plain Layout
26330 \begin_inset Formula $\textrm{Ł}$
26340 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26343 \begin_layout Plain Layout
26345 \begin_inset space \hspace{}
26350 \begin_inset space \textvisiblespace{}
26358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26361 \begin_layout Plain Layout
26362 \begin_inset Formula $\textrm{!`}$
26372 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26375 \begin_layout Plain Layout
26377 \begin_inset space \hspace{}
26382 \begin_inset space \textvisiblespace{}
26390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26393 \begin_layout Plain Layout
26394 \begin_inset Formula $\textrm{?`}$
26404 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26407 \begin_layout Plain Layout
26415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26418 \begin_layout Plain Layout
26419 \begin_inset Formula $\textrm{ȷ}$
26433 \begin_inset space \hfill{}
26439 \begin_layout Standard
26441 \begin_inset Formula $\textrm{\textrm{Å}}$
26445 \begin_inset Formula $\textrm{\textrm{Ø}}$
26448 can also be inserted via the math toolbar button
26451 arg "math-insert \\digamma"
26457 \begin_layout Standard
26458 An exception are the commands
26461 \begin_inset space \hspace{}
26470 \begin_inset space \hspace{}
26476 , because they can be inserted in \SpecialChar LyX
26480 \begin_layout Subsection
26482 \begin_inset CommandInset label
26484 name "subsec:Accents-in-Text"
26489 \begin_inset Index idx
26492 \begin_layout Plain Layout
26501 \begin_layout Standard
26502 With the following commands all letters can be accented.
26503 The commands must be inserted in \SpecialChar TeX
26507 \begin_layout Standard
26508 \begin_inset space \hfill{}
26512 \begin_inset Tabular
26513 <lyxtabular version="3" rows="8" columns="2">
26514 <features booktabs="true" tabularvalignment="middle">
26515 <column alignment="left" valignment="top" width="0pt">
26516 <column alignment="block" valignment="top">
26518 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26521 \begin_layout Plain Layout
26527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26530 \begin_layout Plain Layout
26538 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26545 \begin_inset Quotes grd
26553 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26556 \begin_layout Plain Layout
26560 \begin_layout Plain Layout
26576 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26579 \begin_layout Plain Layout
26587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26590 \begin_layout Plain Layout
26594 \begin_layout Plain Layout
26610 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26613 \begin_layout Plain Layout
26617 \begin_inset space \textvisiblespace{}
26625 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26628 \begin_layout Plain Layout
26632 \begin_layout Plain Layout
26648 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26651 \begin_layout Plain Layout
26659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26662 \begin_layout Plain Layout
26666 \begin_layout Plain Layout
26682 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26685 \begin_layout Plain Layout
26689 \begin_inset space \textvisiblespace{}
26697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26700 \begin_layout Plain Layout
26704 \begin_layout Plain Layout
26720 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26723 \begin_layout Plain Layout
26727 \begin_inset space \textvisiblespace{}
26735 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26738 \begin_layout Plain Layout
26742 \begin_layout Plain Layout
26758 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26761 \begin_layout Plain Layout
26765 \begin_inset space \textvisiblespace{}
26773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26776 \begin_layout Plain Layout
26780 \begin_layout Plain Layout
26800 \begin_inset space \hfill{}
26804 \begin_inset Tabular
26805 <lyxtabular version="3" rows="8" columns="2">
26806 <features booktabs="true" tabularvalignment="middle">
26807 <column alignment="left" valignment="top" width="0pt">
26808 <column alignment="center" valignment="top">
26810 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26813 \begin_layout Plain Layout
26819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26822 \begin_layout Plain Layout
26830 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26833 \begin_layout Plain Layout
26837 \begin_inset space \textvisiblespace{}
26845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26848 \begin_layout Plain Layout
26852 \begin_layout Plain Layout
26868 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26871 \begin_layout Plain Layout
26879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26882 \begin_layout Plain Layout
26886 \begin_layout Plain Layout
26902 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26905 \begin_layout Plain Layout
26909 \begin_inset Index idx
26912 \begin_layout Plain Layout
26923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26926 \begin_layout Plain Layout
26930 \begin_layout Plain Layout
26946 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26949 \begin_layout Plain Layout
26957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26960 \begin_layout Plain Layout
26964 \begin_layout Plain Layout
26980 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26983 \begin_layout Plain Layout
26987 \begin_inset space \textvisiblespace{}
26995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26998 \begin_layout Plain Layout
27002 \begin_layout Plain Layout
27018 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27021 \begin_layout Plain Layout
27025 \begin_inset space \textvisiblespace{}
27033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27036 \begin_layout Plain Layout
27040 \begin_layout Plain Layout
27056 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27059 \begin_layout Plain Layout
27063 \begin_inset space \textvisiblespace{}
27071 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27074 \begin_layout Plain Layout
27078 \begin_layout Plain Layout
27098 \begin_inset space \hfill{}
27104 \begin_layout Standard
27105 \begin_inset VSpace medskip
27114 also two different characters can be accented.
27120 \begin_inset space \textvisiblespace{}
27129 \begin_layout Plain Layout
27141 \begin_layout Standard
27154 can in combination with vowels directly be inserted with the keyboard without
27155 using \SpecialChar TeX
27157 The same applies for the tilde
27161 \begin_layout Plain Layout
27162 This only applies for keyboards where the tilde is defined as accent.
27171 in combination with
27186 \begin_layout Standard
27229 and accents that are inserted directly with the keyboard are also available
27230 in mathematical text.
27231 For the other accents there are special math commands to be used in formulas,
27233 \begin_inset CommandInset ref
27235 reference "subsec:Accents-for-one"
27242 \begin_layout Standard
27243 \begin_inset VSpace bigskip
27246 Furthermore, with the command
27253 \begin_inset Index idx
27256 \begin_layout Plain Layout
27264 all numbers and letters can be set into a circle, quasi accented with a
27265 circle, similar to the copyright symbol.
27268 \begin_layout Standard
27270 \begin_inset Tabular
27271 <lyxtabular version="3" rows="3" columns="2">
27272 <features booktabs="true" tabularvalignment="middle">
27273 <column alignment="center" valignment="top" width="0pt">
27274 <column alignment="center" valignment="top">
27276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27279 \begin_layout Plain Layout
27285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27288 \begin_layout Plain Layout
27296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27299 \begin_layout Plain Layout
27307 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27310 \begin_layout Plain Layout
27314 \begin_layout Plain Layout
27329 <row topspace="1mm">
27330 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27333 \begin_layout Plain Layout
27344 raisebox{-1.5pt}{W}}
27349 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27352 \begin_layout Plain Layout
27356 \begin_layout Plain Layout
27386 \begin_layout Standard
27387 One has to take care that the character fits in the circle.
27398 \begin_layout Plain Layout
27400 \begin_inset CommandInset ref
27402 reference "subsec:Font-Sizes"
27411 specifies thereby the size of the circle.
27422 \begin_layout Plain Layout
27424 \begin_inset CommandInset ref
27426 reference "subsec:Boxes-without-Frame"
27435 the character can be centered.
27438 \begin_layout Subsection
27440 \begin_inset Index idx
27443 \begin_layout Plain Layout
27452 \begin_layout Standard
27453 Old-style figures (also known as old-style numerals) are created with the
27461 \begin_inset Index idx
27464 \begin_layout Plain Layout
27473 The command can be used in formulas and in \SpecialChar TeX
27475 The command scheme is:
27478 \begin_layout Standard
27483 oldstylenums{number}
27486 \begin_layout Standard
27491 oldstylenums{0123456789
27494 \begin_inset Formula $\oldstylenums{0123456789}$
27500 \begin_layout Section
27502 \begin_inset CommandInset label
27504 name "sec:Formula-Styles"
27509 \begin_inset Index idx
27512 \begin_layout Plain Layout
27521 \begin_layout Itemize
27522 There are two different alignment styles:
27526 \begin_layout Description
27527 Centered is the predefined standard.
27530 \begin_layout Description
27531 Indented this can be set using the menu
27533 Document\SpecialChar menuseparator
27539 \begin_inset space ~
27545 \begin_layout Standard
27550 is used, the indentation can be adjusted.
27551 The default value depends on the used document class.
27555 \begin_layout Itemize
27556 And two different numbering styles that can be set in the menu
27558 Document\SpecialChar menuseparator
27564 \begin_inset space ~
27573 \begin_layout Description
27574 Right is in most cases the default.
27577 \begin_layout Description
27582 \begin_layout Standard
27583 The chosen styles are used for all displayed formulas of the document.
27584 When both, centered and indented formulas should be created in a document,
27590 The indented formulas are then set in a flalign environment, see
27591 \begin_inset CommandInset ref
27593 reference "subsec:Flalign-Environment"
27600 \begin_layout Section
27602 \begin_inset CommandInset label
27604 name "sec:Multiline-Formulas"
27609 \begin_inset Index idx
27612 \begin_layout Plain Layout
27613 Formula ! multiline
27621 \begin_layout Subsection
27625 \begin_layout Standard
27626 In \SpecialChar LyX
27627 multiline formulas are created by pressing
27630 arg "newline-insert newline"
27634 This creates either an
27638 that is described in
27639 \begin_inset CommandInset ref
27641 reference "subsec:Standard-align-Environment"
27645 or, when automatically loading the package
27649 is disabled in the document settings, an
27651 eqnarray environment
27653 that is described in
27654 \begin_inset CommandInset ref
27656 reference "subsec:Eqnarray-Environment"
27661 The align environment is recommended because it provides in any case a
27662 typographically correct output.
27665 \begin_layout Standard
27666 There are other multiline formula environments that can be created via the
27669 Insert\SpecialChar menuseparator
27673 These environments are described in the following sections.
27676 \begin_layout Standard
27677 In all multiline formula environments a new line is created by pressing
27681 arg "newline-insert newline"
27685 To add or delete lines, the math toolbar buttons
27688 arg "tabular-feature append-row"
27694 arg "tabular-feature delete-row"
27697 , respectively, or the menu
27699 Edit\SpecialChar menuseparator
27705 \begin_layout Subsubsection
27707 \begin_inset CommandInset label
27709 name "subsec:Line-Separation"
27714 \begin_inset Index idx
27717 \begin_layout Plain Layout
27718 Formula ! multiline ! Line separation
27726 \begin_layout Standard
27727 There is sometimes not enough space in multiline formulas between the lines:
27728 \begin_inset Formula
27730 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}\\
27731 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
27739 \begin_layout Standard
27740 In \SpecialChar LaTeX
27741 additional line space is specified as optional argument of the new line
27743 This is not yet possible in \SpecialChar LyX
27748 \begin_layout Plain Layout
27750 \begin_inset CommandInset href
27752 name "LyX-bug #1505"
27753 target "https://www.lyx.org/trac/ticket/1505"
27763 , therefore the whole formula must be inserted in \SpecialChar TeX
27765 To add in our example space, the command
27773 is inserted at the end of the first line.
27778 \begin_layout Plain Layout
27785 \begin_layout Plain Layout
27787 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27790 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27797 \begin_layout Plain Layout
27801 left(B^{2}+x_{0}^{2}
27809 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27814 \begin_layout Plain Layout
27826 \begin_layout Standard
27827 \begin_inset VSpace bigskip
27830 To set the line separation for all lines in a formula, the length
27837 \begin_inset Index idx
27840 \begin_layout Plain Layout
27850 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27861 \begin_inset space \thinspace{}
27866 \begin_inset space \thinspace{}
27869 mm additional line separation as in the previous example, the command
27872 \begin_layout Standard
27882 \begin_layout Standard
27883 is inserted in \SpecialChar TeX
27884 mode before the formula.
27885 This requires that the \SpecialChar LaTeX
27894 \begin_layout Plain Layout
27899 is part of every \SpecialChar LaTeX
27900 standard installation.
27906 \begin_inset Index idx
27909 \begin_layout Plain Layout
27915 was loaded in \SpecialChar LaTeX
27916 -preamble with the line
27919 \begin_layout Standard
27927 \begin_layout Standard
27932 \begin_layout Plain Layout
27944 \begin_inset Formula
27946 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}\\
27947 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
27955 \begin_layout Standard
27959 \begin_layout Plain Layout
27970 To get back to the predefined distance,
27976 is set to the value 3
27977 \begin_inset space \thinspace{}
27983 \begin_layout Subsubsection
27985 \begin_inset CommandInset label
27987 name "subsec:Column-Separation"
27992 \begin_inset Index idx
27995 \begin_layout Plain Layout
27996 Formula ! multiline ! Column separation
28004 \begin_layout Standard
28005 Multiline formulas form a matrix.
28006 A formula in the eqnarray environment is for example a matrix with three
28008 By changing the column separation in this environment, the space beside
28009 the relation sign can be changed.
28012 \begin_layout Standard
28013 The column separation is specified with the length
28020 \begin_inset Index idx
28023 \begin_layout Plain Layout
28032 \begin_inset Newline newline
28035 column separation = 2
28036 \begin_inset space \thinspace{}
28046 \begin_inset Newline newline
28052 \begin_layout Standard
28062 \begin_layout Standard
28063 inserted in \SpecialChar TeX
28064 mode, sets for all following formulas a column separation of
28066 \begin_inset space \thinspace{}
28070 To get back to the predefined distance,
28077 \begin_inset space \thinspace{}
28083 \begin_layout Standard
28085 \begin_inset space \thinspace{}
28088 cm column separation:
28092 \begin_layout Plain Layout
28104 \begin_inset Formula
28112 A formula with the predefined column separation for matrices of 10
28113 \begin_inset space \thinspace{}
28120 \begin_layout Plain Layout
28132 \begin_inset Formula
28143 \begin_layout Standard
28144 \begin_inset Newpage newpage
28150 \begin_layout Subsubsection
28152 \begin_inset Index idx
28155 \begin_layout Plain Layout
28164 \begin_layout Standard
28165 Long formulas can be typeset using these methods:
28168 \begin_layout Itemize
28169 When one side of the equation is much shorter than the line width, this
28170 one is chosen for the left side and the right side is typeset over two
28172 \begin_inset Formula
28174 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 \\
28175 & & -\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}
28180 The minus sign at the beginning of the second line does normally not appear
28181 as an operator because it is the first character of the line.
28182 Thus it would not be surrounded by space and could not be distinguished
28183 from the fraction bar.
28185 \begin_inset space \thinspace{}
28188 pt space was inserted behind the minus sign with the command
28198 \begin_layout Plain Layout
28206 \begin_inset CommandInset ref
28208 reference "subsec:Variable-Space"
28218 \begin_inset Index idx
28221 \begin_layout Plain Layout
28232 \begin_layout Itemize
28233 When both sides of the equation are too long, the command
28240 \begin_inset Index idx
28243 \begin_layout Plain Layout
28252 It is inserted in the first column of the first line and causes all further
28253 insertions to overwrite the following columns:
28254 \begin_inset Formula
28256 \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 \\
28257 & & -\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 \\
28258 & & =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}
28263 After the insertion of
28269 , the cursor is in a purple box that is a bit shifted to the left from the
28271 In this the formula is inserted.
28272 \begin_inset Newline newline
28275 The content of the further lines is inserted to the second or another formula
28277 The greater the column number where it was inserted, the larger the indentation.
28278 \begin_inset VSpace medskip
28282 \begin_inset Newline newline
28286 \begin_inset Note Greyedout
28289 \begin_layout Plain Layout
28290 Note the following when using
28299 \begin_layout Itemize
28300 The formula doesn't use the full page width.
28302 \begin_inset space \thinspace{}
28306 \begin_inset space \space{}
28310 \begin_inset Formula $-B^{2}$
28313 is added to the first line in the above example, it would have been outside
28315 To better use the width, negative space can be inserted at the beginning
28319 \begin_layout Itemize
28320 Due to a bug in \SpecialChar LyX
28321 the cursor cannot be set with the mouse into the first
28326 \begin_layout Plain Layout
28327 \begin_inset CommandInset href
28329 name "LyX-bug #1429"
28330 target "https://www.lyx.org/trac/ticket/1429"
28340 One can only set the cursor at the beginning of the line and move it with
28349 \begin_layout Itemize
28350 Other methods to set long formulas are offered by the environments described
28352 \begin_inset CommandInset ref
28354 reference "subsec:Multline-Environment"
28359 \begin_inset CommandInset ref
28361 reference "subsec:Multiline-Formula-Parts"
28368 \begin_layout Subsubsection
28369 Multiline Fractions
28370 \begin_inset CommandInset label
28372 name "subsec:Multiline-Fractions"
28377 \begin_inset Index idx
28380 \begin_layout Plain Layout
28381 Fractions ! multiline
28389 \begin_layout Standard
28390 There are cases where the denominator and/or the numerator of a fraction
28391 is so long that the fraction does not fit into one line.
28392 It is then necessary to add a line break within the fraction.
28393 This can be done using the command
28400 \begin_inset Index idx
28403 \begin_layout Plain Layout
28412 To activate it, set in the document settings under
28415 \begin_inset space ~
28425 \begin_inset Index idx
28428 \begin_layout Plain Layout
28429 Packages ! mathtools
28437 \begin_inset space ~
28452 \begin_layout Standard
28457 splitfrac{first line}{second line}
28460 \begin_layout Standard
28461 and is used as denominator and/or numerator:
28464 \begin_layout Standard
28465 \begin_inset Formula
28467 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}
28472 The command for the first numerator above is:
28475 \begin_layout Standard
28480 splitfrac{xy+xy+xy+xy+xy
28481 \begin_inset space \textvisiblespace{}
28489 \begin_layout Subsubsection
28491 \begin_inset CommandInset label
28493 name "subsec:Multiline-Brackets"
28498 \begin_inset Index idx
28501 \begin_layout Plain Layout
28502 Brackets ! for multiline expressions
28510 \begin_layout Standard
28511 For brackets spanning multiple lines the following problem occurs:
28512 \begin_inset Formula
28514 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28515 & & \left.\cdots+B-D\right]
28523 \begin_layout Standard
28524 The closing bracket is smaller than the opening bracket because brackets
28525 with variable size may not span multiple lines.
28528 \begin_layout Standard
28529 To set the bracket size for the second line correctly, the first line is
28537 \begin_inset Index idx
28540 \begin_layout Plain Layout
28548 and the second line with
28556 \begin_layout Plain Layout
28570 \begin_inset CommandInset ref
28572 reference "subsec:Automatic-Bracket-Size"
28584 \begin_inset Index idx
28587 \begin_layout Plain Layout
28610 \begin_inset space \textvisiblespace{}
28620 \begin_inset space \textvisiblespace{}
28630 \begin_inset space \textvisiblespace{}
28636 \begin_inset Formula $\downarrow$
28642 \begin_inset Index idx
28645 \begin_layout Plain Layout
28653 is inserted, because the multiplication operator with its limits is the
28654 largest symbol in the first line and this should be the size for the bracket
28655 in the second line.
28658 \begin_layout Standard
28659 The result is this:
28660 \begin_inset Formula
28662 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28663 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28671 \begin_layout Subsection
28675 \begin_layout Standard
28676 Align environments can be used for every kind of multiline formulas.
28677 They are especially useful to set several formulas side by side.
28680 \begin_layout Standard
28681 Align environments consist of columns.
28682 The odd columns are right aligned, the even ones left aligned.
28683 Every line in an Align environment can be numbered.
28686 \begin_layout Standard
28687 Align environments are created via the menu
28689 Insert\SpecialChar menuseparator
28695 Edit\SpecialChar menuseparator
28696 Math\SpecialChar menuseparator
28697 Change Formula Type
28699 already existing formulas can be converted to Align environments.
28702 \begin_layout Standard
28703 To add or delete columns, the math toolbar buttons
28706 arg "tabular-feature append-column"
28712 arg "tabular-feature delete-column"
28715 , respectively, or the menu
28717 Edit\SpecialChar menuseparator
28723 \begin_layout Subsubsection
28724 Standard align Environment
28725 \begin_inset CommandInset label
28727 name "subsec:Standard-align-Environment"
28732 \begin_inset Index idx
28735 \begin_layout Plain Layout
28736 Formula ! multiline ! align environment
28744 \begin_layout Standard
28745 This Align environment is created by pressing
28748 arg "newline-insert newline"
28751 in a formula or by the menu
28753 Insert\SpecialChar menuseparator
28754 Math\SpecialChar menuseparator
28755 AMS align Environment
28760 \begin_layout Standard
28761 An example for two formulas set side by side, that are created with a four
28762 column align environment:
28763 \begin_inset Formula
28765 A & =\sin(B) & C & =D\\
28766 C & \ne A & B & \ne D
28771 As it can be seen, the formulas in this environment are placed so as if
28780 \begin_layout Plain Layout
28788 \begin_inset CommandInset ref
28790 reference "subsec:Variable-Space"
28801 before the first and after every even column.
28802 When the formula style
28808 \begin_layout Plain Layout
28810 \begin_inset CommandInset ref
28812 reference "sec:Formula-Styles"
28823 is used, the formula is set without the
28829 before the first column.
28832 \begin_layout Subsubsection
28833 Alignat Environment
28834 \begin_inset Index idx
28837 \begin_layout Plain Layout
28838 Formula ! multiline ! alignat environment
28846 \begin_layout Standard
28847 The alignat environment has no predefined column separation.
28848 It can be inserted manually with the spaces that are described
28849 \begin_inset CommandInset ref
28851 reference "subsec:Space"
28858 \begin_layout Standard
28859 The above example in the alignat environment where 1
28860 \begin_inset space \thinspace{}
28863 cm space was inserted at the beginning of the second formula:
28864 \begin_inset Formula
28865 \begin{alignat*}{2}
28866 A & =\sin(B) & \hspace{1cm}C & =D\\
28867 C & \ne A & B & \ne D
28872 Because the column separation can be set separately for every column, this
28873 environment is especially suitable to set three and more formulas side
28877 \begin_layout Subsubsection
28878 Flalign Environment
28879 \begin_inset CommandInset label
28881 name "subsec:Flalign-Environment"
28886 \begin_inset Index idx
28889 \begin_layout Plain Layout
28890 Formula ! multiline ! flalign environment
28898 \begin_layout Standard
28899 In this environment the first two columns are always set as much as possible
28900 to the left and the last two ones to the right.
28902 \begin_inset Formula
28904 A & =1 & B & =2 & C & =3\\
28905 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28913 \begin_layout Standard
28914 By creating a flalign environment with an odd number of columns where an
28915 empty \SpecialChar TeX
28916 brace is inserted to the last column, several formulas in a document
28917 can be set to the left, although the formula style
28922 As example the indented formula
28923 \begin_inset CommandInset ref
28925 reference "eq:VolInt"
28930 \begin_inset Formula
28932 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28937 The first two columns contain the formula.
28938 To indent it as with the formula style
28943 \begin_inset space \thinspace{}
28946 pt space was inserted at the beginning of the first column.
28949 \begin_layout Subsection
28950 Eqnarray Environment
28951 \begin_inset CommandInset label
28953 name "subsec:Eqnarray-Environment"
28958 \begin_inset Index idx
28961 \begin_layout Plain Layout
28962 Formula ! multiline ! eqnarray environment
28970 \begin_layout Standard
28971 When this environment has been created, three blue boxes appear.
28972 The content of the first box is right aligned, the content of the last
28974 The content of the middle box appears centered and a bit smaller, because
28975 it is designed to insert there only relation characters.
28976 \begin_inset Formula
28978 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28988 \begin_layout Subsection
28990 \begin_inset Index idx
28993 \begin_layout Plain Layout
28994 Formula ! multiline ! gather environment
29002 \begin_layout Standard
29003 This environment consists of only one centered column.
29004 Every line can be numbered.
29005 \begin_inset Formula
29016 \begin_layout Subsection
29017 Multline Environment
29018 \begin_inset CommandInset label
29020 name "subsec:Multline-Environment"
29025 \begin_inset Index idx
29028 \begin_layout Plain Layout
29029 Formula ! multiline ! multline environment
29037 \begin_layout Standard
29038 The multline environment consists, like the gather environment, of only
29040 But the first line is left aligned, the last one right aligned.
29041 All other lines are centered.
29042 Therefore this environment is suitable for long formulas.
29044 \begin_inset CommandInset ref
29046 reference "eq:lefteqn"
29050 in the multline environment:
29051 \begin_inset Formula
29053 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}\\
29054 -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}\\
29055 =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}}
29063 \begin_layout Standard
29064 In the output only the last (first) line of a multline environment appears
29065 numbered when the document numbering is right (left).
29069 \begin_layout Plain Layout
29070 numbering styles see
29071 \begin_inset CommandInset ref
29073 reference "sec:Formula-Styles"
29085 \begin_layout Standard
29093 \begin_inset Index idx
29096 \begin_layout Plain Layout
29111 \begin_inset Index idx
29114 \begin_layout Plain Layout
29122 a centered line can be right or left aligned, respectively.
29123 The commands are used as follows:
29126 \begin_layout Standard
29131 shoveright{line content}
29137 shoveleft{line content}
29140 \begin_layout Standard
29141 \begin_inset VSpace medskip
29151 \begin_inset Index idx
29154 \begin_layout Plain Layout
29162 specifies the distance of the first line from the left page margin.
29163 Predefined is the length 0
29164 \begin_inset space \thinspace{}
29170 \begin_layout Standard
29171 As example the above formula where the command
29174 \begin_layout Standard
29184 \begin_layout Standard
29185 was inserted in \SpecialChar TeX
29190 \begin_layout Plain Layout
29202 \begin_inset Formula
29204 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}\\
29205 \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}}\\
29206 =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}}
29215 \begin_layout Plain Layout
29226 The second line was left aligned using
29235 \begin_layout Subsection
29236 Multiline Formula Parts
29237 \begin_inset CommandInset label
29239 name "subsec:Multiline-Formula-Parts"
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29248 Formula ! multiline ! formula parts
29256 \begin_layout Standard
29257 To display only parts of a formula with multiple lines, one of the following
29258 environments is used:
29275 They can be inserted via the menu
29277 Insert\SpecialChar menuseparator
29280 or by using the commands described in this section.
29283 \begin_layout Standard
29284 The first three have the same properties as the corresponding multiline
29285 formula environments, but it is possible to set further formula parts beside
29288 \begin_inset Formula
29290 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29291 \Delta E\Delta t & \ge\frac{\hbar}{2}
29293 \right\} \textrm{Uncertainty relations}
29301 \begin_layout Standard
29302 To get this formula, a displayed formula is created where the command
29309 \begin_inset Index idx
29312 \begin_layout Plain Layout
29321 A purple box appears around the blue formula box where now columns and
29322 lines can be added.
29323 Outside the multiline environment other formula parts can be set, like
29327 \begin_layout Standard
29328 The aligned environment is also suitable for long formulas whose lines are
29329 horizontally aligned.
29330 Using aligned in a displayed formula has the advantage that the formula
29331 number is vertically centered behind the lines.
29333 \begin_inset CommandInset ref
29335 reference "eq:shortlong"
29339 in the aligned environment:
29340 \begin_inset Formula
29342 \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}|}\\
29343 & -\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}|}
29352 \begin_layout Standard
29353 To use the environments
29372 \begin_inset Index idx
29375 \begin_layout Plain Layout
29390 \begin_inset Index idx
29393 \begin_layout Plain Layout
29408 \begin_inset Index idx
29411 \begin_layout Plain Layout
29419 are inserted, respectively.
29420 The split environment has the same properties as the aligned environment
29421 but it can only have two columns.
29424 \begin_layout Subsection
29425 Text in multiline Formulas
29426 \begin_inset CommandInset label
29428 name "subsec:Text-in-multiline"
29433 \begin_inset Index idx
29436 \begin_layout Plain Layout
29443 \begin_inset Index idx
29446 \begin_layout Plain Layout
29447 Formula ! multiline ! text
29455 \begin_layout Standard
29456 In the Align environments, and the multline and gather environment, text
29457 can be inserted that will appear in a separate line and doesn't affect
29458 the column alignment.
29459 To do this, the command
29466 \begin_inset Index idx
29469 \begin_layout Plain Layout
29477 is used in the following scheme:
29480 \begin_layout Standard
29488 \begin_layout Standard
29489 The text should not be longer than a line because it cannot be hyphenated.
29490 As \SpecialChar LyX
29491 doesn't yet support
29497 directly, the text is written as mathematical text.
29504 must hereby be at the beginning of a line and appears in the output above
29506 An example where the text was inserted at the beginning of the second line:
29507 \begin_inset Formula
29509 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29510 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29518 \begin_layout Standard
29525 always creates some vertical space between the text and the formula lines.
29526 To avoid this space, set in the document settings under
29529 \begin_inset space ~
29539 \begin_inset Index idx
29542 \begin_layout Plain Layout
29543 Packages ! mathtools
29551 \begin_inset space ~
29557 Then you can use the command
29564 \begin_inset Index idx
29567 \begin_layout Plain Layout
29584 \begin_layout Standard
29585 \begin_inset Formula
29587 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29588 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29596 \begin_layout Section
29598 \begin_inset Index idx
29601 \begin_layout Plain Layout
29608 \begin_inset Index idx
29611 \begin_layout Plain Layout
29612 Formula ! numbering|see
29616 \begin_layout Plain Layout
29627 \begin_layout Plain Layout
29642 \begin_layout Subsection
29646 \begin_layout Standard
29647 Numbered formulas can be created with the menu
29649 Insert\SpecialChar menuseparator
29650 Math\SpecialChar menuseparator
29652 \begin_inset space ~
29660 \begin_inset space ~
29666 Existing formulas can be numbered with the menu
29668 Edit\SpecialChar menuseparator
29669 Math\SpecialChar menuseparator
29671 \begin_inset space ~
29679 arg "math-number-toggle"
29683 The formula number is displayed in \SpecialChar LyX
29684 behind the formula as a number sign
29686 The number sign is replaced in the output by the formula number.
29689 \begin_layout Standard
29690 When numbering is turned on in multiline formulas, all lines will be numbered.
29691 But the numbering can be controlled with the menu
29693 Edit\SpecialChar menuseparator
29694 Math\SpecialChar menuseparator
29696 \begin_inset space ~
29700 \begin_inset space ~
29704 \begin_inset space ~
29712 arg "math-number-line-toggle"
29718 \begin_layout Standard
29719 Except for inline formulas, all formulas can be numbered with two different
29721 \begin_inset CommandInset ref
29723 reference "sec:Formula-Styles"
29730 \begin_layout Subsection
29732 \begin_inset Index idx
29735 \begin_layout Plain Layout
29736 Cross-references ! to formulas
29744 \begin_layout Standard
29745 All labeled formulas can be cross-referenced.
29746 A label is added by the menu
29748 Insert\SpecialChar menuseparator
29751 or the toolbar button
29758 The cursor must hereby be inside a displayed formula.
29759 Alternatively you can right-click on the formula and choose
29764 A dialog pops up displaying the prefix
29769 The label is inserted there behind the prefix.
29770 The predefined prefix means
29771 \begin_inset Quotes eld
29775 \begin_inset Quotes erd
29778 and makes it easier to find labels in large documents because it marks
29779 it as formula label to divide it from e.
29780 \begin_inset space \thinspace{}
29784 \begin_inset space \space{}
29788 To change a label, the menu
29790 Insert\SpecialChar menuseparator
29793 is used again or you right-click on a formula and then on
29800 \begin_layout Standard
29801 The name of the label is displayed in \SpecialChar LyX
29802 within two parentheses behind formula.
29803 A formula with a label is always numbered.
29806 \begin_layout Standard
29807 Cross-references are inserted via the menu
29809 Insert\SpecialChar menuseparator
29812 or with the toolbar button
29815 arg "dialog-show-new-inset ref"
29819 A formula cross-reference appears in the output as formula number.
29820 When in the cross-reference dialog window the format
29824 is chosen, the cross-reference appears in the output as formula number
29826 \begin_inset Newline newline
29829 By right-clicking on a cross-reference in \SpecialChar LyX
29830 , one jumps to the formula that
29834 \begin_layout Standard
29835 Here are as examples cross-references to formulas of the following subsections:
29836 \begin_inset Note Note
29839 \begin_layout Plain Layout
29840 Note the different cross-reference types.
29848 \begin_layout Standard
29850 \begin_inset CommandInset ref
29857 \begin_inset CommandInset ref
29865 \begin_inset CommandInset ref
29871 ) big Latin letters are used for the numbering in contrary to (
29872 \begin_inset CommandInset ref
29881 \begin_layout Standard
29882 \begin_inset VSpace medskip
29885 When the argument of
29893 \begin_layout Plain Layout
29901 \begin_inset CommandInset ref
29903 reference "subsec:User-defined-Numbering"
29914 contains a box like in
29915 \begin_inset CommandInset ref
29917 reference "subsec:Paragraph-Boxes"
29921 , the formula cannot be referenced.
29924 \begin_layout Subsection
29926 \begin_inset Index idx
29929 \begin_layout Plain Layout
29930 Formula numbering ! subnumbering
29938 \begin_layout Standard
29939 Formulas can be numbered as subequations.
29940 To activate this feature, add the module
29944 to the document in the menu
29946 Document\SpecialChar menuseparator
29947 Settings\SpecialChar menuseparator
29951 To insert subequations use the menu
29953 Insert\SpecialChar menuseparator
29954 Custom Insets\SpecialChar menuseparator
29960 \begin_layout Standard
29961 The equations to be subnumbered are put into the
29967 \begin_inset Formula
29975 \begin_inset VSpace -5mm
29979 \begin_inset Flex Subequations
29982 \begin_layout Plain Layout
29983 \begin_inset Formula
29991 \begin_inset Formula
30006 \begin_layout Standard
30007 Every formula in the
30011 inset will be subnumbered with a, b, c, \SpecialChar ldots
30013 For multiline formulas every line will be subnumbered.
30016 \begin_layout Standard
30017 Referencing subequations work like for normal equations:
30018 \begin_inset CommandInset ref
30025 \begin_inset CommandInset ref
30032 If you want to reference the subequations collectively, insert a label
30033 as first thing in the
30039 \begin_inset CommandInset ref
30041 reference "eq:Here-is-an"
30051 \begin_layout Standard
30052 By inserting subequations vertical space is added before it.
30053 To remove this, insert -5
30054 \begin_inset space \thinspace{}
30057 mm vertical space right before the
30062 If the formula style
30068 \begin_layout Plain Layout
30070 \begin_inset CommandInset ref
30072 reference "sec:Formula-Styles"
30084 \begin_inset space \thinspace{}
30090 \begin_layout Standard
30091 To get another subnumber instead of small Latin letters, insert this command
30092 as \SpecialChar TeX
30093 code before the equations in the
30100 \begin_layout Standard
30109 theparentequation -
30114 \begin_layout Standard
30121 creates hereby the parent number and
30127 adds a small Roman number as subnumber.
30128 For more information about the customization of the numbering, see
30129 \begin_inset CommandInset ref
30131 reference "subsec:Numbering-with-Roman"
30138 \begin_layout Standard
30139 Here is an example for a multiline formula where the numbering is customized
30140 and turned off for the second line:
30141 \begin_inset Flex Subequations
30144 \begin_layout Plain Layout
30145 \begin_inset CommandInset label
30147 name "eq:Here-is-an"
30155 \begin_layout Plain Layout
30163 theparentequation -
30171 \begin_inset Formula
30173 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30174 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30175 & = & B^{2}-2BZ+Z^{2}
30188 \begin_layout Subsection
30189 Numbering with Roman Numbers and Letters
30190 \begin_inset CommandInset label
30192 name "subsec:Numbering-with-Roman"
30197 \begin_inset Index idx
30200 \begin_layout Plain Layout
30201 Formula numbering ! with letters
30207 \begin_inset Index idx
30210 \begin_layout Plain Layout
30211 Formula numbering ! with Roman numbers
30219 \begin_layout Standard
30220 Formulas can also be numbered with Roman numbers and Latin letters.
30221 To number for example with small Roman numbers, the command
30224 \begin_layout Standard
30236 \begin_layout Standard
30237 is inserted before the formula in \SpecialChar TeX
30246 \begin_inset Index idx
30249 \begin_layout Plain Layout
30257 redefines the predefined command
30273 \begin_layout Plain Layout
30280 has the same scheme like the command
30286 that is described in
30287 \begin_inset CommandInset ref
30289 reference "subsec:The-Command-newcommand"
30302 is the formula counter.
30309 is used as prefix for a counter, the value of the counter is output as
30311 When a formula is numbered, \SpecialChar LaTeX
30312 sets internally the command
30318 behind the formula.
30324 \begin_inset Index idx
30327 \begin_layout Plain Layout
30337 outputs the counter as small Roman number.
30340 \begin_layout Standard
30341 All formulas behind the command
30351 are now numbered Roman.
30352 To switch to numbering with big Roman numbers, the command is inserted
30366 \begin_inset Index idx
30369 \begin_layout Plain Layout
30381 \begin_inset Quotes eld
30385 \begin_inset Quotes erd
30388 with small Latin letters there is the command
30395 \begin_inset Index idx
30398 \begin_layout Plain Layout
30406 , for big ones there is the command
30413 \begin_inset Index idx
30416 \begin_layout Plain Layout
30429 \begin_layout Standard
30430 \begin_inset Note Greyedout
30433 \begin_layout Plain Layout
30439 \begin_inset space ~
30442 formulas can be numbered with Latin letters in one document.
30450 \begin_layout Standard
30454 \begin_layout Plain Layout
30470 \begin_layout Standard
30471 \begin_inset Formula
30473 A=\textrm{small roman}
30482 \begin_layout Plain Layout
30496 \begin_inset Formula
30498 B=\textrm{big Roman}\label{eq:Rom}
30507 \begin_layout Plain Layout
30521 \begin_inset Formula
30523 C=\textrm{small Latin}
30532 \begin_layout Plain Layout
30546 \begin_inset Formula
30548 D=\textrm{big Latin}\label{eq:Lat}
30556 \begin_layout Standard
30557 To switch back to the default numbering, insert the command:
30560 \begin_layout Standard
30570 \begin_inset Index idx
30573 \begin_layout Plain Layout
30584 \begin_layout Standard
30588 \begin_layout Plain Layout
30602 \begin_inset Formula
30612 \begin_layout Standard
30613 \begin_inset VSpace medskip
30616 As you see, formulas are numbered serially independent from the numbering
30618 When then numbering should start with
30619 \begin_inset Quotes eld
30623 \begin_inset Quotes erd
30626 when the style is changed, new equation counters have to be defined.
30627 A description about this can be found in the file
30628 \begin_inset CommandInset href
30630 name "Formula-numbering.lyx"
30631 target "run:Formula-numbering.lyx"
30639 \begin_layout Subsection
30640 User-defined Numbering
30641 \begin_inset CommandInset label
30643 name "subsec:User-defined-Numbering"
30648 \begin_inset Index idx
30651 \begin_layout Plain Layout
30652 Formula numbering ! user-defined
30660 \begin_layout Standard
30661 \begin_inset Note Greyedout
30664 \begin_layout Plain Layout
30669 If the document language is a right-to-left language such as Arabic, you
30670 must add this to the to the \SpecialChar LaTeX
30671 -preamble to be able to use the commands described
30673 \begin_inset Newline newline
30681 \begin_inset Newline newline
30685 \begin_inset Phantom HPhantom
30688 \begin_layout Plain Layout
30691 \begin_inset space ~
30717 \begin_layout Standard
30718 \begin_inset Index idx
30721 \begin_layout Plain Layout
30722 Formula numbering ! self-defined delimiters
30727 With the standard numbering parentheses are set around the formula number.
30728 To replace the parentheses for example by vertical bars, the following
30729 line is added to the \SpecialChar LaTeX
30733 \begin_layout Standard
30739 \begin_inset Newline newline
30743 \begin_inset Phantom HPhantom
30746 \begin_layout Plain Layout
30749 \begin_inset space ~
30763 maketag@@@{|#1|}} }
30766 \begin_inset Note Note
30769 \begin_layout Plain Layout
30770 This macro is already declared in the \SpecialChar LaTeX
30771 -preamble for testing.
30772 To activate it, remove the percent signs at the beginning.
30780 \begin_layout Standard
30781 To use other characters, the vertical bars besides the
30785 are replaced by one ore more characters.
30786 To get only the formula number the vertical bars are omitted.
30789 \begin_layout Standard
30790 \begin_inset VSpace bigskip
30793 When there should be an expression of your choice instead of the consecutive
30794 formula number in parentheses behind the formula, the command
30801 \begin_inset Index idx
30804 \begin_layout Plain Layout
30813 \begin_inset Formula
30815 A+B=C\tag{something}\label{eq:tag}
30820 In this example the command
30825 \begin_inset space \textvisiblespace{}
30830 was inserted in the formula.
30833 \begin_layout Standard
30839 \begin_inset space \textvisiblespace{}
30844 is inserted instead, the star prevents the parentheses around the expression:
30845 \begin_inset Formula
30847 A+B=C\tag*{something}
30855 \begin_layout Standard
30856 \begin_inset VSpace bigskip
30859 To restart the formula numbering with new document parts or sections, the
30860 following command is used:
30863 \begin_layout Standard
30868 @addtoreset{equation}{part}
30871 \begin_inset Index idx
30874 \begin_layout Plain Layout
30879 \begin_layout Plain Layout
30890 \begin_layout Plain Layout
30903 \begin_layout Plain Layout
30914 \begin_layout Plain Layout
30927 \begin_inset Newline newline
30931 \begin_inset Newline newline
30938 @addtoreset{equation}{section}
30941 \begin_layout Standard
30942 To be able to use these commands in \SpecialChar TeX
30944 \begin_inset Quotes eld
30948 \begin_inset Quotes erd
30951 character has to be made
30952 \begin_inset Quotes eld
30956 \begin_inset Quotes erd
30959 for \SpecialChar LaTeX
30974 So the command sequence in \SpecialChar TeX
30978 \begin_layout Standard
30984 \begin_inset Newline newline
30989 @addtoreset{equation}{section}
30990 \begin_inset Newline newline
30998 \begin_layout Standard
30999 In the \SpecialChar LaTeX
31012 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31016 \begin_layout Standard
31031 \begin_layout Plain Layout
31036 is part of the \SpecialChar LaTeX
31042 \begin_inset Index idx
31045 \begin_layout Plain Layout
31046 Packages ! carlisle
31051 that is part of every \SpecialChar LaTeX
31052 standard installation.
31058 \begin_inset Index idx
31061 \begin_layout Plain Layout
31062 Packages ! remreset
31067 has to be loaded in the \SpecialChar LaTeX
31068 -preamble with the line
31071 \begin_layout Standard
31076 usepackage{remreset}
31079 \begin_layout Standard
31087 \begin_inset Index idx
31090 \begin_layout Plain Layout
31095 \begin_layout Plain Layout
31106 \begin_layout Plain Layout
31119 \begin_layout Plain Layout
31130 \begin_layout Plain Layout
31142 can be used with the same scheme as
31151 \begin_layout Standard
31152 \begin_inset VSpace bigskip
31155 Sometimes formulas should be numbered in the following form:
31158 \begin_layout Standard
31161 (section number.formula number)
31164 \begin_layout Standard
31165 The formula number should start with every section with
31166 \begin_inset Quotes eld
31170 \begin_inset Quotes erd
31176 \begin_layout Standard
31177 For this case there is the command
31184 \begin_inset Index idx
31187 \begin_layout Plain Layout
31195 , which is used with the following scheme:
31198 \begin_layout Standard
31203 numberwithin{counter}{sectioning}
31206 \begin_layout Standard
31207 Counter denotes what kind of numbering is affected, sectioning denotes what
31208 number is before the dot.
31211 \begin_layout Standard
31212 Thus in our case the following \SpecialChar LaTeX
31213 preamble or \SpecialChar TeX
31217 \begin_layout Standard
31222 numberwithin{equation}{section}
31225 \begin_layout Standard
31226 This is the result:
31230 \begin_layout Plain Layout
31234 numberwithin{equation}{section}
31240 \begin_inset Formula
31250 \begin_layout Standard
31252 \begin_inset space \thinspace{}
31256 \begin_inset space \space{}
31259 tables so that the number of the part is the sectioning,
31260 \begin_inset Newline newline
31267 numberwithin{table}{part}
31272 \begin_layout Standard
31273 To go back to the standard numbering or to prevent this kind of numbering
31274 when it is defined by the document class, the following command is inserted
31275 as \SpecialChar TeX
31276 code or to the \SpecialChar LaTeX
31280 \begin_layout Standard
31290 \begin_inset Index idx
31293 \begin_layout Plain Layout
31307 \begin_layout Plain Layout
31323 \begin_inset Newline newline
31331 \begin_inset Newline newline
31343 \begin_layout Standard
31350 uses internally the command
31356 , described above, that also needs to be reverted.
31360 \begin_layout Plain Layout
31367 \begin_layout Plain Layout
31371 @removefromreset{equation}{section}
31374 \begin_layout Plain Layout
31386 \begin_layout Section
31387 Chemical Symbols and Equations
31388 \begin_inset CommandInset label
31390 name "subsec:Chemical-Symbols-and"
31395 \begin_inset Index idx
31398 \begin_layout Plain Layout
31399 Chemical characters ! Symbols
31405 \begin_inset Index idx
31408 \begin_layout Plain Layout
31415 \begin_inset Index idx
31418 \begin_layout Plain Layout
31427 \begin_layout Standard
31428 An example text from chemistry:
31431 \begin_layout Quote
31433 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31436 -ion reacts with two
31437 \begin_inset Formula $\mathrm{Na^{+}}$
31440 -ions to sodium sulfate
31441 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31445 The chemical equation for this is:
31446 \begin_inset Formula
31448 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31456 \begin_layout Standard
31457 This chemical equation can directly be created as formula.
31458 To avoid that the symbols appear italic, everything is highlighted and
31459 changed by the shortcut
31465 to the upright font style.
31469 \begin_layout Plain Layout
31475 \begin_inset CommandInset ref
31477 reference "subsec:Font-Styles"
31489 \begin_layout Standard
31490 A more convenient way to typeset chemical formulas is to use the command
31498 \begin_inset Index idx
31501 \begin_layout Plain Layout
31509 that is available when the \SpecialChar LaTeX
31515 \begin_inset Index idx
31518 \begin_layout Plain Layout
31531 to a formula a new blue box appears where chemical formulas can be inserted
31532 in an intuitive way.
31535 \begin_layout Standard
31537 \begin_inset Tabular
31538 <lyxtabular version="3" rows="10" columns="2">
31539 <features booktabs="true" tabularvalignment="middle">
31540 <column alignment="center" valignment="top" width="0pt">
31541 <column alignment="center" valignment="top">
31543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31546 \begin_layout Plain Layout
31552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31555 \begin_layout Plain Layout
31563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31566 \begin_layout Plain Layout
31570 \begin_inset space \textvisiblespace{}
31578 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31581 \begin_layout Plain Layout
31582 \begin_inset Formula $\ce{H2CO3}$
31591 <row topspace="1.5mm">
31592 <cell alignment="center" valignment="top" usebox="none">
31595 \begin_layout Plain Layout
31599 \begin_inset space \textvisiblespace{}
31607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31610 \begin_layout Plain Layout
31611 \begin_inset Formula $\ce{SO4^{2-}}$
31620 <row topspace="1.5mm">
31621 <cell alignment="center" valignment="top" usebox="none">
31624 \begin_layout Plain Layout
31628 \begin_inset space \textvisiblespace{}
31636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31639 \begin_layout Plain Layout
31640 \begin_inset Formula $\ce{(NH4)2S}$
31649 <row topspace="1.5mm">
31650 <cell alignment="center" valignment="top" usebox="none">
31653 \begin_layout Plain Layout
31657 \begin_inset space \textvisiblespace{}
31665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31678 <row topspace="1.5mm">
31679 <cell alignment="center" valignment="top" usebox="none">
31682 \begin_layout Plain Layout
31686 \begin_inset space \textvisiblespace{}
31692 \begin_inset space \textvisiblespace{}
31698 \begin_inset space \textvisiblespace{}
31706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31709 \begin_layout Plain Layout
31710 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31719 <row topspace="1.5mm">
31720 <cell alignment="center" valignment="top" usebox="none">
31723 \begin_layout Plain Layout
31727 \begin_inset space \textvisiblespace{}
31731 \begin_inset Formula $\downarrow$
31735 \begin_inset Formula $\to$
31743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31746 \begin_layout Plain Layout
31747 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31760 \begin_layout Plain Layout
31764 \begin_inset space \textvisiblespace{}
31770 \begin_inset space \textvisiblespace{}
31776 \begin_inset space \textvisiblespace{}
31784 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31787 \begin_layout Plain Layout
31788 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31801 \begin_layout Plain Layout
31805 \begin_inset space \textvisiblespace{}
31809 \begin_inset space \textvisiblespace{}
31813 \begin_inset space \textvisiblespace{}
31817 \begin_inset space \textvisiblespace{}
31821 \begin_inset space \textvisiblespace{}
31829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31832 \begin_layout Plain Layout
31833 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31842 <row topspace="1.5mm">
31843 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31846 \begin_layout Plain Layout
31850 \begin_inset space \textvisiblespace{}
31854 \begin_inset space \textvisiblespace{}
31858 \begin_inset space \textvisiblespace{}
31862 \begin_inset space \textvisiblespace{}
31870 \begin_inset space \textvisiblespace{}
31878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31881 \begin_layout Plain Layout
31882 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31898 \begin_layout Standard
31899 \begin_inset Note Greyedout
31902 \begin_layout Plain Layout
31907 It is not possible in \SpecialChar LyX
31908 to use the character ^ to get an up-arrow as described
31914 One instead uses a negative thin space followed by the command
31921 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31932 \begin_layout Standard
31939 the command for equation
31940 \begin_inset space ~
31944 \begin_inset CommandInset ref
31946 reference "eq:chem-reaction"
31951 \begin_inset Newline newline
31959 \begin_inset space \textvisiblespace{}
31963 \begin_inset space \textvisiblespace{}
31967 \begin_inset space \textvisiblespace{}
31971 \begin_inset space \textvisiblespace{}
31975 \begin_inset space \textvisiblespace{}
31979 \begin_inset space \textvisiblespace{}
31985 \begin_layout Standard
31986 To create multiline chemical equations first a multiline formula is created
31988 \begin_inset CommandInset ref
31990 reference "sec:Multiline-Formulas"
31995 Afterwards the command
32001 is used in every small blue box of the formula.
32003 \begin_inset CommandInset ref
32005 reference "eq:TEOS-reaction-1"
32010 \begin_inset CommandInset ref
32012 reference "eq:TEOS-reaction-2"
32016 are an example of a multi-stage chemical reaction where every equation
32017 has its own number.
32018 \begin_inset Formula
32020 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32021 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32029 \begin_layout Standard
32040 package provides the command
32047 \begin_inset Index idx
32050 \begin_layout Plain Layout
32058 that has to be used for special cases.
32059 For more information about
32065 and more examples have a look at the documentation of
32070 \begin_inset CommandInset citation
32080 \begin_layout Section
32084 \begin_layout Standard
32086 supports two types of commutative diagrams:
32094 that are explained in the following.
32097 \begin_layout Subsection
32099 \begin_inset Index idx
32102 \begin_layout Plain Layout
32111 \begin_layout Standard
32112 Diagrams of this type visualize relations by vertical and horizontal lines
32114 \begin_inset Formula
32116 \begin{CD}A@>>>B@>>>C\\
32127 \begin_layout Standard
32128 To get them, the command
32133 \begin_inset Index idx
32136 \begin_layout Plain Layout
32146 is inserted to a formula.
32147 A blue box appears with two dashed lines where further commands can be
32152 arg "newline-insert newline"
32155 a new line is created.
32156 Horizontal relations are inserted in odd, vertical in even formula lines.
32159 \begin_layout Standard
32160 To create the relations there are the following commands:
32163 \begin_layout Itemize
32168 creates a left arrow,
32179 \begin_layout Itemize
32184 creates an up arrow,
32192 a vertical equal sign
32195 \begin_layout Itemize
32201 is a placeholder for non-existent relations
32204 \begin_layout Standard
32205 All arrows can be labeled as follows:
32208 \begin_layout Itemize
32209 If text inserted between the first and second < or >, resp., it is placed
32211 When it is inserted between the second and third one, it appears under
32215 \begin_layout Itemize
32216 When text for vertical arrows is inserted between the first and second A
32217 or V, resp., it is placed left beside the arrow.
32218 When it is inserted between the second and third one, it appears right
32220 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32224 \begin_layout Standard
32225 As example a diagram with all possible relations:
32228 \begin_layout Standard
32229 \begin_inset Formula
32231 \begin{CD}A@>j>>B@>>k>C@=F\\
32242 \begin_layout Standard
32243 The command for this is:
32244 \begin_inset Newline newline
32252 \begin_inset space \textvisiblespace{}
32255 A@>j>>B@>>k>C@=F Ctrl+Return
32256 \begin_inset Newline newline
32260 \begin_inset Phantom HPhantom
32263 \begin_layout Plain Layout
32269 \begin_inset space \textvisiblespace{}
32282 \begin_inset Formula $\to$
32288 \begin_inset Newline newline
32292 \begin_inset Phantom HPhantom
32295 \begin_layout Plain Layout
32301 \begin_inset space \textvisiblespace{}
32312 \begin_layout Subsection
32314 \begin_inset Index idx
32317 \begin_layout Plain Layout
32318 Diagrams ! xymatrix
32326 \begin_layout Standard
32327 To be able to use xymatrices, the \SpecialChar LaTeX
32333 A xymatrix is created by inserting the command
32340 Then you are able to add new matrix columns and rows like for normal matrices,
32342 \begin_inset CommandInset ref
32344 reference "sec:Matrices"
32351 \begin_layout Standard
32352 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32354 All possibilities to create commutative diagrams and decorations are explained
32359 that you find in the menu
32361 Help\SpecialChar menuseparator
32363 \begin_inset space ~
32371 \begin_layout Subsection
32377 \begin_inset Index idx
32380 \begin_layout Plain Layout
32389 \begin_layout Standard
32394 -diagrams, the \SpecialChar LaTeX
32404 -diagram is created by inserting the command
32411 Then you are able to add new matrix columns and rows like for normal matrices,
32413 \begin_inset CommandInset ref
32415 reference "sec:Matrices"
32422 \begin_layout Standard
32423 Examples how to create
32427 diagrams in \SpecialChar LyX
32430 Feynman-diagram manual
32432 that you find in the menu
32434 Help\SpecialChar menuseparator
32436 \begin_inset space ~
32444 \begin_layout Section
32445 User-defined Commands
32446 \begin_inset Index idx
32449 \begin_layout Plain Layout
32450 User-defined commands
32458 \begin_layout Standard
32459 \begin_inset Note Greyedout
32462 \begin_layout Plain Layout
32467 The names of user-defined commands and macros may only consist of Latin
32476 \begin_layout Subsection
32480 \begin_inset CommandInset label
32482 name "subsec:The-Command-newcommand"
32487 \begin_inset Index idx
32490 \begin_layout Plain Layout
32491 User-defined commands !
32499 \begin_inset Index idx
32502 \begin_layout Plain Layout
32513 \begin_layout Standard
32514 Many \SpecialChar LaTeX
32515 -commands are too long to be used frequently.
32516 But it is possible to define with the command
32522 new shorter commands.
32525 \begin_layout Standard
32526 The command scheme of
32535 \begin_layout Standard
32540 newcommand{new command name}[number of arguments][optional
32545 \begin_inset Newline newline
32549 \begin_inset Phantom HPhantom
32552 \begin_layout Plain Layout
32562 {command definition}
32565 \begin_layout Standard
32566 \begin_inset Note Greyedout
32569 \begin_layout Plain Layout
32574 Assure that the name of the new command is not already used in your document
32575 or by \SpecialChar LaTeX
32576 -packages that you use.
32577 When you for example define the command
32589 , you get an error message because
32595 is already defined as command for
32596 \begin_inset Quotes eld
32600 \begin_inset Formula $\le$
32604 \begin_inset Quotes erd
32615 \begin_layout Standard
32616 The number of arguments is an integer in the range 0
32617 \begin_inset space \thinspace{}
32621 \begin_inset space \thinspace{}
32624 9 and specifies how many arguments the new command should have.
32625 With the optional value a value for an optional argument can be predefined.
32626 When this is done, the
32634 rgument of the new command is automatically an optional one.
32637 \begin_layout Standard
32638 Here are some examples:
32641 \begin_layout Itemize
32642 To define the command
32654 , the \SpecialChar LaTeX
32656 \begin_inset VSpace medskip
32660 \begin_inset Newline newline
32674 \begin_layout Itemize
32675 To define the command
32687 , the argument (that should be underlined) must be taken into account.
32688 For this the preamble line is:
32689 \begin_inset VSpace medskip
32693 \begin_inset Newline newline
32707 \begin_inset VSpace medskip
32711 \begin_inset Newline newline
32718 acts as argument placeholder, the
32722 behind it denotes that it is the placeholder for the first argument.
32725 \begin_layout Itemize
32733 \begin_inset space \thinspace{}
32737 \begin_inset space \space{}
32747 \begin_inset VSpace medskip
32751 \begin_inset Newline newline
32762 framebox#1#2{$#3$}}
32765 \begin_inset VSpace medskip
32769 \begin_inset Newline newline
32772 The two Dollar signs creates the extra formula needed for
32779 \begin_inset CommandInset ref
32781 reference "subsec:Boxes-with-Frame"
32788 \begin_layout Itemize
32789 To create a new command for
32795 where the color for the box need not be specified, the argument for the
32796 color is defined optional:
32797 \begin_inset VSpace medskip
32801 \begin_inset Newline newline
32812 fcolorbox{#2}{#1}{$#3$}}
32815 \begin_inset VSpace medskip
32819 \begin_inset Newline newline
32822 When the color is not specified when using
32828 , the predefined color
32835 \begin_layout Standard
32836 A test of the new defined commands:
32839 \begin_layout Standard
32841 \begin_inset Tabular
32842 <lyxtabular version="3" rows="6" columns="2">
32843 <features booktabs="true" tabularvalignment="middle">
32844 <column alignment="center" valignment="top" width="0pt">
32845 <column alignment="center" valignment="top">
32847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32850 \begin_layout Plain Layout
32856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32859 \begin_layout Plain Layout
32867 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32870 \begin_layout Plain Layout
32874 \begin_inset space \textvisiblespace{}
32882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32885 \begin_layout Plain Layout
32886 \begin_inset Formula $A\gr B$
32896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32899 \begin_layout Plain Layout
32907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32910 \begin_layout Plain Layout
32911 \begin_inset Formula $\us{ABcd}$
32920 <row topspace="1mm">
32921 <cell alignment="center" valignment="top" usebox="none">
32924 \begin_layout Plain Layout
32928 \begin_inset Formula $\to$
32934 \begin_inset Formula $\to$
32942 \begin_inset space \textvisiblespace{}
32950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32953 \begin_layout Plain Layout
32954 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
32963 <row topspace="1.5mm">
32964 <cell alignment="center" valignment="top" usebox="none">
32967 \begin_layout Plain Layout
32971 \begin_inset Formula $\to$
32979 \begin_inset space \textvisiblespace{}
32987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32990 \begin_layout Plain Layout
32991 \begin_inset Formula $\cb{red}{\int A=B}$
33000 <row topspace="1.5mm" bottomspace="1mm">
33001 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33004 \begin_layout Plain Layout
33010 \begin_inset Formula $\to$
33018 \begin_inset space \textvisiblespace{}
33026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33029 \begin_layout Plain Layout
33030 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33046 \begin_layout Subsection
33048 \begin_inset Index idx
33051 \begin_layout Plain Layout
33052 User-defined commands! Math macros
33058 \begin_inset Index idx
33061 \begin_layout Plain Layout
33070 \begin_layout Standard
33071 User-defined commands are especially convenient for complex expressions.
33072 When you are for example dealing with a document that has quadratic equations,
33073 the same solution type occurs several times.
33074 The general form of a quadratic equation is
33075 \begin_inset Formula
33077 0=\lambda^{2}+p\lambda+q
33082 The general form of the solution is
33083 \begin_inset Formula
33085 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33093 \begin_layout Standard
33094 To define a command for the solution formula where only the three parameters
33096 \begin_inset Formula $\lambda$
33100 \begin_inset Formula $p$
33104 \begin_inset Formula $q$
33107 need to be specified and the index of
33108 \begin_inset Formula $\lambda$
33111 can be given optionally, the \SpecialChar LaTeX
33113 \begin_inset Newline newline
33129 \begin_inset Newline newline
33133 \begin_inset Phantom HPhantom
33136 \begin_layout Plain Layout
33150 frac{#3^{2}}{4}-#4}}
33153 \begin_layout Standard
33154 To create with this the solution formula, the command
33155 \begin_inset Newline newline
33165 \begin_inset Formula $\to$
33171 \begin_inset Formula $\to$
33178 is inserted to a formula
33183 \begin_layout Standard
33184 The definition of the new command is unintuitive because one has to know
33185 the schemes of all used \SpecialChar LaTeX
33187 \begin_inset space \thinspace{}
33191 \begin_inset space \space{}
33194 that a fraction is inserted in \SpecialChar LaTeX
33199 frac{numerator}{denominator}
33202 Furthermore one can easily forget a brace in the definition and cannot
33203 see in \SpecialChar LyX
33204 what the new command is doing.
33205 To avoid these problems \SpecialChar LyX
33206 offers the possibility to use math macros instead
33216 \begin_layout Standard
33217 A math macro is created by using the menu
33219 Insert\SpecialChar menuseparator
33220 Math\SpecialChar menuseparator
33223 or the toolbar button
33226 arg "math-macro newmacroname_newcommand"
33230 The math macro toolbar appears together with the following box where the
33232 \begin_inset Newline newline
33236 \begin_inset space \hspace*{\fill}
33240 \begin_inset Graphics
33241 filename clipart/macrobox.png
33247 \begin_inset space \hspace*{\fill}
33251 \begin_inset Newline newline
33255 \begin_inset FormulaMacro
33256 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33261 newmacroname is the default name of the macro that should be changed to
33262 something sensible.
33263 The wanted formula is inserted in the first blue box.
33264 An argument placeholder is inserted with the command
33271 \begin_inset space \thinspace{}
33275 \begin_inset space \space{}
33284 or by using the macro toolbar button
33287 arg "math-macro-add-param"
33291 Argument placeholders are displayed red.
33293 \begin_inset space ~
33296 arguments are possible.
33297 Optional arguments are created with the toolbar button
33300 arg "math-macro-add-optional-param"
33304 The first non-optional argument can be transformed to an optional one with
33308 arg "math-macro-make-optional"
33312 In the second blue box the appearance of the macro in \SpecialChar LyX
33314 Normally you want to see it as it is defined, so the box is kept empty.
33315 But when you have created a macro that needs lot of space on the screen,
33316 you can insert in the box for example
33317 \begin_inset Newline newline
33347 \begin_inset Newline newline
33352 For the macro only the arguments with the macro name in front of them will
33353 then be displayed in \SpecialChar LyX
33354 , leading to a better overview.
33355 The formula appears in the output as defined in the first box.
33356 \begin_inset Newline newline
33359 The appearance of macros in formulas can furthermore be changed for single
33360 macros by setting the cursor in the macro and using the menu
33362 View\SpecialChar menuseparator
33364 \begin_inset space ~
33368 \begin_inset space ~
33376 \begin_layout Standard
33377 To use a macro, the macro name is inserted as command to a formula, in our
33385 Our macro looks in \SpecialChar LyX
33387 \begin_inset Newline newline
33391 \begin_inset space \hspace*{\fill}
33395 \begin_inset Graphics
33396 filename clipart/macrouse.png
33402 \begin_inset space \hspace*{\fill}
33406 \begin_inset Newline newline
33409 Here is our macro example with the arguments
33410 \begin_inset Formula $x$
33414 \begin_inset Formula $\ln(x)$
33418 \begin_inset Formula $B$
33424 \begin_layout Standard
33425 \begin_inset Formula
33435 \begin_layout Standard
33439 Tools\SpecialChar menuseparator
33440 Preferences\SpecialChar menuseparator
33441 Editing\SpecialChar menuseparator
33444 different styles to edit macros.
33445 To find the style that suits you the most, choose a style and set the cursor
33446 in a macro formula to see the difference.
33449 \begin_layout Standard
33450 A math macro is transformed internally to a
33456 command when exporting the document.
33463 command is not placed in the \SpecialChar LaTeX
33464 -preamble, therefore macros can only be used
33465 in formulas that are in the document below the macro definition box.
33468 \begin_layout Standard
33469 Math macros can also be directly created from a
33476 When writing for example the command
33479 \begin_inset Newline newline
33488 xleftarrow[#2]{#1}}
33489 \begin_inset Newline newline
33494 in \SpecialChar LyX
33495 as normal text, highlighting it completely and using then the shortcut
33500 , the command will be transformed to a math macro.
33501 Using this method you need to be careful that the
33507 command is typed correctly, otherwise you get a faulty macro leading to
33512 \begin_layout Standard
33513 Math macros currently have the problem that further formulas in macro definition
33514 s are handled wrongly.
33515 Therefore the example
33522 \begin_inset CommandInset ref
33524 reference "subsec:The-Command-newcommand"
33528 cannot be created as macro.
33531 \begin_layout Standard
33532 When the cursor is in a macro definition box, you will see the macro toolbar
33533 in \SpecialChar LyX
33537 \begin_layout Standard
33538 \begin_inset VSpace defskip
33544 \begin_layout Standard
33545 \begin_inset Graphics
33546 filename clipart/MacroToolbar.png
33551 \begin_inset Index idx
33554 \begin_layout Plain Layout
33563 \begin_layout Standard
33564 \begin_inset VSpace defskip
33570 \begin_layout Standard
33571 The macro toolbar contains from left to right the following buttons:
33574 \begin_layout Standard
33575 \begin_inset VSpace defskip
33581 \begin_layout Standard
33582 \begin_inset Tabular
33583 <lyxtabular version="3" rows="9" columns="2">
33584 <features islongtable="true" longtabularalignment="center">
33585 <column alignment="left" valignment="top">
33586 <column alignment="left" valignment="top" width="85col%">
33587 <row interlinespace="2.5mm">
33588 <cell alignment="center" valignment="top" usebox="none">
33591 \begin_layout Plain Layout
33594 arg "math-macro-remove-param"
33602 <cell alignment="center" valignment="top" usebox="none">
33605 \begin_layout Plain Layout
33608 Edit\SpecialChar menuseparator
33609 Math\SpecialChar menuseparator
33611 \begin_inset space ~
33614 Definition\SpecialChar menuseparator
33615 Remove Last Argument
33621 <row interlinespace="2.5mm">
33622 <cell alignment="center" valignment="top" usebox="none">
33625 \begin_layout Plain Layout
33628 arg "math-macro-add-param"
33636 <cell alignment="center" valignment="top" usebox="none">
33639 \begin_layout Plain Layout
33642 Edit\SpecialChar menuseparator
33643 Math\SpecialChar menuseparator
33645 \begin_inset space ~
33648 Definition\SpecialChar menuseparator
33655 <row interlinespace="2.5mm">
33656 <cell alignment="center" valignment="top" usebox="none">
33659 \begin_layout Plain Layout
33662 arg "math-macro-make-optional"
33670 <cell alignment="center" valignment="top" usebox="none">
33673 \begin_layout Plain Layout
33676 Edit\SpecialChar menuseparator
33677 Math\SpecialChar menuseparator
33679 \begin_inset space ~
33682 Definition\SpecialChar menuseparator
33683 Transform First Non-Optional to
33684 \begin_inset Newline newline
33688 \begin_inset Phantom HPhantom
33691 \begin_layout Plain Layout
33694 Edit\SpecialChar menuseparator
33695 Math\SpecialChar menuseparator
33697 \begin_inset space ~
33700 Definition\SpecialChar menuseparator
33712 <row interlinespace="2.5mm">
33713 <cell alignment="center" valignment="top" usebox="none">
33716 \begin_layout Plain Layout
33719 arg "math-macro-make-nonoptional"
33727 <cell alignment="center" valignment="top" usebox="none">
33730 \begin_layout Plain Layout
33733 Edit\SpecialChar menuseparator
33734 Math\SpecialChar menuseparator
33736 \begin_inset space ~
33739 Definition\SpecialChar menuseparator
33740 Transform Last Optional to
33741 \begin_inset Newline newline
33745 \begin_inset Phantom HPhantom
33748 \begin_layout Plain Layout
33751 Edit\SpecialChar menuseparator
33752 Math\SpecialChar menuseparator
33754 \begin_inset space ~
33757 Definition\SpecialChar menuseparator
33763 Non-Optional Argument
33769 <row interlinespace="2.5mm">
33770 <cell alignment="center" valignment="top" usebox="none">
33773 \begin_layout Plain Layout
33776 arg "math-macro-remove-optional-param"
33784 <cell alignment="center" valignment="top" usebox="none">
33787 \begin_layout Plain Layout
33790 Edit\SpecialChar menuseparator
33791 Math\SpecialChar menuseparator
33793 \begin_inset space ~
33796 Definition\SpecialChar menuseparator
33797 Remove Optional Argument
33803 <row interlinespace="2.5mm">
33804 <cell alignment="center" valignment="top" usebox="none">
33807 \begin_layout Plain Layout
33810 arg "math-macro-add-optional-param"
33818 <cell alignment="center" valignment="top" usebox="none">
33821 \begin_layout Plain Layout
33824 Edit\SpecialChar menuseparator
33825 Math\SpecialChar menuseparator
33827 \begin_inset space ~
33830 Definition\SpecialChar menuseparator
33831 Insert Optional Argument
33837 <row interlinespace="2.5mm">
33838 <cell alignment="center" valignment="top" usebox="none">
33841 \begin_layout Plain Layout
33844 arg "math-macro-remove-greedy-param"
33852 <cell alignment="center" valignment="top" usebox="none">
33855 \begin_layout Plain Layout
33858 Edit\SpecialChar menuseparator
33859 Math\SpecialChar menuseparator
33861 \begin_inset space ~
33864 Definition\SpecialChar menuseparator
33865 Remove Last Argument
33866 \begin_inset Newline newline
33870 \begin_inset Phantom HPhantom
33873 \begin_layout Plain Layout
33876 Edit\SpecialChar menuseparator
33877 Math\SpecialChar menuseparator
33879 \begin_inset space ~
33882 Definition\SpecialChar menuseparator
33888 Spitting Out To The Right
33894 <row interlinespace="2.5mm">
33895 <cell alignment="center" valignment="top" usebox="none">
33898 \begin_layout Plain Layout
33901 arg "math-macro-append-greedy-param"
33909 <cell alignment="center" valignment="top" usebox="none">
33912 \begin_layout Plain Layout
33915 Edit\SpecialChar menuseparator
33916 Math\SpecialChar menuseparator
33918 \begin_inset space ~
33921 Definition\SpecialChar menuseparator
33923 \begin_inset Newline newline
33927 \begin_inset Phantom HPhantom
33930 \begin_layout Plain Layout
33933 Edit\SpecialChar menuseparator
33934 Math\SpecialChar menuseparator
33936 \begin_inset space ~
33939 Definition\SpecialChar menuseparator
33945 Eating From The Right
33951 <row interlinespace="2.5mm">
33952 <cell alignment="center" valignment="top" usebox="none">
33955 \begin_layout Plain Layout
33958 arg "math-macro-add-greedy-optional-param"
33966 <cell alignment="center" valignment="top" usebox="none">
33969 \begin_layout Plain Layout
33972 Edit\SpecialChar menuseparator
33973 Math\SpecialChar menuseparator
33975 \begin_inset space ~
33978 Definition\SpecialChar menuseparator
33979 Append Optional Argument
33980 \begin_inset Newline newline
33984 \begin_inset Phantom HPhantom
33987 \begin_layout Plain Layout
33990 Edit\SpecialChar menuseparator
33991 Math\SpecialChar menuseparator
33993 \begin_inset space ~
33996 Definition\SpecialChar menuseparator
34002 Eating From The Right
34015 \begin_layout Section
34016 Computer Algebra Systems
34019 \begin_layout Standard
34021 offers the exchange between mathematical expressions written in \SpecialChar LyX
34023 editor and external applications or user defined scripts.
34024 Currently supported applications are
34041 Note that the set of supported mathematical constructs is limited only
34042 to very simple cases.
34045 \begin_layout Subsection
34049 \begin_layout Standard
34050 Write some expression in a formula, go to the
34052 Edit\SpecialChar menuseparator
34053 Math\SpecialChar menuseparator
34054 Use Computer Algebra System
34056 menu and choose the application you have installed on the computer.
34057 After that the result of computation should show on the right side of the
34058 expression together with the
34059 \begin_inset Quotes eld
34063 \begin_inset Quotes erd
34069 \begin_layout Standard
34070 Here are few simple examples (with results from
34074 ) to show what kind of computations can be performed:
34077 \begin_layout Itemize
34078 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34084 \begin_layout Itemize
34085 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34091 \begin_layout Itemize
34092 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34098 \begin_layout Itemize
34099 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34103 \begin_inset Newline newline
34107 \begin_inset Note Greyedout
34110 \begin_layout Plain Layout
34115 One needs to use proper delimiter insets
34116 \begin_inset Formula $\left(\right)$
34119 instead of simple '(' ')' characters.
34127 \begin_layout Itemize
34128 \begin_inset Formula $\det\left[\begin{array}{ccc}
34132 \end{array}\right]=-56$
34138 \begin_layout Itemize
34139 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34145 \begin_layout Itemize
34146 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34152 \begin_layout Itemize
34153 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34159 \begin_layout Subsection
34163 \begin_layout Standard
34164 Currently there is no keyboard shortcut for calling the algebra applications.
34165 One can easily bind a shortcut to the
34179 \begin_inset space \thinspace{}
34183 \begin_inset space \space{}
34190 key inside the math editor.
34195 one would use this shortcut definition command:
34198 \begin_layout Standard
34201 command-alternatives paragraph-break;math-extern maxima
34204 \begin_layout Section
34206 \begin_inset Index idx
34209 \begin_layout Plain Layout
34218 \begin_layout Subsection
34220 \begin_inset Index idx
34223 \begin_layout Plain Layout
34232 \begin_layout Standard
34233 Negative numbers often look ugly in formulas because the minus sign before
34234 the number is set with the same length as the minus operator sign.
34235 When writing the negative number in normal text, the minus sign appears
34239 \begin_layout Standard
34240 Thus, the problem disappears when converting the minus sign to mathematical
34244 \begin_layout Standard
34245 An example to visualize the problem:
34248 \begin_layout Standard
34250 \begin_inset Tabular
34251 <lyxtabular version="3" rows="3" columns="2">
34252 <features booktabs="true" tabularvalignment="middle">
34253 <column alignment="right" valignment="top" width="0pt">
34254 <column alignment="left" valignment="top">
34256 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34259 \begin_layout Plain Layout
34265 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34268 \begin_layout Plain Layout
34276 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34279 \begin_layout Plain Layout
34285 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34288 \begin_layout Plain Layout
34289 \begin_inset Formula $x=-2$
34299 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34302 \begin_layout Plain Layout
34308 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34311 \begin_layout Plain Layout
34312 \begin_inset Formula $x=\textrm{-}2$
34328 \begin_layout Subsection
34329 Comma as decimal Separator
34330 \begin_inset Index idx
34333 \begin_layout Plain Layout
34342 \begin_layout Standard
34343 In \SpecialChar LaTeX
34344 a comma inside a formula is used, according to the English convention,
34345 as number group separator.
34346 So there will be space added behind all commas in formulas.
34349 \begin_layout Standard
34350 To avoid this, the comma is highlighted and changed to mathematical text
34360 \begin_layout Standard
34361 To use all formula commas in the document as decimal separator, the file
34370 \begin_layout Plain Layout
34375 is part of the \SpecialChar LaTeX
34381 \begin_inset Index idx
34384 \begin_layout Plain Layout
34389 \begin_layout Plain Layout
34409 \begin_inset Index idx
34412 \begin_layout Plain Layout
34418 is loaded with the \SpecialChar LaTeX
34422 \begin_layout Standard
34430 \begin_layout Subsection
34432 \begin_inset CommandInset label
34434 name "subsec:Physical-Vectors"
34439 \begin_inset Index idx
34442 \begin_layout Plain Layout
34451 \begin_layout Standard
34452 Predefined vectors are offered by the \SpecialChar LaTeX
34458 \begin_inset Index idx
34461 \begin_layout Plain Layout
34467 that is loaded with the \SpecialChar LaTeX
34471 \begin_layout Standard
34479 \begin_layout Standard
34483 \begin_layout Plain Layout
34493 \begin_inset Note Note
34496 \begin_layout Plain Layout
34497 The following table will only be displayed when the \SpecialChar LaTeX
34510 \begin_layout Standard
34511 The following commands are defined:
34514 \begin_layout Standard
34516 \begin_inset Tabular
34517 <lyxtabular version="3" rows="4" columns="2">
34518 <features booktabs="true" tabularvalignment="middle">
34519 <column alignment="center" valignment="top" width="0pt">
34520 <column alignment="center" valignment="top">
34522 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34525 \begin_layout Plain Layout
34531 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34534 \begin_layout Plain Layout
34542 <cell alignment="center" valignment="top" usebox="none">
34545 \begin_layout Plain Layout
34555 <cell alignment="center" valignment="top" usebox="none">
34558 \begin_layout Plain Layout
34559 \begin_inset Formula $\Bra{\psi}$
34569 <cell alignment="center" valignment="top" usebox="none">
34572 \begin_layout Plain Layout
34582 <cell alignment="center" valignment="top" usebox="none">
34585 \begin_layout Plain Layout
34586 \begin_inset Formula $\Ket{\psi}$
34596 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34599 \begin_layout Plain Layout
34611 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34614 \begin_layout Plain Layout
34615 \begin_inset Formula $\Braket{\psi|\phi}$
34631 \begin_layout Standard
34638 assures that all vertical bars are set in the size of the surrounding brackets:
34639 \begin_inset Formula
34641 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34650 \begin_layout Plain Layout
34660 \begin_inset Note Note
34663 \begin_layout Plain Layout
34664 The following will be displayed when the \SpecialChar LaTeX
34677 \begin_layout Standard
34678 You need to install the \SpecialChar LaTeX
34683 to see the rest of this subsection in the output.
34686 \begin_layout Standard
34690 \begin_layout Plain Layout
34702 \begin_layout Standard
34709 can also be achieved using the command
34715 , that is described in
34716 \begin_inset CommandInset ref
34718 reference "subsec:Automatic-Bracket-Size"
34725 \begin_layout Subsection
34726 Self-defined Fractions
34727 \begin_inset CommandInset label
34729 name "subsec:Self-defined-Fractions"
34734 \begin_inset Index idx
34737 \begin_layout Plain Layout
34738 Fractions ! self-defined
34746 \begin_layout Standard
34747 To define custom commands for fractions, the command
34754 \begin_inset Index idx
34757 \begin_layout Plain Layout
34764 \begin_layout Plain Layout
34778 is used in the following scheme:
34781 \begin_layout Standard
34794 bracket}{fraction bar thickness}{style}
34795 \begin_inset Newline newline
34799 \begin_inset Phantom HPhantom
34802 \begin_layout Plain Layout
34812 {numerator}{denominator}
34815 \begin_layout Standard
34816 The style is a number in the range of 0
34817 \begin_inset space \thinspace{}
34821 \begin_inset space \thinspace{}
34827 \begin_layout Standard
34829 \begin_inset Tabular
34830 <lyxtabular version="3" rows="5" columns="2">
34831 <features booktabs="true" tabularvalignment="middle">
34832 <column alignment="center" valignment="top" width="0pt">
34833 <column alignment="center" valignment="top">
34835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34838 \begin_layout Plain Layout
34844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34847 \begin_layout Plain Layout
34855 <cell alignment="center" valignment="top" usebox="none">
34858 \begin_layout Plain Layout
34864 <cell alignment="center" valignment="top" usebox="none">
34867 \begin_layout Plain Layout
34868 display style formula
34875 <cell alignment="center" valignment="top" usebox="none">
34878 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" usebox="none">
34887 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" usebox="none">
34898 \begin_layout Plain Layout
34904 <cell alignment="center" valignment="top" usebox="none">
34907 \begin_layout Plain Layout
34915 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34918 \begin_layout Plain Layout
34924 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34927 \begin_layout Plain Layout
34941 \begin_layout Standard
34942 When no style is given, the size is adjusted to the surrounding environment
34943 like for the command
34952 \begin_layout Standard
34953 When no fraction bar thickness is given, the predefined value of 0.4
34954 \begin_inset space \thinspace{}
34960 \begin_layout Standard
34961 \begin_inset VSpace medskip
34964 For example, the commands
34977 \begin_inset CommandInset ref
34979 reference "subsec:Fractions"
34983 are defined with the commands
34986 \begin_layout Standard
34995 genfrac{}{}{}{0}{#1}{#2}}
34998 \begin_layout Standard
35002 \begin_layout Standard
35011 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35014 \begin_layout Standard
35015 \begin_inset VSpace medskip
35018 To define a fraction where the fraction bar thickness can be given as optional
35019 argument, the following line is inserted to the \SpecialChar LaTeX
35023 \begin_layout Standard
35032 genfrac{}{}{#1}{}{#2}{#3}}
35035 \begin_layout Standard
35037 \begin_inset Formula
35039 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35040 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35045 As one can see, the distance of the numerator and the denominator to the
35046 fraction bar is round about three times the bar thickness.
35049 \begin_layout Subsection
35051 \begin_inset Index idx
35054 \begin_layout Plain Layout
35063 \begin_layout Standard
35064 There are four ways to cancel formulas or parts of formulas:
35067 \begin_layout Standard
35071 \begin_layout Plain Layout
35081 \begin_inset Note Note
35084 \begin_layout Plain Layout
35085 The following table will only be displayed when the \SpecialChar LaTeX
35098 \begin_layout Standard
35100 \begin_inset Tabular
35101 <lyxtabular version="3" rows="5" columns="2">
35102 <features booktabs="true" tabularvalignment="middle">
35103 <column alignment="center" valignment="top" width="0pt">
35104 <column alignment="center" valignment="top">
35106 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35109 \begin_layout Plain Layout
35115 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35118 \begin_layout Plain Layout
35126 <cell alignment="center" valignment="top" usebox="none">
35129 \begin_layout Plain Layout
35133 \begin_inset space \textvisiblespace{}
35139 \begin_inset space \textvisiblespace{}
35147 <cell alignment="center" valignment="top" usebox="none">
35150 \begin_layout Plain Layout
35151 \begin_inset Formula $\cancel{\int A=B}$
35160 <row topspace="1.5mm">
35161 <cell alignment="center" valignment="top" usebox="none">
35164 \begin_layout Plain Layout
35168 \begin_inset space \textvisiblespace{}
35174 \begin_inset space \textvisiblespace{}
35182 <cell alignment="center" valignment="top" usebox="none">
35185 \begin_layout Plain Layout
35186 \begin_inset Formula $\bcancel{\int A=B}$
35195 <row topspace="1.5mm">
35196 <cell alignment="center" valignment="top" usebox="none">
35199 \begin_layout Plain Layout
35203 \begin_inset space \textvisiblespace{}
35209 \begin_inset space \textvisiblespace{}
35217 <cell alignment="center" valignment="top" usebox="none">
35220 \begin_layout Plain Layout
35221 \begin_inset Formula $\xcancel{\int A=B}$
35231 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35234 \begin_layout Plain Layout
35238 \begin_inset space \textvisiblespace{}
35244 \begin_inset space \textvisiblespace{}
35248 \begin_inset Formula $\to$
35256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35259 \begin_layout Plain Layout
35260 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35276 \begin_layout Standard
35283 is especially suitable to visualize the reduction of fractions within formulas:
35284 \begin_inset Formula
35286 \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}}}
35294 \begin_layout Standard
35295 To change the size of
35302 \begin_inset Quotes eld
35306 \begin_inset Quotes erd
35309 value one can add the \SpecialChar LaTeX
35313 \begin_layout Standard
35318 PassOptionsToPackage{option}{cancel}
35321 \begin_layout Standard
35330 which leads to the same size as for the canceled value, or
35334 which makes is it a bit smaller than normal.
35337 \begin_layout Standard
35338 To color the cancellation bar one adds this command as \SpecialChar TeX
35342 \begin_layout Standard
35354 \begin_layout Standard
35359 can be replaced by a color of your choice.
35362 \begin_layout Standard
35366 \begin_layout Plain Layout
35382 \begin_layout Standard
35383 \begin_inset Formula
35385 \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}}}
35393 \begin_layout Standard
35397 \begin_layout Plain Layout
35411 \begin_inset Note Note
35414 \begin_layout Plain Layout
35423 \begin_layout Standard
35424 For further customizations, see the documentation of the package
35429 \begin_inset CommandInset citation
35437 \begin_inset Index idx
35440 \begin_layout Plain Layout
35449 \begin_layout Standard
35453 \begin_layout Plain Layout
35463 \begin_inset Note Note
35466 \begin_layout Plain Layout
35467 The following will be displayed when the \SpecialChar LaTeX
35480 \begin_layout Standard
35481 You need to install the \SpecialChar LaTeX
35486 to see the rest of this subsection in the output.
35489 \begin_layout Standard
35493 \begin_layout Plain Layout
35505 \begin_layout Subsection
35506 Formulas in Section Headings
35507 \begin_inset CommandInset label
35509 name "subsec:Formulas-in-Section"
35514 \begin_inset Index idx
35517 \begin_layout Plain Layout
35518 Formula ! in section headings
35526 \begin_layout Standard
35527 When formulas are used in section headings, the following has to be taken
35531 \begin_layout Standard
35532 \begin_inset Note Greyedout
35535 \begin_layout Plain Layout
35541 \begin_inset Index idx
35544 \begin_layout Plain Layout
35545 Packages ! hyperref
35550 support is enabled in the document settings dialog under
35553 \begin_inset space ~
35558 , PDF-bookmarks are created for every section heading in the table of contents.
35559 If a section heading contains formulas, they are incorrectly displayed
35560 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35569 \begin_layout Standard
35570 Both problems can be solved by inserting at the end of the section heading
35571 a short title with the menu
35573 Insert\SpecialChar menuseparator
35575 \begin_inset space ~
35581 Short titles are used as alternative for multiline section headings to
35582 keep the table of contents clearly arranged.
35583 Only the short title appears in the table of contents and therefore also
35584 in the PDF-bookmark.
35587 \begin_layout Standard
35588 When formulas should be used in the table of contents but
35592 is used, one can use the following command in \SpecialChar TeX
35596 \begin_layout Standard
35601 texorpdfstring{part}{alternative}
35602 \begin_inset Index idx
35605 \begin_layout Plain Layout
35616 \begin_layout Standard
35617 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35618 This can be characters, formulas, footnotes, but also cross-references.
35619 The alternative is used instead of the part for the bookmark.
35622 \begin_layout Standard
35623 Here are two example headings:
35624 \begin_inset VSpace -3mm
35631 \begin_layout Plain Layout
35643 \begin_layout Subsubsection
35644 Heading without formula in table of contents
35645 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35649 \begin_inset Argument 1
35652 \begin_layout Plain Layout
35653 Heading without formula in table of contents
35661 \begin_layout Subsubsection
35662 Heading with formula in table of contents
35666 \begin_layout Plain Layout
35676 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35683 \begin_layout Plain Layout
35693 \begin_layout Standard
35697 \begin_layout Plain Layout
35706 In the first heading a short title was used, in the second one
35715 \begin_layout Standard
35716 To get the same formatting as for the other headings, the complete heading
35725 \begin_layout Plain Layout
35727 \begin_inset CommandInset ref
35729 reference "subsec:Bold-Formulas"
35741 \begin_layout Subsection
35742 Formulas in multi-column Text
35743 \begin_inset Index idx
35746 \begin_layout Plain Layout
35747 Formula ! in multi-column text
35755 \begin_layout Standard
35756 Formulas in multi-column text are often too wide to fit into a column and
35757 thus need to be set over the whole page width.
35758 This is done by using the \SpecialChar LaTeX
35767 \begin_layout Plain Layout
35772 is part of every \SpecialChar LaTeX
35773 standard installation.
35779 \begin_inset Index idx
35782 \begin_layout Plain Layout
35783 Packages ! multicol
35788 , that is loaded with the \SpecialChar LaTeX
35792 \begin_layout Standard
35797 usepackage{multicol}
35800 \begin_layout Standard
35801 \begin_inset Note Greyedout
35804 \begin_layout Plain Layout
35805 Note that in this case the setting
35808 \begin_inset space ~
35815 Document\SpecialChar menuseparator
35821 \begin_inset space ~
35841 \begin_layout Standard
35842 Before the multi-column text the command
35845 \begin_layout Standard
35850 begin{multicols}{column number}
35853 \begin_layout Standard
35854 is written in \SpecialChar TeX
35856 The column number is a number in the range of 2
35857 \begin_inset space \thinspace{}
35861 \begin_inset space \thinspace{}
35865 Before the formula the multi-column text is ended by inserting the command
35868 \begin_layout Standard
35876 \begin_layout Standard
35877 in \SpecialChar TeX
35881 \begin_layout Standard
35882 Due to the command some space is automatically added before the formula.
35884 \begin_inset space \thinspace{}
35887 mm vertical space is inserted before the formula.
35888 When the formula style
35894 \begin_layout Plain Layout
35896 \begin_inset CommandInset ref
35898 reference "sec:Formula-Styles"
35910 \begin_inset space \thinspace{}
35913 mm space is inserted instead.
35916 \begin_layout Standard
35917 As example a multi-column text with a displayed formula:
35920 \begin_layout Standard
35926 \begin_layout Plain Layout
35930 begin{multicols}{2}
35935 Das Spektrum wird fouriertransformiert.
35936 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35937 , Lösungsmittel) zu trennen.
35938 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35939 nun das Aussehen des Ausgangssignals.
35940 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35941 über alle Phasen integrieren muss.
35943 \begin_inset Formula $S$
35946 unser normiertes Ausgangssignal und
35947 \begin_inset Formula $P$
35950 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35954 \begin_layout Plain Layout
35964 \begin_inset VSpace -6mm
35968 \begin_inset Formula
35970 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35979 \begin_layout Plain Layout
35983 begin{multicols}{2}
35989 \begin_inset Formula $S_{0}$
35992 das Signal ohne Gradient ist und die Normierungsbedingung
35993 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35997 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35999 \begin_inset Formula $\nicefrac{\pi}{2}$
36003 \begin_inset space \thinspace{}
36006 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36007 das Signal zusätzlich abschwächt.
36008 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36010 \begin_inset Formula $T_{2}$
36016 \begin_layout Standard
36022 \begin_layout Plain Layout
36034 \begin_layout Subsection
36035 Formulas with Description of Variables
36036 \begin_inset Index idx
36039 \begin_layout Plain Layout
36040 Formula ! with description of variables
36048 \begin_layout Standard
36049 To describe variables within a formula, like in formula
36050 \begin_inset CommandInset ref
36052 reference "eq:within"
36061 \begin_inset Formula $n$
36065 \begin_inset space ~
36068 matrix is used with left aligned columns for the
36069 \begin_inset Formula $n$
36076 \begin_layout Plain Layout
36078 \begin_inset CommandInset ref
36080 reference "sec:Matrices"
36089 To set the description in a smaller size, before the matrix e.
36090 \begin_inset space \thinspace{}
36094 \begin_inset space \space{}
36107 \begin_layout Plain Layout
36109 \begin_inset CommandInset ref
36111 reference "subsec:Font-Sizes"
36123 \begin_layout Standard
36124 When the formula style
36130 \begin_layout Plain Layout
36132 \begin_inset CommandInset ref
36134 reference "sec:Formula-Styles"
36155 \begin_layout Plain Layout
36162 only works in formulas with the style
36167 \begin_inset CommandInset ref
36169 reference "subsec:Variable-Space"
36178 is inserted before and after the matrix to have the same separation of
36179 the matrix from the equation and the side margin.
36182 \begin_layout Standard
36183 When the formula style
36187 is used, the method described in
36188 \begin_inset CommandInset ref
36190 reference "subsec:Flalign-Environment"
36194 is used to indent formulas.
36196 \begin_inset CommandInset ref
36198 reference "eq:within"
36202 consists of five columns where in the first two columns contain the equation,
36203 the third the matrix and the last one an empty \SpecialChar TeX
36205 \begin_inset Formula
36207 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36208 \rho & \textrm{density}\\
36209 V & \textrm{volume}\\
36210 g & \textrm{gravitational acceleration}
36211 \end{array} & & {}\label{eq:within}
36219 \begin_layout Subsection
36220 Upright small Greek Letters
36221 \begin_inset CommandInset label
36223 name "subsec:Upright-small-Greek"
36228 \begin_inset Index idx
36231 \begin_layout Plain Layout
36232 Greek letters ! upright
36240 \begin_layout Standard
36241 Most of the math fonts only provide italic small Greek letters.
36242 But for symbols of elementary particles like pions and neutrinos, upright
36243 Greek letters are needed.
36252 \begin_layout Plain Layout
36257 is part of the \SpecialChar LaTeX
36263 \begin_inset Index idx
36266 \begin_layout Plain Layout
36271 \begin_layout Plain Layout
36291 \begin_inset Index idx
36294 \begin_layout Plain Layout
36300 that is loaded with the \SpecialChar LaTeX
36304 \begin_layout Standard
36309 usepackage{upgreek}
36312 \begin_layout Standard
36318 \begin_layout Plain Layout
36328 \begin_inset Note Note
36331 \begin_layout Plain Layout
36332 The following table will only be displayed when the \SpecialChar LaTeX
36342 They are created when the command for a small Greek letter is started with
36348 For example the command
36355 \begin_inset Formula $\uptau$
36361 \begin_layout Standard
36362 With these commands reactions of elementary particles can be typeset:
36363 \begin_inset Formula
36365 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36373 \begin_layout Standard
36374 The upright letters are more bold and wider than the italic ones.
36375 They should therefore not be used for units like
36376 \begin_inset Quotes eld
36380 \begin_inset Quotes erd
36386 \begin_layout Standard
36390 \begin_layout Plain Layout
36400 \begin_inset Note Note
36403 \begin_layout Plain Layout
36404 The following will be displayed when the \SpecialChar LaTeX
36417 \begin_layout Standard
36418 You need to install the \SpecialChar LaTeX
36423 to see the rest of this subsection in the output.
36426 \begin_layout Standard
36430 \begin_layout Plain Layout
36442 \begin_layout Subsection
36443 Text Characters in Formulas
36444 \begin_inset Index idx
36447 \begin_layout Plain Layout
36456 \begin_layout Standard
36457 In some cases you might want to insert text characters directly into formulas.
36458 When for example the centered dot · is often used in formulas like
36459 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36462 , one would have to insert the command
36472 \begin_layout Plain Layout
36474 \begin_inset CommandInset ref
36476 reference "subsec:Binary-Operators"
36485 all the time, because this character is defined in all encodings as text
36487 But the encoding can be changed by this \SpecialChar LaTeX
36491 \begin_layout Standard
36496 Declare Inputtext{183}{
36506 f\SpecialChar ligaturebreak
36510 \begin_layout Standard
36511 The character encoding (menu
36513 Document\SpecialChar menuseparator
36514 Settings\SpecialChar menuseparator
36517 ) specifies what character appears when a keyboard key is pressed.
36518 When the key for the character '·' is pressed, internally the command
36525 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36527 With the changed encoding the right command is chosen automatically, depending
36528 on if the character was inserted into a formula or not.
36531 \begin_layout Standard
36532 The encoding of several characters is saved in definition files.
36533 For example the encoding
36537 is defined in the file
36541 which is in the installation folder of \SpecialChar LaTeX
36543 Encodings should only be changed via the \SpecialChar LaTeX
36544 -preamble and not in the definition
36546 Otherwise documents could not be edited by other \SpecialChar LyX
36547 users working on other
36551 \begin_layout Standard
36552 \begin_inset VSpace medskip
36555 Besides the centered dot, in this document the degree sign ° is defined
36556 with the following \SpecialChar LaTeX
36557 -preamble line so that it can be directly inserted into
36561 \begin_layout Standard
36566 DeclareInputtext{176}{
36576 f\SpecialChar ligaturebreak
36580 \begin_layout Subsection
36582 -comments in formulas
36583 \begin_inset Index idx
36586 \begin_layout Plain Layout
36596 \begin_layout Standard
36597 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36599 code of your file with the menu
36601 Insert\SpecialChar menuseparator
36602 Note\SpecialChar menuseparator
36606 This is not possible in a formula but you can insert \SpecialChar LaTeX
36611 \begin_layout Standard
36619 \begin_layout Standard
36620 This creates a box in which you can write your comment.
36621 Due to a bug in \SpecialChar LyX
36626 \begin_layout Plain Layout
36627 \begin_inset CommandInset href
36629 name "LyX-bug #9002"
36630 target "https://www.lyx.org/trac/ticket/9002"
36640 you cannot write normal text inside the comment, even when you use mathematical
36641 text, you will see its \SpecialChar LaTeX
36642 -commands in the \SpecialChar LaTeX
36644 \begin_inset Newline newline
36647 This a formula with a \SpecialChar LaTeX
36649 \begin_inset Formula
36651 A=B%\text{This is the comment}
36659 \begin_layout Standard
36660 \begin_inset Newpage newpage
36666 \begin_layout Section
36669 \begin_inset Index idx
36672 \begin_layout Plain Layout
36681 \begin_layout Standard
36682 This section is a summary of the most important typographic rules, listed
36687 \begin_layout Plain Layout
36688 This collection was partly taken from the German semi-official dictionary
36690 \begin_inset Quotes eld
36694 \begin_inset Quotes erd
36698 \begin_inset CommandInset citation
36705 that lists some of the ISO rules.
36706 More rules are listed in
36707 \begin_inset CommandInset citation
36722 \begin_layout Itemize
36731 \begin_layout Plain Layout
36732 done with font styles, see
36733 \begin_inset CommandInset ref
36735 reference "subsec:Font-Styles"
36744 , no matter if they appear in italic text: 30
36745 \begin_inset space \thinspace{}
36749 \begin_inset Newline newline
36752 Between the value and the unit is the smallest space, see
36753 \begin_inset CommandInset ref
36755 reference "subsec:Predefined-Space"
36760 \begin_inset Newline newline
36763 This convention is automatically fulfilled when the command
36770 When it is entered to a formula, two boxes appear.
36771 In the first one the value is inserted, in the second one the unit, and
36773 \begin_inset Formula $\unit[30]{km/h}$
36777 \begin_inset space \thinspace{}
36787 is not a real \SpecialChar LaTeX
36788 command but the command
36794 , therefore you cannot use it in \SpecialChar TeX
36798 \begin_layout Itemize
36799 Percent and perthousand signs are set like physical units:
36800 \begin_inset Newline newline
36804 \begin_inset space \thinspace{}
36810 \begin_layout Itemize
36811 The degree sign follows directly on the value: 15°, but not when it is used
36813 \begin_inset space \thinspace{}
36819 \begin_layout Itemize
36820 In numbers with more than four digits the smallest space is inserted before
36821 every third digit to group them:
36831 \begin_inset space \thinspace{}
36835 \begin_inset space \thinspace{}
36841 \begin_layout Itemize
36842 For dimensions like 120×90×40
36843 \begin_inset space \thinspace{}
36846 cm the multiplication sign
36847 \begin_inset Quotes eld
36851 \begin_inset Quotes erd
36855 It is available either via the command
36863 Insert\SpecialChar menuseparator
36864 Special Character\SpecialChar menuseparator
36870 \begin_layout Itemize
36871 Functions with names consisting of several letters are set upright to avoid
36873 \begin_inset CommandInset ref
36875 reference "subsec:Predefined-Functions"
36882 \begin_layout Itemize
36883 Indices consisting of several letters, are set upright:
36884 \begin_inset Formula $E_{\mathrm{kin}}$
36888 \begin_inset Newline newline
36891 Components of matrices are set italic:
36892 \begin_inset Formula $\hat{H}_{kl}$
36898 \begin_layout Itemize
36899 The differentiation/integration operator 'd', the Euler's number 'e' and
36900 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36904 \begin_layout Itemize
36905 The character that denotes a
36909 transformation is inserted either by the command
36914 \begin_inset space \textvisiblespace{}
36921 Insert\SpecialChar menuseparator
36922 Special Character\SpecialChar menuseparator
36923 Symbols\SpecialChar menuseparator
36925 \begin_inset space ~
36931 \begin_inset Formula $\mathscr{F}$
36937 \begin_layout Standard
36938 \begin_inset Newpage newpage
36944 \begin_layout Section
36946 \begin_inset Index idx
36949 \begin_layout Plain Layout
36958 \begin_layout Standard
36959 Some characters and symbols can be created with several commands.
36960 Here is a list of the synonym commands:
36963 \begin_layout Standard
36964 \begin_inset VSpace bigskip
36968 \begin_inset space \hfill{}
36972 \begin_inset Tabular
36973 <lyxtabular version="3" rows="12" columns="2">
36974 <features booktabs="true" tabularvalignment="middle">
36975 <column alignment="center" valignment="top" width="0pt">
36976 <column alignment="center" valignment="top" width="0pt">
36978 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36981 \begin_layout Plain Layout
36987 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36990 \begin_layout Plain Layout
36998 <cell alignment="center" valignment="top" usebox="none">
37001 \begin_layout Plain Layout
37009 <cell alignment="center" valignment="top" usebox="none">
37012 \begin_layout Plain Layout
37020 <cell alignment="center" valignment="top" usebox="none">
37023 \begin_layout Plain Layout
37031 <cell alignment="center" valignment="top" usebox="none">
37034 \begin_layout Plain Layout
37044 <cell alignment="center" valignment="top" usebox="none">
37047 \begin_layout Plain Layout
37055 <cell alignment="center" valignment="top" usebox="none">
37058 \begin_layout Plain Layout
37068 <cell alignment="center" valignment="top" usebox="none">
37071 \begin_layout Plain Layout
37079 <cell alignment="center" valignment="top" usebox="none">
37082 \begin_layout Plain Layout
37090 <cell alignment="center" valignment="top" usebox="none">
37093 \begin_layout Plain Layout
37101 <cell alignment="center" valignment="top" usebox="none">
37104 \begin_layout Plain Layout
37112 <cell alignment="center" valignment="top" usebox="none">
37115 \begin_layout Plain Layout
37123 <cell alignment="center" valignment="top" usebox="none">
37126 \begin_layout Plain Layout
37136 <cell alignment="center" valignment="top" usebox="none">
37139 \begin_layout Plain Layout
37147 <cell alignment="center" valignment="top" usebox="none">
37150 \begin_layout Plain Layout
37160 <cell alignment="center" valignment="top" usebox="none">
37163 \begin_layout Plain Layout
37171 <cell alignment="center" valignment="top" usebox="none">
37174 \begin_layout Plain Layout
37184 <cell alignment="center" valignment="top" usebox="none">
37187 \begin_layout Plain Layout
37195 <cell alignment="center" valignment="top" usebox="none">
37198 \begin_layout Plain Layout
37208 <cell alignment="center" valignment="top" usebox="none">
37211 \begin_layout Plain Layout
37219 <cell alignment="center" valignment="top" usebox="none">
37222 \begin_layout Plain Layout
37230 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37233 \begin_layout Plain Layout
37241 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37244 \begin_layout Plain Layout
37256 \begin_inset space \hfill{}
37260 \begin_inset Tabular
37261 <lyxtabular version="3" rows="12" columns="2">
37262 <features booktabs="true" tabularvalignment="middle">
37263 <column alignment="center" valignment="top" width="0pt">
37264 <column alignment="center" valignment="top" width="0pt">
37266 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37269 \begin_layout Plain Layout
37275 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37278 \begin_layout Plain Layout
37286 <cell alignment="center" valignment="top" usebox="none">
37289 \begin_layout Plain Layout
37297 <cell alignment="center" valignment="top" usebox="none">
37300 \begin_layout Plain Layout
37312 <cell alignment="center" valignment="top" usebox="none">
37315 \begin_layout Plain Layout
37323 <cell alignment="center" valignment="top" usebox="none">
37326 \begin_layout Plain Layout
37336 <cell alignment="center" valignment="top" usebox="none">
37339 \begin_layout Plain Layout
37347 <cell alignment="center" valignment="top" usebox="none">
37350 \begin_layout Plain Layout
37360 <cell alignment="center" valignment="top" usebox="none">
37363 \begin_layout Plain Layout
37371 <cell alignment="center" valignment="top" usebox="none">
37374 \begin_layout Plain Layout
37382 <cell alignment="center" valignment="top" usebox="none">
37385 \begin_layout Plain Layout
37393 <cell alignment="center" valignment="top" usebox="none">
37396 \begin_layout Plain Layout
37404 <cell alignment="center" valignment="top" usebox="none">
37407 \begin_layout Plain Layout
37415 <cell alignment="center" valignment="top" usebox="none">
37418 \begin_layout Plain Layout
37428 <cell alignment="center" valignment="top" usebox="none">
37431 \begin_layout Plain Layout
37439 <cell alignment="center" valignment="top" usebox="none">
37442 \begin_layout Plain Layout
37452 <cell alignment="center" valignment="top" usebox="none">
37455 \begin_layout Plain Layout
37463 <cell alignment="center" valignment="top" usebox="none">
37466 \begin_layout Plain Layout
37476 <cell alignment="center" valignment="top" usebox="none">
37479 \begin_layout Plain Layout
37487 <cell alignment="center" valignment="top" usebox="none">
37490 \begin_layout Plain Layout
37500 <cell alignment="center" valignment="top" usebox="none">
37503 \begin_layout Plain Layout
37511 <cell alignment="center" valignment="top" usebox="none">
37514 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37527 \begin_layout Plain Layout
37535 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37538 \begin_layout Plain Layout
37552 \begin_inset space \hfill{}
37556 \begin_inset CommandInset href
37559 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37567 \begin_layout Standard
37568 \begin_inset Newpage newpage
37574 \begin_layout Bibliography
37575 \begin_inset CommandInset bibitem
37576 LatexCommand bibitem
37590 The \SpecialChar LaTeX
37594 Addison Wesley, 2004
37597 \begin_layout Bibliography
37598 \begin_inset CommandInset bibitem
37599 LatexCommand bibitem
37606 \begin_inset CommandInset href
37609 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37614 of \SpecialChar LaTeX
37618 \begin_layout Bibliography
37619 \begin_inset CommandInset bibitem
37620 LatexCommand bibitem
37627 \begin_inset CommandInset href
37630 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
37639 \begin_layout Plain Layout
37648 -\SpecialChar LaTeX
37652 \begin_layout Bibliography
37653 \begin_inset CommandInset bibitem
37654 LatexCommand bibitem
37661 \begin_inset CommandInset href
37664 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37669 of all symbols available with \SpecialChar LaTeX
37673 \begin_layout Bibliography
37674 \begin_inset CommandInset bibitem
37675 LatexCommand bibitem
37682 \begin_inset CommandInset href
37684 name "Documentation"
37685 target "https://www.ctan.org/tex-archive/macros/latex/contrib/cancel/cancel.pdf"
37690 of the \SpecialChar LaTeX
37696 \begin_inset Index idx
37699 \begin_layout Plain Layout
37708 \begin_layout Bibliography
37709 \begin_inset CommandInset bibitem
37710 LatexCommand bibitem
37717 \begin_inset CommandInset href
37719 name "Documentation"
37720 target "https://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/doc/manual.pdf"
37725 of the \SpecialChar LaTeX
37731 \begin_inset Index idx
37734 \begin_layout Plain Layout
37735 Packages ! hyperref
37743 \begin_layout Bibliography
37744 \begin_inset CommandInset bibitem
37745 LatexCommand bibitem
37752 \begin_inset CommandInset href
37754 name "Documentation"
37755 target "https://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37760 of the \SpecialChar LaTeX
37766 \begin_inset Index idx
37769 \begin_layout Plain Layout
37778 \begin_layout Bibliography
37779 \begin_inset CommandInset bibitem
37780 LatexCommand bibitem
37789 \begin_inset space ~
37796 \begin_inset space ~
37799 Auflage, Dudenverlag, 2000
37802 \begin_layout Bibliography
37803 \begin_inset CommandInset bibitem
37804 LatexCommand bibitem
37811 \begin_inset CommandInset href
37814 target "https://www.nist.gov/physical-measurement-laboratory/special-publication-811"
37819 for reviewing manuscripts
37822 \begin_layout Standard
37823 \begin_inset CommandInset index_print
37824 LatexCommand printindex