1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
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54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
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126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children false
143 \language_package default
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147 \font_sans "lmss" "default"
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149 \font_math "auto" "auto"
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151 \use_non_tex_fonts false
153 \font_roman_osf false
155 \font_typewriter_osf false
156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command default
168 \pdf_title "LyX's Math Manual"
169 \pdf_author "LyX Team, Uwe Stöhr"
170 \pdf_subject "LyX-documentation about math"
171 \pdf_keywords "LyX, Mathed"
173 \pdf_bookmarksnumbered true
174 \pdf_bookmarksopen true
175 \pdf_bookmarksopenlevel 1
176 \pdf_breaklinks false
180 \pdf_pdfusetitle false
181 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
184 \use_package amsmath 2
185 \use_package amssymb 2
186 \use_package cancel 1
188 \use_package mathdots 1
189 \use_package mathtools 2
190 \use_package mhchem 1
191 \use_package stackrel 1
192 \use_package stmaryrd 1
193 \use_package undertilde 0
195 \cite_engine_type default
199 \paperorientation portrait
205 \notefontcolor #0000ff
212 \paragraph_separation skip
215 \math_numbering_side default
216 \quotes_style english
220 \paperpagestyle plain
225 \tracking_changes true
226 \output_changes false
229 \html_be_strict false
230 \author -563046850 "Jean-Marc LASGOUTTES"
231 \author 47243155 "Jean-Marc"
238 's detailed Math manual
242 by the \SpecialChar LyX
247 \begin_layout Plain Layout
249 If you have comments or error corrections, please send them to the \SpecialChar LyX
254 \begin_inset CommandInset href
256 name "lyx-docs@lists.lyx.org"
257 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
269 \begin_inset Note Note
272 \begin_layout Plain Layout
279 \begin_inset Newline newline
283 \begin_inset Newline newline
289 \change_inserted 47243155 1563226038
291 \change_deleted 47243155 1563226038
297 \begin_layout Standard
298 \begin_inset CommandInset toc
299 LatexCommand tableofcontents
306 \begin_layout Standard
307 \begin_inset Note Note
310 \begin_layout Plain Layout
311 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
314 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
321 If they are not installed the document can be exported anyway but the sections
322 where the packages are required will not appear in the output.
327 ; if it is not installed, this file cannot be exported.
330 \begin_layout Plain Layout
331 The latest PDF-version of this document can be found here:
332 \begin_inset Newline newline
337 https://wiki.lyx.org/LyX/Manuals#Math
345 \begin_layout Standard
346 \begin_inset Newpage newpage
352 \begin_layout Section
356 \begin_layout Standard
357 This document explains \SpecialChar LyX
358 's math features and is furthermore a collection
359 of \SpecialChar LaTeX
360 -commands used for mathematical characters and constructs.
361 The explanations are designed for the usage of commands.
362 It is therefore required that you have read the section
373 \begin_layout Standard
374 Most of the characters and many constructs explained in this manual are
375 also accessible via the menu
379 \SpecialChar menuseparator
395 But everybody who has to write lots of formulas will notice that it is
396 much faster to use commands instead of the math toolbar.
397 Therefore this manual is focused on commands but also mentions the correspondin
398 g toolbar buttons when available.
401 \begin_layout Standard
402 If not specially mentioned the commands are only available within formulas.
403 To be able to use all commands explained in this document, the option
407 must be checked in the document settings (menu
409 Document\SpecialChar menuseparator
410 Settings\SpecialChar menuseparator
421 \begin_layout Plain Layout
424 Use AMS math package automatically
430 \begin_layout Plain Layout
439 -math when math constructs are found that are supported by \SpecialChar LyX
448 \begin_layout Standard
449 This document doesn't list all
453 \begin_layout Plain Layout
466 \begin_layout Plain Layout
471 \begin_layout Plain Layout
480 -math commands is in the file
483 \begin_inset CommandInset href
486 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
493 , which is part of every \SpecialChar LaTeX
494 standard installation.
499 for lucidity reasons.
502 \begin_layout Section
506 \begin_layout Standard
507 To create an inline formula
508 \begin_inset Index idx
511 \begin_layout Plain Layout
517 that is embedded into a text line, use one of the shortcuts
523 or the toolbar button
530 \begin_inset Newline newline
533 To create a display style formula
534 \begin_inset Index idx
537 \begin_layout Plain Layout
538 Formula ! display style
543 which will appear bigger, has a different format, and will be in a separate
544 paragraph, use one of these shortcuts:
553 \begin_layout Standard
554 To change a display style formula to an inline formula, set the cursor into
555 the formula and use one of the shortcuts
563 Edit\SpecialChar menuseparator
564 Math\SpecialChar menuseparator
568 The same way is used to change an inline formula to a display style formula.
571 \begin_layout Standard
572 To display parts of an inline formula in the size of a display style formula,
580 \begin_inset Index idx
583 \begin_layout Plain Layout
592 Then a new blue box appears in which the desired formula part is inserted.
595 \begin_layout Standard
596 Only inline formulas are allowed inside tables.
599 \begin_layout Standard
604 can be turned on in the menu
606 View\SpecialChar menuseparator
610 When you click there on
611 \begin_inset Quotes eld
615 \begin_inset Quotes erd
618 the toolbar will be shown permanently at the bottom; this state is visualized
623 menu with a checkmark.
624 When you click in this state again on
625 \begin_inset Quotes eld
629 \begin_inset Quotes erd
640 is only shown when the cursor is within a formula; this state is visualized
641 by the renaming of the menu entry from
642 \begin_inset Quotes eld
646 \begin_inset Quotes erd
650 \begin_inset Quotes eld
658 \begin_inset Quotes erd
664 \begin_layout Standard
667 \begin_inset Index idx
670 \begin_layout Plain Layout
677 is invoked by pressing the toolbar button
685 Insert\SpecialChar menuseparator
697 \begin_layout Standard
698 To change the \SpecialChar LaTeX
700 \begin_inset Index idx
703 \begin_layout Plain Layout
712 Document\SpecialChar menuseparator
713 Settings\SpecialChar menuseparator
723 \begin_layout Standard
724 To edit matrices, case differentiations and multiline formulas subsequently,
727 Edit\SpecialChar menuseparator
732 Edit\SpecialChar menuseparator
734 \begin_inset space \thinspace{}
738 \begin_inset space \thinspace{}
748 When lines and columns are swapped via the menu, the column or line where
749 the cursor is in is exchanged with the column to the right or the line
751 Is the cursor in the last column or row, the exchange is done with the
752 column to the left or the line above.
755 \begin_layout Standard
756 To write text in formulas
760 \begin_layout Plain Layout
761 For multiline formulas the command
768 \begin_inset CommandInset ref
770 reference "subsec:Text-in-multiline"
784 \begin_inset Index idx
787 \begin_layout Plain Layout
794 \begin_inset Index idx
797 \begin_layout Plain Layout
804 This mode is invoked with the shortcut
810 or by the insertion of the command
817 \begin_inset Index idx
820 \begin_layout Plain Layout
829 The text appears black in \SpecialChar LyX
830 and can therefore be distinguished from the
831 other formula parts which appear blue.
832 In the output mathematical text is set upright, in contrary to other formula
836 \begin_layout Subsection*
840 \begin_layout Standard
841 Most of the \SpecialChar LaTeX
842 -commands for math constructs have the following scheme:
845 \begin_layout Standard
861 \begin_layout Standard
862 A command always starts with a backslash
863 \begin_inset Quotes gld
873 \begin_inset Quotes grd
877 To omit optional arguments, also omit the associated brackets.
878 The braces around the required arguments are named in this document as
881 \begin_inset Index idx
884 \begin_layout Plain Layout
892 If you add in a formula a left brace to a command name, \SpecialChar LyX
894 creates a \SpecialChar TeX
896 In all other cases \SpecialChar TeX
897 braces are created in formulas with the command
905 braces appear red in \SpecialChar LyX
906 , in contrary to normal braces which appear blue.
908 mode no command is needed to get \SpecialChar TeX
911 braces don't appear in the output.
914 \begin_layout Standard
915 When commands without arguments, like commands for symbols are entered in
917 mode, a space character must
921 be behind the command to end it.
922 This space doesn't appear in the output.
923 When the space should appear in the output, the space must be followed
924 by a protected space in normal text.
927 \begin_layout Standard
928 A protected space is inserted with
931 arg "command-alternatives space-insert protected ; math-space"
937 \begin_layout Subsection*
938 \begin_inset Newpage newpage
944 \begin_layout Itemize
946 \begin_inset space \textvisiblespace{}
949 denotes a space character to be input.
952 \begin_layout Itemize
954 \begin_inset Formula $\to$
957 denotes the usage of the corresponding arrow key on the keyboard.
962 key can often be used instead of
963 \begin_inset Formula $\to$
967 \begin_inset Formula $\downarrow$
975 \begin_inset Formula $\leftarrow$
979 \begin_inset Formula $\uparrow$
985 \begin_layout Subsection*
989 \begin_layout Standard
991 \begin_inset Float table
998 \begin_layout Plain Layout
1000 \begin_inset Caption Standard
1002 \begin_layout Plain Layout
1003 \begin_inset CommandInset label
1005 name "tab:Available-units"
1017 \begin_layout Plain Layout
1019 \begin_inset Tabular
1020 <lyxtabular version="3" rows="13" columns="2">
1021 <features booktabs="true" tabularvalignment="middle">
1022 <column alignment="center" valignment="top">
1023 <column alignment="center" valignment="top" width="0pt">
1025 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1099 \begin_inset space \thinspace{}
1103 \begin_inset space \thinspace{}
1113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1116 \begin_layout Plain Layout
1122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1125 \begin_layout Plain Layout
1127 \begin_inset space \thinspace{}
1131 \begin_inset space \thinspace{}
1141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1155 \begin_inset space \thinspace{}
1159 \begin_inset space \thinspace{}
1169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1172 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1181 \begin_layout Plain Layout
1183 \begin_inset space \thinspace{}
1187 \begin_inset space \thinspace{}
1197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1200 \begin_layout Plain Layout
1206 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1209 \begin_layout Plain Layout
1211 \begin_inset space \thinspace{}
1215 \begin_inset space \thinspace{}
1225 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1228 \begin_layout Plain Layout
1234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1237 \begin_layout Plain Layout
1239 \begin_inset space \thinspace{}
1243 \begin_inset Formula $\approx$
1247 \begin_inset space \thinspace{}
1257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1260 \begin_layout Plain Layout
1266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1269 \begin_layout Plain Layout
1271 \begin_inset space \thinspace{}
1275 \begin_inset space \thinspace{}
1285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1288 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1297 \begin_layout Plain Layout
1301 \begin_inset Quotes eld
1307 \begin_inset Quotes erd
1317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1320 \begin_layout Plain Layout
1326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1329 \begin_layout Plain Layout
1331 \begin_inset Quotes eld
1339 \begin_inset Quotes erd
1349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1352 \begin_layout Plain Layout
1358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1361 \begin_layout Plain Layout
1363 \begin_inset space \thinspace{}
1367 \begin_inset Formula $\nicefrac{1}{18}$
1371 \begin_inset space \thinspace{}
1392 \begin_layout Standard
1393 \begin_inset Newpage newpage
1399 \begin_layout Section
1403 \begin_layout Subsection
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1415 \begin_inset Index idx
1418 \begin_layout Plain Layout
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1444 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1476 \begin_layout Plain Layout
1491 \begin_layout Standard
1492 Indices are created with an underscore
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-subscript"
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1517 arg "math-superscript"
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features booktabs="true" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1543 \begin_layout Plain Layout
1551 <cell alignment="center" valignment="top" usebox="none">
1554 \begin_layout Plain Layout
1560 <cell alignment="center" valignment="top" usebox="none">
1563 \begin_layout Plain Layout
1564 \begin_inset Formula $B_{V}$
1573 <row topspace="1.5mm">
1574 <cell alignment="center" valignment="top" usebox="none">
1577 \begin_layout Plain Layout
1583 <cell alignment="center" valignment="top" usebox="none">
1586 \begin_layout Plain Layout
1587 \begin_inset Formula $B^{V}$
1596 <row topspace="1.5mm">
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1600 \begin_layout Plain Layout
1602 \begin_inset space \textvisiblespace{}
1610 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1613 \begin_layout Plain Layout
1614 \begin_inset Formula $B^{A}$
1630 \begin_layout Standard
1631 As the caret is in some languages an accent, vowels will be accentuated
1632 in this case and not set as exponents
1636 \begin_layout Plain Layout
1637 Depending on the used keyboard settings this can also happen for characters
1644 To get exponents in this case, press
1648 after the caret as in the last example.
1651 \begin_layout Subsection
1653 \begin_inset CommandInset label
1655 name "subsec:Fractions"
1660 \begin_inset Index idx
1663 \begin_layout Plain Layout
1672 \begin_layout Standard
1673 Fractions are generated with the command
1680 \begin_inset Index idx
1683 \begin_layout Plain Layout
1691 or via the math toolbar button
1694 arg "math-insert \\frac"
1698 The font size is adjusted automatically, depending on whether the fraction
1699 is in an inline or display style formula.
1700 With the math toolbar button
1703 arg "math-insert \\frac-square"
1706 you can select different fraction types.
1709 \begin_layout Standard
1717 \begin_inset Index idx
1720 \begin_layout Plain Layout
1728 a fraction can be created that always has the size of a display style formula.
1736 \begin_inset Index idx
1739 \begin_layout Plain Layout
1747 the fraction appears always with the size of an inline formula.
1751 \begin_layout Standard
1752 A line with the fraction
1753 \begin_inset Formula $\frac{1}{2}$
1756 that was created with the command
1765 \begin_layout Standard
1766 A line with the fraction
1767 \begin_inset Formula $\dfrac{1}{2}$
1770 that was created with the command
1779 \begin_layout Standard
1781 \begin_inset Tabular
1782 <lyxtabular version="3" rows="4" columns="2">
1783 <features booktabs="true" tabularvalignment="middle">
1784 <column alignment="center" valignment="top" width="0pt">
1785 <column alignment="center" valignment="top" width="0pt">
1787 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1790 \begin_layout Plain Layout
1796 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1799 \begin_layout Plain Layout
1806 <row topspace="1.5mm">
1807 <cell alignment="center" valignment="top" usebox="none">
1810 \begin_layout Plain Layout
1814 \begin_inset space \textvisiblespace{}
1818 \begin_inset Formula $\downarrow$
1826 <cell alignment="center" valignment="top" usebox="none">
1829 \begin_layout Plain Layout
1830 \begin_inset Formula $\frac{A}{B}$
1839 <row topspace="2mm">
1840 <cell alignment="center" valignment="top" usebox="none">
1843 \begin_layout Plain Layout
1847 \begin_inset space \textvisiblespace{}
1851 \begin_inset Formula $\downarrow$
1859 <cell alignment="center" valignment="top" usebox="none">
1862 \begin_layout Plain Layout
1863 \begin_inset Formula $\dfrac{A}{B}$
1872 <row topspace="2mm" bottomspace="1mm">
1873 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1876 \begin_layout Plain Layout
1880 \begin_inset space \textvisiblespace{}
1886 \begin_inset space \textvisiblespace{}
1890 \begin_inset Formula $\downarrow$
1894 \begin_inset Formula $\downarrow\downarrow$
1902 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1905 \begin_layout Plain Layout
1906 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1922 \begin_layout Standard
1923 \begin_inset VSpace bigskip
1927 \begin_inset Newpage newpage
1930 For nested fractions the command
1937 \begin_inset Index idx
1940 \begin_layout Plain Layout
1950 \begin_inset VSpace -3mm
1956 \begin_layout Standard
1957 \begin_inset Formula
1959 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1960 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1968 \begin_layout Standard
1969 The command for the example above is:
1972 \begin_layout Standard
1978 \begin_inset space \textvisiblespace{}
1982 \begin_inset Formula $\downarrow$
1988 \begin_inset space \textvisiblespace{}
1994 \begin_inset space \textvisiblespace{}
1998 \begin_inset Formula $\downarrow$
2002 \begin_inset Formula $\downarrow$
2008 \begin_layout Standard
2009 \begin_inset VSpace medskip
2015 \begin_layout Standard
2022 sets the fraction always in the size of a displayed formula, also when
2023 it is part of another fraction.
2026 \begin_layout Standard
2027 It is possible to specify the alignment of the numerator.
2034 is used to left align it, the command
2047 centers the numerator.
2048 These fractions demonstrate the different alignments:
2051 \begin_layout Standard
2054 \begin_inset Formula
2056 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2064 \begin_layout Standard
2065 \begin_inset Note Greyedout
2068 \begin_layout Plain Layout
2085 are no real \SpecialChar LaTeX
2086 commands but represent the command
2090 cfrac[alignment]{numerator}{denominator}
2093 Therefore you cannot use them in \SpecialChar TeX
2102 \begin_layout Standard
2103 \begin_inset VSpace medskip
2106 It is often advantageous to combine
2119 \begin_inset Formula
2121 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2129 \begin_layout Standard
2130 For inline fractions with a sloped fraction stroke you can use the command
2138 \begin_inset Index idx
2141 \begin_layout Plain Layout
2150 \begin_inset Formula $\nicefrac{5}{31}$
2160 \begin_inset Index idx
2163 \begin_layout Plain Layout
2172 \begin_inset Formula $\unitfrac{5}{31}$
2175 There is furthermore the command
2181 that offers to write a fraction in combination with a number:
2182 \begin_inset Formula $\unitfrac[2]{1}{3}$
2188 \begin_layout Standard
2189 \begin_inset Note Greyedout
2192 \begin_layout Plain Layout
2203 is not a real \SpecialChar LaTeX
2204 command but the command
2205 \begin_inset Newline newline
2212 unitfrac[number]{numerator}{denominator}
2215 Therefore you cannot use it in \SpecialChar TeX
2224 \begin_layout Standard
2225 How to define own fractions where the fraction stroke can be changed, is
2227 \begin_inset CommandInset ref
2229 reference "subsec:Self-defined-Fractions"
2236 \begin_layout Standard
2237 Multiline fractions are explained in
2238 \begin_inset CommandInset ref
2240 reference "subsec:Multiline-Fractions"
2247 \begin_layout Subsection
2249 \begin_inset Index idx
2252 \begin_layout Plain Layout
2261 \begin_layout Standard
2262 Square roots are created with
2269 \begin_inset Index idx
2272 \begin_layout Plain Layout
2280 or the math toolbar button
2283 arg "math-insert \\sqrt"
2286 , all other roots with the command
2293 \begin_inset Index idx
2296 \begin_layout Plain Layout
2304 or with the math toolbar button
2307 arg "math-insert \\root"
2313 \begin_layout Standard
2315 \begin_inset Tabular
2316 <lyxtabular version="3" rows="3" columns="2">
2317 <features booktabs="true" tabularvalignment="middle">
2318 <column alignment="center" valignment="top" width="0pt">
2319 <column alignment="center" valignment="top" width="0pt">
2321 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2324 \begin_layout Plain Layout
2330 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2333 \begin_layout Plain Layout
2340 <row topspace="1mm">
2341 <cell alignment="center" valignment="top" usebox="none">
2344 \begin_layout Plain Layout
2348 \begin_inset space \textvisiblespace{}
2356 <cell alignment="center" valignment="top" usebox="none">
2359 \begin_layout Plain Layout
2360 \begin_inset Formula $\sqrt{A-B}$
2369 <row topspace="1mm">
2370 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2373 \begin_layout Plain Layout
2377 \begin_inset space \textvisiblespace{}
2381 \begin_inset Formula $\downarrow$
2389 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2392 \begin_layout Plain Layout
2393 \begin_inset Formula $\sqrt[3]{A-B}$
2409 \begin_layout Standard
2410 A square root can also be created with
2416 when the root index field is left empty.
2419 \begin_layout Standard
2420 With certain indices the distance to the root is too small, like in this
2422 \begin_inset Formula $\sqrt[\beta]{B}$
2426 \begin_inset Newline newline
2430 \begin_inset Formula $\beta$
2434 To avoid this, the commands
2441 \begin_inset Index idx
2444 \begin_layout Plain Layout
2459 \begin_inset Index idx
2462 \begin_layout Plain Layout
2470 are used with the following scheme:
2473 \begin_layout Standard
2487 \begin_layout Standard
2488 Distance is the number of Big Points (unit bp;
2489 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2492 ), that the index should be moved to the left or top, resp..
2493 The commands are written to the index.
2494 This way the command
2495 \begin_inset Newline newline
2505 \begin_inset Formula $\to$
2511 \begin_inset Formula $\to$
2517 \begin_inset space \textvisiblespace{}
2521 \begin_inset Formula $\to$
2525 \begin_inset Newline newline
2530 produces a correct typeset formula:
2531 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2537 \begin_layout Subsection
2538 Binomial Coefficients
2539 \begin_inset Index idx
2542 \begin_layout Plain Layout
2543 Binomial coefficients
2551 \begin_layout Standard
2552 Binomial coefficients are inserted with the command
2559 \begin_inset Index idx
2562 \begin_layout Plain Layout
2570 or with the submenu of the math toolbar button
2573 arg "math-insert \\frac-square"
2589 there are the commands
2596 \begin_inset Index idx
2599 \begin_layout Plain Layout
2614 \begin_inset Index idx
2617 \begin_layout Plain Layout
2626 For other brackets around binomial coeficients there are the commands
2633 \begin_inset Index idx
2636 \begin_layout Plain Layout
2651 \begin_inset Index idx
2654 \begin_layout Plain Layout
2665 \begin_layout Standard
2667 \begin_inset Tabular
2668 <lyxtabular version="3" rows="6" columns="2">
2669 <features booktabs="true" tabularvalignment="middle">
2670 <column alignment="center" valignment="top" width="0pt">
2671 <column alignment="center" valignment="top" width="0pt">
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2685 \begin_layout Plain Layout
2692 <row topspace="1mm">
2693 <cell alignment="center" valignment="top" usebox="none">
2696 \begin_layout Plain Layout
2700 \begin_inset space \textvisiblespace{}
2704 \begin_inset Formula $\downarrow$
2712 <cell alignment="center" valignment="top" usebox="none">
2715 \begin_layout Plain Layout
2716 \begin_inset Formula $\binom{A}{B}$
2725 <row topspace="2mm">
2726 <cell alignment="center" valignment="top" usebox="none">
2729 \begin_layout Plain Layout
2733 \begin_inset space \textvisiblespace{}
2737 \begin_inset Formula $\downarrow$
2745 <cell alignment="center" valignment="top" usebox="none">
2748 \begin_layout Plain Layout
2749 \begin_inset Formula $\dbinom{A}{B}$
2758 <row topspace="2mm" bottomspace="0.5mm">
2759 <cell alignment="center" valignment="top" usebox="none">
2762 \begin_layout Plain Layout
2766 \begin_inset space \textvisiblespace{}
2770 \begin_inset Formula $\downarrow$
2778 <cell alignment="center" valignment="top" usebox="none">
2781 \begin_layout Plain Layout
2782 \begin_inset Formula $\tbinom{A}{B}$
2791 <row topspace="1mm">
2792 <cell alignment="center" valignment="top" topline="true" usebox="none">
2795 \begin_layout Plain Layout
2799 \begin_inset space \textvisiblespace{}
2803 \begin_inset Formula $\downarrow$
2811 <cell alignment="center" valignment="top" topline="true" usebox="none">
2814 \begin_layout Plain Layout
2815 \begin_inset Formula ${A \brack B}$
2824 <row topspace="2mm" bottomspace="0.5mm">
2825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2828 \begin_layout Plain Layout
2832 \begin_inset space \textvisiblespace{}
2836 \begin_inset Formula $\downarrow$
2844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2847 \begin_layout Plain Layout
2848 \begin_inset Formula ${A \brace B}$
2864 \begin_layout Subsection
2865 Case Differentiations
2866 \begin_inset Index idx
2869 \begin_layout Plain Layout
2870 Case differentiations
2878 \begin_layout Standard
2880 \begin_inset Tabular
2881 <lyxtabular version="3" rows="3" columns="2">
2882 <features booktabs="true" tabularvalignment="middle">
2883 <column alignment="center" valignment="top" width="0pt">
2884 <column alignment="center" valignment="top" width="0pt">
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2898 \begin_layout Plain Layout
2906 <cell alignment="center" valignment="top" usebox="none">
2909 \begin_layout Plain Layout
2913 \begin_inset space \textvisiblespace{}
2917 \begin_inset Formula $\to$
2921 \begin_inset Index idx
2924 \begin_layout Plain Layout
2937 <cell alignment="center" valignment="top" usebox="none">
2940 \begin_layout Plain Layout
2941 \begin_inset Formula $\begin{cases}
2951 <row topspace="1.5mm">
2952 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2955 \begin_layout Plain Layout
2959 \begin_inset space \textvisiblespace{}
2965 arg "newline-insert newline"
2973 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2976 \begin_layout Plain Layout
2977 \begin_inset Formula $\begin{cases}
2978 A & \textrm{for }x>0\\
2979 B & \textrm{for }x=0
2996 \begin_layout Standard
3003 or pressing the math toolbar button
3006 arg "math-insert \\cases"
3009 you can create new lines with the shortcut
3012 arg "newline-insert newline"
3015 or the table toolbar button
3018 arg "tabular-feature append-row"
3024 \begin_layout Standard
3031 is also available via the menu
3033 Insert\SpecialChar menuseparator
3034 Math\SpecialChar menuseparator
3040 \begin_layout Subsection
3042 \begin_inset Index idx
3045 \begin_layout Plain Layout
3054 \begin_layout Standard
3062 \begin_inset Index idx
3065 \begin_layout Plain Layout
3073 every character can be displayed canceled.
3074 The characters are quasi accentuated by a slash.
3077 \begin_layout Standard
3079 \begin_inset Tabular
3080 <lyxtabular version="3" rows="4" columns="2">
3081 <features booktabs="true" tabularvalignment="middle">
3082 <column alignment="center" valignment="top" width="0pt">
3083 <column alignment="center" valignment="top" width="0pt">
3085 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3088 \begin_layout Plain Layout
3094 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3097 \begin_layout Plain Layout
3105 <cell alignment="center" valignment="top" usebox="none">
3108 \begin_layout Plain Layout
3116 <cell alignment="center" valignment="top" usebox="none">
3119 \begin_layout Plain Layout
3120 \begin_inset Formula $\not=$
3130 <cell alignment="center" valignment="top" usebox="none">
3133 \begin_layout Plain Layout
3143 <cell alignment="center" valignment="top" usebox="none">
3146 \begin_layout Plain Layout
3147 \begin_inset Formula $\not\le$
3157 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3160 \begin_layout Plain Layout
3170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3173 \begin_layout Plain Layout
3174 \begin_inset Formula $\not\parallel$
3190 \begin_layout Standard
3191 The last example shows that not all negations look good.
3192 Therefore there are special commands for some negations (see
3193 \begin_inset CommandInset ref
3195 reference "subsec:Mathematical-Symbols"
3200 \begin_inset CommandInset ref
3202 reference "sec:Relations"
3209 \begin_layout Subsection
3211 \begin_inset CommandInset label
3213 name "subsec:Placeholders"
3218 \begin_inset Index idx
3221 \begin_layout Plain Layout
3228 \begin_inset Index idx
3231 \begin_layout Plain Layout
3232 Chemical characters ! Isotopes
3238 \begin_inset Index idx
3241 \begin_layout Plain Layout
3246 \begin_layout Plain Layout
3257 \begin_layout Plain Layout
3272 \begin_layout Standard
3274 \begin_inset space \thinspace{}
3278 \begin_inset space \space{}
3285 \begin_layout Plain Layout
3286 Typesetting isotopes and chemical symbols is described in
3287 \begin_inset CommandInset ref
3289 reference "subsec:Chemical-Symbols-and"
3298 the following problem occurs:
3301 \begin_layout Standard
3303 \begin_inset Tabular
3304 <lyxtabular version="3" rows="2" columns="2">
3305 <features booktabs="true" tabularvalignment="middle">
3306 <column alignment="center" valignment="top" width="0pt">
3307 <column alignment="center" valignment="top" width="0pt">
3309 <cell alignment="center" valignment="top" usebox="none">
3312 \begin_layout Plain Layout
3313 Indices created with sub- and superscripts:
3318 <cell alignment="center" valignment="top" usebox="none">
3321 \begin_layout Plain Layout
3322 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3331 <row topspace="1.5mm">
3332 <cell alignment="center" valignment="top" usebox="none">
3335 \begin_layout Plain Layout
3341 <cell alignment="center" valignment="top" usebox="none">
3344 \begin_layout Plain Layout
3345 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3361 \begin_layout Standard
3362 The shorter index is by default placed below or above the first character
3363 of the longer index.
3364 To avoid this there is the command
3371 \begin_inset Index idx
3374 \begin_layout Plain Layout
3382 or the math toolbar button
3383 \begin_inset space \thinspace{}
3390 \begin_layout Plain Layout
3391 can be found in the submenu of the toolbar button
3394 arg "math-insert \\space"
3408 that creates one or more phantom characters.
3415 a small blue box appears that is superposed with two red arrows.
3416 The arrows indicate that the complete width and height of the box content
3417 will be created as placeholder.
3418 Phantom characters are accordingly placeholders with the size of the characters.
3421 \begin_layout Standard
3423 \begin_inset Tabular
3424 <lyxtabular version="3" rows="4" columns="2">
3425 <features booktabs="true" tabularvalignment="middle">
3426 <column alignment="center" valignment="top" width="0pt">
3427 <column alignment="center" valignment="top" width="0pt">
3429 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3432 \begin_layout Plain Layout
3438 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3441 \begin_layout Plain Layout
3448 <row topspace="1.5mm">
3449 <cell alignment="center" valignment="top" usebox="none">
3452 \begin_layout Plain Layout
3454 \begin_inset space \textvisiblespace{}
3460 \begin_inset space \textvisiblespace{}
3464 \begin_inset Formula $\to$
3468 \begin_inset space \textvisiblespace{}
3476 <cell alignment="center" valignment="top" usebox="none">
3479 \begin_layout Plain Layout
3480 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3489 <row topspace="1.5mm" bottomspace="0.5mm">
3490 <cell alignment="center" valignment="top" usebox="none">
3493 \begin_layout Plain Layout
3495 \begin_inset space \textvisiblespace{}
3501 \begin_inset space \textvisiblespace{}
3505 \begin_inset Formula $\to$
3509 \begin_inset space \textvisiblespace{}
3517 <cell alignment="center" valignment="top" usebox="none">
3520 \begin_layout Plain Layout
3521 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3530 <row topspace="1.5mm" bottomspace="0.5mm">
3531 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3534 \begin_layout Plain Layout
3538 \begin_inset space \textvisiblespace{}
3544 \begin_inset space \textvisiblespace{}
3548 \begin_inset Formula $\to$
3552 \begin_inset space \textvisiblespace{}
3560 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3563 \begin_layout Plain Layout
3564 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3580 \begin_layout Standard
3581 Furthermore there are the commands
3588 \begin_inset Index idx
3591 \begin_layout Plain Layout
3612 \begin_inset Index idx
3615 \begin_layout Plain Layout
3636 creates only space for the maximal height of the characters in the box
3637 but not for its width.
3644 creates only space for the width of the box content.
3645 Therefore the boxes of both commands have only one red arrow.
3648 \begin_layout Standard
3649 For example the command
3654 \begin_inset space \textvisiblespace{}
3661 creates space for the height of the integral sign,
3665 \begin_layout Plain Layout
3672 creates an integral sign, see
3673 \begin_inset CommandInset ref
3675 reference "subsec:Big-Operators"
3684 because this is the larger character.
3685 An example application is in
3686 \begin_inset CommandInset ref
3688 reference "subsec:Multiline-Brackets"
3695 \begin_layout Standard
3696 Placeholders can also be used for text when they are inserted via the menu
3699 Insert\SpecialChar menuseparator
3700 Formatting\SpecialChar menuseparator
3706 \begin_layout Standard
3708 \begin_inset Newline newline
3712 \begin_inset Phantom Phantom
3715 \begin_layout Plain Layout
3724 \begin_layout Subsection
3726 \begin_inset Index idx
3729 \begin_layout Plain Layout
3736 \begin_inset Index idx
3739 \begin_layout Plain Layout
3740 Formula ! underlined
3748 \begin_layout Standard
3750 \begin_inset Tabular
3751 <lyxtabular version="3" rows="4" columns="2">
3752 <features booktabs="true" tabularvalignment="middle">
3753 <column alignment="center" valignment="top" width="0pt">
3754 <column alignment="center" valignment="top" width="0pt">
3756 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3759 \begin_layout Plain Layout
3765 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3768 \begin_layout Plain Layout
3775 <row topspace="2mm">
3776 <cell alignment="center" valignment="top" usebox="none">
3779 \begin_layout Plain Layout
3783 \begin_inset space \textvisiblespace{}
3787 \begin_inset Index idx
3790 \begin_layout Plain Layout
3803 <cell alignment="center" valignment="top" usebox="none">
3806 \begin_layout Plain Layout
3807 \begin_inset Formula $\overline{A+B}$
3816 <row bottomspace="1mm">
3817 <cell alignment="center" valignment="top" usebox="none">
3820 \begin_layout Plain Layout
3824 \begin_inset space \textvisiblespace{}
3828 \begin_inset Index idx
3831 \begin_layout Plain Layout
3844 <cell alignment="center" valignment="top" usebox="none">
3847 \begin_layout Plain Layout
3848 \begin_inset Formula $\underline{A+B}$
3857 <row topspace="2mm" bottomspace="1mm">
3858 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3861 \begin_layout Plain Layout
3865 \begin_inset space \textvisiblespace{}
3871 \begin_inset space \textvisiblespace{}
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3882 \begin_layout Plain Layout
3883 \begin_inset Formula $\overline{\underline{A+B}}$
3899 \begin_layout Standard
3900 In the last example it doesn't matter if first
3915 \begin_layout Standard
3916 To double underline use
3925 \begin_layout Standard
3926 It is possible to place up to 6 lines above or below characters.
3929 \begin_layout Standard
3930 \begin_inset VSpace bigskip
3933 Custom lines can be created using the command
3940 \begin_inset Index idx
3943 \begin_layout Plain Layout
3951 which has the following scheme:
3954 \begin_layout Standard
3959 rule[vertical offset]{length}{thickness}
3962 \begin_layout Standard
3963 The optional vertical offset shifts the line upwards (or downwards, when
3964 the value is negative).
3966 \begin_inset CommandInset ref
3968 reference "tab:Available-units"
3972 can be used for the values.
3973 Here are two example lines created with the commands
3974 \begin_inset Newline newline
3981 rule[-2ex]{3cm}{2pt}
3992 \begin_layout Standard
3994 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4000 \begin_layout Standard
4007 can also be used for text when a line is inserted via the menu
4009 Insert\SpecialChar menuseparator
4010 Formatting\SpecialChar menuseparator
4012 \begin_inset space ~
4020 \begin_layout Standard
4022 \begin_inset CommandInset line
4033 \begin_layout Subsection
4035 \begin_inset CommandInset label
4037 name "subsec:Ellipses"
4042 \begin_inset Index idx
4045 \begin_layout Plain Layout
4054 \begin_layout Standard
4055 There are different types of ellipses available.
4059 \begin_layout Plain Layout
4060 In the math toolbar in the submenu of the button
4063 arg "math-insert \\ldots"
4071 For listings dots at the baseline are used (
4078 \begin_inset Index idx
4081 \begin_layout Plain Layout
4089 ), while for operations dots are needed that are on the same height as the
4097 \begin_inset Index idx
4100 \begin_layout Plain Layout
4109 When using the command
4116 \begin_inset Index idx
4119 \begin_layout Plain Layout
4127 , \SpecialChar LaTeX
4128 decides on the basis of the next character what type is used.
4131 \begin_layout Standard
4133 \begin_inset Tabular
4134 <lyxtabular version="3" rows="9" columns="2">
4135 <features booktabs="true" tabularvalignment="middle">
4136 <column alignment="center" valignment="top" width="0pt">
4137 <column alignment="center" valignment="top" width="0pt">
4139 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4142 \begin_layout Plain Layout
4148 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4151 \begin_layout Plain Layout
4159 <cell alignment="center" valignment="top" usebox="none">
4162 \begin_layout Plain Layout
4164 \begin_inset space \textvisiblespace{}
4170 \begin_inset space \textvisiblespace{}
4178 <cell alignment="center" valignment="top" usebox="none">
4181 \begin_layout Plain Layout
4182 \begin_inset Formula $A_{1},\dots,A_{n}$
4192 <cell alignment="center" valignment="top" usebox="none">
4195 \begin_layout Plain Layout
4197 \begin_inset space \textvisiblespace{}
4203 \begin_inset space \textvisiblespace{}
4211 <cell alignment="center" valignment="top" usebox="none">
4214 \begin_layout Plain Layout
4215 \begin_inset Formula $A_{1}+\dots+A_{n}$
4225 <cell alignment="center" valignment="top" usebox="none">
4228 \begin_layout Plain Layout
4230 \begin_inset space \textvisiblespace{}
4236 \begin_inset space \textvisiblespace{}
4244 <cell alignment="center" valignment="top" usebox="none">
4247 \begin_layout Plain Layout
4248 \begin_inset Formula $A_{1},\ldots,A_{n}$
4258 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4261 \begin_layout Plain Layout
4263 \begin_inset space \textvisiblespace{}
4269 \begin_inset space \textvisiblespace{}
4277 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4280 \begin_layout Plain Layout
4281 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4291 <cell alignment="center" valignment="top" usebox="none">
4294 \begin_layout Plain Layout
4302 <cell alignment="center" valignment="top" usebox="none">
4305 \begin_layout Plain Layout
4306 \begin_inset Formula $\vdots$
4316 <cell alignment="center" valignment="top" usebox="none">
4319 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\ddots$
4341 <cell alignment="center" valignment="top" usebox="none">
4344 \begin_layout Plain Layout
4352 <cell alignment="center" valignment="top" usebox="none">
4355 \begin_layout Plain Layout
4356 \begin_inset Formula $\iddots$
4366 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4369 \begin_layout Plain Layout
4371 \begin_inset space \thinspace{}
4374 matrix with the different dots
4379 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4382 \begin_layout Plain Layout
4383 \begin_inset Formula $\begin{array}{ccc}
4384 A_{11} & \cdots & A_{1m}\\
4385 \vdots & \ddots & \vdots\\
4386 A_{n1} & \cdots & A_{nm}
4403 \begin_layout Standard
4404 The ellipses available in menu
4406 Insert\SpecialChar menuseparator
4408 \begin_inset space ~
4422 \begin_layout Standard
4423 \begin_inset VSpace medskip
4432 , one of the options
4434 Use mathdots package (automatically)
4436 must be set in the document settings under
4439 \begin_inset space ~
4445 \begin_inset Newline newline
4450 Use mathdots package
4452 will improve the appearance of all dots in the documents if their font
4453 style or size is not the default.
4456 \begin_layout Standard
4457 \begin_inset VSpace medskip
4460 Specially for matrices there are ellipses that span over several columns.
4461 They are created with the command
4468 \begin_inset Index idx
4471 \begin_layout Plain Layout
4479 , that has the following scheme:
4482 \begin_layout Standard
4487 hdotsfor[distance]{number of columns}
4490 \begin_layout Standard
4491 The number of columns specifies how many columns should be spanned.
4492 Distance is a factor for the distance between the dots.
4495 \begin_layout Standard
4496 In the following matrix the command
4502 was inserted in the first box of the second line, to get an ellipsis with
4503 a dot distance twice as long as with the command
4510 \begin_inset Formula
4512 \left(\begin{array}{cccc}
4521 Note that the matrix fields that should be spanned must be empty, otherwise
4522 you get \SpecialChar LaTeX
4526 \begin_layout Standard
4527 \begin_inset VSpace bigskip
4530 Furthermore you can fill with the command
4537 \begin_inset Index idx
4540 \begin_layout Plain Layout
4548 the rest of a line with dots.
4549 The effect of these commands is the same as with
4556 \begin_inset CommandInset ref
4558 reference "subsec:Variable-Space"
4565 \begin_layout Standard
4566 For example the command
4571 \begin_inset space \textvisiblespace{}
4579 \begin_layout Standard
4580 \begin_inset Formula $A\dotfill B$
4586 \begin_layout Standard
4593 there is for a line the command
4600 \begin_inset Index idx
4603 \begin_layout Plain Layout
4614 \begin_layout Standard
4615 \begin_inset Formula $A\hrulefill B$
4621 \begin_layout Standard
4622 To use the commands for text, they have to be inserted in \SpecialChar TeX
4626 \begin_layout Section
4628 \begin_inset CommandInset label
4635 \begin_inset Index idx
4638 \begin_layout Plain Layout
4647 \begin_layout Standard
4648 Matrices can be inserted via the math toolbar button
4651 arg "dialog-show mathmatrix"
4656 Insert\SpecialChar menuseparator
4657 Math\SpecialChar menuseparator
4661 In the matrix dialog you can specify the number of columns and rows, the
4662 alignment and the decoration.
4663 The vertical alignment is only of importance for matrices in inline formulas:
4666 \begin_layout Standard
4667 The first matrix is top
4668 \begin_inset Formula $\begin{array}[t]{cccc}
4676 \begin_inset Formula $\begin{array}{cccc}
4683 and the third bottom
4684 \begin_inset Formula $\begin{array}[b]{cccc}
4694 \begin_layout Standard
4695 The horizontal alignment specifies how the column entries should be aligned.
4696 It is set by entering a letter for every column.
4701 denotes left aligned,
4710 To create for example a 4
4715 \begin_inset space ~
4718 matrix where the first column is left aligned, the second and third are
4719 centered and the last one is right aligned, one enters for the horizontal
4725 Normally in a matrix all columns are centered, therefore the default for
4733 \begin_layout Standard
4734 Horizontal alignment:
4737 \begin_layout Standard
4743 \begin_inset Formula $\begin{array}{lll}
4755 \begin_inset Formula $\begin{array}{ccc}
4767 \begin_inset Formula $\begin{array}{rrr}
4777 \begin_layout Standard
4778 To add or delete rows and columns subsequently, the math toolbar buttons
4782 arg "tabular-feature append-row"
4788 arg "tabular-feature delete-row"
4792 \begin_inset space \thinspace{}
4797 Edit\SpecialChar menuseparator
4801 New rows can also be created with
4804 arg "newline-insert newline"
4810 \begin_layout Standard
4811 \begin_inset VSpace bigskip
4815 \change_deleted 47243155 1563226130
4817 \change_deleted -563046850 1563190969
4821 \change_inserted -563046850 1563190971
4827 \change_deleted -563046850 1563192602
4829 \change_inserted -563046850 1563192607
4832 parentheses in the selected style around the matrix
4833 \change_inserted -563046850 1563192780
4838 style, suitable for an inline matrix like this one
4839 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
4841 \end{smallmatrix}\bigr)$
4848 \change_inserted -563046850 1563192943
4849 Here the parentheses have been added manually using commands
4862 \begin_layout Standard
4864 \change_deleted -563046850 1563192735
4867 Alternatively, parentheses can can
4868 \change_deleted -563046850 1563192971
4871 be created with the commands
4878 \begin_inset Index idx
4881 \begin_layout Plain Layout
4896 \begin_inset Index idx
4899 \begin_layout Plain Layout
4910 \begin_inset space ~
4916 \begin_inset CommandInset ref
4918 reference "subsec:Automatic-Bracket-Size"
4922 , or by using the following commands:
4923 \begin_inset VSpace medskip
4929 \begin_layout Standard
4930 \begin_inset space \hfill{}
4934 \begin_inset Tabular
4935 <lyxtabular version="3" rows="4" columns="2">
4936 <features booktabs="true" tabularvalignment="middle">
4937 <column alignment="center" valignment="top" width="0pt">
4938 <column alignment="center" valignment="top">
4940 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4943 \begin_layout Plain Layout
4949 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4952 \begin_layout Plain Layout
4959 <row topspace="1.5mm">
4960 <cell alignment="center" valignment="top" usebox="none">
4963 \begin_layout Plain Layout
4967 \begin_inset space \textvisiblespace{}
4975 \begin_inset space \thinspace{}
4983 <cell alignment="center" valignment="top" usebox="none">
4986 \begin_layout Plain Layout
4987 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4988 0 & \textrm{-}\mathrm{i}\\
4990 \end{array}\end{bmatrix}$
4999 <row topspace="1.5mm" bottomspace="0.5mm">
5000 <cell alignment="center" valignment="top" usebox="none">
5003 \begin_layout Plain Layout
5007 \begin_inset space \textvisiblespace{}
5015 \begin_inset space \thinspace{}
5023 <cell alignment="center" valignment="top" usebox="none">
5026 \begin_layout Plain Layout
5027 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5028 0 & \textrm{-}\mathrm{i}\\
5030 \end{array}\end{Bmatrix}$
5040 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5043 \begin_layout Plain Layout
5047 \begin_inset space \textvisiblespace{}
5055 \begin_inset space \thinspace{}
5063 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5066 \begin_layout Plain Layout
5067 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5068 0 & \textrm{-}\mathrm{i}\\
5070 \end{array}\end{pmatrix}$
5084 \begin_inset space \hfill{}
5088 \begin_inset Tabular
5089 <lyxtabular version="3" rows="4" columns="2">
5090 <features booktabs="true" tabularvalignment="middle">
5091 <column alignment="center" valignment="top" width="0pt">
5092 <column alignment="center" valignment="top">
5094 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5097 \begin_layout Plain Layout
5103 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5106 \begin_layout Plain Layout
5113 <row topspace="1.5mm">
5114 <cell alignment="center" valignment="top" usebox="none">
5117 \begin_layout Plain Layout
5121 \begin_inset space \textvisiblespace{}
5129 \begin_inset space \thinspace{}
5137 <cell alignment="center" valignment="top" usebox="none">
5140 \begin_layout Plain Layout
5141 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5142 0 & \textrm{-}\mathrm{i}\\
5144 \end{array}\end{vmatrix}$
5153 <row topspace="1.5mm" bottomspace="0.5mm">
5154 <cell alignment="center" valignment="top" usebox="none">
5157 \begin_layout Plain Layout
5161 \begin_inset space \textvisiblespace{}
5169 \begin_inset space \thinspace{}
5177 <cell alignment="center" valignment="top" usebox="none">
5180 \begin_layout Plain Layout
5181 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5182 0 & \textrm{-}\mathrm{i}\\
5184 \end{array}\end{Vmatrix}$
5194 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5197 \begin_layout Plain Layout
5201 \begin_inset space \textvisiblespace{}
5209 \begin_inset space \thinspace{}
5217 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5220 \begin_layout Plain Layout
5221 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5222 0 & \textrm{-}\mathrm{i}\\
5224 \end{array}\end{matrix}$
5238 \begin_inset space \hfill{}
5244 \begin_layout Standard
5245 \begin_inset VSpace medskip
5249 \begin_inset space \thinspace{}
5253 \begin_inset space \space{}
5262 is inserted, a blue box appears between two vertical lines where the matrix
5264 \begin_inset Newline newline
5267 Note that decorated matrices ignore the vertical alignment.
5270 \begin_layout Standard
5271 \begin_inset VSpace bigskip
5274 As all multiline formulas are matrices, the length
5281 \begin_inset Index idx
5284 \begin_layout Plain Layout
5292 that is described in
5293 \begin_inset CommandInset ref
5295 reference "subsec:Column-Separation"
5299 can also be used to change the column separation of matrices.
5302 \begin_layout Standard
5303 To change the row separation, the command
5310 \begin_inset Index idx
5313 \begin_layout Plain Layout
5322 It is used as follows:
5325 \begin_layout Standard
5332 arraystretch}{stretch factor}
5333 \begin_inset Index idx
5336 \begin_layout Plain Layout
5347 \begin_layout Standard
5354 assigns the stretch factor to the predefined command
5362 \begin_inset space \thinspace{}
5366 \begin_inset space \space{}
5369 the row separation, use the factor 2.
5370 This is then used for all following matrices.
5371 To go back to the original separation, assign the factor 1 to
5380 \begin_layout Standard
5382 \change_inserted 47243155 1563226178
5383 Small inline matrices can also be obtained using
5384 \change_deleted 47243155 1563226182
5385 To set matrices into a text line,
5394 \begin_inset Index idx
5397 \begin_layout Plain Layout
5406 \change_deleted 47243155 1563226186
5410 When it is inserted a blue box with two dashed lines appears.
5411 In this box the matrix is inserted.
5414 \begin_layout Standard
5416 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5418 \end{smallmatrix}\right)$
5422 \change_inserted 47243155 1563226243
5423 with automatic delimiters around it
5428 \begin_layout Section
5429 Brackets and Delimiters
5430 \begin_inset Index idx
5433 \begin_layout Plain Layout
5440 \begin_inset Index idx
5443 \begin_layout Plain Layout
5452 \begin_layout Subsection
5453 Vertical Brackets and Delimiters
5454 \begin_inset Index idx
5457 \begin_layout Plain Layout
5466 \begin_layout Standard
5467 \begin_inset space \hfill{}
5471 \begin_inset Tabular
5472 <lyxtabular version="3" rows="9" columns="2">
5473 <features booktabs="true" tabularvalignment="middle">
5474 <column alignment="center" valignment="top" width="0pt">
5475 <column alignment="center" valignment="top" width="0pt">
5477 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5480 \begin_layout Plain Layout
5486 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5489 \begin_layout Plain Layout
5497 <cell alignment="center" valignment="top" usebox="none">
5500 \begin_layout Plain Layout
5506 <cell alignment="center" valignment="top" usebox="none">
5509 \begin_layout Plain Layout
5510 \begin_inset Formula $($
5520 <cell alignment="center" valignment="top" usebox="none">
5523 \begin_layout Plain Layout
5529 <cell alignment="center" valignment="top" usebox="none">
5532 \begin_layout Plain Layout
5533 \begin_inset Formula $\{$
5543 <cell alignment="center" valignment="top" usebox="none">
5546 \begin_layout Plain Layout
5552 <cell alignment="center" valignment="top" usebox="none">
5555 \begin_layout Plain Layout
5556 \begin_inset Formula $[$
5566 <cell alignment="center" valignment="top" usebox="none">
5569 \begin_layout Plain Layout
5577 <cell alignment="center" valignment="top" usebox="none">
5580 \begin_layout Plain Layout
5581 \begin_inset Formula $\langle$
5591 <cell alignment="center" valignment="top" usebox="none">
5594 \begin_layout Plain Layout
5602 <cell alignment="center" valignment="top" usebox="none">
5605 \begin_layout Plain Layout
5606 \begin_inset Formula $\lceil$
5616 <cell alignment="center" valignment="top" usebox="none">
5619 \begin_layout Plain Layout
5627 <cell alignment="center" valignment="top" usebox="none">
5630 \begin_layout Plain Layout
5631 \begin_inset Formula $\lfloor$
5641 <cell alignment="center" valignment="top" usebox="none">
5644 \begin_layout Plain Layout
5650 <cell alignment="center" valignment="top" usebox="none">
5653 \begin_layout Plain Layout
5654 \begin_inset Formula $/$
5664 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5667 \begin_layout Plain Layout
5673 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5676 \begin_layout Plain Layout
5677 \begin_inset Formula $|$
5691 \begin_inset space \hfill{}
5695 \begin_inset Tabular
5696 <lyxtabular version="3" rows="9" columns="2">
5697 <features booktabs="true" tabularvalignment="middle">
5698 <column alignment="center" valignment="top" width="0pt">
5699 <column alignment="center" valignment="top" width="0pt">
5701 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5704 \begin_layout Plain Layout
5710 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5713 \begin_layout Plain Layout
5721 <cell alignment="center" valignment="top" usebox="none">
5724 \begin_layout Plain Layout
5730 <cell alignment="center" valignment="top" usebox="none">
5733 \begin_layout Plain Layout
5734 \begin_inset Formula $)$
5744 <cell alignment="center" valignment="top" usebox="none">
5747 \begin_layout Plain Layout
5753 <cell alignment="center" valignment="top" usebox="none">
5756 \begin_layout Plain Layout
5757 \begin_inset Formula $\}$
5767 <cell alignment="center" valignment="top" usebox="none">
5770 \begin_layout Plain Layout
5776 <cell alignment="center" valignment="top" usebox="none">
5779 \begin_layout Plain Layout
5780 \begin_inset Formula $]$
5790 <cell alignment="center" valignment="top" usebox="none">
5793 \begin_layout Plain Layout
5801 <cell alignment="center" valignment="top" usebox="none">
5804 \begin_layout Plain Layout
5805 \begin_inset Formula $\rangle$
5815 <cell alignment="center" valignment="top" usebox="none">
5818 \begin_layout Plain Layout
5826 <cell alignment="center" valignment="top" usebox="none">
5829 \begin_layout Plain Layout
5830 \begin_inset Formula $\rceil$
5840 <cell alignment="center" valignment="top" usebox="none">
5843 \begin_layout Plain Layout
5851 <cell alignment="center" valignment="top" usebox="none">
5854 \begin_layout Plain Layout
5855 \begin_inset Formula $\rfloor$
5865 <cell alignment="center" valignment="top" usebox="none">
5868 \begin_layout Plain Layout
5878 <cell alignment="center" valignment="top" usebox="none">
5881 \begin_layout Plain Layout
5882 \begin_inset Formula $\backslash$
5892 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5895 \begin_layout Plain Layout
5903 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5906 \begin_layout Plain Layout
5907 \begin_inset Formula $\|$
5921 \begin_inset space \hfill{}
5927 \begin_layout Standard
5930 \begin_inset Note Greyedout
5933 \begin_layout Plain Layout
5946 \begin_inset Index idx
5949 \begin_layout Plain Layout
5957 must be used for the backslash, because the command
5965 produces a line break there.
5973 \begin_layout Standard
5974 For all characters listed above the size can be adjusted with the commands
5975 described in the following two subsections.
5976 When using these commands, the characters < and > can directly be used
5977 instead of the commands
5992 \begin_layout Subsubsection
5994 \begin_inset CommandInset label
5996 name "subsec:Manual-Bracket-Size"
6001 \begin_inset Index idx
6004 \begin_layout Plain Layout
6005 Bracket size ! manual
6013 \begin_layout Standard
6014 The bracket size can be specified manually by the \SpecialChar LaTeX
6022 \begin_inset Index idx
6025 \begin_layout Plain Layout
6058 denotes the smallest and
6064 the largest bracket size.
6067 \begin_layout Standard
6068 These commands are used to emphasize levels of brackets:
6071 \begin_layout Standard
6073 \begin_inset Tabular
6074 <lyxtabular version="3" rows="2" columns="2">
6075 <features booktabs="true" tabularvalignment="middle">
6076 <column alignment="center" valignment="top" width="0pt">
6077 <column alignment="center" valignment="top" width="0pt">
6079 <cell alignment="center" valignment="top" usebox="none">
6082 \begin_layout Plain Layout
6083 all brackets in the same size:
6088 <cell alignment="center" valignment="top" usebox="none">
6091 \begin_layout Plain Layout
6092 \begin_inset Formula $((A+B)(A-B))^{C}$
6101 <row topspace="2mm">
6102 <cell alignment="center" valignment="top" usebox="none">
6105 \begin_layout Plain Layout
6111 <cell alignment="center" valignment="top" usebox="none">
6114 \begin_layout Plain Layout
6115 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6131 \begin_layout Standard
6132 For the second formula the command
6139 \begin_inset space \textvisiblespace{}
6147 \begin_layout Standard
6148 Here is an overview about all bracket sizes:
6151 \begin_layout Standard
6168 \begin_inset space \textvisiblespace{}
6176 \begin_inset space \textvisiblespace{}
6180 \begin_inset space \textvisiblespace{}
6190 \begin_layout Standard
6192 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6198 \begin_layout Standard
6205 -commands there is the variant
6212 \begin_inset Index idx
6215 \begin_layout Plain Layout
6223 that adds a bit more space between the bracket and its content, and the
6237 \begin_inset Index idx
6240 \begin_layout Plain Layout
6250 , that don't add additional space.
6255 at the end of the command
6261 is for a left bracket; for a right bracket this will be replaced by an
6267 A left or right bracket can each be an opening or closing bracket.
6270 \begin_layout Standard
6271 In the following table is a comparison of the variants:
6274 \begin_layout Standard
6276 \begin_inset Tabular
6277 <lyxtabular version="3" rows="5" columns="2">
6278 <features booktabs="true" tabularvalignment="middle">
6279 <column alignment="center" valignment="top" width="0pt">
6280 <column alignment="center" valignment="middle">
6282 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6285 \begin_layout Plain Layout
6291 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6294 \begin_layout Plain Layout
6301 <row topspace="2mm">
6302 <cell alignment="center" valignment="top" usebox="none">
6305 \begin_layout Plain Layout
6315 \begin_inset space \textvisiblespace{}
6325 <cell alignment="center" valignment="top" usebox="none">
6328 \begin_layout Plain Layout
6329 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6338 <row topspace="2mm">
6339 <cell alignment="center" valignment="top" usebox="none">
6342 \begin_layout Plain Layout
6352 \begin_inset space \textvisiblespace{}
6362 <cell alignment="center" valignment="top" usebox="none">
6365 \begin_layout Plain Layout
6366 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6375 <row topspace="2mm" bottomspace="0.5mm">
6376 <cell alignment="center" valignment="top" usebox="none">
6379 \begin_layout Plain Layout
6389 \begin_inset space \textvisiblespace{}
6399 <cell alignment="center" valignment="top" usebox="none">
6402 \begin_layout Plain Layout
6403 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6412 <row topspace="1.5mm" bottomspace="0.5mm">
6413 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6416 \begin_layout Plain Layout
6428 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6431 \begin_layout Plain Layout
6432 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6448 \begin_layout Subsubsection
6449 Automatic Bracket Size
6450 \begin_inset CommandInset label
6452 name "subsec:Automatic-Bracket-Size"
6457 \begin_inset Index idx
6460 \begin_layout Plain Layout
6461 Bracket size ! automatic
6469 \begin_layout Standard
6470 Brackets with variable size can be inserted with the commands
6477 \begin_inset Index idx
6480 \begin_layout Plain Layout
6495 \begin_inset Index idx
6498 \begin_layout Plain Layout
6506 or via the math toolbar button
6509 arg "dialog-show mathdelimiter"
6525 the wanted bracket must be inserted.
6526 The bracket size will then automatically be calculated for the output.
6529 \begin_layout Standard
6531 normal bracket: The command
6538 \begin_inset space \textvisiblespace{}
6542 \begin_inset Formula $\downarrow$
6546 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula
6562 \begin_layout Standard
6564 multiline bracket: The command
6573 \begin_inset space \textvisiblespace{}
6577 \begin_inset Formula $\downarrow$
6581 \begin_inset space \textvisiblespace{}
6589 \begin_inset Formula
6591 \ln\left(\frac{A}{C}\right)
6599 \begin_layout Standard
6615 \begin_inset space ~
6621 This has the advantage that you can see in \SpecialChar LyX
6622 immediately the real bracket
6623 size and that the matching right bracket will be created too.
6624 \begin_inset Newline newline
6627 The command for the last example would then be:
6638 \begin_inset space \textvisiblespace{}
6642 \begin_inset Formula $\downarrow$
6648 \begin_layout Standard
6649 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6650 For example the command
6657 \begin_inset space \textvisiblespace{}
6661 \begin_inset Formula $\downarrow$
6665 \begin_inset space \textvisiblespace{}
6675 \begin_inset Formula
6677 \left.\frac{A}{B}\right\}
6696 will be converted by \SpecialChar LyX
6697 to brackets in the right size when the document is
6698 reloaded and an omitted bracket will appear as dashed line.
6701 \begin_layout Standard
6702 \begin_inset VSpace bigskip
6705 Because all popular \SpecialChar LaTeX
6706 distributions use e\SpecialChar TeX
6707 , an extension to \SpecialChar LaTeX
6716 \begin_inset Index idx
6719 \begin_layout Plain Layout
6727 is additionally available for all brackets and limits.
6728 With this command the height of the following character is adapted to the
6729 one of the surrounding brackets, what is e.
6730 \begin_inset space \thinspace{}
6734 \begin_inset space \space{}
6737 needed for physical vectors:
6738 \begin_inset Formula
6740 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6745 For physical vectors there is a special \SpecialChar LaTeX
6746 -package, described in
6747 \begin_inset CommandInset ref
6749 reference "subsec:Physical-Vectors"
6756 \begin_layout Subsection
6758 \begin_inset Index idx
6761 \begin_layout Plain Layout
6762 Brackets ! horizontal
6770 \begin_layout Standard
6772 \begin_inset Tabular
6773 <lyxtabular version="3" rows="4" columns="2">
6774 <features booktabs="true" tabularvalignment="middle">
6775 <column alignment="center" valignment="top" width="0pt">
6776 <column alignment="center" valignment="top" width="0pt">
6778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6781 \begin_layout Plain Layout
6787 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6790 \begin_layout Plain Layout
6798 <cell alignment="center" valignment="top" usebox="none">
6801 \begin_layout Plain Layout
6805 \begin_inset space \textvisiblespace{}
6809 \begin_inset space \textvisiblespace{}
6813 \begin_inset Index idx
6816 \begin_layout Plain Layout
6829 <cell alignment="center" valignment="top" usebox="none">
6832 \begin_layout Plain Layout
6833 \begin_inset Formula $\overbrace{A+B}^{3}$
6842 <row topspace="2mm">
6843 <cell alignment="center" valignment="top" usebox="none">
6846 \begin_layout Plain Layout
6850 \begin_inset space \textvisiblespace{}
6854 \begin_inset space \textvisiblespace{}
6858 \begin_inset Index idx
6861 \begin_layout Plain Layout
6874 <cell alignment="center" valignment="top" usebox="none">
6877 \begin_layout Plain Layout
6878 \begin_inset Formula $\underbrace{A+B}_{5}$
6888 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6891 \begin_layout Plain Layout
6895 \begin_inset space \textvisiblespace{}
6901 \begin_inset space \textvisiblespace{}
6905 \begin_inset space \textvisiblespace{}
6909 \begin_inset space \textvisiblespace{}
6913 \begin_inset space \textvisiblespace{}
6917 \begin_inset space \textvisiblespace{}
6921 \begin_inset space \textvisiblespace{}
6929 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6932 \begin_layout Plain Layout
6933 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6949 \begin_layout Standard
6950 In the last example it doesn't matter if
6962 is inserted at first.
6965 \begin_layout Standard
6966 \begin_inset VSpace medskip
6972 \begin_layout Standard
6973 If you set in the document settings under
6976 \begin_inset space ~
6986 \begin_inset Index idx
6989 \begin_layout Plain Layout
6990 Packages ! mathtools
6998 \begin_inset space ~
7003 , you have access to square backets:
7006 \begin_layout Standard
7008 \begin_inset Tabular
7009 <lyxtabular version="3" rows="4" columns="2">
7010 <features booktabs="true" tabularvalignment="middle">
7011 <column alignment="center" valignment="top" width="0pt">
7012 <column alignment="center" valignment="top" width="0pt">
7014 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7017 \begin_layout Plain Layout
7023 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7026 \begin_layout Plain Layout
7034 <cell alignment="center" valignment="top" usebox="none">
7037 \begin_layout Plain Layout
7065 \begin_inset space \textvisiblespace{}
7069 \begin_inset Index idx
7072 \begin_layout Plain Layout
7085 <cell alignment="center" valignment="top" usebox="none">
7088 \begin_layout Plain Layout
7089 \begin_inset Formula $\overbracket{A+B}^{3}$
7098 <row topspace="2mm">
7099 <cell alignment="center" valignment="top" usebox="none">
7102 \begin_layout Plain Layout
7130 \begin_inset space \textvisiblespace{}
7134 \begin_inset Index idx
7137 \begin_layout Plain Layout
7162 <cell alignment="center" valignment="top" usebox="none">
7165 \begin_layout Plain Layout
7166 \begin_inset Formula $\underbracket{A+B}_{5}$
7176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7179 \begin_layout Plain Layout
7185 \begin_inset space \textvisiblespace{}
7189 \begin_inset space \textvisiblespace{}
7193 \begin_inset space \textvisiblespace{}
7197 \begin_inset space \textvisiblespace{}
7201 \begin_inset space \textvisiblespace{}
7209 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7212 \begin_layout Plain Layout
7213 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7229 \begin_layout Standard
7242 you can change the thickness of the bracket's stroke by specifying the
7243 desired thickness in square brackets behind the command:
7246 \begin_layout Standard
7248 \begin_inset Tabular
7249 <lyxtabular version="3" rows="3" columns="2">
7250 <features booktabs="true" tabularvalignment="middle">
7251 <column alignment="center" valignment="top" width="0pt">
7252 <column alignment="center" valignment="top" width="0pt">
7254 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7257 \begin_layout Plain Layout
7263 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7266 \begin_layout Plain Layout
7274 <cell alignment="center" valignment="top" usebox="none">
7277 \begin_layout Plain Layout
7307 \begin_inset space \textvisiblespace{}
7315 <cell alignment="center" valignment="top" usebox="none">
7318 \begin_layout Plain Layout
7319 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7328 <row topspace="2mm">
7329 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7332 \begin_layout Plain Layout
7362 \begin_inset space \textvisiblespace{}
7370 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7373 \begin_layout Plain Layout
7374 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7390 \begin_layout Standard
7391 \begin_inset VSpace bigskip
7394 When brackets should overlap each other, multiline formulas, as described
7396 \begin_inset CommandInset ref
7398 reference "sec:Multiline-Formulas"
7403 \begin_inset Formula
7405 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7406 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7411 In the first row the formula is inserted together with the first brace.
7412 It is hereby important that the space command
7416 \begin_layout Plain Layout
7417 Space commands are explained in
7418 \begin_inset CommandInset ref
7420 reference "subsec:Predefined-Space"
7435 is inserted before the first
7436 \begin_inset Formula $d$
7439 , because the brace that ends behind the
7440 \begin_inset Formula $q$
7443 prevents that the following
7444 \begin_inset Quotes eld
7448 \begin_inset Quotes erd
7451 is surrounded by space.
7455 \begin_layout Plain Layout
7456 because a bracket is not handled as a character, see
7457 \begin_inset CommandInset ref
7459 reference "subsec:Binary-Operators"
7468 In the second row the second brace is inserted.
7469 As it should begin before the
7470 \begin_inset Formula $b$
7485 \begin_layout Plain Layout
7493 \begin_inset CommandInset ref
7495 reference "subsec:Placeholders"
7504 This space is needed because the
7505 \begin_inset Quotes eld
7509 \begin_inset Quotes erd
7512 is also surrounded by space in the formula.
7513 The brace is placed under the command
7522 \begin_layout Standard
7523 It gets more complicated when brackets overlap each other above and under
7524 the formula, like in the following example:
7528 \begin_layout Plain Layout
7540 \begin_inset Formula
7542 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7543 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7552 \begin_layout Plain Layout
7563 The first formula row is the same as the second row of the previous example,
7564 with the difference that the brace is above.
7565 The second row contains the formula together with the second brace.
7566 To avoid that there is space between the upper brace in the first row and
7567 the formula, the row spacing needs to be reduced.
7568 This is not easily possible due to a bug in \SpecialChar LyX
7573 \begin_layout Plain Layout
7574 \begin_inset CommandInset href
7576 name "LyX-bug #1505"
7577 target "https://www.lyx.org/trac/ticket/1505"
7587 As a solution for the problem, the global formula row separation
7594 \begin_inset Index idx
7597 \begin_layout Plain Layout
7605 must be changed to -6
7606 \begin_inset space \thinspace{}
7609 pt before the formula with the command
7625 is set back after the formula to the standard value of 3
7626 \begin_inset space \thinspace{}
7629 pt using the same command.
7630 More about the row separation in formulas is explained in
7631 \begin_inset CommandInset ref
7633 reference "subsec:Line-Separation"
7640 \begin_layout Section
7642 \begin_inset Index idx
7645 \begin_layout Plain Layout
7654 \begin_layout Standard
7655 Arrows can be inserted via the math toolbar button
7658 arg "math-insert \\leftarrow"
7661 or the commands listed in the following subsections.
7664 \begin_layout Subsection
7666 \begin_inset Index idx
7669 \begin_layout Plain Layout
7678 \begin_layout Standard
7679 \begin_inset space \hfill{}
7683 \begin_inset Tabular
7684 <lyxtabular version="3" rows="8" columns="2">
7685 <features booktabs="true" tabularvalignment="middle">
7686 <column alignment="center" valignment="top" width="0pt">
7687 <column alignment="center" valignment="top" width="0pt">
7689 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7692 \begin_layout Plain Layout
7698 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7701 \begin_layout Plain Layout
7709 <cell alignment="center" valignment="top" usebox="none">
7712 \begin_layout Plain Layout
7720 <cell alignment="center" valignment="top" usebox="none">
7723 \begin_layout Plain Layout
7724 \begin_inset Formula $\gets$
7734 <cell alignment="center" valignment="top" usebox="none">
7737 \begin_layout Plain Layout
7745 <cell alignment="center" valignment="top" usebox="none">
7748 \begin_layout Plain Layout
7749 \begin_inset Formula $\Leftarrow$
7759 <cell alignment="center" valignment="top" usebox="none">
7762 \begin_layout Plain Layout
7770 <cell alignment="center" valignment="top" usebox="none">
7773 \begin_layout Plain Layout
7774 \begin_inset Formula $\longleftarrow$
7784 <cell alignment="center" valignment="top" usebox="none">
7787 \begin_layout Plain Layout
7795 <cell alignment="center" valignment="top" usebox="none">
7798 \begin_layout Plain Layout
7799 \begin_inset Formula $\Longleftarrow$
7809 <cell alignment="center" valignment="top" usebox="none">
7812 \begin_layout Plain Layout
7820 <cell alignment="center" valignment="top" usebox="none">
7823 \begin_layout Plain Layout
7824 \begin_inset Formula $\leftharpoonup$
7834 <cell alignment="center" valignment="top" usebox="none">
7837 \begin_layout Plain Layout
7845 <cell alignment="center" valignment="top" usebox="none">
7848 \begin_layout Plain Layout
7849 \begin_inset Formula $\leftharpoondown$
7859 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7862 \begin_layout Plain Layout
7870 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7873 \begin_layout Plain Layout
7874 \begin_inset Formula $\hookleftarrow$
7888 \begin_inset space \hfill{}
7892 \begin_inset Tabular
7893 <lyxtabular version="3" rows="8" columns="2">
7894 <features booktabs="true" tabularvalignment="middle">
7895 <column alignment="center" valignment="top" width="0pt">
7896 <column alignment="center" valignment="top" width="0pt">
7898 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7901 \begin_layout Plain Layout
7907 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7910 \begin_layout Plain Layout
7918 <cell alignment="center" valignment="top" usebox="none">
7921 \begin_layout Plain Layout
7929 <cell alignment="center" valignment="top" usebox="none">
7932 \begin_layout Plain Layout
7933 \begin_inset Formula $\to$
7943 <cell alignment="center" valignment="top" usebox="none">
7946 \begin_layout Plain Layout
7954 <cell alignment="center" valignment="top" usebox="none">
7957 \begin_layout Plain Layout
7958 \begin_inset Formula $\Rightarrow$
7968 <cell alignment="center" valignment="top" usebox="none">
7971 \begin_layout Plain Layout
7979 <cell alignment="center" valignment="top" usebox="none">
7982 \begin_layout Plain Layout
7983 \begin_inset Formula $\longrightarrow$
7993 <cell alignment="center" valignment="top" usebox="none">
7996 \begin_layout Plain Layout
8004 <cell alignment="center" valignment="top" usebox="none">
8007 \begin_layout Plain Layout
8008 \begin_inset Formula $\Longrightarrow$
8018 <cell alignment="center" valignment="top" usebox="none">
8021 \begin_layout Plain Layout
8029 <cell alignment="center" valignment="top" usebox="none">
8032 \begin_layout Plain Layout
8033 \begin_inset Formula $\rightharpoonup$
8043 <cell alignment="center" valignment="top" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\rightharpoondown$
8068 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8082 \begin_layout Plain Layout
8083 \begin_inset Formula $\hookrightarrow$
8097 \begin_inset space \hfill{}
8103 \begin_layout Standard
8104 \begin_inset space \hfill{}
8108 \begin_inset Tabular
8109 <lyxtabular version="3" rows="6" columns="2">
8110 <features booktabs="true" tabularvalignment="middle">
8111 <column alignment="center" valignment="top" width="0pt">
8112 <column alignment="center" valignment="top" width="0pt">
8114 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8117 \begin_layout Plain Layout
8123 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8126 \begin_layout Plain Layout
8134 <cell alignment="center" valignment="top" usebox="none">
8137 \begin_layout Plain Layout
8145 <cell alignment="center" valignment="top" usebox="none">
8148 \begin_layout Plain Layout
8149 \begin_inset Formula $\leftrightarrow$
8159 <cell alignment="center" valignment="top" usebox="none">
8162 \begin_layout Plain Layout
8170 <cell alignment="center" valignment="top" usebox="none">
8173 \begin_layout Plain Layout
8174 \begin_inset Formula $\Leftrightarrow$
8184 <cell alignment="center" valignment="top" usebox="none">
8187 \begin_layout Plain Layout
8195 <cell alignment="center" valignment="top" usebox="none">
8198 \begin_layout Plain Layout
8199 \begin_inset Formula $\longleftrightarrow$
8209 <cell alignment="center" valignment="top" usebox="none">
8212 \begin_layout Plain Layout
8220 <cell alignment="center" valignment="top" usebox="none">
8223 \begin_layout Plain Layout
8224 \begin_inset Formula $\Longleftrightarrow$
8234 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8237 \begin_layout Plain Layout
8245 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8248 \begin_layout Plain Layout
8249 \begin_inset Formula $\rightleftharpoons$
8263 \begin_inset space \hspace{}
8268 \begin_inset space \hfill{}
8272 \begin_inset Tabular
8273 <lyxtabular version="3" rows="5" columns="2">
8274 <features booktabs="true" tabularvalignment="middle">
8275 <column alignment="center" valignment="top" width="0pt">
8276 <column alignment="center" valignment="top" width="0pt">
8278 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8281 \begin_layout Plain Layout
8287 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8290 \begin_layout Plain Layout
8298 <cell alignment="center" valignment="top" usebox="none">
8301 \begin_layout Plain Layout
8309 <cell alignment="center" valignment="top" usebox="none">
8312 \begin_layout Plain Layout
8313 \begin_inset Formula $\mapsto$
8323 <cell alignment="center" valignment="top" usebox="none">
8326 \begin_layout Plain Layout
8334 <cell alignment="center" valignment="top" usebox="none">
8337 \begin_layout Plain Layout
8338 \begin_inset Formula $\longmapsto$
8348 <cell alignment="center" valignment="top" usebox="none">
8351 \begin_layout Plain Layout
8359 <cell alignment="center" valignment="top" usebox="none">
8362 \begin_layout Plain Layout
8363 \begin_inset Formula $\leadsto$
8373 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8376 \begin_layout Plain Layout
8384 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8387 \begin_layout Plain Layout
8388 \begin_inset Formula $\dasharrow$
8402 \begin_inset space \hfill{}
8408 \begin_layout Standard
8409 \begin_inset VSpace medskip
8412 Arrows used as accents like e.
8413 \begin_inset space \thinspace{}
8417 \begin_inset space \space{}
8420 vector arrows are listed in
8421 \begin_inset CommandInset ref
8423 reference "sec:Accents"
8430 \begin_layout Standard
8431 \begin_inset VSpace bigskip
8434 Furthermore there are the labeled arrows
8435 \begin_inset Index idx
8438 \begin_layout Plain Layout
8451 \begin_inset Index idx
8454 \begin_layout Plain Layout
8469 \begin_inset Index idx
8472 \begin_layout Plain Layout
8479 \begin_layout Plain Layout
8494 When inserting one of these commands in a formula, an arrow with two blue
8495 boxes appear where the label can be inserted.
8496 The length of the arrow adapts to the label width.
8499 \begin_layout Standard
8501 \begin_inset Tabular
8502 <lyxtabular version="3" rows="3" columns="2">
8503 <features booktabs="true" tabularvalignment="middle">
8504 <column alignment="center" valignment="top" width="0pt">
8505 <column alignment="center" valignment="top" width="0pt">
8507 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8510 \begin_layout Plain Layout
8516 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8519 \begin_layout Plain Layout
8527 <cell alignment="center" valignment="top" usebox="none">
8530 \begin_layout Plain Layout
8534 \begin_inset space \textvisiblespace{}
8538 \begin_inset Formula $\downarrow$
8542 \begin_inset Formula $\to$
8550 <cell alignment="center" valignment="top" usebox="none">
8553 \begin_layout Plain Layout
8554 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8563 <row topspace="2mm">
8564 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8567 \begin_layout Plain Layout
8571 \begin_inset space \textvisiblespace{}
8575 \begin_inset Formula $\downarrow$
8579 \begin_inset Formula $\to$
8587 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8590 \begin_layout Plain Layout
8591 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8607 \begin_layout Standard
8608 \begin_inset VSpace medskip
8614 \begin_layout Standard
8615 If you set in the document settings under
8618 \begin_inset space ~
8628 \begin_inset Index idx
8631 \begin_layout Plain Layout
8632 Packages ! mathtools
8640 \begin_inset space ~
8645 , you have access to the following labeled arrows:
8648 \begin_layout Standard
8649 \begin_inset Newpage newpage
8655 \begin_layout Standard
8657 \begin_inset space \hspace*{\fill}
8661 \begin_inset Tabular
8662 <lyxtabular version="3" rows="7" columns="2">
8663 <features booktabs="true" tabularvalignment="middle">
8664 <column alignment="center" valignment="top" width="0pt">
8665 <column alignment="center" valignment="top" width="0pt">
8667 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8670 \begin_layout Plain Layout
8676 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8679 \begin_layout Plain Layout
8687 <cell alignment="center" valignment="top" usebox="none">
8690 \begin_layout Plain Layout
8710 <cell alignment="center" valignment="top" usebox="none">
8713 \begin_layout Plain Layout
8714 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8723 <row topspace="2mm">
8724 <cell alignment="center" valignment="top" usebox="none">
8727 \begin_layout Plain Layout
8747 <cell alignment="center" valignment="top" usebox="none">
8750 \begin_layout Plain Layout
8751 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8760 <row topspace="2mm">
8761 <cell alignment="center" valignment="top" usebox="none">
8764 \begin_layout Plain Layout
8784 <cell alignment="center" valignment="top" usebox="none">
8787 \begin_layout Plain Layout
8788 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8797 <row topspace="2mm">
8798 <cell alignment="center" valignment="top" usebox="none">
8801 \begin_layout Plain Layout
8821 <cell alignment="center" valignment="top" usebox="none">
8824 \begin_layout Plain Layout
8825 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8834 <row topspace="2mm">
8835 <cell alignment="center" valignment="top" usebox="none">
8838 \begin_layout Plain Layout
8858 <cell alignment="center" valignment="top" usebox="none">
8861 \begin_layout Plain Layout
8862 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8871 <row topspace="2mm">
8872 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8875 \begin_layout Plain Layout
8895 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8898 \begin_layout Plain Layout
8899 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8913 \begin_inset space \hspace*{\fill}
8917 \begin_inset Tabular
8918 <lyxtabular version="3" rows="7" columns="2">
8919 <features booktabs="true" tabularvalignment="middle">
8920 <column alignment="center" valignment="top" width="0pt">
8921 <column alignment="center" valignment="top" width="0pt">
8923 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8926 \begin_layout Plain Layout
8932 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8935 \begin_layout Plain Layout
8943 <cell alignment="center" valignment="top" usebox="none">
8946 \begin_layout Plain Layout
8966 <cell alignment="center" valignment="top" usebox="none">
8969 \begin_layout Plain Layout
8970 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8979 <row topspace="2mm">
8980 <cell alignment="center" valignment="top" usebox="none">
8983 \begin_layout Plain Layout
9003 <cell alignment="center" valignment="top" usebox="none">
9006 \begin_layout Plain Layout
9007 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9016 <row topspace="2mm">
9017 <cell alignment="center" valignment="top" usebox="none">
9020 \begin_layout Plain Layout
9040 <cell alignment="center" valignment="top" usebox="none">
9043 \begin_layout Plain Layout
9044 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9053 <row topspace="2mm">
9054 <cell alignment="center" valignment="top" usebox="none">
9057 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" usebox="none">
9080 \begin_layout Plain Layout
9081 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9090 <row topspace="2mm">
9091 <cell alignment="center" valignment="top" usebox="none">
9094 \begin_layout Plain Layout
9114 <cell alignment="center" valignment="top" usebox="none">
9117 \begin_layout Plain Layout
9118 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9127 <row topspace="2mm">
9128 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9131 \begin_layout Plain Layout
9151 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9154 \begin_layout Plain Layout
9155 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9169 \begin_inset space \hspace*{\fill}
9175 \begin_layout Standard
9176 The command scheme is for all these arrows:
9179 \begin_layout Standard
9181 \begin_inset Tabular
9182 <lyxtabular version="3" rows="2" columns="2">
9183 <features booktabs="true" tabularvalignment="middle">
9184 <column alignment="center" valignment="top" width="0pt">
9185 <column alignment="center" valignment="top" width="0pt">
9187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9190 \begin_layout Plain Layout
9196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9199 \begin_layout Plain Layout
9206 <row bottomspace="0.5mm">
9207 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9210 \begin_layout Plain Layout
9213 xleftrightarrow[x=a]
9216 \begin_inset Formula $\to$
9224 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9227 \begin_layout Plain Layout
9228 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9244 \begin_layout Subsection
9245 Vertical and diagonal Arrows
9246 \begin_inset Index idx
9249 \begin_layout Plain Layout
9256 \begin_inset Index idx
9259 \begin_layout Plain Layout
9268 \begin_layout Standard
9269 \begin_inset space \hfill{}
9273 \begin_inset Tabular
9274 <lyxtabular version="3" rows="7" columns="2">
9275 <features booktabs="true" tabularvalignment="middle">
9276 <column alignment="center" valignment="top" width="0pt">
9277 <column alignment="center" valignment="top" width="0pt">
9279 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9282 \begin_layout Plain Layout
9288 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9291 \begin_layout Plain Layout
9299 <cell alignment="center" valignment="top" usebox="none">
9302 \begin_layout Plain Layout
9310 <cell alignment="center" valignment="top" usebox="none">
9313 \begin_layout Plain Layout
9314 \begin_inset Formula $\uparrow$
9324 <cell alignment="center" valignment="top" usebox="none">
9327 \begin_layout Plain Layout
9335 <cell alignment="center" valignment="top" usebox="none">
9338 \begin_layout Plain Layout
9339 \begin_inset Formula $\Uparrow$
9349 <cell alignment="center" valignment="top" usebox="none">
9352 \begin_layout Plain Layout
9360 <cell alignment="center" valignment="top" usebox="none">
9363 \begin_layout Plain Layout
9364 \begin_inset Formula $\updownarrow$
9374 <cell alignment="center" valignment="top" usebox="none">
9377 \begin_layout Plain Layout
9385 <cell alignment="center" valignment="top" usebox="none">
9388 \begin_layout Plain Layout
9389 \begin_inset Formula $\Updownarrow$
9399 <cell alignment="center" valignment="top" usebox="none">
9402 \begin_layout Plain Layout
9410 <cell alignment="center" valignment="top" usebox="none">
9413 \begin_layout Plain Layout
9414 \begin_inset Formula $\Downarrow$
9424 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9427 \begin_layout Plain Layout
9435 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9438 \begin_layout Plain Layout
9439 \begin_inset Formula $\downarrow$
9453 \begin_inset space \hfill{}
9457 \begin_inset Tabular
9458 <lyxtabular version="3" rows="5" columns="2">
9459 <features booktabs="true" tabularvalignment="middle">
9460 <column alignment="center" valignment="top" width="0pt">
9461 <column alignment="center" valignment="top" width="0pt">
9463 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9466 \begin_layout Plain Layout
9472 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9475 \begin_layout Plain Layout
9483 <cell alignment="center" valignment="top" usebox="none">
9486 \begin_layout Plain Layout
9494 <cell alignment="center" valignment="top" usebox="none">
9497 \begin_layout Plain Layout
9498 \begin_inset Formula $\nearrow$
9508 <cell alignment="center" valignment="top" usebox="none">
9511 \begin_layout Plain Layout
9519 <cell alignment="center" valignment="top" usebox="none">
9522 \begin_layout Plain Layout
9523 \begin_inset Formula $\searrow$
9533 <cell alignment="center" valignment="top" usebox="none">
9536 \begin_layout Plain Layout
9544 <cell alignment="center" valignment="top" usebox="none">
9547 \begin_layout Plain Layout
9548 \begin_inset Formula $\swarrow$
9558 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9561 \begin_layout Plain Layout
9569 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9572 \begin_layout Plain Layout
9573 \begin_inset Formula $\nwarrow$
9587 \begin_inset space \hfill{}
9593 \begin_layout Standard
9594 \begin_inset VSpace medskip
9597 Vertical arrows can be used also as delimiters together with the commands
9599 \begin_inset CommandInset ref
9601 reference "subsec:Manual-Bracket-Size"
9606 \begin_inset CommandInset ref
9608 reference "subsec:Automatic-Bracket-Size"
9615 \begin_layout Section
9617 \begin_inset CommandInset label
9624 \begin_inset Index idx
9627 \begin_layout Plain Layout
9636 \begin_layout Standard
9637 Accents can be inserted via the math toolbar button
9640 arg "math-insert \\hat"
9643 or the commands listed in the following subsections.
9646 \begin_layout Subsection
9647 Accents for one Character
9651 \begin_layout Plain Layout
9664 \begin_layout Plain Layout
9666 \begin_inset CommandInset ref
9668 reference "subsec:Accents-in-Text"
9681 \begin_layout Plain Layout
9689 \begin_inset Note Note
9692 \begin_layout Plain Layout
9699 is used to avoid that the footnote appears in the PDF-bookmark.
9702 \begin_layout Plain Layout
9710 \begin_inset CommandInset ref
9712 reference "subsec:Formulas-in-Section"
9722 \begin_inset CommandInset label
9724 name "subsec:Accents-for-one"
9729 \begin_inset Index idx
9732 \begin_layout Plain Layout
9733 Accents ! for one character
9741 \begin_layout Standard
9742 \begin_inset space \hfill{}
9746 \begin_inset Tabular
9747 <lyxtabular version="3" rows="8" columns="2">
9748 <features booktabs="true" tabularvalignment="middle">
9749 <column alignment="center" valignment="top" width="0pt">
9750 <column alignment="center" valignment="top" width="0pt">
9752 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9755 \begin_layout Plain Layout
9761 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9764 \begin_layout Plain Layout
9771 <row topspace="1.5mm">
9772 <cell alignment="center" valignment="top" usebox="none">
9775 \begin_layout Plain Layout
9779 \begin_inset space \textvisiblespace{}
9787 <cell alignment="center" valignment="top" usebox="none">
9790 \begin_layout Plain Layout
9791 \begin_inset Formula $\dot{A}$
9800 <row topspace="1.5mm">
9801 <cell alignment="center" valignment="top" usebox="none">
9804 \begin_layout Plain Layout
9808 \begin_inset space \textvisiblespace{}
9816 <cell alignment="center" valignment="top" usebox="none">
9819 \begin_layout Plain Layout
9820 \begin_inset Formula $\ddot{A}$
9829 <row topspace="1.5mm">
9830 <cell alignment="center" valignment="top" usebox="none">
9833 \begin_layout Plain Layout
9837 \begin_inset space \textvisiblespace{}
9845 <cell alignment="center" valignment="top" usebox="none">
9848 \begin_layout Plain Layout
9849 \begin_inset Formula $\dddot{A}$
9858 <row topspace="1.5mm">
9859 <cell alignment="center" valignment="top" usebox="none">
9862 \begin_layout Plain Layout
9866 \begin_inset space \textvisiblespace{}
9874 <cell alignment="center" valignment="top" usebox="none">
9877 \begin_layout Plain Layout
9878 \begin_inset Formula $\ddddot{A}$
9887 <row topspace="1.5mm">
9888 <cell alignment="center" valignment="top" usebox="none">
9891 \begin_layout Plain Layout
9895 \begin_inset space \textvisiblespace{}
9899 \begin_inset Index idx
9902 \begin_layout Plain Layout
9913 <cell alignment="center" valignment="top" usebox="none">
9916 \begin_layout Plain Layout
9917 \begin_inset Formula $\vec{A}$
9926 <row topspace="1.5mm">
9927 <cell alignment="center" valignment="top" usebox="none">
9930 \begin_layout Plain Layout
9934 \begin_inset space \textvisiblespace{}
9942 <cell alignment="center" valignment="top" usebox="none">
9945 \begin_layout Plain Layout
9946 \begin_inset Formula $\bar{A}$
9955 <row topspace="1.5mm">
9956 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9959 \begin_layout Plain Layout
9963 \begin_inset space \textvisiblespace{}
9971 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9974 \begin_layout Plain Layout
9975 \begin_inset Formula $\mathring{A}$
9989 \begin_inset space \hfill{}
9993 \begin_inset Tabular
9994 <lyxtabular version="3" rows="7" columns="2">
9995 <features booktabs="true" tabularvalignment="middle">
9996 <column alignment="center" valignment="top" width="0pt">
9997 <column alignment="center" valignment="top" width="0pt">
9999 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10002 \begin_layout Plain Layout
10008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10011 \begin_layout Plain Layout
10018 <row topspace="1.5mm">
10019 <cell alignment="center" valignment="top" usebox="none">
10022 \begin_layout Plain Layout
10026 \begin_inset space \textvisiblespace{}
10034 <cell alignment="center" valignment="top" usebox="none">
10037 \begin_layout Plain Layout
10038 \begin_inset Formula $\tilde{A}$
10047 <row topspace="1.5mm">
10048 <cell alignment="center" valignment="top" usebox="none">
10051 \begin_layout Plain Layout
10055 \begin_inset space \textvisiblespace{}
10063 <cell alignment="center" valignment="top" usebox="none">
10066 \begin_layout Plain Layout
10067 \begin_inset Formula $\hat{A}$
10076 <row topspace="1.5mm">
10077 <cell alignment="center" valignment="top" usebox="none">
10080 \begin_layout Plain Layout
10084 \begin_inset space \textvisiblespace{}
10092 <cell alignment="center" valignment="top" usebox="none">
10095 \begin_layout Plain Layout
10096 \begin_inset Formula $\check{A}$
10105 <row topspace="1.5mm">
10106 <cell alignment="center" valignment="top" usebox="none">
10109 \begin_layout Plain Layout
10113 \begin_inset space \textvisiblespace{}
10121 <cell alignment="center" valignment="top" usebox="none">
10124 \begin_layout Plain Layout
10125 \begin_inset Formula $\acute{A}$
10134 <row topspace="1.5mm">
10135 <cell alignment="center" valignment="top" usebox="none">
10138 \begin_layout Plain Layout
10142 \begin_inset space \textvisiblespace{}
10150 <cell alignment="center" valignment="top" usebox="none">
10153 \begin_layout Plain Layout
10154 \begin_inset Formula $\grave{A}$
10163 <row topspace="1.5mm">
10164 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10167 \begin_layout Plain Layout
10171 \begin_inset space \textvisiblespace{}
10179 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10182 \begin_layout Plain Layout
10183 \begin_inset Formula $\breve{A}$
10197 \begin_inset space \hfill{}
10203 \begin_layout Standard
10204 \begin_inset VSpace bigskip
10210 \begin_layout Standard
10211 You can directly insert accents like é to formulas.
10213 will transform them to the corresponding accent command.
10215 \begin_inset Index idx
10218 \begin_layout Plain Layout
10224 it is better to insert a quotation mark before the vowel.
10225 These two characters are then treated by \SpecialChar LaTeX
10230 character when the formula part with the umlaut is marked as German.
10238 \begin_inset Quotes eld
10242 \begin_inset Quotes erd
10245 umlauts are created as demonstrated in the following example:
10248 \begin_layout Standard
10249 \begin_inset VSpace -2mm
10255 \begin_layout Standard
10257 \begin_inset Tabular
10258 <lyxtabular version="3" rows="3" columns="2">
10259 <features booktabs="true" tabularvalignment="middle">
10260 <column alignment="center" valignment="top" width="0pt">
10261 <column alignment="center" valignment="top">
10263 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10266 \begin_layout Plain Layout
10272 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10275 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" usebox="none">
10286 \begin_layout Plain Layout
10287 \begin_inset Quotes grd
10295 <cell alignment="center" valignment="top" usebox="none">
10298 \begin_layout Plain Layout
10299 \begin_inset space \hspace{}
10306 \begin_inset Formula $"i$
10315 <row topspace="1.5mm">
10316 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10319 \begin_layout Plain Layout
10323 \begin_inset space \textvisiblespace{}
10331 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10334 \begin_layout Plain Layout
10335 \begin_inset Formula $\ddot{i}$
10351 \begin_layout Standard
10352 Another advantage to
10358 is that umlauts can directly be converted to mathematical text because
10359 the accent commands above are
10365 in mathematical text
10368 To convert an accented character to mathematical text, only the character
10369 under the accent may be converted.
10370 This applies also for all other conversions, e.
10371 \begin_inset space \thinspace{}
10375 \begin_inset space \space{}
10381 \begin_layout Standard
10382 In mathematical text, umlauts and other accented characters can directly
10386 \begin_layout Standard
10387 \begin_inset VSpace bigskip
10393 \begin_layout Standard
10395 also supports a tilde under the character if the \SpecialChar LaTeX
10401 \begin_inset Index idx
10404 \begin_layout Plain Layout
10405 Packages ! undertilde
10410 is installed on your system:
10413 \begin_layout Standard
10417 \begin_layout Plain Layout
10427 \begin_inset Note Note
10430 \begin_layout Plain Layout
10431 The following table will only be displayed when the \SpecialChar LaTeX
10444 \begin_layout Standard
10447 \begin_inset Tabular
10448 <lyxtabular version="3" rows="2" columns="2">
10449 <features booktabs="true" tabularvalignment="middle">
10450 <column alignment="center" valignment="top" width="0pt">
10451 <column alignment="center" valignment="top" width="0pt">
10453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10456 \begin_layout Plain Layout
10462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10465 \begin_layout Plain Layout
10473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10476 \begin_layout Plain Layout
10480 \begin_inset space \textvisiblespace{}
10488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10491 \begin_layout Plain Layout
10492 \begin_inset Formula $\utilde{A}$
10508 \begin_layout Standard
10512 \begin_layout Plain Layout
10522 \begin_inset Note Note
10525 \begin_layout Plain Layout
10526 The following will be displayed when the \SpecialChar LaTeX
10539 \begin_layout Standard
10540 You need to install the \SpecialChar LaTeX
10545 to see the rest of this subsection in the output.
10548 \begin_layout Standard
10552 \begin_layout Plain Layout
10564 \begin_layout Standard
10565 \begin_inset Newpage newpage
10571 \begin_layout Subsection
10572 Accents for several Characters
10573 \begin_inset Index idx
10576 \begin_layout Plain Layout
10577 Accents ! for several characters
10585 \begin_layout Standard
10586 \begin_inset space \hfill{}
10590 \begin_inset Tabular
10591 <lyxtabular version="3" rows="5" columns="2">
10592 <features booktabs="true" tabularvalignment="middle">
10593 <column alignment="center" valignment="top" width="0pt">
10594 <column alignment="center" valignment="top" width="0pt">
10596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10599 \begin_layout Plain Layout
10605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10608 \begin_layout Plain Layout
10615 <row topspace="1.5mm">
10616 <cell alignment="center" valignment="top" usebox="none">
10619 \begin_layout Plain Layout
10623 \begin_inset space \textvisiblespace{}
10631 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10634 \begin_layout Plain Layout
10635 \begin_inset Formula $\overleftarrow{A=B}$
10644 <row topspace="1.5mm">
10645 <cell alignment="center" valignment="top" usebox="none">
10648 \begin_layout Plain Layout
10652 \begin_inset space \textvisiblespace{}
10660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10663 \begin_layout Plain Layout
10664 \begin_inset Formula $\underleftarrow{A=B}$
10673 <row topspace="1.5mm">
10674 <cell alignment="center" valignment="top" usebox="none">
10677 \begin_layout Plain Layout
10681 \begin_inset space \textvisiblespace{}
10689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10692 \begin_layout Plain Layout
10693 \begin_inset Formula $\overleftrightarrow{A=B}$
10702 <row topspace="1.5mm" bottomspace="1mm">
10703 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10706 \begin_layout Plain Layout
10709 underleftrightarrow
10710 \begin_inset space \textvisiblespace{}
10718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10721 \begin_layout Plain Layout
10722 \begin_inset Formula $\underleftrightarrow{A=B}$
10736 \begin_inset space \hfill{}
10740 \begin_inset Tabular
10741 <lyxtabular version="3" rows="5" columns="2">
10742 <features booktabs="true" tabularvalignment="middle">
10743 <column alignment="center" valignment="top" width="0pt">
10744 <column alignment="center" valignment="top" width="0pt">
10746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10749 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10765 <row topspace="1.5mm">
10766 <cell alignment="center" valignment="top" usebox="none">
10769 \begin_layout Plain Layout
10773 \begin_inset space \textvisiblespace{}
10781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10784 \begin_layout Plain Layout
10785 \begin_inset Formula $\overrightarrow{A=B}$
10794 <row topspace="1.5mm">
10795 <cell alignment="center" valignment="top" usebox="none">
10798 \begin_layout Plain Layout
10802 \begin_inset space \textvisiblespace{}
10810 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10813 \begin_layout Plain Layout
10814 \begin_inset Formula $\underrightarrow{A=B}$
10823 <row topspace="1.5mm">
10824 <cell alignment="center" valignment="top" usebox="none">
10827 \begin_layout Plain Layout
10831 \begin_inset space \textvisiblespace{}
10839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10842 \begin_layout Plain Layout
10843 \begin_inset Formula $\widetilde{A=B}$
10852 <row topspace="1.5mm" bottomspace="1mm">
10853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10856 \begin_layout Plain Layout
10860 \begin_inset space \textvisiblespace{}
10868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10871 \begin_layout Plain Layout
10872 \begin_inset Formula $\widehat{A=B}$
10886 \begin_inset space \hfill{}
10892 \begin_layout Standard
10893 \begin_inset VSpace medskip
10896 With these commands as many characters as you like can be accented.
10909 will only be set in the output with a length of three characters, as shown
10910 in the following example:
10911 \begin_inset Formula
10913 \widetilde{A+B=C-D}
10921 \begin_layout Standard
10929 \begin_inset Index idx
10932 \begin_layout Plain Layout
10947 \begin_inset Index idx
10950 \begin_layout Plain Layout
10958 described in the previous subsection it is also possible to accent several
10965 \begin_inset space \textvisiblespace{}
10969 \begin_inset Formula $\downarrow$
10975 \begin_inset Formula
10977 \underset{***}{A=B}
10985 \begin_layout Section
10987 \begin_inset CommandInset label
10989 name "subsec:Space"
10994 \begin_inset Index idx
10997 \begin_layout Plain Layout
11006 \begin_layout Subsection
11008 \begin_inset CommandInset label
11010 name "subsec:Predefined-Space"
11015 \begin_inset Index idx
11018 \begin_layout Plain Layout
11019 Space ! horizontal ! predefined
11027 \begin_layout Standard
11028 Sometimes it is necessary to insert horizontal space into a formula.
11029 This is done by inserting a protected space (shortcut
11032 arg "command-alternatives space-insert protected ; math-space"
11037 \begin_inset Quotes eld
11043 \begin_inset space \textvisiblespace{}
11049 \begin_inset Quotes erd
11052 appears and by pressing
11056 several times one can select one of eight different space sizes.
11057 The spaces can also be inserted using the math toolbar button
11060 arg "math-insert \\space"
11063 or special commands.
11064 Independent from the inserted command, one can select the size again by
11072 \begin_layout Standard
11075 \begin_inset Tabular
11076 <lyxtabular version="3" rows="6" columns="3">
11077 <features booktabs="true" tabularvalignment="middle">
11078 <column alignment="center" valignment="top">
11079 <column alignment="center" valignment="top" width="15col%">
11080 <column alignment="center" valignment="top">
11082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11085 \begin_layout Plain Layout
11091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11094 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11107 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11118 \begin_layout Plain Layout
11126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11138 \begin_layout Plain Layout
11139 \begin_inset Formula $A\,B$
11149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11152 \begin_layout Plain Layout
11160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11172 \begin_layout Plain Layout
11173 \begin_inset Formula $A\:B$
11183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11186 \begin_layout Plain Layout
11194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11197 \begin_layout Plain Layout
11203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11206 \begin_layout Plain Layout
11207 \begin_inset Formula $A\;B$
11217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11220 \begin_layout Plain Layout
11228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11231 \begin_layout Plain Layout
11237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11240 \begin_layout Plain Layout
11241 \begin_inset Formula $A\quad B$
11251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11254 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11274 \begin_layout Plain Layout
11275 \begin_inset Formula $A\qquad B$
11289 \begin_inset space \hfill{}
11293 \begin_inset Tabular
11294 <lyxtabular version="3" rows="6" columns="3">
11295 <features booktabs="true" tabularvalignment="middle">
11296 <column alignment="center" valignment="top">
11297 <column alignment="center" valignment="top" width="15col%">
11298 <column alignment="center" valignment="top">
11300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11303 \begin_layout Plain Layout
11309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11312 \begin_layout Plain Layout
11322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11325 \begin_layout Plain Layout
11333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11336 \begin_layout Plain Layout
11344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11356 \begin_layout Plain Layout
11357 \begin_inset Formula $A\hfill B$
11367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11370 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11381 \begin_layout Plain Layout
11387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11390 \begin_layout Plain Layout
11391 \begin_inset Formula $A\hspace*{1em}B$
11401 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11404 \begin_layout Plain Layout
11412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11415 \begin_layout Plain Layout
11421 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11424 \begin_layout Plain Layout
11425 \begin_inset Formula $A\hspace{1em}B$
11435 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11438 \begin_layout Plain Layout
11442 \begin_inset space \textvisiblespace{}
11450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11453 \begin_layout Plain Layout
11459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11462 \begin_layout Plain Layout
11463 \begin_inset Formula $A\ B$
11473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11476 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11487 \begin_layout Plain Layout
11493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11496 \begin_layout Plain Layout
11497 \begin_inset Formula $A\!B$
11513 \begin_layout Standard
11515 \begin_inset space ~
11519 \begin_inset space \thinspace{}
11523 \begin_inset space \thinspace{}
11526 7 are variable spaces which are explained in
11527 \begin_inset CommandInset ref
11529 reference "subsec:Variable-Space"
11535 \begin_inset space ~
11538 9 seems to produce no space.
11539 It is displayed red in \SpecialChar LyX
11540 contrary to the other sizes, because it is a negative
11542 There are two more negative spaces:
11545 \begin_layout Standard
11547 \begin_inset Tabular
11548 <lyxtabular version="3" rows="3" columns="3">
11549 <features booktabs="true" tabularvalignment="middle">
11550 <column alignment="center" valignment="middle" width="6.8cm">
11551 <column alignment="center" valignment="top" width="0pt">
11552 <column alignment="center" valignment="top" width="0pt">
11554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11557 \begin_layout Plain Layout
11563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11566 \begin_layout Plain Layout
11574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11577 \begin_layout Plain Layout
11587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11590 \begin_layout Plain Layout
11595 keystrokes after inserting the protected space
11600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11603 \begin_layout Plain Layout
11609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11612 \begin_layout Plain Layout
11620 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11623 \begin_layout Plain Layout
11629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11632 \begin_layout Plain Layout
11633 \begin_inset Formula $A\negmedspace B$
11641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11644 \begin_layout Plain Layout
11645 \begin_inset Formula $A\negthickspace B$
11661 \begin_layout Standard
11662 Negative spaces can lead to characters overlapping each other.
11663 Thus they can be used to enforce ligatures, which are e.
11664 \begin_inset space \thinspace{}
11668 \begin_inset space \space{}
11671 useful for summation operators:
11674 \begin_layout Standard
11676 \begin_inset Tabular
11677 <lyxtabular version="3" rows="3" columns="2">
11678 <features booktabs="true" tabularvalignment="middle">
11679 <column alignment="center" valignment="top" width="0pt">
11680 <column alignment="center" valignment="top">
11682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11685 \begin_layout Plain Layout
11691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11694 \begin_layout Plain Layout
11702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11705 \begin_layout Plain Layout
11711 \begin_inset space \textvisiblespace{}
11719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11722 \begin_layout Plain Layout
11723 \begin_inset Formula $\sum\sum f_{kl}$
11733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11736 \begin_layout Plain Layout
11744 \begin_inset space \textvisiblespace{}
11752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11755 \begin_layout Plain Layout
11756 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11772 \begin_layout Standard
11774 \begin_inset VSpace medskip
11780 \begin_layout Standard
11782 Relations like for example equal signs, are always surrounded by space.
11783 To suppress this, the equal sign is placed into a \SpecialChar TeX
11785 The following example demonstrates this:
11788 \begin_layout Standard
11790 \begin_inset Tabular
11791 <lyxtabular version="3" rows="2" columns="2">
11792 <features tabularvalignment="middle">
11793 <column alignment="center" valignment="top" width="0pt">
11794 <column alignment="center" valignment="top" width="0pt">
11796 <cell alignment="center" valignment="top" usebox="none">
11799 \begin_layout Plain Layout
11805 <cell alignment="center" valignment="top" usebox="none">
11808 \begin_layout Plain Layout
11809 \begin_inset Formula $A=B$
11819 <cell alignment="center" valignment="top" usebox="none">
11822 \begin_layout Plain Layout
11823 equation without space
11828 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11831 \begin_layout Plain Layout
11832 \begin_inset Formula $A{=}B$
11848 \begin_layout Standard
11850 The command for the last formula is:
11855 \begin_inset Formula $\to$
11861 \begin_layout Standard
11862 \begin_inset VSpace bigskip
11868 \begin_layout Standard
11869 Spaces are needed for physical units, because the space between the value
11870 and the unit is the smallest one and not a normal space.
11871 For units in text, the smallest space is inserted via the menu
11873 Insert\SpecialChar menuseparator
11874 Formatting\SpecialChar menuseparator
11876 \begin_inset space ~
11884 arg "space-insert thin"
11890 \begin_layout Standard
11891 An example to visualize the difference:
11894 \begin_layout Standard
11895 \begin_inset Tabular
11896 <lyxtabular version="3" rows="2" columns="2">
11897 <features tabularvalignment="middle">
11898 <column alignment="left" valignment="top">
11899 <column alignment="left" valignment="top">
11901 <cell alignment="center" valignment="top" usebox="none">
11904 \begin_layout Plain Layout
11906 \begin_inset Formula $\cdot$
11914 <cell alignment="center" valignment="top" usebox="none">
11917 \begin_layout Plain Layout
11918 space between value and unit
11925 <cell alignment="center" valignment="top" usebox="none">
11928 \begin_layout Plain Layout
11930 \begin_inset space \thinspace{}
11934 \begin_inset Formula $\cdot$
11942 <cell alignment="center" valignment="top" usebox="none">
11945 \begin_layout Plain Layout
11946 smallest space between value and unit
11959 \begin_layout Subsection
11964 \begin_layout Plain Layout
11977 \begin_layout Plain Layout
11978 for vertical space in formulas see
11979 \begin_inset CommandInset ref
11981 reference "subsec:Line-Separation"
11994 \begin_layout Plain Layout
12002 \begin_inset Note Note
12005 \begin_layout Plain Layout
12008 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12011 \begin_layout Plain Layout
12014 texorpdfstring is in section
12015 \begin_inset CommandInset ref
12017 reference "subsec:Formulas-in-Section"
12027 \begin_inset CommandInset label
12029 name "subsec:Variable-Space"
12034 \begin_inset Index idx
12037 \begin_layout Plain Layout
12038 Space ! horizontal ! variable
12046 \begin_layout Standard
12047 Space with a defined length can be inserted with the command
12054 \begin_inset Index idx
12057 \begin_layout Plain Layout
12067 \begin_inset Quotes eld
12073 \begin_inset space \textvisiblespace{}
12079 \begin_inset Quotes erd
12083 The length can be specified by left-clicking on the
12084 \begin_inset Quotes eld
12090 \begin_inset space \textvisiblespace{}
12096 \begin_inset Quotes erd
12100 The length may also be negative.
12101 When a space would be the first character in a line it would be omitted.
12102 To force its output use the command
12114 or left-click on the
12115 \begin_inset Quotes eld
12121 \begin_inset space \textvisiblespace{}
12127 \begin_inset Quotes erd
12130 and check the option
12135 \begin_inset Newline newline
12138 To insert as much space as is available, the command
12145 \begin_inset Index idx
12148 \begin_layout Plain Layout
12159 \begin_layout Standard
12161 \begin_inset Tabular
12162 <lyxtabular version="3" rows="4" columns="2">
12163 <features booktabs="true" tabularvalignment="middle">
12164 <column alignment="center" valignment="top" width="0pt">
12165 <column alignment="center" valignment="top">
12167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12170 \begin_layout Plain Layout
12178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12181 \begin_layout Plain Layout
12189 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12192 \begin_layout Plain Layout
12196 \begin_inset space \textvisiblespace{}
12202 \begin_inset space \thinspace{}
12210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12213 \begin_layout Plain Layout
12214 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12227 \begin_layout Plain Layout
12231 \begin_inset space \textvisiblespace{}
12237 \begin_inset space \thinspace{}
12245 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12248 \begin_layout Plain Layout
12249 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12262 \begin_layout Plain Layout
12266 \begin_inset space \textvisiblespace{}
12274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12277 \begin_layout Plain Layout
12278 \begin_inset Formula $A=A\hfill B=B$
12294 \begin_layout Standard
12295 In the last example the available space is given by the longest column entry
12297 In an inline formula the space depends on the length of the line in which
12305 Thus, when the line uses the full width, no space will be created.
12312 only has an effect on displayed formulas when the formula style
12317 (Formula styles are explained in
12318 \begin_inset CommandInset ref
12320 reference "sec:Formula-Styles"
12327 \begin_layout Standard
12334 , there are the commands
12346 that fill the space with a pattern, see
12347 \begin_inset CommandInset ref
12349 reference "subsec:Ellipses"
12356 \begin_layout Standard
12357 For text, variable space can be inserted via the menu
12359 Insert\SpecialChar menuseparator
12360 Formatting\SpecialChar menuseparator
12362 \begin_inset space ~
12370 \begin_layout Standard
12371 This is a line with
12372 \begin_inset space \hspace{}
12377 \begin_inset space \thinspace{}
12383 \begin_layout Standard
12384 This is a line with
12385 \begin_inset space \hfill{}
12391 \begin_layout Subsection
12392 Space besides inline Formulas
12393 \begin_inset Index idx
12396 \begin_layout Plain Layout
12397 Space ! besides inline formulas
12405 \begin_layout Standard
12406 The space that surrounds inline formulas can be adjusted with the length
12414 \begin_inset Index idx
12417 \begin_layout Plain Layout
12426 The value of a length is set with the command
12433 \begin_inset Index idx
12436 \begin_layout Plain Layout
12444 which has the following scheme:
12447 \begin_layout Standard
12452 setlength{length name}{value}
12455 \begin_layout Standard
12463 \begin_inset space \thinspace{}
12469 \begin_layout Standard
12479 \begin_layout Standard
12480 is inserted in \SpecialChar TeX
12483 \begin_inset space \thinspace{}
12486 mm space will now be set around all inline formulas:
12490 \begin_layout Plain Layout
12504 \begin_layout Standard
12505 This is a line with an inline formula
12506 \begin_inset Formula $A=B$
12510 \begin_inset space \thinspace{}
12513 mm surrounding space.
12517 \begin_layout Plain Layout
12531 \begin_layout Standard
12532 To return to the predefined value,
12538 is set to the value 0
12539 \begin_inset space \thinspace{}
12545 \begin_layout Standard
12546 \begin_inset Newpage newpage
12552 \begin_layout Section
12554 \begin_inset Index idx
12557 \begin_layout Plain Layout
12564 \begin_inset Index idx
12567 \begin_layout Plain Layout
12572 \begin_layout Plain Layout
12583 \begin_layout Plain Layout
12598 \begin_layout Standard
12599 Boxes for text are described in chapter
12606 \begin_inset space ~
12614 \begin_layout Subsection
12616 \begin_inset CommandInset label
12618 name "subsec:Boxes-with-Frame"
12623 \begin_inset Index idx
12626 \begin_layout Plain Layout
12635 \begin_layout Standard
12636 It is possible to frame a formula or part of one with the commands
12643 \begin_inset Index idx
12646 \begin_layout Plain Layout
12661 \begin_inset Index idx
12664 \begin_layout Plain Layout
12675 \begin_layout Standard
12676 When one of these commands is inserted in a formula, a blue box appears
12677 within a frame to enter formula parts.
12684 an additional formula has to be created by
12688 within this box, because the box content will otherwise be treated as mathemati
12696 is used, a new formula is automatically created inside the frame.
12699 \begin_layout Standard
12706 is not suitable to frame displayed formulas because the formula will always
12707 be set in the size of the text.
12714 is in contrary not suitable to frame inline formulas, because the formula
12715 will always be set in the size of a displayed formula.
12718 \begin_layout Standard
12732 \begin_inset Index idx
12735 \begin_layout Plain Layout
12743 where additionally the frame width and the alignment can be specified.
12750 is used in the following scheme:
12753 \begin_layout Standard
12758 framebox[frame width][position]{box content}
12761 \begin_layout Standard
12762 The position can either be
12779 right aligns the formula in the box.
12780 When no position is given, the formula will be centered.
12781 \begin_inset Newline newline
12784 If no width is given, also no position can be given.
12785 In this case the frame width is adjusted to the box content like for
12794 \begin_layout Standard
12801 is inserted, a box appears containing three blue boxes.
12802 The first two boxes are surrounded by brackets and denote the two optional
12804 The third box is for formula parts like for
12813 \begin_layout Standard
12815 \begin_inset Tabular
12816 <lyxtabular version="3" rows="5" columns="2">
12817 <features booktabs="true" tabularvalignment="middle">
12818 <column alignment="center" valignment="top" width="0pt">
12819 <column alignment="center" valignment="top">
12821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12824 \begin_layout Plain Layout
12830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12833 \begin_layout Plain Layout
12840 <row topspace="1.5mm">
12841 <cell alignment="center" valignment="top" usebox="none">
12844 \begin_layout Plain Layout
12848 \begin_inset space \textvisiblespace{}
12858 \begin_inset space \textvisiblespace{}
12866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12869 \begin_layout Plain Layout
12870 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12879 <row topspace="1.5mm">
12880 <cell alignment="center" valignment="top" usebox="none">
12883 \begin_layout Plain Layout
12887 \begin_inset space \textvisiblespace{}
12893 \begin_inset space \textvisiblespace{}
12901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12904 \begin_layout Plain Layout
12905 \begin_inset Formula $\boxed{\int A=B}$
12914 <row topspace="1.5mm">
12915 <cell alignment="center" valignment="top" usebox="none">
12918 \begin_layout Plain Layout
12922 \begin_inset space \textvisiblespace{}
12930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12933 \begin_layout Plain Layout
12934 \begin_inset Formula $A+\fbox{B}$
12943 <row topspace="1.5mm" bottomspace="1mm">
12944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12947 \begin_layout Plain Layout
12951 \begin_inset space \textvisiblespace{}
12955 \begin_inset Formula $\to$
12959 \begin_inset Formula $\to$
12969 \begin_inset space \textvisiblespace{}
12973 \begin_inset Formula $\downarrow$
12981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12984 \begin_layout Plain Layout
12985 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13001 \begin_layout Standard
13002 The frame thickness can also be adjusted.
13003 To do this the following commands have to be inserted in \SpecialChar TeX
13008 \begin_layout Standard
13018 \begin_inset Quotes eld
13022 \begin_inset Quotes erd
13036 \begin_inset Quotes eld
13040 \begin_inset Quotes erd
13046 \begin_layout Standard
13047 \begin_inset Quotes eld
13051 \begin_inset Quotes erd
13054 specifies the minimal distance between the frame and the first character
13056 An example for this is the following framed formula:
13060 \begin_layout Plain Layout
13072 \begin_inset Formula
13079 Before this formula the commands
13082 \begin_layout Standard
13104 \begin_layout Standard
13105 were inserted in \SpecialChar TeX
13107 The given values are used for all following boxes.
13110 \begin_layout Standard
13111 To return to the standard frame size, the command
13114 \begin_layout Standard
13139 \begin_layout Plain Layout
13153 \begin_layout Standard
13154 is inserted in \SpecialChar TeX
13155 mode before the next formula.
13158 \begin_layout Subsection
13159 Boxes without Frame
13160 \begin_inset CommandInset label
13162 name "subsec:Boxes-without-Frame"
13167 \begin_inset Index idx
13170 \begin_layout Plain Layout
13171 Boxes ! without frame
13179 \begin_layout Standard
13180 For boxes without a frame there are the following box commands:
13187 \begin_inset Index idx
13190 \begin_layout Plain Layout
13205 \begin_inset Index idx
13208 \begin_layout Plain Layout
13223 \begin_inset Index idx
13226 \begin_layout Plain Layout
13237 \begin_layout Standard
13244 a box can be super- or subscripted.
13245 But in contrary to normal super- and subscripting, the characters in the
13246 box keep their font size.
13253 is used in the following scheme:
13256 \begin_layout Standard
13261 raisebox{height}{box content}
13264 \begin_layout Standard
13265 When the box should contain a formula, an extra formula is needed like for
13276 \begin_inset Note Greyedout
13279 \begin_layout Plain Layout
13290 this extra formula is created by pressing
13294 twice instead of once because \SpecialChar LyX
13295 doesn't yet support
13309 \begin_layout Standard
13311 \begin_inset Tabular
13312 <lyxtabular version="3" rows="4" columns="2">
13313 <features booktabs="true" tabularvalignment="middle">
13314 <column alignment="center" valignment="top" width="0pt">
13315 <column alignment="center" valignment="top">
13317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13320 \begin_layout Plain Layout
13326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13329 \begin_layout Plain Layout
13337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13340 \begin_layout Plain Layout
13344 \begin_inset Formula $\to$
13350 \begin_inset Formula $\to$
13358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13361 \begin_layout Plain Layout
13362 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13375 \begin_layout Plain Layout
13379 \begin_inset Formula $\to$
13385 \begin_inset Formula $\to$
13393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13396 \begin_layout Plain Layout
13397 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13410 \begin_layout Plain Layout
13414 \begin_inset Formula $\to$
13430 \begin_inset space \textvisiblespace{}
13438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13441 \begin_layout Plain Layout
13442 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13458 \begin_layout Standard
13483 , with the difference that there is no frame.
13486 \begin_layout Subsection
13488 \begin_inset CommandInset label
13490 name "subsec:Colored-Boxes"
13495 \begin_inset Index idx
13498 \begin_layout Plain Layout
13507 \begin_layout Standard
13508 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13517 \begin_layout Plain Layout
13518 The \SpecialChar LaTeX
13523 is part of every \SpecialChar LaTeX
13524 standard installation.
13530 \begin_inset Index idx
13533 \begin_layout Plain Layout
13539 has to be loaded in the \SpecialChar LaTeX
13540 -preamble with the line
13544 \begin_layout Plain Layout
13545 When text is colored somewhere in the document with a predefined color,
13547 loads the \SpecialChar LaTeX
13553 Thus it is possible that the package is loaded twice, but this does not
13560 \begin_inset Note Note
13563 \begin_layout Plain Layout
13564 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13573 \begin_layout Standard
13581 \begin_layout Standard
13582 \begin_inset VSpace medskip
13585 To color boxes, the command
13592 \begin_inset Index idx
13595 \begin_layout Plain Layout
13603 is used in the following scheme:
13606 \begin_layout Standard
13611 colorbox{color}{box content}
13614 \begin_layout Standard
13615 The box content can also be a box and a
13621 can also be part of another box (see the 2nd and 3rd example).
13622 When the box should contain a formula, an extra formula has to be created,
13623 the same way as for
13633 \begin_layout Plain Layout
13634 This also applies for the command
13648 \begin_layout Standard
13649 One of the following predefined colors can be chosen:
13652 \begin_layout Standard
13686 \begin_layout Standard
13688 \begin_inset Tabular
13689 <lyxtabular version="3" rows="4" columns="2">
13690 <features booktabs="true" tabularvalignment="middle">
13691 <column alignment="center" valignment="top" width="0pt">
13692 <column alignment="center" valignment="top">
13694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13697 \begin_layout Plain Layout
13703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13706 \begin_layout Plain Layout
13714 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13717 \begin_layout Plain Layout
13721 \begin_inset Formula $\to$
13731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13734 \begin_layout Plain Layout
13735 \begin_inset Formula $\colorbox{yellow}{A=B}$
13744 <row topspace="1.5mm">
13745 <cell alignment="center" valignment="top" usebox="none">
13748 \begin_layout Plain Layout
13752 \begin_inset Formula $\to$
13760 \begin_inset space \textvisiblespace{}
13768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13771 \begin_layout Plain Layout
13772 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13781 <row topspace="1.5mm" bottomspace="1mm">
13782 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13785 \begin_layout Plain Layout
13789 \begin_inset space \textvisiblespace{}
13795 \begin_inset Formula $\to$
13811 \begin_inset space \textvisiblespace{}
13819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13822 \begin_layout Plain Layout
13823 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13839 \begin_layout Standard
13846 only colors the box but not the characters in the box.
13847 To color all characters, the whole formula is highlighted and the desired
13848 color is chosen in the
13851 \begin_inset space ~
13857 The dialog can be called with the toolbar button
13860 arg "dialog-show character"
13865 Edit\SpecialChar menuseparator
13867 \begin_inset space ~
13870 Style\SpecialChar menuseparator
13874 The formula number then has the same color as the formula.
13875 When the formula number should get another color than the formula characters,
13876 the color must be changed within the formula.
13879 \begin_layout Standard
13883 \begin_layout Standard
13886 \begin_inset Formula
13888 \int A=B\label{eq:red}
13896 \begin_inset Formula
13898 \textcolor{red}{\int A=B}\label{eq:redgreen}
13906 \begin_layout Standard
13908 \begin_inset CommandInset ref
13914 is completely colored red.
13915 \begin_inset Newline newline
13919 \begin_inset CommandInset ref
13921 reference "eq:redgreen"
13925 was first completely colored green to set the color for the formula number.
13926 Subsequently the formula characters were colored red.
13929 \begin_layout Standard
13930 \begin_inset VSpace bigskip
13933 To color the frame different than the rest of the box, the command
13940 \begin_inset Index idx
13943 \begin_layout Plain Layout
13951 is used in the following scheme:
13954 \begin_layout Standard
13959 fcolorbox{frame color}{color}{box content}
13962 \begin_layout Standard
13969 is an extension of the command
13976 The frame width is set, like for
13999 \begin_layout Plain Layout
14011 \begin_inset Formula
14013 \fcolorbox{cyan}{magenta}{A=B}
14022 \begin_layout Plain Layout
14036 \begin_layout Standard
14037 This formula was created with the command
14038 \begin_inset Newline newline
14046 \begin_inset Formula $\to$
14052 \begin_inset Formula $\to$
14062 \begin_layout Standard
14063 \begin_inset VSpace bigskip
14066 To use other colors than the predefined ones, they have to be defined first.
14069 \begin_layout Standard
14070 One can for example define the color
14071 \begin_inset Quotes eld
14079 \begin_inset Quotes erd
14082 with the \SpecialChar LaTeX
14086 \begin_layout Standard
14091 definecolor{darkgreen}{cmyk}{0.5,
14106 \begin_inset Index idx
14109 \begin_layout Plain Layout
14120 \begin_layout Standard
14125 is the color space that denotes the colors
14142 The four comma separated numbers are the portion factor for the corresponding
14143 colors of the color space.
14144 The factors can be in the range of 0
14145 \begin_inset space \thinspace{}
14149 \begin_inset space \thinspace{}
14157 also the color space
14161 can be used for definitions.
14178 , so that there are in this case three portion factors for the corresponding
14180 Furthermore there is the color space
14184 with one portion factor for the gray value.
14187 \begin_layout Standard
14188 As example a framed box with the new defined color
14192 where the characters have been colored
14197 \begin_inset Formula
14199 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14207 \begin_layout Standard
14208 Self-defined colors can also be used for text with the help of the command
14216 \begin_inset Index idx
14219 \begin_layout Plain Layout
14228 \begin_layout Standard
14232 \begin_layout Plain Layout
14236 textcolor{darkgreen}{
14242 \begin_inset Quotes eld
14246 \begin_inset Quotes erd
14253 \begin_layout Plain Layout
14263 \begin_layout Standard
14271 \begin_inset Index idx
14274 \begin_layout Plain Layout
14282 is used in the scheme
14286 textcolor{color}{characters to color}
14291 \begin_layout Subsection
14293 \begin_inset CommandInset label
14295 name "subsec:Paragraph-Boxes"
14300 \begin_inset Index idx
14303 \begin_layout Plain Layout
14304 Boxes ! as paragraph
14312 \begin_layout Standard
14313 A box that can contain several lines and paragraphs, a so-called paragraph
14314 box (parbox), can be created with the menu
14316 Insert\SpecialChar menuseparator
14319 or the toolbar button
14328 \begin_layout Standard
14329 The following example shows a framed parbox in a line:
14332 \begin_layout Standard
14333 \begin_inset VSpace medskip
14337 \begin_inset Box Boxed
14347 height_special "totalheight"
14352 backgroundcolor "none"
14355 \begin_layout Plain Layout
14356 This is a paragraph box.
14358 \begin_inset space \thinspace{}
14361 cm long and can also contain formulas:
14362 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14373 \begin_layout Standard
14374 \begin_inset VSpace medskip
14380 \begin_layout Standard
14381 Such a box is created by right-clicking on the gray box inset.
14382 A dialog pops up showing the box properties.
14396 \begin_inset space \thinspace{}
14401 Vertical Box Alignment
14406 \begin_layout Standard
14407 \begin_inset VSpace medskip
14410 In \SpecialChar LaTeX
14411 a parbox is created with the command
14418 \begin_inset Index idx
14421 \begin_layout Plain Layout
14429 which has the following scheme:
14432 \begin_layout Standard
14437 parbox[position]{width}{box content}
14440 \begin_layout Standard
14455 \begin_inset Quotes eld
14459 \begin_inset Quotes erd
14462 means that the box is aligned within the surrounding text with its last
14469 \begin_inset Quotes eld
14473 \begin_inset Quotes erd
14476 this is done with the first line.
14477 When no position is given, the box will be vertically centered, see section
14485 \begin_inset space ~
14490 manual for examples.
14493 \begin_layout Standard
14494 \begin_inset VSpace bigskip
14497 To frame formulas completely, including the formula number, the formula
14498 must be set into a parbox.
14499 To do this, the command
14513 is inserted in \SpecialChar TeX
14514 mode before the formula.
14522 \begin_inset Index idx
14525 \begin_layout Plain Layout
14533 is hereby the line width set for the document.
14534 Because the frame is outside the parbox, 2
14535 \begin_inset space \thinspace{}
14538 times the frame separation and the frame thickness must be subtracted from
14540 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14549 \begin_layout Plain Layout
14554 is part of every \SpecialChar LaTeX
14555 standard installation.
14561 \begin_inset Index idx
14564 \begin_layout Plain Layout
14570 must be loaded in the \SpecialChar LaTeX
14571 -preamble with the line
14574 \begin_layout Standard
14582 \begin_layout Standard
14583 Behind the formula both boxes are closed by entering
14587 in \SpecialChar TeX
14589 Here is an example:
14593 \begin_layout Plain Layout
14607 \begin_layout Standard
14611 \begin_layout Plain Layout
14629 \begin_inset Formula
14631 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14640 \begin_layout Plain Layout
14651 \begin_layout Plain Layout
14665 \begin_layout Standard
14666 \begin_inset VSpace medskip
14669 As a parbox is used as the argument of
14675 , there is in this case no difference between
14690 \begin_layout Standard
14691 \begin_inset VSpace bigskip
14694 Paragraph boxes are very useful to comment formulas directly.
14701 is used in combination with the command
14715 \begin_inset CommandInset ref
14717 reference "subsec:User-defined-Numbering"
14724 \begin_layout Standard
14725 An example of a formula commented with
14734 \begin_layout Standard
14738 \begin_layout Plain Layout
14751 This is a description.
14752 It is distinctly separated from the formula and multiline.
14756 \begin_layout Plain Layout
14768 \begin_layout Standard
14769 Such a formula must be inserted completely in \SpecialChar TeX
14770 mode because \SpecialChar LyX
14772 support the command
14779 The formula is created with the following command sequence:
14782 \begin_layout Standard
14795 is inserted in \SpecialChar TeX
14800 \begin_layout Plain Layout
14801 When the formula style
14813 can also be replaced by
14820 (formula styles see
14821 \begin_inset CommandInset ref
14823 reference "sec:Formula-Styles"
14832 Then the description follows as normal text and finally
14838 is inserted in \SpecialChar TeX
14852 hereby create a displayed formula.
14855 \begin_layout Standard
14862 can be seen in this example that was
14863 \begin_inset Quotes eld
14867 \begin_inset Quotes erd
14870 using the mathematical textmode:
14871 \begin_inset Formula
14873 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14881 \begin_layout Section
14883 \begin_inset Index idx
14886 \begin_layout Plain Layout
14895 \begin_layout Subsection
14897 \begin_inset CommandInset label
14899 name "subsec:Big-Operators"
14904 \begin_inset Index idx
14907 \begin_layout Plain Layout
14914 \begin_inset Index idx
14917 \begin_layout Plain Layout
14924 \begin_inset Index idx
14927 \begin_layout Plain Layout
14936 \begin_layout Standard
14937 To be able to use all integral operators listed here, the option
14939 Use esint package automatically
14941 must be set in the document settings under
14944 \begin_inset space ~
14952 \begin_layout Standard
14953 \begin_inset space \hfill{}
14957 \begin_inset Tabular
14958 <lyxtabular version="3" rows="11" columns="2">
14959 <features booktabs="true" tabularvalignment="middle">
14960 <column alignment="center" valignment="top" width="0pt">
14961 <column alignment="center" valignment="top" width="0pt">
14963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14966 \begin_layout Plain Layout
14972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14975 \begin_layout Plain Layout
14983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14986 \begin_layout Plain Layout
14990 \begin_inset Index idx
14993 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15010 \begin_inset Formula $\int$
15020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15023 \begin_layout Plain Layout
15031 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15034 \begin_layout Plain Layout
15035 \begin_inset Formula $\oint$
15045 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15048 \begin_layout Plain Layout
15056 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15059 \begin_layout Plain Layout
15060 \begin_inset Formula $\ointctrclockwise$
15070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15073 \begin_layout Plain Layout
15081 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15084 \begin_layout Plain Layout
15085 \begin_inset Formula $\ointclockwise$
15095 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15109 \begin_layout Plain Layout
15110 \begin_inset Formula $\sqint$
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
15136 \begin_inset Formula $\fint$
15146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15149 \begin_layout Plain Layout
15157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15160 \begin_layout Plain Layout
15162 \begin_inset Formula $\landupint$
15172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15175 \begin_layout Plain Layout
15183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15186 \begin_layout Plain Layout
15188 \begin_inset Formula $\landdownint$
15198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15201 \begin_layout Plain Layout
15209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15212 \begin_layout Plain Layout
15213 \begin_inset Formula $\bigcap$
15223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15226 \begin_layout Plain Layout
15234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15237 \begin_layout Plain Layout
15238 \begin_inset Formula $\bigcup$
15252 \begin_inset space \hfill{}
15256 \begin_inset Tabular
15257 <lyxtabular version="3" rows="11" columns="2">
15258 <features booktabs="true" tabularvalignment="middle">
15259 <column alignment="center" valignment="top" width="0pt">
15260 <column alignment="center" valignment="top" width="0pt">
15262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15265 \begin_layout Plain Layout
15271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15274 \begin_layout Plain Layout
15282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15285 \begin_layout Plain Layout
15289 \begin_inset Index idx
15292 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15309 \begin_inset Formula $\sum$
15319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15326 \begin_inset Index idx
15329 \begin_layout Plain Layout
15336 \begin_layout Plain Layout
15355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15358 \begin_layout Plain Layout
15359 \begin_inset Formula $\prod$
15369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15372 \begin_layout Plain Layout
15380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15383 \begin_layout Plain Layout
15384 \begin_inset Formula $\coprod$
15394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15397 \begin_layout Plain Layout
15405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15408 \begin_layout Plain Layout
15409 \begin_inset Formula $\bigodot$
15419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15422 \begin_layout Plain Layout
15430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Plain Layout
15434 \begin_inset Formula $\bigotimes$
15444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15447 \begin_layout Plain Layout
15455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15458 \begin_layout Plain Layout
15459 \begin_inset Formula $\bigoplus$
15469 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15472 \begin_layout Plain Layout
15480 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15483 \begin_layout Plain Layout
15484 \begin_inset Formula $\bigwedge$
15494 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15497 \begin_layout Plain Layout
15505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15508 \begin_layout Plain Layout
15509 \begin_inset Formula $\bigvee$
15519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15522 \begin_layout Plain Layout
15530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15533 \begin_layout Plain Layout
15534 \begin_inset Formula $\bigsqcup$
15544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15547 \begin_layout Plain Layout
15555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15558 \begin_layout Plain Layout
15559 \begin_inset Formula $\biguplus$
15573 \begin_inset space \hfill{}
15579 \begin_layout Standard
15580 All big operators can also be inserted via the math toolbar button
15583 arg "math-insert \\intop"
15589 \begin_layout Standard
15590 The operators are called big because they are bigger than the sometimes
15591 equal looking binary operators.
15592 All big operators can have limits as described in the next subsection.
15595 \begin_layout Standard
15596 For all integral operators there is a second version available, ending in
15614 These operators are different from
15621 \begin_inset space \space{}
15624 in the style the operator limits are displayed, see
15625 \begin_inset CommandInset ref
15627 reference "subsec:Operator-Limits"
15635 \begin_layout Subsubsection*
15636 Advice for Integrals
15639 \begin_layout Standard
15644 in an integral is an operator, that therefore has to be set upright.
15645 This is done by highlighting the
15649 and using the keyboard shortcut
15659 \begin_layout Plain Layout
15665 \begin_inset CommandInset ref
15667 reference "subsec:Font-Styles"
15677 Finally the smallest space is inserted before the
15681 , as this is usual for operators.
15685 \begin_layout Standard
15687 \begin_inset Formula $\int A(x)dx$
15691 \begin_inset Newline newline
15695 \begin_inset Phantom HPhantom
15698 \begin_layout Plain Layout
15705 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15711 \begin_layout Standard
15712 For multiple integrals there are the following commands:
15713 \begin_inset VSpace medskip
15719 \begin_layout Standard
15720 \begin_inset space \hfill{}
15724 \begin_inset Tabular
15725 <lyxtabular version="3" rows="4" columns="2">
15726 <features booktabs="true" tabularvalignment="middle">
15727 <column alignment="center" valignment="top" width="0pt">
15728 <column alignment="center" valignment="top" width="0pt">
15730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15733 \begin_layout Plain Layout
15739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15742 \begin_layout Plain Layout
15749 <row bottomspace="1mm">
15750 <cell alignment="center" valignment="top" usebox="none">
15753 \begin_layout Plain Layout
15761 <cell alignment="center" valignment="top" usebox="none">
15764 \begin_layout Plain Layout
15765 \begin_inset Formula $\iint$
15774 <row bottomspace="1mm">
15775 <cell alignment="center" valignment="top" usebox="none">
15778 \begin_layout Plain Layout
15786 <cell alignment="center" valignment="top" usebox="none">
15789 \begin_layout Plain Layout
15790 \begin_inset Formula $\oiint$
15799 <row bottomspace="1mm">
15800 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15803 \begin_layout Plain Layout
15811 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15814 \begin_layout Plain Layout
15815 \begin_inset Formula $\sqiint$
15829 \begin_inset space \hfill{}
15833 \begin_inset Tabular
15834 <lyxtabular version="3" rows="4" columns="2">
15835 <features booktabs="true" tabularvalignment="middle">
15836 <column alignment="center" valignment="top" width="0pt">
15837 <column alignment="center" valignment="top" width="0pt">
15839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15842 \begin_layout Plain Layout
15848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15851 \begin_layout Plain Layout
15858 <row bottomspace="1mm">
15859 <cell alignment="center" valignment="top" usebox="none">
15862 \begin_layout Plain Layout
15870 <cell alignment="center" valignment="top" usebox="none">
15873 \begin_layout Plain Layout
15874 \begin_inset Formula $\iiint$
15883 <row bottomspace="1mm">
15884 <cell alignment="center" valignment="top" usebox="none">
15887 \begin_layout Plain Layout
15895 <cell alignment="center" valignment="top" usebox="none">
15898 \begin_layout Plain Layout
15899 \begin_inset Formula $\iiiint$
15908 <row bottomspace="1mm">
15909 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15912 \begin_layout Plain Layout
15920 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15923 \begin_layout Plain Layout
15924 \begin_inset Formula $\dotsint$
15938 \begin_inset space \hfill{}
15944 \begin_layout Subsection
15946 \begin_inset CommandInset label
15948 name "subsec:Operator-Limits"
15953 \begin_inset Index idx
15956 \begin_layout Plain Layout
15965 \begin_layout Standard
15966 Limits are created by super- and subscripts:
15969 \begin_layout Standard
15971 \begin_inset Tabular
15972 <lyxtabular version="3" rows="2" columns="2">
15973 <features booktabs="true" tabularvalignment="middle">
15974 <column alignment="center" valignment="top" width="0pt">
15975 <column alignment="center" valignment="top" width="0pt">
15977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15980 \begin_layout Plain Layout
15986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15989 \begin_layout Plain Layout
15997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16000 \begin_layout Plain Layout
16006 \begin_inset space \textvisiblespace{}
16010 \begin_inset Formula $\to$
16014 \begin_inset Formula $\to$
16022 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16025 \begin_layout Plain Layout
16026 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16042 \begin_layout Standard
16043 Limits of inline formulas are set right beside the operator.
16044 Limits in displayed formulas are set above or below the operator, except
16045 for integral limits.
16048 \begin_layout Standard
16049 To force that the limits are set beside the operator, the cursor is set
16050 directly behind the operator and the limits type is changed with the menu
16053 Edit\SpecialChar menuseparator
16054 Math\SpecialChar menuseparator
16073 \begin_layout Standard
16074 The default limits type is this:
16075 \begin_inset Formula
16077 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16082 This is how it looks when the limits type was changed to
16089 \begin_inset Formula
16091 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16096 For integrals, except those ending with
16112 etc., the limits are by default set beside the operator.
16113 But for multiple integrals the limits are often set below the operator.
16114 In the following example the limits type was therefore set to
16118 and so set below the integrals:
16119 \begin_inset Formula
16121 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16129 \begin_layout Standard
16130 \begin_inset VSpace medskip
16133 To specify conditions for limits, the commands
16140 \begin_inset Index idx
16143 \begin_layout Plain Layout
16158 \begin_inset Index idx
16161 \begin_layout Plain Layout
16170 To create for example this expression
16171 \begin_inset Formula
16173 \sum_{\begin{subarray}{c}
16177 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16185 \begin_layout Standard
16186 the following has to be done:
16187 \begin_inset Newline newline
16199 \begin_inset space \textvisiblespace{}
16205 One is now in a blue box under the summation operator and insert there
16211 \begin_inset space \textvisiblespace{}
16217 The blue box is now within a purple box and now several lines can be written
16219 A new line is created by inserting a line break (
16222 arg "newline-insert newline"
16227 \begin_inset Newline newline
16232 0<k<1000 Ctrl+Return
16233 \begin_inset Newline newline
16238 is typed in, a new box appears below for the new line.
16241 \begin_layout Standard
16242 The alignment of the lines can be changed to left aligned with the
16252 Edit\SpecialChar menuseparator
16256 To get right alignment,
16261 \begin_inset space \textvisiblespace{}
16266 is inserted at the beginning of the line.
16269 \begin_layout Standard
16282 with the difference that the lines are always centered.
16285 \begin_layout Standard
16286 \begin_inset VSpace bigskip
16290 \begin_inset CommandInset ref
16292 reference "eq:substack"
16296 there can be too much space beside an operator, because the characters
16297 following the operator are set beside the limits.
16298 To avoid this the command
16305 \begin_inset Index idx
16308 \begin_layout Plain Layout
16317 To activate it, set in the document settings under
16320 \begin_inset space ~
16330 \begin_inset Index idx
16333 \begin_layout Plain Layout
16334 Packages ! mathtools
16342 \begin_inset space ~
16354 sets the space besides the operator to 0
16355 \begin_inset space \thinspace{}
16359 \begin_inset Newline newline
16363 \begin_inset CommandInset ref
16365 reference "eq:substack"
16369 , one uses the command
16372 \begin_layout Standard
16380 \begin_layout Standard
16381 and inserts the operator with its limits into the braces.
16382 Behind the brace one continues the formula:
16383 \begin_inset Formula
16385 \smashoperator{\sum_{\begin{subarray}{c}
16389 \end{subarray}}^{n}}k^{-2}
16397 \begin_layout Standard
16398 It is possible to set the space of only one side of the operator to 0
16399 \begin_inset space \thinspace{}
16403 To do this write either
16422 stands for the left and
16426 for the right side of the operator.
16427 Here is an example of the possible
16436 \begin_layout Standard
16437 \begin_inset Formula
16439 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}
16447 \begin_layout Standard
16448 \begin_inset VSpace bigskip
16454 \begin_layout Standard
16455 When several consecutive operators have limits the typesetting of the limits
16456 looks often imperfect in the output, see this example:
16457 \begin_inset Formula
16459 \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}
16464 To improve the typesetting set in the document settings under
16467 \begin_inset space ~
16477 \begin_inset Index idx
16480 \begin_layout Plain Layout
16481 Packages ! mathtools
16489 \begin_inset space ~
16495 Then insert into your formula the command
16502 \begin_inset Index idx
16505 \begin_layout Plain Layout
16513 directly before the first operator.
16514 The example will then look like this:
16515 \begin_inset Formula
16517 \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}
16525 \begin_layout Standard
16526 \begin_inset VSpace bigskip
16529 How to use one limit for several operators is described in
16530 \begin_inset CommandInset ref
16532 reference "subsec:Self-defined-Operators"
16539 \begin_layout Subsection
16540 Decoration for Operators
16541 \begin_inset Index idx
16544 \begin_layout Plain Layout
16545 Operators ! Decoration
16553 \begin_layout Standard
16561 \begin_inset Index idx
16564 \begin_layout Plain Layout
16579 \begin_inset Index idx
16582 \begin_layout Plain Layout
16590 characters can be placed above or below an operator, respectively.
16598 \begin_inset Index idx
16601 \begin_layout Plain Layout
16609 characters can be set before and behind a big operator.
16612 \begin_layout Standard
16614 \begin_inset space ~
16626 \begin_layout Itemize
16633 is used to set characters at the corners of the operator
16636 \begin_layout Itemize
16643 is used to set characters before and/or behind the operator (this variant
16644 represents \SpecialChar LaTeX
16654 \begin_layout Itemize
16661 is used to set characters at the left corners and/or behind the operator
16664 \begin_layout Itemize
16671 is used to set characters at the right corners and/or before the operator
16674 \begin_layout Standard
16675 For example the command
16680 \begin_inset space \textvisiblespace{}
16686 \begin_inset space \textvisiblespace{}
16690 \begin_inset Formula $\to$
16694 \begin_inset Formula $\to$
16698 \begin_inset space \textvisiblespace{}
16708 \begin_inset Formula
16710 \sideset{}{'}\sum_{k=1}^{n}
16718 \begin_layout Standard
16719 \begin_inset Note Greyedout
16722 \begin_layout Plain Layout
16729 can only be used to decorate big operators, binary operators are not allowed.
16737 \begin_layout Standard
16750 can also be used to decorate symbols and characters.
16751 For example, the command
16756 \begin_inset space \textvisiblespace{}
16762 \begin_inset space \textvisiblespace{}
16768 \begin_inset Formula $\uparrow$
16776 \begin_inset Formula
16778 \overset{a}{\maltese}
16786 \begin_layout Subsection
16788 \begin_inset CommandInset label
16790 name "subsec:Binary-Operators"
16795 \begin_inset Index idx
16798 \begin_layout Plain Layout
16807 \begin_layout Standard
16808 Binary operators are surrounded by space when there is a character before
16810 \begin_inset VSpace medskip
16816 \begin_layout Standard
16817 \begin_inset Tabular
16818 <lyxtabular version="3" rows="13" columns="2">
16819 <features booktabs="true" tabularvalignment="middle">
16820 <column alignment="center" valignment="top" width="0pt">
16821 <column alignment="center" valignment="top" width="0pt">
16823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16826 \begin_layout Plain Layout
16828 \begin_inset Note Note
16831 \begin_layout Plain Layout
16838 is only used as spacer.
16848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16851 \begin_layout Plain Layout
16859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16862 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $+$
16882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16894 \begin_layout Plain Layout
16895 \begin_inset Formula $-$
16905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16908 \begin_layout Plain Layout
16916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16919 \begin_layout Plain Layout
16920 \begin_inset Formula $\pm$
16930 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16933 \begin_layout Plain Layout
16941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16944 \begin_layout Plain Layout
16945 \begin_inset Formula $\mp$
16955 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16958 \begin_layout Plain Layout
16966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16969 \begin_layout Plain Layout
16970 \begin_inset Formula $\cdot$
16980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16983 \begin_layout Plain Layout
16991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16994 \begin_layout Plain Layout
16995 \begin_inset Formula $\times$
17005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17008 \begin_layout Plain Layout
17016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17019 \begin_layout Plain Layout
17020 \begin_inset Formula $\div$
17030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17033 \begin_layout Plain Layout
17037 \begin_layout Plain Layout
17050 \begin_layout Plain Layout
17062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17065 \begin_layout Plain Layout
17066 \begin_inset Formula $*$
17076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17079 \begin_layout Plain Layout
17087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17090 \begin_layout Plain Layout
17091 \begin_inset Formula $\star$
17101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17104 \begin_layout Plain Layout
17112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17115 \begin_layout Plain Layout
17116 \begin_inset Formula $\circ$
17126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17129 \begin_layout Plain Layout
17137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17140 \begin_layout Plain Layout
17141 \begin_inset Formula $\diamond$
17151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17154 \begin_layout Plain Layout
17162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17165 \begin_layout Plain Layout
17166 \begin_inset Formula $\bullet$
17180 \begin_inset space \hfill{}
17184 \begin_inset Tabular
17185 <lyxtabular version="3" rows="13" columns="2">
17186 <features booktabs="true" tabularvalignment="middle">
17187 <column alignment="center" valignment="top" width="0pt">
17188 <column alignment="center" valignment="top" width="0pt">
17190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17193 \begin_layout Plain Layout
17199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17202 \begin_layout Plain Layout
17210 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17213 \begin_layout Plain Layout
17221 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17224 \begin_layout Plain Layout
17225 \begin_inset Formula $\nabla$
17235 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17238 \begin_layout Plain Layout
17246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17249 \begin_layout Plain Layout
17250 \begin_inset Formula $\bigtriangledown$
17260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17263 \begin_layout Plain Layout
17271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17274 \begin_layout Plain Layout
17275 \begin_inset Formula $\bigtriangleup$
17285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17288 \begin_layout Plain Layout
17296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17299 \begin_layout Plain Layout
17300 \begin_inset Formula $\Box$
17310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17313 \begin_layout Plain Layout
17321 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17324 \begin_layout Plain Layout
17325 \begin_inset Formula $\cap$
17335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17338 \begin_layout Plain Layout
17346 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17349 \begin_layout Plain Layout
17350 \begin_inset Formula $\cup$
17360 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17363 \begin_layout Plain Layout
17371 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17374 \begin_layout Plain Layout
17375 \begin_inset Formula $\dagger$
17385 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17388 \begin_layout Plain Layout
17396 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17399 \begin_layout Plain Layout
17400 \begin_inset Formula $\ddagger$
17410 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17413 \begin_layout Plain Layout
17421 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17424 \begin_layout Plain Layout
17425 \begin_inset Formula $\wr$
17435 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17438 \begin_layout Plain Layout
17446 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17449 \begin_layout Plain Layout
17450 \begin_inset Formula $\bigcirc$
17460 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17471 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17474 \begin_layout Plain Layout
17475 \begin_inset Formula $\wedge$
17485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17488 \begin_layout Plain Layout
17496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17499 \begin_layout Plain Layout
17500 \begin_inset Formula $\vee$
17514 \begin_inset space \hfill{}
17518 \begin_inset Tabular
17519 <lyxtabular version="3" rows="13" columns="2">
17520 <features booktabs="true" tabularvalignment="middle">
17521 <column alignment="center" valignment="top" width="0pt">
17522 <column alignment="center" valignment="top" width="0pt">
17524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17527 \begin_layout Plain Layout
17533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17536 \begin_layout Plain Layout
17544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17547 \begin_layout Plain Layout
17555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17558 \begin_layout Plain Layout
17559 \begin_inset Formula $\oplus$
17569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17572 \begin_layout Plain Layout
17580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17583 \begin_layout Plain Layout
17584 \begin_inset Formula $\ominus$
17594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17597 \begin_layout Plain Layout
17605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17608 \begin_layout Plain Layout
17609 \begin_inset Formula $\otimes$
17619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17622 \begin_layout Plain Layout
17630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17633 \begin_layout Plain Layout
17634 \begin_inset Formula $\oslash$
17644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17647 \begin_layout Plain Layout
17655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17658 \begin_layout Plain Layout
17659 \begin_inset Formula $\odot$
17669 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17672 \begin_layout Plain Layout
17680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17683 \begin_layout Plain Layout
17684 \begin_inset Formula $\amalg$
17694 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17697 \begin_layout Plain Layout
17705 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17708 \begin_layout Plain Layout
17709 \begin_inset Formula $\uplus$
17719 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17722 \begin_layout Plain Layout
17730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17733 \begin_layout Plain Layout
17734 \begin_inset Formula $\setminus$
17744 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17747 \begin_layout Plain Layout
17755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17758 \begin_layout Plain Layout
17759 \begin_inset Formula $\sqcap$
17769 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17772 \begin_layout Plain Layout
17780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17783 \begin_layout Plain Layout
17784 \begin_inset Formula $\sqcup$
17794 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17797 \begin_layout Plain Layout
17805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17808 \begin_layout Plain Layout
17809 \begin_inset Formula $\triangleleft$
17819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17822 \begin_layout Plain Layout
17830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17833 \begin_layout Plain Layout
17834 \begin_inset Formula $\triangleright$
17850 \begin_layout Standard
17851 All binary operators can also be inserted via the math toolbar button
17854 arg "math-insert \\pm"
17860 \begin_layout Standard
17861 To typeset the Laplace operator also
17878 \begin_inset Formula $\nabla^{2}$
17881 ) can be used instead of
17890 \begin_layout Standard
17897 Insert\SpecialChar menuseparator
17909 \begin_layout Subsection
17910 Self-defined Operators
17911 \begin_inset CommandInset label
17913 name "subsec:Self-defined-Operators"
17918 \begin_inset Index idx
17921 \begin_layout Plain Layout
17922 Operators ! self-defined
17930 \begin_layout Standard
17931 With the help of the command
17935 DeclareMathOperator
17938 \begin_inset Index idx
17941 \begin_layout Plain Layout
17946 DeclareMathOperator
17951 custom operators can be defined in the \SpecialChar LaTeX
17953 Its command scheme is:
17956 \begin_layout Standard
17961 DeclareMathOperator{new command}{display}
17964 \begin_layout Standard
17965 Display can be characters or symbols that define how the operator looks
17967 To define a big operator a * is set behind the command.
17968 All self-defined big operators can have limits as described in
17969 \begin_inset CommandInset ref
17971 reference "subsec:Operator-Limits"
17978 \begin_layout Standard
17979 For example the \SpecialChar LaTeX
17983 \begin_layout Standard
17988 DeclareMathOperator*{
17995 \begin_layout Standard
17996 defines the command
18002 , that inserts a big operator consisting of the lozenge symbol from
18003 \begin_inset CommandInset ref
18005 reference "subsec:Miscellaneous-Symbols"
18010 \begin_inset Formula
18012 \Lozenge_{n=1}^{\infty}
18017 The command for this formula is:
18028 \begin_inset Formula $\to$
18034 \begin_layout Standard
18035 \begin_inset VSpace bigskip
18038 When self-defined operators are not used several times in the document,
18039 they can also be defined with the commands
18046 \begin_inset Index idx
18049 \begin_layout Plain Layout
18064 \begin_inset Index idx
18067 \begin_layout Plain Layout
18075 , which have the following scheme:
18078 \begin_layout Standard
18092 \begin_layout Standard
18099 defines big operators,
18108 \begin_layout Standard
18116 \begin_inset space \thinspace{}
18120 \begin_inset space \space{}
18123 be used to use one limit for several operators:
18126 \begin_layout Standard
18127 \begin_inset Formula
18129 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18137 \begin_layout Standard
18138 The command for the formula above is:
18139 \begin_inset Newline newline
18155 \begin_inset space \textvisiblespace{}
18161 \begin_inset Formula $\to$
18167 \begin_inset space \textvisiblespace{}
18175 \begin_layout Section
18177 \begin_inset Index idx
18180 \begin_layout Plain Layout
18189 \begin_layout Subsection
18191 \begin_inset CommandInset label
18193 name "subsec:Font-Styles"
18198 \begin_inset Index idx
18201 \begin_layout Plain Layout
18210 \begin_layout Standard
18211 Latin letters in formulas can be set in one of the following font styles:
18214 \begin_layout Standard
18216 \begin_inset Tabular
18217 <lyxtabular version="3" rows="6" columns="3">
18218 <features booktabs="true" tabularvalignment="middle">
18219 <column alignment="center" valignment="top" width="0pt">
18220 <column alignment="center" valignment="top">
18221 <column alignment="center" valignment="top">
18223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18226 \begin_layout Plain Layout
18232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18235 \begin_layout Plain Layout
18241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18244 \begin_layout Plain Layout
18252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18255 \begin_layout Plain Layout
18261 \begin_inset space \textvisiblespace{}
18271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18275 \begin_inset Formula $\mathbb{ABC}$
18283 <cell alignment="center" valignment="top" usebox="none">
18286 \begin_layout Plain Layout
18294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18297 \begin_layout Plain Layout
18303 \begin_inset space \textvisiblespace{}
18313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18316 \begin_layout Plain Layout
18317 \begin_inset Formula $\mathbf{AbC}$
18325 <cell alignment="center" valignment="top" usebox="none">
18328 \begin_layout Plain Layout
18341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18344 \begin_layout Plain Layout
18350 \begin_inset space \textvisiblespace{}
18360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18363 \begin_layout Plain Layout
18364 \begin_inset Formula $\boldsymbol{AbC}$
18372 <cell alignment="center" valignment="top" usebox="none">
18375 \begin_layout Plain Layout
18378 arg "font-boldsymbol"
18388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18391 \begin_layout Plain Layout
18397 \begin_inset space \textvisiblespace{}
18407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18410 \begin_layout Plain Layout
18411 \begin_inset Formula $\mathcal{ABC}$
18419 <cell alignment="center" valignment="top" usebox="none">
18422 \begin_layout Plain Layout
18430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18433 \begin_layout Plain Layout
18439 \begin_inset space \textvisiblespace{}
18449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18452 \begin_layout Plain Layout
18453 \begin_inset Formula $\mathfrak{AbC}$
18461 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18464 \begin_layout Plain Layout
18478 \begin_layout Standard
18480 \begin_inset Tabular
18481 <lyxtabular version="3" rows="6" columns="3">
18482 <features booktabs="true" tabularvalignment="middle">
18483 <column alignment="center" valignment="top" width="0pt">
18484 <column alignment="center" valignment="top">
18485 <column alignment="center" valignment="top">
18487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18490 \begin_layout Plain Layout
18496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18499 \begin_layout Plain Layout
18505 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18508 \begin_layout Plain Layout
18516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18519 \begin_layout Plain Layout
18525 \begin_inset space \textvisiblespace{}
18535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18538 \begin_layout Plain Layout
18539 \begin_inset Formula $\mathit{AbC}$
18547 <cell alignment="center" valignment="top" usebox="none">
18550 \begin_layout Plain Layout
18558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18561 \begin_layout Plain Layout
18567 \begin_inset space \textvisiblespace{}
18577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18580 \begin_layout Plain Layout
18581 \begin_inset Formula $\mathrm{AbC}$
18589 <cell alignment="center" valignment="top" usebox="none">
18592 \begin_layout Plain Layout
18605 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18608 \begin_layout Plain Layout
18614 \begin_inset space \textvisiblespace{}
18624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18627 \begin_layout Plain Layout
18628 \begin_inset Formula $\mathsf{AbC}$
18636 <cell alignment="center" valignment="top" usebox="none">
18639 \begin_layout Plain Layout
18652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18655 \begin_layout Plain Layout
18661 \begin_inset space \textvisiblespace{}
18671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18674 \begin_layout Plain Layout
18675 \begin_inset Formula $\mathtt{AbC}$
18683 <cell alignment="center" valignment="top" usebox="none">
18686 \begin_layout Plain Layout
18689 arg "font-typewriter"
18699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18702 \begin_layout Plain Layout
18708 \begin_inset space \textvisiblespace{}
18718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18721 \begin_layout Plain Layout
18722 \begin_inset Formula $\mathscr{ABC}$
18730 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18733 \begin_layout Plain Layout
18747 \begin_layout Standard
18748 \begin_inset Note Greyedout
18751 \begin_layout Plain Layout
18774 can only be used for big letters.
18782 \begin_layout Standard
18783 Predefined is the style
18792 \begin_layout Standard
18793 The style commands work also for letters in mathematical constructs:
18794 \begin_inset Formula
18796 \mathfrak{A=\frac{b}{C}}
18804 \begin_layout Standard
18805 Characters in mathematical text don't appear in a math font style but in
18806 the text font style
18813 That their style can't be set correctly via the text style dialog is a
18814 bug in \SpecialChar LyX
18819 \begin_layout Plain Layout
18820 \begin_inset CommandInset href
18822 name "LyX-bug #4629"
18823 target "https://www.lyx.org/trac/ticket/4629"
18836 \begin_layout Standard
18837 Instead of the style commands the dialog
18839 Edit\SpecialChar menuseparator
18840 Math\SpecialChar menuseparator
18843 or the toolbar button
18846 arg "math-insert \\font"
18852 \begin_layout Subsection
18854 \begin_inset CommandInset label
18856 name "subsec:Bold-Formulas"
18861 \begin_inset Index idx
18864 \begin_layout Plain Layout
18873 \begin_layout Standard
18874 To make a complete formula bold, the command
18880 from the previous subsection cannot be used, because it doesn't work for
18881 small Greek letters.
18882 Furthermore it prints Latin letters always upright, like in the following
18886 \begin_layout Standard
18887 \begin_inset Formula
18889 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18897 \begin_layout Standard
18898 To display the formula correctly, the command
18905 \begin_inset Formula
18907 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18912 It is also possible to set the formula in a
18914 boldmath environment
18917 This environment is created by inserting the command
18924 \begin_inset Index idx
18927 \begin_layout Plain Layout
18935 in \SpecialChar TeX
18937 To end the environment, the command
18944 \begin_inset Index idx
18947 \begin_layout Plain Layout
18955 is inserted in \SpecialChar TeX
18960 \begin_layout Plain Layout
18970 \begin_inset Formula
18972 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18981 \begin_layout Plain Layout
18993 \begin_layout Subsection
18995 \begin_inset Index idx
18998 \begin_layout Plain Layout
19007 \begin_layout Standard
19008 Formulas can be colored like normal text: Highlight a formula or a formula
19014 Here is a formula in magenta:
19015 \begin_inset Formula
19017 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19025 \begin_layout Standard
19026 You can also define your own colors as described in
19027 \begin_inset CommandInset ref
19029 reference "subsec:Colored-Boxes"
19034 They can be used with the \SpecialChar TeX
19042 \begin_inset Index idx
19045 \begin_layout Plain Layout
19056 \begin_layout Standard
19061 textcolor{color}{characters or formula}
19064 \begin_layout Standard
19065 The following example was colored completely dark green and partly red:
19068 \begin_layout Standard
19072 \begin_layout Plain Layout
19076 textcolor{darkgreen}{
19082 \begin_inset Formula
19084 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19093 \begin_layout Plain Layout
19103 \begin_layout Standard
19104 Due to a bug in \SpecialChar LyX
19105 only complete formulas can be colored with self-defined
19110 \begin_layout Plain Layout
19111 \begin_inset CommandInset href
19113 name "LyX-bug #5269"
19114 target "https://www.lyx.org/trac/ticket/5269"
19127 \begin_layout Subsection
19129 \begin_inset CommandInset label
19131 name "subsec:Font-Sizes"
19136 \begin_inset Index idx
19139 \begin_layout Plain Layout
19148 \begin_layout Standard
19149 For characters in formulas there are, analog to characters in text, the
19150 following size commands:
19153 \begin_layout Standard
19197 \begin_inset Newline newline
19219 \begin_layout Standard
19220 The size produced by the commands depends on the document font size, which
19221 corresponds to the command
19228 The other commands produce smaller or larger sizes than
19235 The font size can however not exceed a certain value.
19236 Is for example the document font size 12
19237 \begin_inset space \thinspace{}
19246 switches to the same size as
19256 \begin_layout Standard
19257 A size command is inserted in \SpecialChar TeX
19258 mode before the formula and sets the size
19259 for all following formula and text characters.
19260 To switch back to the initial size, the command
19266 is inserted behind the formula in \SpecialChar TeX
19270 \begin_layout Standard
19271 Within a formula the size can be changed using the following size commands
19272 or the toolbar button
19275 arg "math-insert \\style"
19281 \begin_layout Standard
19284 \begin_inset Tabular
19285 <lyxtabular version="3" rows="5" columns="2">
19286 <features booktabs="true" tabularvalignment="middle">
19287 <column alignment="center" valignment="top" width="0pt">
19288 <column alignment="center" valignment="top">
19290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19302 \begin_layout Plain Layout
19310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19317 \begin_inset Index idx
19320 \begin_layout Plain Layout
19333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19336 \begin_layout Plain Layout
19337 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19346 <row topspace="1mm">
19347 <cell alignment="center" valignment="top" usebox="none">
19350 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19362 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19375 \begin_layout Plain Layout
19383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19386 \begin_layout Plain Layout
19387 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19400 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19411 \begin_layout Plain Layout
19412 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19428 \begin_layout Standard
19429 After entering these commands, a blue box appears in which the formula parts
19433 \begin_layout Standard
19434 There is a further method to change the font size, that though only works
19435 for symbols or letters in mathematical text.
19436 To use it, one of the above text size commands is inserted in mathematical
19438 All following characters until the end of the mathematical text or until
19439 another size command will have the selected size.
19441 \begin_inset VSpace -2mm
19447 \begin_layout Standard
19451 \begin_layout Plain Layout
19461 \begin_inset Formula
19463 A=\frac{B}{c}\cdot\maltese
19469 \begin_inset Formula
19471 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19480 \begin_layout Plain Layout
19492 \begin_layout Standard
19493 \begin_inset VSpace medskip
19496 Before both formulas the command
19503 The command for the second formula is:
19504 \begin_inset Newline newline
19512 \begin_inset space \textvisiblespace{}
19518 \begin_inset space \textvisiblespace{}
19524 \begin_inset space \textvisiblespace{}
19530 \begin_inset space \textvisiblespace{}
19534 \begin_inset Formula $\to$
19538 \begin_inset Formula $\to$
19542 \begin_inset Newline newline
19546 \begin_inset space \hspace*{}
19557 \begin_inset space \textvisiblespace{}
19563 \begin_inset space \textvisiblespace{}
19569 \begin_inset space \textvisiblespace{}
19575 \begin_layout Standard
19576 If a symbol cannot be displayed in different sizes, it will always be displayed
19577 in the default size.
19580 \begin_layout Section
19582 \begin_inset Index idx
19585 \begin_layout Plain Layout
19594 \begin_layout Standard
19595 Greek letters can also be inserted via the toolbar button
19598 arg "math-insert \\alpha"
19602 All international typesetting norms purport that Greek letters in math
19603 have to be typeset italic/slanted.
19604 In some languages, like French or Russian, they are nevertheless sometimes
19608 \begin_layout Subsection
19610 \begin_inset Index idx
19613 \begin_layout Plain Layout
19614 Greek letters ! small
19622 \begin_layout Standard
19623 \begin_inset space \hfill{}
19627 \begin_inset Tabular
19628 <lyxtabular version="3" rows="11" columns="2">
19629 <features booktabs="true" tabularvalignment="middle">
19630 <column alignment="center" valignment="top" width="0pt">
19631 <column alignment="center" valignment="top" width="0pt">
19633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19636 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19645 \begin_layout Plain Layout
19653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19656 \begin_layout Plain Layout
19664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19667 \begin_layout Plain Layout
19668 \begin_inset Formula $\alpha$
19678 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19681 \begin_layout Plain Layout
19689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19692 \begin_layout Plain Layout
19693 \begin_inset Formula $\beta$
19703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19706 \begin_layout Plain Layout
19714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19717 \begin_layout Plain Layout
19718 \begin_inset Formula $\gamma$
19728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19731 \begin_layout Plain Layout
19739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19742 \begin_layout Plain Layout
19743 \begin_inset Formula $\delta$
19753 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19756 \begin_layout Plain Layout
19764 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19767 \begin_layout Plain Layout
19768 \begin_inset Formula $\epsilon$
19778 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19781 \begin_layout Plain Layout
19789 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19792 \begin_layout Plain Layout
19793 \begin_inset Formula $\varepsilon$
19803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19806 \begin_layout Plain Layout
19814 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19817 \begin_layout Plain Layout
19818 \begin_inset Formula $\zeta$
19828 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19831 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19843 \begin_inset Formula $\eta$
19853 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19856 \begin_layout Plain Layout
19864 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19867 \begin_layout Plain Layout
19868 \begin_inset Formula $\theta$
19878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19881 \begin_layout Plain Layout
19889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19892 \begin_layout Plain Layout
19893 \begin_inset Formula $\vartheta$
19907 \begin_inset space \hfill{}
19911 \begin_inset Tabular
19912 <lyxtabular version="3" rows="12" columns="2">
19913 <features booktabs="true" tabularvalignment="middle">
19914 <column alignment="center" valignment="top" width="0pt">
19915 <column alignment="center" valignment="top" width="0pt">
19917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19920 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19937 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19940 \begin_layout Plain Layout
19948 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19951 \begin_layout Plain Layout
19952 \begin_inset Formula $\iota$
19962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19965 \begin_layout Plain Layout
19973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19976 \begin_layout Plain Layout
19977 \begin_inset Formula $\kappa$
19987 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19990 \begin_layout Plain Layout
19998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20001 \begin_layout Plain Layout
20002 \begin_inset Formula $\varkappa$
20012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20015 \begin_layout Plain Layout
20023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20026 \begin_layout Plain Layout
20027 \begin_inset Formula $\lambda$
20037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20051 \begin_layout Plain Layout
20052 \begin_inset Formula $\mu$
20062 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20065 \begin_layout Plain Layout
20073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20076 \begin_layout Plain Layout
20077 \begin_inset Formula $\nu$
20087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20090 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $\xi$
20112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20121 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20124 \begin_layout Plain Layout
20125 \begin_inset Formula $o$
20135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20138 \begin_layout Plain Layout
20146 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20149 \begin_layout Plain Layout
20150 \begin_inset Formula $\pi$
20160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20163 \begin_layout Plain Layout
20171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20174 \begin_layout Plain Layout
20175 \begin_inset Formula $\varpi$
20185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20188 \begin_layout Plain Layout
20196 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20199 \begin_layout Plain Layout
20200 \begin_inset Formula $\rho$
20214 \begin_inset space \hfill{}
20218 \begin_inset Tabular
20219 <lyxtabular version="3" rows="11" columns="2">
20220 <features booktabs="true" tabularvalignment="middle">
20221 <column alignment="center" valignment="top" width="0pt">
20222 <column alignment="center" valignment="top" width="0pt">
20224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20227 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20236 \begin_layout Plain Layout
20244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20247 \begin_layout Plain Layout
20255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20258 \begin_layout Plain Layout
20259 \begin_inset Formula $\varrho$
20269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20272 \begin_layout Plain Layout
20280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20283 \begin_layout Plain Layout
20284 \begin_inset Formula $\sigma$
20294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20297 \begin_layout Plain Layout
20305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20308 \begin_layout Plain Layout
20309 \begin_inset Formula $\varsigma$
20319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20333 \begin_layout Plain Layout
20334 \begin_inset Formula $\tau$
20344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20347 \begin_layout Plain Layout
20355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20358 \begin_layout Plain Layout
20359 \begin_inset Formula $\upsilon$
20369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20372 \begin_layout Plain Layout
20380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20383 \begin_layout Plain Layout
20384 \begin_inset Formula $\phi$
20394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20397 \begin_layout Plain Layout
20405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20408 \begin_layout Plain Layout
20409 \begin_inset Formula $\varphi$
20419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20422 \begin_layout Plain Layout
20430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20433 \begin_layout Plain Layout
20434 \begin_inset Formula $\chi$
20444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20447 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Plain Layout
20459 \begin_inset Formula $\psi$
20469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20483 \begin_layout Plain Layout
20484 \begin_inset Formula $\omega$
20498 \begin_inset space \hfill{}
20504 \begin_layout Standard
20505 \begin_inset VSpace medskip
20511 \begin_layout Standard
20512 How to create special upright Greek letters is explained in
20513 \begin_inset CommandInset ref
20515 reference "subsec:Upright-small-Greek"
20522 \begin_layout Subsection
20524 \begin_inset Index idx
20527 \begin_layout Plain Layout
20528 Greek letters ! big
20536 \begin_layout Standard
20537 \begin_inset space \hfill{}
20541 \begin_inset Tabular
20542 <lyxtabular version="3" rows="7" columns="2">
20543 <features booktabs="true" tabularvalignment="middle">
20544 <column alignment="center" valignment="top" width="0pt">
20545 <column alignment="center" valignment="top" width="0pt">
20547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20550 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20570 \begin_layout Plain Layout
20578 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20581 \begin_layout Plain Layout
20582 \begin_inset Formula $\Gamma$
20592 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20595 \begin_layout Plain Layout
20603 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20606 \begin_layout Plain Layout
20607 \begin_inset Formula $\Delta$
20617 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20620 \begin_layout Plain Layout
20628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20631 \begin_layout Plain Layout
20632 \begin_inset Formula $\Theta$
20642 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20645 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20657 \begin_inset Formula $\Lambda$
20667 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20670 \begin_layout Plain Layout
20678 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20681 \begin_layout Plain Layout
20682 \begin_inset Formula $\Xi$
20692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20695 \begin_layout Plain Layout
20703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20706 \begin_layout Plain Layout
20707 \begin_inset Formula $\Pi$
20721 \begin_inset space \hfill{}
20725 \begin_inset Tabular
20726 <lyxtabular version="3" rows="6" columns="2">
20727 <features booktabs="true" tabularvalignment="middle">
20728 <column alignment="center" valignment="top" width="0pt">
20729 <column alignment="center" valignment="top" width="0pt">
20731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20743 \begin_layout Plain Layout
20751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20754 \begin_layout Plain Layout
20762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20765 \begin_layout Plain Layout
20766 \begin_inset Formula $\Sigma$
20776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20779 \begin_layout Plain Layout
20787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20790 \begin_layout Plain Layout
20791 \begin_inset Formula $\Upsilon$
20801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20804 \begin_layout Plain Layout
20812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20815 \begin_layout Plain Layout
20816 \begin_inset Formula $\Phi$
20826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20829 \begin_layout Plain Layout
20837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20840 \begin_layout Plain Layout
20841 \begin_inset Formula $\Psi$
20851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20854 \begin_layout Plain Layout
20862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20865 \begin_layout Plain Layout
20866 \begin_inset Formula $\Omega$
20880 \begin_inset space \hfill{}
20886 \begin_layout Standard
20887 \begin_inset VSpace medskip
20890 That the big Greek letters appear upright is caused by a design bug when
20893 To get correct italic big letters, begin every command with
20898 For example the command
20905 \begin_inset Formula $\varGamma$
20909 Another way is to load the package
20917 \begin_layout Plain Layout
20922 is part of the \SpecialChar LaTeX
20928 \begin_inset Index idx
20931 \begin_layout Plain Layout
20936 \begin_layout Plain Layout
20956 \begin_inset Index idx
20959 \begin_layout Plain Layout
20965 with the \SpecialChar LaTeX
20969 \begin_layout Standard
20974 usepackage{fixmath}
20977 \begin_layout Standard
20978 Then all big Greek letters in a document will automatically be typeset italic.
20981 \begin_layout Subsection
20983 \begin_inset Index idx
20986 \begin_layout Plain Layout
20987 Greek letters ! bold
20995 \begin_layout Standard
20996 Greek letters cannot be set with different font styles like Latin letters.
20997 They can only be made bold with the command
21004 \begin_inset Index idx
21007 \begin_layout Plain Layout
21018 \begin_layout Standard
21020 \begin_inset Tabular
21021 <lyxtabular version="3" rows="3" columns="2">
21022 <features booktabs="true" tabularvalignment="middle">
21023 <column alignment="center" valignment="top" width="0pt">
21024 <column alignment="center" valignment="top">
21026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21029 \begin_layout Plain Layout
21035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21038 \begin_layout Plain Layout
21046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21049 \begin_layout Plain Layout
21061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21064 \begin_layout Plain Layout
21065 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21078 \begin_layout Plain Layout
21090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21093 \begin_layout Plain Layout
21094 \begin_inset Formula $\theta\boldsymbol{\theta}$
21110 \begin_layout Section
21115 \begin_layout Plain Layout
21128 \begin_layout Plain Layout
21129 A list with all symbols of most of the \SpecialChar LaTeX
21130 -packages can be found in
21131 \begin_inset CommandInset citation
21147 \begin_layout Plain Layout
21155 \begin_inset Note Note
21158 \begin_layout Plain Layout
21161 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21164 \begin_layout Plain Layout
21167 texorpdfstring is in section
21168 \begin_inset CommandInset ref
21170 reference "subsec:Formulas-in-Section"
21180 \begin_inset Index idx
21183 \begin_layout Plain Layout
21192 \begin_layout Standard
21193 Many of the symbols listed in this section can also be inserted via the
21197 arg "math-insert \\nabla"
21203 arg "math-insert \\digamma"
21209 \begin_layout Subsection
21210 Mathematical Symbols
21211 \begin_inset CommandInset label
21213 name "subsec:Mathematical-Symbols"
21218 \begin_inset Index idx
21221 \begin_layout Plain Layout
21222 Symbols ! mathematical
21230 \begin_layout Standard
21231 \begin_inset Tabular
21232 <lyxtabular version="3" rows="10" columns="2">
21233 <features booktabs="true" tabularvalignment="middle">
21234 <column alignment="center" valignment="top" width="0pt">
21235 <column alignment="center" valignment="top" width="0pt">
21237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21240 \begin_layout Plain Layout
21246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21249 \begin_layout Plain Layout
21257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21260 \begin_layout Plain Layout
21268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21271 \begin_layout Plain Layout
21272 \begin_inset Formula $\neg$
21282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21285 \begin_layout Plain Layout
21293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21296 \begin_layout Plain Layout
21297 \begin_inset Formula $\Im$
21307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21310 \begin_layout Plain Layout
21318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21321 \begin_layout Plain Layout
21322 \begin_inset Formula $\Re$
21332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21335 \begin_layout Plain Layout
21343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21346 \begin_layout Plain Layout
21347 \begin_inset Formula $\aleph$
21357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21360 \begin_layout Plain Layout
21368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21371 \begin_layout Plain Layout
21372 \begin_inset Formula $\partial$
21382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21385 \begin_layout Plain Layout
21393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21396 \begin_layout Plain Layout
21397 \begin_inset Formula $\infty$
21407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21410 \begin_layout Plain Layout
21418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21421 \begin_layout Plain Layout
21422 \begin_inset Formula $\wp$
21432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21435 \begin_layout Plain Layout
21443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21446 \begin_layout Plain Layout
21447 \begin_inset Formula $\imath$
21457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21460 \begin_layout Plain Layout
21468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21471 \begin_layout Plain Layout
21472 \begin_inset Formula $\jmath$
21486 \begin_inset space \hfill{}
21490 \begin_inset Tabular
21491 <lyxtabular version="3" rows="10" columns="2">
21492 <features booktabs="true" tabularvalignment="middle">
21493 <column alignment="center" valignment="top" width="0pt">
21494 <column alignment="center" valignment="top" width="0pt">
21496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21499 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21508 \begin_layout Plain Layout
21510 \begin_inset Note Note
21513 \begin_layout Plain Layout
21520 is only used as spacer.
21532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21535 \begin_layout Plain Layout
21543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21546 \begin_layout Plain Layout
21547 \begin_inset Formula $\forall$
21557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21560 \begin_layout Plain Layout
21568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21571 \begin_layout Plain Layout
21572 \begin_inset Formula $\exists$
21582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21585 \begin_layout Plain Layout
21593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21596 \begin_layout Plain Layout
21597 \begin_inset Formula $\nexists$
21607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21610 \begin_layout Plain Layout
21618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21621 \begin_layout Plain Layout
21622 \begin_inset Formula $\emptyset$
21632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21635 \begin_layout Plain Layout
21643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21646 \begin_layout Plain Layout
21647 \begin_inset Formula $\varnothing$
21657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21660 \begin_layout Plain Layout
21668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21671 \begin_layout Plain Layout
21672 \begin_inset Formula $\dag$
21682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21685 \begin_layout Plain Layout
21693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21696 \begin_layout Plain Layout
21697 \begin_inset Formula $\ddag$
21707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21710 \begin_layout Plain Layout
21718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21721 \begin_layout Plain Layout
21725 \begin_layout Plain Layout
21735 \begin_inset Formula $\complement$
21742 \begin_layout Plain Layout
21756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21759 \begin_layout Plain Layout
21767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21770 \begin_layout Plain Layout
21771 \begin_inset Formula $\Bbbk$
21785 \begin_inset space \hfill{}
21789 \begin_inset Tabular
21790 <lyxtabular version="3" rows="10" columns="2">
21791 <features booktabs="true" tabularvalignment="middle">
21792 <column alignment="center" valignment="top" width="0pt">
21793 <column alignment="center" valignment="top" width="0pt">
21795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21798 \begin_layout Plain Layout
21804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21807 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21818 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21829 \begin_layout Plain Layout
21830 \begin_inset Formula $\prime$
21840 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21843 \begin_layout Plain Layout
21851 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21854 \begin_layout Plain Layout
21855 \begin_inset Formula $\backprime$
21865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21868 \begin_layout Plain Layout
21876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21879 \begin_layout Plain Layout
21880 \begin_inset Formula $\mho$
21890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21893 \begin_layout Plain Layout
21901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21904 \begin_layout Plain Layout
21905 \begin_inset Formula $\triangle$
21915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21918 \begin_layout Plain Layout
21926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21929 \begin_layout Plain Layout
21930 \begin_inset Formula $\angle$
21940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21943 \begin_layout Plain Layout
21951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21954 \begin_layout Plain Layout
21955 \begin_inset Formula $\measuredangle$
21965 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21968 \begin_layout Plain Layout
21976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21979 \begin_layout Plain Layout
21980 \begin_inset Formula $\sphericalangle$
21990 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21993 \begin_layout Plain Layout
22001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22004 \begin_layout Plain Layout
22005 \begin_inset Formula $\top$
22015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22018 \begin_layout Plain Layout
22026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22029 \begin_layout Plain Layout
22030 \begin_inset Formula $\bot$
22046 \begin_layout Subsection
22047 Miscellaneous Symbols
22048 \begin_inset CommandInset label
22050 name "subsec:Miscellaneous-Symbols"
22055 \begin_inset Index idx
22058 \begin_layout Plain Layout
22059 Symbols ! miscellaneous
22067 \begin_layout Standard
22070 \begin_inset Tabular
22071 <lyxtabular version="3" rows="10" columns="2">
22072 <features booktabs="true" tabularvalignment="middle">
22073 <column alignment="center" valignment="top" width="0pt">
22074 <column alignment="center" valignment="top" width="0pt">
22076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22079 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22099 \begin_layout Plain Layout
22107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22110 \begin_layout Plain Layout
22111 \begin_inset Formula $\flat$
22121 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22124 \begin_layout Plain Layout
22132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22135 \begin_layout Plain Layout
22136 \begin_inset Formula $\natural$
22146 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22149 \begin_layout Plain Layout
22157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22160 \begin_layout Plain Layout
22161 \begin_inset Formula $\sharp$
22171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22174 \begin_layout Plain Layout
22182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22185 \begin_layout Plain Layout
22186 \begin_inset Formula $\surd$
22196 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22199 \begin_layout Plain Layout
22207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22210 \begin_layout Plain Layout
22211 \begin_inset Formula $\checkmark$
22221 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Plain Layout
22232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22235 \begin_layout Plain Layout
22236 \begin_inset Formula $\yen$
22246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22261 \begin_inset Formula $\pounds$
22271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22284 \begin_inset Formula $\$$
22294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22306 \begin_layout Plain Layout
22307 \begin_inset Formula $§$
22321 \begin_inset space \hfill{}
22325 \begin_inset Tabular
22326 <lyxtabular version="3" rows="10" columns="2">
22327 <features booktabs="true" tabularvalignment="middle">
22328 <column alignment="center" valignment="top" width="0pt">
22329 <column alignment="center" valignment="top">
22331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22354 \begin_layout Plain Layout
22362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22365 \begin_layout Plain Layout
22366 \begin_inset Formula $\hbar$
22376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22379 \begin_layout Plain Layout
22387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22390 \begin_layout Plain Layout
22391 \begin_inset Formula $\hslash$
22401 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22404 \begin_layout Plain Layout
22412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22415 \begin_layout Plain Layout
22416 \begin_inset Formula $\clubsuit$
22426 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22429 \begin_layout Plain Layout
22437 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22440 \begin_layout Plain Layout
22441 \begin_inset Formula $\spadesuit$
22451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22454 \begin_layout Plain Layout
22462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22465 \begin_layout Plain Layout
22466 \begin_inset Formula $\bigstar$
22476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22479 \begin_layout Plain Layout
22487 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22490 \begin_layout Plain Layout
22491 \begin_inset Formula $\blacklozenge$
22501 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22504 \begin_layout Plain Layout
22512 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22515 \begin_layout Plain Layout
22516 \begin_inset Formula $\blacktriangle$
22526 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22529 \begin_layout Plain Layout
22537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22540 \begin_layout Plain Layout
22541 \begin_inset Formula $\blacktriangledown$
22551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22554 \begin_layout Plain Layout
22562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22565 \begin_layout Plain Layout
22566 \begin_inset Formula $\bullet$
22580 \begin_inset space \hfill{}
22584 \begin_inset Tabular
22585 <lyxtabular version="3" rows="10" columns="2">
22586 <features booktabs="true" tabularvalignment="middle">
22587 <column alignment="center" valignment="top" width="0pt">
22588 <column alignment="center" valignment="top" width="0pt">
22590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22593 \begin_layout Plain Layout
22599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22602 \begin_layout Plain Layout
22610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\diamondsuit$
22635 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22638 \begin_layout Plain Layout
22646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22649 \begin_layout Plain Layout
22650 \begin_inset Formula $\Diamond$
22660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\heartsuit$
22685 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22700 \begin_inset Formula $\P$
22710 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22713 \begin_layout Plain Layout
22721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Plain Layout
22725 \begin_inset Formula $\copyright$
22735 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22738 \begin_layout Plain Layout
22746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22749 \begin_layout Plain Layout
22750 \begin_inset Formula $\circledR$
22760 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\maltese$
22785 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\diagup$
22810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22825 \begin_inset Formula $\diagdown$
22841 \begin_layout Standard
22842 \begin_inset VSpace medskip
22848 \begin_layout Standard
22849 Some symbols can be displayed in different sizes, see
22850 \begin_inset CommandInset ref
22852 reference "subsec:Font-Sizes"
22859 \begin_layout Subsection
22861 \begin_inset Index idx
22864 \begin_layout Plain Layout
22865 Symbols ! Euro-symbol
22871 \begin_inset Index idx
22874 \begin_layout Plain Layout
22881 \begin_layout Plain Layout
22898 \begin_layout Standard
22899 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22905 \begin_inset Index idx
22908 \begin_layout Plain Layout
22914 must be installed and loaded with the \SpecialChar LaTeX
22918 \begin_layout Standard
22923 usepackage[gennarrow]{eurosym}
22926 \begin_layout Standard
22927 The Euro symbol can now be inserted with the command
22934 \begin_inset Index idx
22937 \begin_layout Plain Layout
22948 \begin_layout Standard
22949 The Euro symbol can directly be inserted with the € key in mathematical
22950 text, without having
22965 can also be inserted in \SpecialChar TeX
22967 The official currency symbol can then be inserted with the command
22974 \begin_inset Index idx
22977 \begin_layout Plain Layout
22985 , that is only available in \SpecialChar TeX
22989 \begin_layout Standard
22993 \begin_layout Plain Layout
23003 \begin_inset Note Note
23006 \begin_layout Plain Layout
23007 The following table will only be displayed when the \SpecialChar LaTeX
23020 \begin_layout Standard
23021 An overview about the different Euro symbols:
23024 \begin_layout Standard
23026 \begin_inset Tabular
23027 <lyxtabular version="3" rows="4" columns="3">
23028 <features booktabs="true" tabularvalignment="middle">
23029 <column alignment="center" valignment="top" width="0pt">
23030 <column alignment="center" valignment="top" width="0pt">
23031 <column alignment="center" valignment="top" width="0pt">
23033 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23036 \begin_layout Plain Layout
23040 \begin_layout Plain Layout
23044 cmidrule[0.08em]{2-3}
23054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23057 \begin_layout Plain Layout
23063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23066 \begin_layout Plain Layout
23074 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23077 \begin_layout Plain Layout
23083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23086 \begin_layout Plain Layout
23094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23097 \begin_layout Plain Layout
23098 \begin_inset Formula $\euro$
23108 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23111 \begin_layout Plain Layout
23117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23129 \begin_layout Plain Layout
23130 \begin_inset Formula $\mbox{€}$
23140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23143 \begin_layout Plain Layout
23150 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23153 \begin_layout Plain Layout
23161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23164 \begin_layout Plain Layout
23168 \begin_layout Plain Layout
23188 \begin_inset Note Note
23191 \begin_layout Plain Layout
23198 is used here only for table borders.
23208 manual for details.
23216 \begin_layout Standard
23220 \begin_layout Plain Layout
23230 \begin_inset Note Note
23233 \begin_layout Plain Layout
23234 The following will be displayed when the \SpecialChar LaTeX
23247 \begin_layout Standard
23248 You need to install the \SpecialChar LaTeX
23253 to see the rest of this subsection in the output.
23256 \begin_layout Standard
23260 \begin_layout Plain Layout
23272 \begin_layout Section
23274 \begin_inset CommandInset label
23276 name "sec:Relations"
23281 \begin_inset Index idx
23284 \begin_layout Plain Layout
23291 \begin_inset Index idx
23294 \begin_layout Plain Layout
23299 \begin_layout Plain Layout
23310 \begin_layout Plain Layout
23325 \begin_layout Standard
23326 All following relations can also be inserted via the toolbar button
23329 arg "math-insert \\leq"
23335 \begin_layout Standard
23336 \begin_inset Tabular
23337 <lyxtabular version="3" rows="17" columns="2">
23338 <features booktabs="true" tabularvalignment="middle">
23339 <column alignment="center" valignment="top" width="0pt">
23340 <column alignment="center" valignment="top" width="0pt">
23342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23345 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23354 \begin_layout Plain Layout
23362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23371 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23374 \begin_layout Plain Layout
23375 \begin_inset Formula $<$
23385 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23388 \begin_layout Plain Layout
23396 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23399 \begin_layout Plain Layout
23400 \begin_inset Formula $\le$
23410 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23413 \begin_layout Plain Layout
23421 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23424 \begin_layout Plain Layout
23425 \begin_inset Formula $\ll$
23435 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23438 \begin_layout Plain Layout
23446 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23449 \begin_layout Plain Layout
23450 \begin_inset Formula $\prec$
23460 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23463 \begin_layout Plain Layout
23471 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23474 \begin_layout Plain Layout
23475 \begin_inset Formula $\preceq$
23485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23488 \begin_layout Plain Layout
23496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23499 \begin_layout Plain Layout
23500 \begin_inset Formula $\subset$
23510 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23513 \begin_layout Plain Layout
23521 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23524 \begin_layout Plain Layout
23525 \begin_inset Formula $\subseteq$
23535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23538 \begin_layout Plain Layout
23546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23549 \begin_layout Plain Layout
23550 \begin_inset Formula $\sqsubseteq$
23560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23563 \begin_layout Plain Layout
23571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23574 \begin_layout Plain Layout
23575 \begin_inset Formula $\in$
23585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23588 \begin_layout Plain Layout
23596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23599 \begin_layout Plain Layout
23600 \begin_inset Formula $\vdash$
23610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23613 \begin_layout Plain Layout
23621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23624 \begin_layout Plain Layout
23625 \begin_inset Formula $\smile$
23635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23638 \begin_layout Plain Layout
23646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23649 \begin_layout Plain Layout
23650 \begin_inset Formula $\lhd$
23660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23663 \begin_layout Plain Layout
23671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23674 \begin_layout Plain Layout
23675 \begin_inset Formula $\unlhd$
23685 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23688 \begin_layout Plain Layout
23696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23699 \begin_layout Plain Layout
23700 \begin_inset Formula $\gtrless$
23710 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23713 \begin_layout Plain Layout
23721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23724 \begin_layout Plain Layout
23725 \begin_inset Formula $\mid$
23735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23738 \begin_layout Plain Layout
23746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23749 \begin_layout Plain Layout
23750 \begin_inset Formula $\nmid$
23764 \begin_inset space \hfill{}
23768 \begin_inset Tabular
23769 <lyxtabular version="3" rows="17" columns="2">
23770 <features booktabs="true" tabularvalignment="middle">
23771 <column alignment="center" valignment="top" width="0pt">
23772 <column alignment="center" valignment="top" width="0pt">
23774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23777 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23786 \begin_layout Plain Layout
23794 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23797 \begin_layout Plain Layout
23803 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23806 \begin_layout Plain Layout
23807 \begin_inset Formula $=$
23817 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23820 \begin_layout Plain Layout
23828 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23831 \begin_layout Plain Layout
23832 \begin_inset Formula $\not=$
23842 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23845 \begin_layout Plain Layout
23853 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23856 \begin_layout Plain Layout
23857 \begin_inset Formula $\equiv$
23867 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23870 \begin_layout Plain Layout
23878 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23881 \begin_layout Plain Layout
23882 \begin_inset Formula $\sim$
23892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23903 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23906 \begin_layout Plain Layout
23907 \begin_inset Formula $\simeq$
23917 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23920 \begin_layout Plain Layout
23928 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23931 \begin_layout Plain Layout
23932 \begin_inset Formula $\approx$
23942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23945 \begin_layout Plain Layout
23953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23956 \begin_layout Plain Layout
23957 \begin_inset Formula $\cong$
23967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23970 \begin_layout Plain Layout
23978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23981 \begin_layout Plain Layout
23982 \begin_inset Formula $\bowtie$
23992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23995 \begin_layout Plain Layout
24003 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24006 \begin_layout Plain Layout
24007 \begin_inset Formula $\notin$
24017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24020 \begin_layout Plain Layout
24028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24031 \begin_layout Plain Layout
24032 \begin_inset Formula $\perp$
24042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24045 \begin_layout Plain Layout
24053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24056 \begin_layout Plain Layout
24057 \begin_inset Formula $\propto$
24067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24070 \begin_layout Plain Layout
24078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24081 \begin_layout Plain Layout
24082 \begin_inset Formula $\asymp$
24092 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24095 \begin_layout Plain Layout
24103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24106 \begin_layout Plain Layout
24107 \begin_inset Formula $\doteq$
24117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24120 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24131 \begin_layout Plain Layout
24132 \begin_inset Formula $\circeq$
24142 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24145 \begin_layout Plain Layout
24153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24156 \begin_layout Plain Layout
24157 \begin_inset Formula $\models$
24167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24170 \begin_layout Plain Layout
24178 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24181 \begin_layout Plain Layout
24182 \begin_inset Formula $\widehat{=}$
24196 \begin_inset space \hfill{}
24200 \begin_inset Tabular
24201 <lyxtabular version="3" rows="17" columns="2">
24202 <features booktabs="true" tabularvalignment="middle">
24203 <column alignment="center" valignment="top" width="0pt">
24204 <column alignment="center" valignment="top" width="0pt">
24206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24218 \begin_layout Plain Layout
24226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24229 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24238 \begin_layout Plain Layout
24239 \begin_inset Formula $>$
24249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24263 \begin_layout Plain Layout
24264 \begin_inset Formula $\ge$
24274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24277 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24288 \begin_layout Plain Layout
24289 \begin_inset Formula $\gg$
24299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24302 \begin_layout Plain Layout
24310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24313 \begin_layout Plain Layout
24314 \begin_inset Formula $\succ$
24324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24327 \begin_layout Plain Layout
24335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24338 \begin_layout Plain Layout
24339 \begin_inset Formula $\succeq$
24349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24352 \begin_layout Plain Layout
24360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24363 \begin_layout Plain Layout
24364 \begin_inset Formula $\supset$
24374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24388 \begin_layout Plain Layout
24389 \begin_inset Formula $\supseteq$
24399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24402 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24413 \begin_layout Plain Layout
24414 \begin_inset Formula $\sqsupseteq$
24424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24438 \begin_layout Plain Layout
24439 \begin_inset Formula $\ni$
24449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24452 \begin_layout Plain Layout
24460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24463 \begin_layout Plain Layout
24464 \begin_inset Formula $\dashv$
24474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24488 \begin_layout Plain Layout
24489 \begin_inset Formula $\frown$
24499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24502 \begin_layout Plain Layout
24510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24513 \begin_layout Plain Layout
24514 \begin_inset Formula $\rhd$
24524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24539 \begin_inset Formula $\unrhd$
24549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24552 \begin_layout Plain Layout
24560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24563 \begin_layout Plain Layout
24564 \begin_inset Formula $\lessgtr$
24574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24577 \begin_layout Plain Layout
24585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24588 \begin_layout Plain Layout
24589 \begin_inset Formula $\parallel$
24599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24602 \begin_layout Plain Layout
24610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24613 \begin_layout Plain Layout
24614 \begin_inset Formula $\nparallel$
24630 \begin_layout Standard
24631 \begin_inset VSpace medskip
24646 are bigger than the equal looking operators
24661 \begin_layout Standard
24663 supports also many special relations.
24664 Use the toolbar button
24667 arg "math-insert \\leqq"
24670 to see a list of these relations.
24673 \begin_layout Standard
24674 Relations are, in contrary to symbols, always surrounded by space.
24677 \begin_layout Standard
24678 Relations with labels can be created with the command
24685 \begin_inset Index idx
24688 \begin_layout Plain Layout
24699 \begin_layout Standard
24701 \begin_inset Tabular
24702 <lyxtabular version="3" rows="2" columns="2">
24703 <features booktabs="true" tabularvalignment="middle">
24704 <column alignment="center" valignment="top" width="0pt">
24705 <column alignment="center" valignment="top">
24707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24710 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24726 <row topspace="1.5mm">
24727 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24730 \begin_layout Plain Layout
24734 \begin_inset space \textvisiblespace{}
24742 \begin_inset space \textvisiblespace{}
24746 \begin_inset Formula $\downarrow$
24752 \begin_inset space \textvisiblespace{}
24756 \begin_inset space \textvisiblespace{}
24764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Plain Layout
24768 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24784 \begin_layout Section
24788 \begin_layout Subsection
24789 Predefined Functions
24790 \begin_inset CommandInset label
24792 name "subsec:Predefined-Functions"
24797 \begin_inset Index idx
24800 \begin_layout Plain Layout
24801 Functions ! predefined
24809 \begin_layout Standard
24810 In general, variables are set
24814 in mathematical expressions, but not function names, because
24815 \begin_inset Formula $sin$
24818 could be misunderstood as
24819 \begin_inset Formula $s\cdot i\cdot n$
24823 Therefore there are predefined functions which are additionally a bit separated
24825 They are inserted as commands starting with a backslash before their name.
24828 \begin_layout Standard
24830 \begin_inset Tabular
24831 <lyxtabular version="3" rows="2" columns="2">
24832 <features booktabs="true" tabularvalignment="middle">
24833 <column alignment="center" valignment="top" width="0pt">
24834 <column alignment="center" valignment="top" width="0pt">
24836 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24839 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24859 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24868 \begin_layout Plain Layout
24869 \begin_inset Formula $Asin(x)+B$
24883 \begin_inset space \quad{}
24887 \begin_inset Tabular
24888 <lyxtabular version="3" rows="2" columns="2">
24889 <features booktabs="true" tabularvalignment="middle">
24890 <column alignment="center" valignment="top" width="0pt">
24891 <column alignment="center" valignment="top" width="0pt">
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24896 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24905 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24916 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24927 \begin_layout Plain Layout
24928 \begin_inset Formula $A\sin(x)+B$
24944 \begin_layout Standard
24945 The following functions are predefined:
24948 \begin_layout Standard
24949 \begin_inset VSpace -2mm
24955 \begin_layout Standard
24957 \begin_inset Tabular
24958 <lyxtabular version="3" rows="9" columns="4">
24959 <features booktabs="true" tabularvalignment="middle">
24960 <column alignment="center" valignment="top" width="0pt">
24961 <column alignment="center" valignment="top" width="0pt">
24962 <column alignment="center" valignment="top" width="0pt">
24963 <column alignment="center" valignment="top" width="0pt">
24965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24968 \begin_layout Plain Layout
24974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24977 \begin_layout Plain Layout
24983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24986 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25006 \begin_layout Plain Layout
25014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25017 \begin_layout Plain Layout
25025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25028 \begin_layout Plain Layout
25036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25039 \begin_layout Plain Layout
25049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25052 \begin_layout Plain Layout
25060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25063 \begin_layout Plain Layout
25071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25074 \begin_layout Plain Layout
25082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25085 \begin_layout Plain Layout
25095 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25098 \begin_layout Plain Layout
25106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25109 \begin_layout Plain Layout
25117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25120 \begin_layout Plain Layout
25128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25131 \begin_layout Plain Layout
25141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25144 \begin_layout Plain Layout
25152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25155 \begin_layout Plain Layout
25163 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25166 \begin_layout Plain Layout
25174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25177 \begin_layout Plain Layout
25187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25190 \begin_layout Plain Layout
25198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25201 \begin_layout Plain Layout
25209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25212 \begin_layout Plain Layout
25220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25223 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25236 \begin_layout Plain Layout
25244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25247 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25258 \begin_layout Plain Layout
25266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25269 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25282 \begin_layout Plain Layout
25290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25293 \begin_layout Plain Layout
25301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25304 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25315 \begin_layout Plain Layout
25325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25328 \begin_layout Plain Layout
25336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25339 \begin_layout Plain Layout
25347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25350 \begin_layout Plain Layout
25358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25361 \begin_layout Plain Layout
25377 \begin_layout Standard
25378 They can also be inserted with the math toolbar button
25381 arg "math-insert \\functions"
25387 \begin_layout Subsection
25388 Self-defined Functions
25389 \begin_inset Index idx
25392 \begin_layout Plain Layout
25393 Functions ! self-defined
25401 \begin_layout Standard
25402 To use a function that is not predefined, like for example the sign function
25403 sgn(x), there are two possibilities:
25406 \begin_layout Itemize
25407 Define the function by inserting the following line to the \SpecialChar LaTeX
25412 \begin_layout Plain Layout
25417 DeclareMathOperator
25420 \begin_inset CommandInset ref
25422 reference "subsec:Self-defined-Operators"
25432 \begin_inset Newline newline
25436 \begin_inset VSpace -3mm
25440 \begin_inset Newline newline
25447 DeclareMathOperator{
25452 \begin_inset Index idx
25455 \begin_layout Plain Layout
25460 DeclareMathOperator
25466 \begin_inset Newline newline
25470 \begin_inset VSpace -2mm
25474 \begin_inset Newline newline
25477 Now the new defined function can be called with the command
25486 \begin_layout Itemize
25487 Write the formula as usual, mark the formula name, in our example the letters
25492 , and change it to mathematical text.
25493 Finally, a space is inserted between prefactor and function.
25496 \begin_layout Standard
25497 The result is the same with both methods as with a predefined function
25501 \begin_layout Plain Layout
25502 In \SpecialChar LyX
25503 self-defined functions are displayed red, predefined ones black.
25511 \begin_layout Standard
25513 \begin_inset Tabular
25514 <lyxtabular version="3" rows="3" columns="2">
25515 <features booktabs="true" tabularvalignment="middle">
25516 <column alignment="center" valignment="top" width="0pt">
25517 <column alignment="center" valignment="top" width="0pt">
25519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25531 \begin_layout Plain Layout
25539 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25554 \begin_inset Formula $A\sgn(x)+B$
25564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25567 \begin_layout Plain Layout
25571 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25582 \begin_layout Plain Layout
25583 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25599 \begin_layout Standard
25600 The first method is more suitable when the self-defined function should
25601 be used several times.
25604 \begin_layout Subsection
25606 \begin_inset Index idx
25609 \begin_layout Plain Layout
25618 \begin_layout Standard
25619 For limits, in addition to the commands
25626 \begin_inset Index idx
25629 \begin_layout Plain Layout
25649 the following functions are defined:
25652 \begin_layout Standard
25654 \begin_inset Tabular
25655 <lyxtabular version="3" rows="5" columns="2">
25656 <features booktabs="true" tabularvalignment="middle">
25657 <column alignment="center" valignment="top" width="0pt">
25658 <column alignment="center" valignment="top" width="0pt">
25660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25663 \begin_layout Plain Layout
25669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25672 \begin_layout Plain Layout
25680 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25683 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25695 \begin_inset Formula $\varliminf$
25704 <row topspace="1.5mm">
25705 <cell alignment="center" valignment="top" usebox="none">
25708 \begin_layout Plain Layout
25716 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25719 \begin_layout Plain Layout
25720 \begin_inset Formula $\varlimsup$
25729 <row topspace="1.5mm">
25730 <cell alignment="center" valignment="top" usebox="none">
25733 \begin_layout Plain Layout
25741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25744 \begin_layout Plain Layout
25745 \begin_inset Formula $\varprojlim$
25754 <row topspace="1.5mm" bottomspace="1mm">
25755 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25758 \begin_layout Plain Layout
25766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25769 \begin_layout Plain Layout
25770 \begin_inset Formula $\varinjlim$
25786 \begin_layout Standard
25787 \begin_inset VSpace medskip
25790 The limit is created by inserting a subscript.
25791 It is set right beside the function in an inline formula:
25794 \begin_layout Standard
25796 \begin_inset Tabular
25797 <lyxtabular version="3" rows="2" columns="2">
25798 <features booktabs="true" tabularvalignment="middle">
25799 <column alignment="center" valignment="top" width="0pt">
25800 <column alignment="center" valignment="top" width="0pt">
25802 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25805 \begin_layout Plain Layout
25811 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25814 \begin_layout Plain Layout
25822 <cell alignment="center" valignment="top" usebox="none">
25825 \begin_layout Plain Layout
25831 \begin_inset space \textvisiblespace{}
25835 \begin_inset space \textvisiblespace{}
25843 <cell alignment="center" valignment="top" usebox="none">
25846 \begin_layout Plain Layout
25847 \begin_inset Formula $\lim_{x\to A}x=B$
25863 \begin_layout Standard
25864 In a displayed formula the limit is set below the formula, as usual:
25865 \begin_inset Formula
25875 \begin_layout Standard
25876 \begin_inset VSpace medskip
25882 \begin_layout Standard
25883 How to adjust the typesetting of the limits see
25884 \begin_inset CommandInset ref
25886 reference "subsec:Operator-Limits"
25893 \begin_layout Subsection
25895 \begin_inset Index idx
25898 \begin_layout Plain Layout
25899 Functions ! modulo-
25907 \begin_layout Standard
25908 The modulo-function is special, because it exists in four variants.
25909 The variants in a displayed formula are:
25910 \begin_inset Formula
25912 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25913 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25914 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25915 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25916 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25924 \begin_layout Standard
25925 In an inline formula less space is set before the function names for all
25927 By default the modulo-functions take only the first following character
25929 To use more than one character, one has to put them into \SpecialChar TeX
25931 \begin_inset Formula
25933 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25934 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25935 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25943 \begin_layout Section
25945 \begin_inset Index idx
25948 \begin_layout Plain Layout
25957 \begin_layout Standard
25958 The characters ^ and _ would normally create a superscript and subscript,
25960 To get these characters you have to insert them with a leading
25965 \begin_layout Standard
25968 \begin_inset Tabular
25969 <lyxtabular version="3" rows="3" columns="2">
25970 <features booktabs="true" tabularvalignment="middle">
25971 <column alignment="left" valignment="top" width="0pt">
25972 <column alignment="block" valignment="top">
25974 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25977 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25986 \begin_layout Plain Layout
25994 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25997 \begin_layout Plain Layout
26001 \begin_inset space \textvisiblespace{}
26009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26012 \begin_layout Plain Layout
26013 \begin_inset Formula $\mathcircumflex$
26023 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26037 \begin_layout Plain Layout
26038 \begin_inset Formula $\_$
26054 \begin_layout Subsection
26055 Special Characters in Mathematical Text
26058 \begin_layout Standard
26059 The following commands can only be used in mathematical text or in \SpecialChar TeX
26063 \begin_layout Standard
26064 \begin_inset space \hfill{}
26068 \begin_inset Tabular
26069 <lyxtabular version="3" rows="8" columns="2">
26070 <features booktabs="true" tabularvalignment="middle">
26071 <column alignment="left" valignment="top" width="0pt">
26072 <column alignment="block" valignment="top">
26074 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26086 \begin_layout Plain Layout
26094 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26097 \begin_layout Plain Layout
26105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26108 \begin_layout Plain Layout
26109 \begin_inset Formula $\textrm{œ}$
26119 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26122 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26133 \begin_layout Plain Layout
26134 \begin_inset Formula $\textrm{Œ}$
26144 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26147 \begin_layout Plain Layout
26155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26158 \begin_layout Plain Layout
26159 \begin_inset Formula $\textrm{æ}$
26169 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26172 \begin_layout Plain Layout
26180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26183 \begin_layout Plain Layout
26184 \begin_inset Formula $\textrm{Æ}$
26194 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26197 \begin_layout Plain Layout
26205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26208 \begin_layout Plain Layout
26209 \begin_inset Formula $\textrm{å}$
26219 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26222 \begin_layout Plain Layout
26230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26233 \begin_layout Plain Layout
26234 \begin_inset Formula $\textrm{Å}$
26244 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26247 \begin_layout Plain Layout
26255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26258 \begin_layout Plain Layout
26259 \begin_inset Formula $\textrm{ı}$
26273 \begin_inset space \hfill{}
26277 \begin_inset Tabular
26278 <lyxtabular version="3" rows="8" columns="2">
26279 <features booktabs="true" tabularvalignment="middle">
26280 <column alignment="left" valignment="top" width="0pt">
26281 <column alignment="center" valignment="top">
26283 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26286 \begin_layout Plain Layout
26288 \begin_inset Note Note
26291 \begin_layout Plain Layout
26293 \begin_inset space \thinspace{}
26296 mm is used for separation, because otherwise the output will be ¡ and ¿
26307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26310 \begin_layout Plain Layout
26318 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26321 \begin_layout Plain Layout
26329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26332 \begin_layout Plain Layout
26333 \begin_inset Formula $\textrm{ø}$
26343 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26346 \begin_layout Plain Layout
26354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26357 \begin_layout Plain Layout
26358 \begin_inset Formula $\textrm{Ø}$
26368 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26371 \begin_layout Plain Layout
26379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26382 \begin_layout Plain Layout
26383 \begin_inset Formula $\textrm{ł}$
26393 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26396 \begin_layout Plain Layout
26404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26407 \begin_layout Plain Layout
26408 \begin_inset Formula $\textrm{Ł}$
26418 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26421 \begin_layout Plain Layout
26423 \begin_inset space \hspace{}
26428 \begin_inset space \textvisiblespace{}
26436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26439 \begin_layout Plain Layout
26440 \begin_inset Formula $\textrm{!`}$
26450 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26453 \begin_layout Plain Layout
26455 \begin_inset space \hspace{}
26460 \begin_inset space \textvisiblespace{}
26468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26471 \begin_layout Plain Layout
26472 \begin_inset Formula $\textrm{?`}$
26482 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26485 \begin_layout Plain Layout
26493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26496 \begin_layout Plain Layout
26497 \begin_inset Formula $\textrm{ȷ}$
26511 \begin_inset space \hfill{}
26517 \begin_layout Standard
26519 \begin_inset Formula $\textrm{Å}$
26523 \begin_inset Formula $\textrm{Ø}$
26526 can also be inserted via the math toolbar button
26529 arg "math-insert \\digamma"
26535 \begin_layout Standard
26536 An exception are the commands
26539 \begin_inset space \hspace{}
26548 \begin_inset space \hspace{}
26554 , because they can be inserted in \SpecialChar LyX
26558 \begin_layout Subsection
26560 \begin_inset CommandInset label
26562 name "subsec:Accents-in-Text"
26567 \begin_inset Index idx
26570 \begin_layout Plain Layout
26579 \begin_layout Standard
26580 With the following commands all letters can be accented.
26581 The commands must be inserted in \SpecialChar TeX
26585 \begin_layout Standard
26586 \begin_inset space \hfill{}
26590 \begin_inset Tabular
26591 <lyxtabular version="3" rows="8" columns="2">
26592 <features booktabs="true" tabularvalignment="middle">
26593 <column alignment="left" valignment="top" width="0pt">
26594 <column alignment="block" valignment="top">
26596 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26599 \begin_layout Plain Layout
26605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26608 \begin_layout Plain Layout
26616 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26619 \begin_layout Plain Layout
26623 \begin_inset Quotes grd
26631 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26634 \begin_layout Plain Layout
26638 \begin_layout Plain Layout
26654 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26657 \begin_layout Plain Layout
26665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26668 \begin_layout Plain Layout
26672 \begin_layout Plain Layout
26688 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26691 \begin_layout Plain Layout
26695 \begin_inset space \textvisiblespace{}
26703 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26706 \begin_layout Plain Layout
26710 \begin_layout Plain Layout
26726 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26729 \begin_layout Plain Layout
26737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26740 \begin_layout Plain Layout
26744 \begin_layout Plain Layout
26760 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26763 \begin_layout Plain Layout
26767 \begin_inset space \textvisiblespace{}
26775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26778 \begin_layout Plain Layout
26782 \begin_layout Plain Layout
26798 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26801 \begin_layout Plain Layout
26805 \begin_inset space \textvisiblespace{}
26813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26816 \begin_layout Plain Layout
26820 \begin_layout Plain Layout
26836 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26839 \begin_layout Plain Layout
26843 \begin_inset space \textvisiblespace{}
26851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26854 \begin_layout Plain Layout
26858 \begin_layout Plain Layout
26878 \begin_inset space \hfill{}
26882 \begin_inset Tabular
26883 <lyxtabular version="3" rows="8" columns="2">
26884 <features booktabs="true" tabularvalignment="middle">
26885 <column alignment="left" valignment="top" width="0pt">
26886 <column alignment="center" valignment="top">
26888 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26891 \begin_layout Plain Layout
26897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26900 \begin_layout Plain Layout
26908 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26911 \begin_layout Plain Layout
26915 \begin_inset space \textvisiblespace{}
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 Index idx
26990 \begin_layout Plain Layout
27001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27004 \begin_layout Plain Layout
27008 \begin_layout Plain Layout
27024 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27027 \begin_layout Plain Layout
27035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27038 \begin_layout Plain Layout
27042 \begin_layout Plain Layout
27058 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27061 \begin_layout Plain Layout
27065 \begin_inset space \textvisiblespace{}
27073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27076 \begin_layout Plain Layout
27080 \begin_layout Plain Layout
27096 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27099 \begin_layout Plain Layout
27103 \begin_inset space \textvisiblespace{}
27111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27114 \begin_layout Plain Layout
27118 \begin_layout Plain Layout
27134 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27137 \begin_layout Plain Layout
27141 \begin_inset space \textvisiblespace{}
27149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27152 \begin_layout Plain Layout
27156 \begin_layout Plain Layout
27176 \begin_inset space \hfill{}
27182 \begin_layout Standard
27183 \begin_inset VSpace medskip
27192 also two different characters can be accented.
27198 \begin_inset space \textvisiblespace{}
27207 \begin_layout Plain Layout
27219 \begin_layout Standard
27232 can in combination with vowels directly be inserted with the keyboard without
27233 using \SpecialChar TeX
27235 The same applies for the tilde
27239 \begin_layout Plain Layout
27240 This only applies for keyboards where the tilde is defined as accent.
27249 in combination with
27264 \begin_layout Standard
27307 and accents that are inserted directly with the keyboard are also available
27308 in mathematical text.
27309 For the other accents there are special math commands to be used in formulas,
27311 \begin_inset CommandInset ref
27313 reference "subsec:Accents-for-one"
27320 \begin_layout Standard
27321 \begin_inset VSpace bigskip
27324 Furthermore, with the command
27331 \begin_inset Index idx
27334 \begin_layout Plain Layout
27342 all numbers and letters can be set into a circle, quasi accented with a
27343 circle, similar to the copyright symbol.
27346 \begin_layout Standard
27348 \begin_inset Tabular
27349 <lyxtabular version="3" rows="3" columns="2">
27350 <features booktabs="true" tabularvalignment="middle">
27351 <column alignment="center" valignment="top" width="0pt">
27352 <column alignment="center" valignment="top">
27354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27357 \begin_layout Plain Layout
27363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27366 \begin_layout Plain Layout
27374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27377 \begin_layout Plain Layout
27385 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27388 \begin_layout Plain Layout
27392 \begin_layout Plain Layout
27407 <row topspace="1mm">
27408 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27411 \begin_layout Plain Layout
27422 raisebox{-1.5pt}{W}}
27427 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27430 \begin_layout Plain Layout
27434 \begin_layout Plain Layout
27464 \begin_layout Standard
27465 One has to take care that the character fits in the circle.
27476 \begin_layout Plain Layout
27478 \begin_inset CommandInset ref
27480 reference "subsec:Font-Sizes"
27489 specifies thereby the size of the circle.
27500 \begin_layout Plain Layout
27502 \begin_inset CommandInset ref
27504 reference "subsec:Boxes-without-Frame"
27513 the character can be centered.
27516 \begin_layout Subsection
27518 \begin_inset Index idx
27521 \begin_layout Plain Layout
27530 \begin_layout Standard
27531 Old-style figures (also known as old-style numerals) are created with the
27539 \begin_inset Index idx
27542 \begin_layout Plain Layout
27551 The command can be used in formulas and in \SpecialChar TeX
27553 The command scheme is:
27556 \begin_layout Standard
27561 oldstylenums{number}
27564 \begin_layout Standard
27569 oldstylenums{0123456789
27572 \begin_inset Formula $\oldstylenums{0123456789}$
27578 \begin_layout Section
27580 \begin_inset CommandInset label
27582 name "sec:Formula-Styles"
27587 \begin_inset Index idx
27590 \begin_layout Plain Layout
27599 \begin_layout Itemize
27600 There are two different alignment styles:
27604 \begin_layout Description
27605 Centered is the predefined standard.
27608 \begin_layout Description
27609 Indented this can be set using the menu
27611 Document\SpecialChar menuseparator
27617 \begin_inset space ~
27623 \begin_layout Standard
27628 is used, the indentation can be adjusted.
27629 The default value depends on the used document class.
27633 \begin_layout Itemize
27634 And two different numbering styles that can be set in the menu
27636 Document\SpecialChar menuseparator
27642 \begin_inset space ~
27651 \begin_layout Description
27652 Right is in most cases the default.
27655 \begin_layout Description
27660 \begin_layout Standard
27661 The chosen styles are used for all displayed formulas of the document.
27662 When both, centered and indented formulas should be created in a document,
27668 The indented formulas are then set in a flalign environment, see
27669 \begin_inset CommandInset ref
27671 reference "subsec:Flalign-Environment"
27678 \begin_layout Section
27680 \begin_inset CommandInset label
27682 name "sec:Multiline-Formulas"
27687 \begin_inset Index idx
27690 \begin_layout Plain Layout
27691 Formula ! multiline
27699 \begin_layout Subsection
27703 \begin_layout Standard
27704 In \SpecialChar LyX
27705 multiline formulas are created by pressing
27708 arg "newline-insert newline"
27712 This creates either an
27716 that is described in
27717 \begin_inset CommandInset ref
27719 reference "subsec:Standard-align-Environment"
27723 or, when automatically loading the package
27727 is disabled in the document settings, an
27729 eqnarray environment
27731 that is described in
27732 \begin_inset CommandInset ref
27734 reference "subsec:Eqnarray-Environment"
27739 The align environment is recommended because it provides in any case a
27740 typographically correct output.
27743 \begin_layout Standard
27744 There are other multiline formula environments that can be created via the
27747 Insert\SpecialChar menuseparator
27751 These environments are described in the following sections.
27754 \begin_layout Standard
27755 In all multiline formula environments a new line is created by pressing
27759 arg "newline-insert newline"
27763 To add or delete lines, the math toolbar buttons
27766 arg "tabular-feature append-row"
27772 arg "tabular-feature delete-row"
27775 , respectively, or the menu
27777 Edit\SpecialChar menuseparator
27783 \begin_layout Subsubsection
27785 \begin_inset CommandInset label
27787 name "subsec:Line-Separation"
27792 \begin_inset Index idx
27795 \begin_layout Plain Layout
27796 Formula ! multiline ! Line separation
27804 \begin_layout Standard
27805 There is sometimes not enough space in multiline formulas between the lines:
27806 \begin_inset Formula
27808 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}\\
27809 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
27817 \begin_layout Standard
27818 In \SpecialChar LaTeX
27819 additional line space is specified as optional argument of the new line
27821 This is not yet possible in \SpecialChar LyX
27826 \begin_layout Plain Layout
27828 \begin_inset CommandInset href
27830 name "LyX-bug #1505"
27831 target "https://www.lyx.org/trac/ticket/1505"
27841 , therefore the whole formula must be inserted in \SpecialChar TeX
27843 To add in our example space, the command
27851 is inserted at the end of the first line.
27856 \begin_layout Plain Layout
27863 \begin_layout Plain Layout
27865 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27868 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27875 \begin_layout Plain Layout
27879 left(B^{2}+x_{0}^{2}
27887 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27892 \begin_layout Plain Layout
27904 \begin_layout Standard
27905 \begin_inset VSpace bigskip
27908 To set the line separation for all lines in a formula, the length
27915 \begin_inset Index idx
27918 \begin_layout Plain Layout
27928 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27939 \begin_inset space \thinspace{}
27944 \begin_inset space \thinspace{}
27947 mm additional line separation as in the previous example, the command
27950 \begin_layout Standard
27960 \begin_layout Standard
27961 is inserted in \SpecialChar TeX
27962 mode before the formula.
27963 This requires that the \SpecialChar LaTeX
27972 \begin_layout Plain Layout
27977 is part of every \SpecialChar LaTeX
27978 standard installation.
27984 \begin_inset Index idx
27987 \begin_layout Plain Layout
27993 was loaded in \SpecialChar LaTeX
27994 -preamble with the line
27997 \begin_layout Standard
28005 \begin_layout Standard
28010 \begin_layout Plain Layout
28022 \begin_inset Formula
28024 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}\\
28025 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
28033 \begin_layout Standard
28037 \begin_layout Plain Layout
28048 To get back to the predefined distance,
28054 is set to the value 3
28055 \begin_inset space \thinspace{}
28061 \begin_layout Subsubsection
28063 \begin_inset CommandInset label
28065 name "subsec:Column-Separation"
28070 \begin_inset Index idx
28073 \begin_layout Plain Layout
28074 Formula ! multiline ! Column separation
28082 \begin_layout Standard
28083 Multiline formulas form a matrix.
28084 A formula in the eqnarray environment is for example a matrix with three
28086 By changing the column separation in this environment, the space beside
28087 the relation sign can be changed.
28090 \begin_layout Standard
28091 The column separation is specified with the length
28098 \begin_inset Index idx
28101 \begin_layout Plain Layout
28110 \begin_inset Newline newline
28113 column separation = 2
28114 \begin_inset space \thinspace{}
28124 \begin_inset Newline newline
28130 \begin_layout Standard
28140 \begin_layout Standard
28141 inserted in \SpecialChar TeX
28142 mode, sets for all following formulas a column separation of
28144 \begin_inset space \thinspace{}
28148 To get back to the predefined distance,
28155 \begin_inset space \thinspace{}
28161 \begin_layout Standard
28163 \begin_inset space \thinspace{}
28166 cm column separation:
28170 \begin_layout Plain Layout
28182 \begin_inset Formula
28190 A formula with the predefined column separation for matrices of 10
28191 \begin_inset space \thinspace{}
28198 \begin_layout Plain Layout
28210 \begin_inset Formula
28221 \begin_layout Standard
28222 \begin_inset Newpage newpage
28228 \begin_layout Subsubsection
28230 \begin_inset Index idx
28233 \begin_layout Plain Layout
28242 \begin_layout Standard
28243 Long formulas can be typeset using these methods:
28246 \begin_layout Itemize
28247 When one side of the equation is much shorter than the line width, this
28248 one is chosen for the left side and the right side is typeset over two
28250 \begin_inset Formula
28252 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 \\
28253 & & -\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}
28258 The minus sign at the beginning of the second line does normally not appear
28259 as an operator because it is the first character of the line.
28260 Thus it would not be surrounded by space and could not be distinguished
28261 from the fraction bar.
28263 \begin_inset space \thinspace{}
28266 pt space was inserted behind the minus sign with the command
28276 \begin_layout Plain Layout
28284 \begin_inset CommandInset ref
28286 reference "subsec:Variable-Space"
28296 \begin_inset Index idx
28299 \begin_layout Plain Layout
28310 \begin_layout Itemize
28311 When both sides of the equation are too long, the command
28318 \begin_inset Index idx
28321 \begin_layout Plain Layout
28330 It is inserted in the first column of the first line and causes all further
28331 insertions to overwrite the following columns:
28332 \begin_inset Formula
28334 \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 \\
28335 & & -\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 \\
28336 & & =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}
28341 After the insertion of
28347 , the cursor is in a purple box that is a bit shifted to the left from the
28349 In this the formula is inserted.
28350 \begin_inset Newline newline
28353 The content of the further lines is inserted to the second or another formula
28355 The greater the column number where it was inserted, the larger the indentation.
28356 \begin_inset VSpace medskip
28360 \begin_inset Newline newline
28364 \begin_inset Note Greyedout
28367 \begin_layout Plain Layout
28368 Note the following when using
28377 \begin_layout Itemize
28378 The formula doesn't use the full page width.
28380 \begin_inset space \thinspace{}
28384 \begin_inset space \space{}
28388 \begin_inset Formula $-B^{2}$
28391 is added to the first line in the above example, it would have been outside
28393 To better use the width, negative space can be inserted at the beginning
28397 \begin_layout Itemize
28398 Due to a bug in \SpecialChar LyX
28399 the cursor cannot be set with the mouse into the first
28404 \begin_layout Plain Layout
28405 \begin_inset CommandInset href
28407 name "LyX-bug #1429"
28408 target "https://www.lyx.org/trac/ticket/1429"
28418 One can only set the cursor at the beginning of the line and move it with
28427 \begin_layout Itemize
28428 Other methods to set long formulas are offered by the environments described
28430 \begin_inset CommandInset ref
28432 reference "subsec:Multline-Environment"
28437 \begin_inset CommandInset ref
28439 reference "subsec:Multiline-Formula-Parts"
28446 \begin_layout Subsubsection
28447 Multiline Fractions
28448 \begin_inset CommandInset label
28450 name "subsec:Multiline-Fractions"
28455 \begin_inset Index idx
28458 \begin_layout Plain Layout
28459 Fractions ! multiline
28467 \begin_layout Standard
28468 There are cases where the denominator and/or the numerator of a fraction
28469 is so long that the fraction does not fit into one line.
28470 It is then necessary to add a line break within the fraction.
28471 This can be done using the command
28478 \begin_inset Index idx
28481 \begin_layout Plain Layout
28490 To activate it, set in the document settings under
28493 \begin_inset space ~
28503 \begin_inset Index idx
28506 \begin_layout Plain Layout
28507 Packages ! mathtools
28515 \begin_inset space ~
28530 \begin_layout Standard
28535 splitfrac{first line}{second line}
28538 \begin_layout Standard
28539 and is used as denominator and/or numerator:
28542 \begin_layout Standard
28543 \begin_inset Formula
28545 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}
28550 The command for the first numerator above is:
28553 \begin_layout Standard
28558 splitfrac{xy+xy+xy+xy+xy
28559 \begin_inset space \textvisiblespace{}
28567 \begin_layout Subsubsection
28569 \begin_inset CommandInset label
28571 name "subsec:Multiline-Brackets"
28576 \begin_inset Index idx
28579 \begin_layout Plain Layout
28580 Brackets ! for multiline expressions
28588 \begin_layout Standard
28589 For brackets spanning multiple lines the following problem occurs:
28590 \begin_inset Formula
28592 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28593 & & \left.\cdots+B-D\right]
28601 \begin_layout Standard
28602 The closing bracket is smaller than the opening bracket because brackets
28603 with variable size may not span multiple lines.
28606 \begin_layout Standard
28607 To set the bracket size for the second line correctly, the first line is
28615 \begin_inset Index idx
28618 \begin_layout Plain Layout
28626 and the second line with
28634 \begin_layout Plain Layout
28648 \begin_inset CommandInset ref
28650 reference "subsec:Automatic-Bracket-Size"
28662 \begin_inset Index idx
28665 \begin_layout Plain Layout
28688 \begin_inset space \textvisiblespace{}
28698 \begin_inset space \textvisiblespace{}
28708 \begin_inset space \textvisiblespace{}
28714 \begin_inset Formula $\downarrow$
28720 \begin_inset Index idx
28723 \begin_layout Plain Layout
28731 is inserted, because the multiplication operator with its limits is the
28732 largest symbol in the first line and this should be the size for the bracket
28733 in the second line.
28736 \begin_layout Standard
28737 The result is this:
28738 \begin_inset Formula
28740 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28741 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28749 \begin_layout Subsection
28753 \begin_layout Standard
28754 Align environments can be used for every kind of multiline formulas.
28755 They are especially useful to set several formulas side by side.
28758 \begin_layout Standard
28759 Align environments consist of columns.
28760 The odd columns are right aligned, the even ones left aligned.
28761 Every line in an Align environment can be numbered.
28764 \begin_layout Standard
28765 Align environments are created via the menu
28767 Insert\SpecialChar menuseparator
28773 Edit\SpecialChar menuseparator
28774 Math\SpecialChar menuseparator
28775 Change Formula Type
28777 already existing formulas can be converted to Align environments.
28780 \begin_layout Standard
28781 To add or delete columns, the math toolbar buttons
28784 arg "tabular-feature append-column"
28790 arg "tabular-feature delete-column"
28793 , respectively, or the menu
28795 Edit\SpecialChar menuseparator
28801 \begin_layout Subsubsection
28802 Standard align Environment
28803 \begin_inset CommandInset label
28805 name "subsec:Standard-align-Environment"
28810 \begin_inset Index idx
28813 \begin_layout Plain Layout
28814 Formula ! multiline ! align environment
28822 \begin_layout Standard
28823 This Align environment is created by pressing
28826 arg "newline-insert newline"
28829 in a formula or by the menu
28831 Insert\SpecialChar menuseparator
28832 Math\SpecialChar menuseparator
28833 AMS align Environment
28838 \begin_layout Standard
28839 An example for two formulas set side by side, that are created with a four
28840 column align environment:
28841 \begin_inset Formula
28843 A & =\sin(B) & C & =D\\
28844 C & \ne A & B & \ne D
28849 As it can be seen, the formulas in this environment are placed so as if
28858 \begin_layout Plain Layout
28866 \begin_inset CommandInset ref
28868 reference "subsec:Variable-Space"
28879 before the first and after every even column.
28880 When the formula style
28886 \begin_layout Plain Layout
28888 \begin_inset CommandInset ref
28890 reference "sec:Formula-Styles"
28901 is used, the formula is set without the
28907 before the first column.
28910 \begin_layout Subsubsection
28911 Alignat Environment
28912 \begin_inset Index idx
28915 \begin_layout Plain Layout
28916 Formula ! multiline ! alignat environment
28924 \begin_layout Standard
28925 The alignat environment has no predefined column separation.
28926 It can be inserted manually with the spaces that are described
28927 \begin_inset CommandInset ref
28929 reference "subsec:Space"
28936 \begin_layout Standard
28937 The above example in the alignat environment where 1
28938 \begin_inset space \thinspace{}
28941 cm space was inserted at the beginning of the second formula:
28942 \begin_inset Formula
28943 \begin{alignat*}{2}
28944 A & =\sin(B) & \hspace{1cm}C & =D\\
28945 C & \ne A & B & \ne D
28950 Because the column separation can be set separately for every column, this
28951 environment is especially suitable to set three and more formulas side
28955 \begin_layout Subsubsection
28956 Flalign Environment
28957 \begin_inset CommandInset label
28959 name "subsec:Flalign-Environment"
28964 \begin_inset Index idx
28967 \begin_layout Plain Layout
28968 Formula ! multiline ! flalign environment
28976 \begin_layout Standard
28977 In this environment the first two columns are always set as much as possible
28978 to the left and the last two ones to the right.
28980 \begin_inset Formula
28982 A & =1 & B & =2 & C & =3\\
28983 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28991 \begin_layout Standard
28992 By creating a flalign environment with an odd number of columns where an
28993 empty \SpecialChar TeX
28994 brace is inserted to the last column, several formulas in a document
28995 can be set to the left, although the formula style
29000 As example the indented formula
29001 \begin_inset CommandInset ref
29003 reference "eq:VolInt"
29008 \begin_inset Formula
29010 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29015 The first two columns contain the formula.
29016 To indent it as with the formula style
29021 \begin_inset space \thinspace{}
29024 pt space was inserted at the beginning of the first column.
29027 \begin_layout Subsection
29028 Eqnarray Environment
29029 \begin_inset CommandInset label
29031 name "subsec:Eqnarray-Environment"
29036 \begin_inset Index idx
29039 \begin_layout Plain Layout
29040 Formula ! multiline ! eqnarray environment
29048 \begin_layout Standard
29049 When this environment has been created, three blue boxes appear.
29050 The content of the first box is right aligned, the content of the last
29052 The content of the middle box appears centered and a bit smaller, because
29053 it is designed to insert there only relation characters.
29054 \begin_inset Formula
29056 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29066 \begin_layout Subsection
29068 \begin_inset Index idx
29071 \begin_layout Plain Layout
29072 Formula ! multiline ! gather environment
29080 \begin_layout Standard
29081 This environment consists of only one centered column.
29082 Every line can be numbered.
29083 \begin_inset Formula
29094 \begin_layout Subsection
29095 Multline Environment
29096 \begin_inset CommandInset label
29098 name "subsec:Multline-Environment"
29103 \begin_inset Index idx
29106 \begin_layout Plain Layout
29107 Formula ! multiline ! multline environment
29115 \begin_layout Standard
29116 The multline environment consists, like the gather environment, of only
29118 But the first line is left aligned, the last one right aligned.
29119 All other lines are centered.
29120 Therefore this environment is suitable for long formulas.
29122 \begin_inset CommandInset ref
29124 reference "eq:lefteqn"
29128 in the multline environment:
29129 \begin_inset Formula
29131 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}\\
29132 -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}\\
29133 =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}}
29141 \begin_layout Standard
29142 In the output only the last (first) line of a multline environment appears
29143 numbered when the document numbering is right (left).
29147 \begin_layout Plain Layout
29148 numbering styles see
29149 \begin_inset CommandInset ref
29151 reference "sec:Formula-Styles"
29163 \begin_layout Standard
29171 \begin_inset Index idx
29174 \begin_layout Plain Layout
29189 \begin_inset Index idx
29192 \begin_layout Plain Layout
29200 a centered line can be right or left aligned, respectively.
29201 The commands are used as follows:
29204 \begin_layout Standard
29209 shoveright{line content}
29215 shoveleft{line content}
29218 \begin_layout Standard
29219 \begin_inset VSpace medskip
29229 \begin_inset Index idx
29232 \begin_layout Plain Layout
29240 specifies the distance of the first line from the left page margin.
29241 Predefined is the length 0
29242 \begin_inset space \thinspace{}
29248 \begin_layout Standard
29249 As example the above formula where the command
29252 \begin_layout Standard
29262 \begin_layout Standard
29263 was inserted in \SpecialChar TeX
29268 \begin_layout Plain Layout
29280 \begin_inset Formula
29282 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}\\
29283 \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}}\\
29284 =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}}
29293 \begin_layout Plain Layout
29304 The second line was left aligned using
29313 \begin_layout Subsection
29314 Multiline Formula Parts
29315 \begin_inset CommandInset label
29317 name "subsec:Multiline-Formula-Parts"
29322 \begin_inset Index idx
29325 \begin_layout Plain Layout
29326 Formula ! multiline ! formula parts
29334 \begin_layout Standard
29335 To display only parts of a formula with multiple lines, one of the following
29336 environments is used:
29353 They can be inserted via the menu
29355 Insert\SpecialChar menuseparator
29358 or by using the commands described in this section.
29361 \begin_layout Standard
29362 The first three have the same properties as the corresponding multiline
29363 formula environments, but it is possible to set further formula parts beside
29366 \begin_inset Formula
29368 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29369 \Delta E\Delta t & \ge\frac{\hbar}{2}
29371 \right\} \textrm{Uncertainty relations}
29379 \begin_layout Standard
29380 To get this formula, a displayed formula is created where the command
29387 \begin_inset Index idx
29390 \begin_layout Plain Layout
29399 A purple box appears around the blue formula box where now columns and
29400 lines can be added.
29401 Outside the multiline environment other formula parts can be set, like
29405 \begin_layout Standard
29406 The aligned environment is also suitable for long formulas whose lines are
29407 horizontally aligned.
29408 Using aligned in a displayed formula has the advantage that the formula
29409 number is vertically centered behind the lines.
29411 \begin_inset CommandInset ref
29413 reference "eq:shortlong"
29417 in the aligned environment:
29418 \begin_inset Formula
29420 \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}|}\\
29421 & -\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}|}
29430 \begin_layout Standard
29431 To use the environments
29450 \begin_inset Index idx
29453 \begin_layout Plain Layout
29468 \begin_inset Index idx
29471 \begin_layout Plain Layout
29486 \begin_inset Index idx
29489 \begin_layout Plain Layout
29497 are inserted, respectively.
29498 The split environment has the same properties as the aligned environment
29499 but it can only have two columns.
29502 \begin_layout Subsection
29503 Text in multiline Formulas
29504 \begin_inset CommandInset label
29506 name "subsec:Text-in-multiline"
29511 \begin_inset Index idx
29514 \begin_layout Plain Layout
29521 \begin_inset Index idx
29524 \begin_layout Plain Layout
29525 Formula ! multiline ! text
29533 \begin_layout Standard
29534 In the Align environments, and the multline and gather environment, text
29535 can be inserted that will appear in a separate line and doesn't affect
29536 the column alignment.
29537 To do this, the command
29544 \begin_inset Index idx
29547 \begin_layout Plain Layout
29555 is used in the following scheme:
29558 \begin_layout Standard
29566 \begin_layout Standard
29567 The text should not be longer than a line because it cannot be hyphenated.
29568 As \SpecialChar LyX
29569 doesn't yet support
29575 directly, the text is written as mathematical text.
29582 must hereby be at the beginning of a line and appears in the output above
29584 An example where the text was inserted at the beginning of the second line:
29585 \begin_inset Formula
29587 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29588 \intertext{\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 Standard
29603 always creates some vertical space between the text and the formula lines.
29604 To avoid this space, set in the document settings under
29607 \begin_inset space ~
29617 \begin_inset Index idx
29620 \begin_layout Plain Layout
29621 Packages ! mathtools
29629 \begin_inset space ~
29635 Then you can use the command
29642 \begin_inset Index idx
29645 \begin_layout Plain Layout
29662 \begin_layout Standard
29663 \begin_inset Formula
29665 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29666 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29674 \begin_layout Section
29676 \begin_inset Index idx
29679 \begin_layout Plain Layout
29686 \begin_inset Index idx
29689 \begin_layout Plain Layout
29690 Formula ! numbering|see
29694 \begin_layout Plain Layout
29705 \begin_layout Plain Layout
29720 \begin_layout Subsection
29724 \begin_layout Standard
29725 Numbered formulas can be created with the menu
29727 Insert\SpecialChar menuseparator
29728 Math\SpecialChar menuseparator
29730 \begin_inset space ~
29738 \begin_inset space ~
29744 Existing formulas can be numbered with the menu
29746 Edit\SpecialChar menuseparator
29747 Math\SpecialChar menuseparator
29749 \begin_inset space ~
29757 arg "math-number-toggle"
29761 The formula number is displayed in \SpecialChar LyX
29762 behind the formula as a number sign
29764 The number sign is replaced in the output by the formula number.
29767 \begin_layout Standard
29768 When numbering is turned on in multiline formulas, all lines will be numbered.
29769 But the numbering can be controlled with the menu
29771 Edit\SpecialChar menuseparator
29772 Math\SpecialChar menuseparator
29774 \begin_inset space ~
29778 \begin_inset space ~
29782 \begin_inset space ~
29790 arg "math-number-line-toggle"
29796 \begin_layout Standard
29797 Except for inline formulas, all formulas can be numbered with two different
29799 \begin_inset CommandInset ref
29801 reference "sec:Formula-Styles"
29808 \begin_layout Subsection
29810 \begin_inset Index idx
29813 \begin_layout Plain Layout
29814 Cross-references ! to formulas
29822 \begin_layout Standard
29823 All labeled formulas can be cross-referenced.
29824 A label is added by the menu
29826 Insert\SpecialChar menuseparator
29829 or the toolbar button
29836 The cursor must hereby be inside a displayed formula.
29837 Alternatively you can right-click on the formula and choose
29842 A dialog pops up displaying the prefix
29847 The label is inserted there behind the prefix.
29848 The predefined prefix means
29849 \begin_inset Quotes eld
29853 \begin_inset Quotes erd
29856 and makes it easier to find labels in large documents because it marks
29857 it as formula label to divide it from e.
29858 \begin_inset space \thinspace{}
29862 \begin_inset space \space{}
29866 To change a label, the menu
29868 Insert\SpecialChar menuseparator
29871 is used again or you right-click on a formula and then on
29878 \begin_layout Standard
29879 The name of the label is displayed in \SpecialChar LyX
29880 within two parentheses behind formula.
29881 A formula with a label is always numbered.
29884 \begin_layout Standard
29885 Cross-references are inserted via the menu
29887 Insert\SpecialChar menuseparator
29890 or with the toolbar button
29893 arg "dialog-show-new-inset ref"
29897 A formula cross-reference appears in the output as formula number.
29898 When in the cross-reference dialog window the format
29902 is chosen, the cross-reference appears in the output as formula number
29904 \begin_inset Newline newline
29907 By right-clicking on a cross-reference in \SpecialChar LyX
29908 , one jumps to the formula that
29912 \begin_layout Standard
29913 Here are as examples cross-references to formulas of the following subsections:
29914 \begin_inset Note Note
29917 \begin_layout Plain Layout
29918 Note the different cross-reference types.
29926 \begin_layout Standard
29928 \begin_inset CommandInset ref
29935 \begin_inset CommandInset ref
29943 \begin_inset CommandInset ref
29949 ) big Latin letters are used for the numbering in contrary to (
29950 \begin_inset CommandInset ref
29959 \begin_layout Standard
29960 \begin_inset VSpace medskip
29963 When the argument of
29971 \begin_layout Plain Layout
29979 \begin_inset CommandInset ref
29981 reference "subsec:User-defined-Numbering"
29992 contains a box like in
29993 \begin_inset CommandInset ref
29995 reference "subsec:Paragraph-Boxes"
29999 , the formula cannot be referenced.
30002 \begin_layout Subsection
30004 \begin_inset Index idx
30007 \begin_layout Plain Layout
30008 Formula numbering ! subnumbering
30016 \begin_layout Standard
30017 Formulas can be numbered as subequations.
30018 To activate this feature, add the module
30022 to the document in the menu
30024 Document\SpecialChar menuseparator
30025 Settings\SpecialChar menuseparator
30029 To insert subequations use the menu
30031 Insert\SpecialChar menuseparator
30032 Custom Insets\SpecialChar menuseparator
30038 \begin_layout Standard
30039 The equations to be subnumbered are put into the
30045 \begin_inset Formula
30053 \begin_inset VSpace -5mm
30057 \begin_inset Flex Subequations
30060 \begin_layout Plain Layout
30061 \begin_inset Formula
30069 \begin_inset Formula
30084 \begin_layout Standard
30085 Every formula in the
30089 inset will be subnumbered with a, b, c, \SpecialChar ldots
30091 For multiline formulas every line will be subnumbered.
30094 \begin_layout Standard
30095 Referencing subequations work like for normal equations:
30096 \begin_inset CommandInset ref
30103 \begin_inset CommandInset ref
30110 If you want to reference the subequations collectively, insert a label
30111 as first thing in the
30117 \begin_inset CommandInset ref
30119 reference "eq:Here-is-an"
30129 \begin_layout Standard
30130 By inserting subequations vertical space is added before it.
30131 To remove this, insert -5
30132 \begin_inset space \thinspace{}
30135 mm vertical space right before the
30140 If the formula style
30146 \begin_layout Plain Layout
30148 \begin_inset CommandInset ref
30150 reference "sec:Formula-Styles"
30162 \begin_inset space \thinspace{}
30168 \begin_layout Standard
30169 To get another subnumber instead of small Latin letters, insert this command
30170 as \SpecialChar TeX
30171 code before the equations in the
30178 \begin_layout Standard
30187 theparentequation -
30192 \begin_layout Standard
30199 creates hereby the parent number and
30205 adds a small Roman number as subnumber.
30206 For more information about the customization of the numbering, see
30207 \begin_inset CommandInset ref
30209 reference "subsec:Numbering-with-Roman"
30216 \begin_layout Standard
30217 Here is an example for a multiline formula where the numbering is customized
30218 and turned off for the second line:
30219 \begin_inset Flex Subequations
30222 \begin_layout Plain Layout
30223 \begin_inset CommandInset label
30225 name "eq:Here-is-an"
30233 \begin_layout Plain Layout
30241 theparentequation -
30249 \begin_inset Formula
30251 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30252 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30253 & = & B^{2}-2BZ+Z^{2}
30266 \begin_layout Subsection
30267 Numbering with Roman Numbers and Letters
30268 \begin_inset CommandInset label
30270 name "subsec:Numbering-with-Roman"
30275 \begin_inset Index idx
30278 \begin_layout Plain Layout
30279 Formula numbering ! with letters
30285 \begin_inset Index idx
30288 \begin_layout Plain Layout
30289 Formula numbering ! with Roman numbers
30297 \begin_layout Standard
30298 Formulas can also be numbered with Roman numbers and Latin letters.
30299 To number for example with small Roman numbers, the command
30302 \begin_layout Standard
30314 \begin_layout Standard
30315 is inserted before the formula in \SpecialChar TeX
30324 \begin_inset Index idx
30327 \begin_layout Plain Layout
30335 redefines the predefined command
30351 \begin_layout Plain Layout
30358 has the same scheme like the command
30364 that is described in
30365 \begin_inset CommandInset ref
30367 reference "subsec:The-Command-newcommand"
30380 is the formula counter.
30387 is used as prefix for a counter, the value of the counter is output as
30389 When a formula is numbered, \SpecialChar LaTeX
30390 sets internally the command
30396 behind the formula.
30402 \begin_inset Index idx
30405 \begin_layout Plain Layout
30415 outputs the counter as small Roman number.
30418 \begin_layout Standard
30419 All formulas behind the command
30429 are now numbered Roman.
30430 To switch to numbering with big Roman numbers, the command is inserted
30444 \begin_inset Index idx
30447 \begin_layout Plain Layout
30459 \begin_inset Quotes eld
30463 \begin_inset Quotes erd
30466 with small Latin letters there is the command
30473 \begin_inset Index idx
30476 \begin_layout Plain Layout
30484 , for big ones there is the command
30491 \begin_inset Index idx
30494 \begin_layout Plain Layout
30507 \begin_layout Standard
30508 \begin_inset Note Greyedout
30511 \begin_layout Plain Layout
30517 \begin_inset space ~
30520 formulas can be numbered with Latin letters in one document.
30528 \begin_layout Standard
30532 \begin_layout Plain Layout
30548 \begin_layout Standard
30549 \begin_inset Formula
30551 A=\textrm{small roman}
30560 \begin_layout Plain Layout
30574 \begin_inset Formula
30576 B=\textrm{big Roman}\label{eq:Rom}
30585 \begin_layout Plain Layout
30599 \begin_inset Formula
30601 C=\textrm{small Latin}
30610 \begin_layout Plain Layout
30624 \begin_inset Formula
30626 D=\textrm{big Latin}\label{eq:Lat}
30634 \begin_layout Standard
30635 To switch back to the default numbering, insert the command:
30638 \begin_layout Standard
30648 \begin_inset Index idx
30651 \begin_layout Plain Layout
30662 \begin_layout Standard
30666 \begin_layout Plain Layout
30680 \begin_inset Formula
30690 \begin_layout Standard
30691 \begin_inset VSpace medskip
30694 As you see, formulas are numbered serially independent from the numbering
30696 When then numbering should start with
30697 \begin_inset Quotes eld
30701 \begin_inset Quotes erd
30704 when the style is changed, new equation counters have to be defined.
30705 A description about this can be found in the file
30706 \begin_inset CommandInset href
30708 name "Formula-numbering.lyx"
30709 target "run:Formula-numbering.lyx"
30717 \begin_layout Subsection
30718 User-defined Numbering
30719 \begin_inset CommandInset label
30721 name "subsec:User-defined-Numbering"
30726 \begin_inset Index idx
30729 \begin_layout Plain Layout
30730 Formula numbering ! user-defined
30738 \begin_layout Standard
30739 \begin_inset Note Greyedout
30742 \begin_layout Plain Layout
30747 If the document language is a right-to-left language such as Arabic, you
30748 must add this to the to the \SpecialChar LaTeX
30749 -preamble to be able to use the commands described
30751 \begin_inset Newline newline
30759 \begin_inset Newline newline
30763 \begin_inset Phantom HPhantom
30766 \begin_layout Plain Layout
30769 \begin_inset space ~
30795 \begin_layout Standard
30796 \begin_inset Index idx
30799 \begin_layout Plain Layout
30800 Formula numbering ! self-defined delimiters
30805 With the standard numbering parentheses are set around the formula number.
30806 To replace the parentheses for example by vertical bars, the following
30807 line is added to the \SpecialChar LaTeX
30811 \begin_layout Standard
30817 \begin_inset Newline newline
30821 \begin_inset Phantom HPhantom
30824 \begin_layout Plain Layout
30827 \begin_inset space ~
30841 maketag@@@{|#1|}} }
30844 \begin_inset Note Note
30847 \begin_layout Plain Layout
30848 This macro is already declared in the \SpecialChar LaTeX
30849 -preamble for testing.
30850 To activate it, remove the percent signs at the beginning.
30858 \begin_layout Standard
30859 To use other characters, the vertical bars besides the
30863 are replaced by one ore more characters.
30864 To get only the formula number the vertical bars are omitted.
30867 \begin_layout Standard
30868 \begin_inset VSpace bigskip
30871 When there should be an expression of your choice instead of the consecutive
30872 formula number in parentheses behind the formula, the command
30879 \begin_inset Index idx
30882 \begin_layout Plain Layout
30891 \begin_inset Formula
30893 A+B=C\tag{something}\label{eq:tag}
30898 In this example the command
30903 \begin_inset space \textvisiblespace{}
30908 was inserted in the formula.
30911 \begin_layout Standard
30917 \begin_inset space \textvisiblespace{}
30922 is inserted instead, the star prevents the parentheses around the expression:
30923 \begin_inset Formula
30925 A+B=C\tag*{something}
30933 \begin_layout Standard
30934 \begin_inset VSpace bigskip
30937 To restart the formula numbering with new document parts or sections, the
30938 following command is used:
30941 \begin_layout Standard
30946 @addtoreset{equation}{part}
30949 \begin_inset Index idx
30952 \begin_layout Plain Layout
30957 \begin_layout Plain Layout
30968 \begin_layout Plain Layout
30981 \begin_layout Plain Layout
30992 \begin_layout Plain Layout
31005 \begin_inset Newline newline
31009 \begin_inset Newline newline
31016 @addtoreset{equation}{section}
31019 \begin_layout Standard
31020 To be able to use these commands in \SpecialChar TeX
31022 \begin_inset Quotes eld
31026 \begin_inset Quotes erd
31029 character has to be made
31030 \begin_inset Quotes eld
31034 \begin_inset Quotes erd
31037 for \SpecialChar LaTeX
31052 So the command sequence in \SpecialChar TeX
31056 \begin_layout Standard
31062 \begin_inset Newline newline
31067 @addtoreset{equation}{section}
31068 \begin_inset Newline newline
31076 \begin_layout Standard
31077 In the \SpecialChar LaTeX
31090 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31094 \begin_layout Standard
31109 \begin_layout Plain Layout
31114 is part of the \SpecialChar LaTeX
31120 \begin_inset Index idx
31123 \begin_layout Plain Layout
31124 Packages ! carlisle
31129 that is part of every \SpecialChar LaTeX
31130 standard installation.
31136 \begin_inset Index idx
31139 \begin_layout Plain Layout
31140 Packages ! remreset
31145 has to be loaded in the \SpecialChar LaTeX
31146 -preamble with the line
31149 \begin_layout Standard
31154 usepackage{remreset}
31157 \begin_layout Standard
31165 \begin_inset Index idx
31168 \begin_layout Plain Layout
31173 \begin_layout Plain Layout
31184 \begin_layout Plain Layout
31197 \begin_layout Plain Layout
31208 \begin_layout Plain Layout
31220 can be used with the same scheme as
31229 \begin_layout Standard
31230 \begin_inset VSpace bigskip
31233 Sometimes formulas should be numbered in the following form:
31236 \begin_layout Standard
31239 (section number.formula number)
31242 \begin_layout Standard
31243 The formula number should start with every section with
31244 \begin_inset Quotes eld
31248 \begin_inset Quotes erd
31254 \begin_layout Standard
31255 For this case there is the command
31262 \begin_inset Index idx
31265 \begin_layout Plain Layout
31273 , which is used with the following scheme:
31276 \begin_layout Standard
31281 numberwithin{counter}{sectioning}
31284 \begin_layout Standard
31285 Counter denotes what kind of numbering is affected, sectioning denotes what
31286 number is before the dot.
31289 \begin_layout Standard
31290 Thus in our case the following \SpecialChar LaTeX
31291 preamble or \SpecialChar TeX
31295 \begin_layout Standard
31300 numberwithin{equation}{section}
31303 \begin_layout Standard
31304 This is the result:
31308 \begin_layout Plain Layout
31312 numberwithin{equation}{section}
31318 \begin_inset Formula
31328 \begin_layout Standard
31330 \begin_inset space \thinspace{}
31334 \begin_inset space \space{}
31337 tables so that the number of the part is the sectioning,
31338 \begin_inset Newline newline
31345 numberwithin{table}{part}
31350 \begin_layout Standard
31351 To go back to the standard numbering or to prevent this kind of numbering
31352 when it is defined by the document class, the following command is inserted
31353 as \SpecialChar TeX
31354 code or to the \SpecialChar LaTeX
31358 \begin_layout Standard
31368 \begin_inset Index idx
31371 \begin_layout Plain Layout
31385 \begin_layout Plain Layout
31401 \begin_inset Newline newline
31409 \begin_inset Newline newline
31421 \begin_layout Standard
31428 uses internally the command
31434 , described above, that also needs to be reverted.
31438 \begin_layout Plain Layout
31445 \begin_layout Plain Layout
31449 @removefromreset{equation}{section}
31452 \begin_layout Plain Layout
31464 \begin_layout Section
31465 Chemical Symbols and Equations
31466 \begin_inset CommandInset label
31468 name "subsec:Chemical-Symbols-and"
31473 \begin_inset Index idx
31476 \begin_layout Plain Layout
31477 Chemical characters ! Symbols
31483 \begin_inset Index idx
31486 \begin_layout Plain Layout
31493 \begin_inset Index idx
31496 \begin_layout Plain Layout
31505 \begin_layout Standard
31506 An example text from chemistry:
31509 \begin_layout Quote
31511 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31514 -ion reacts with two
31515 \begin_inset Formula $\mathrm{Na^{+}}$
31518 -ions to sodium sulfate
31519 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31523 The chemical equation for this is:
31524 \begin_inset Formula
31526 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31534 \begin_layout Standard
31535 This chemical equation can directly be created as formula.
31536 To avoid that the symbols appear italic, everything is highlighted and
31537 changed by the shortcut
31543 to the upright font style.
31547 \begin_layout Plain Layout
31553 \begin_inset CommandInset ref
31555 reference "subsec:Font-Styles"
31567 \begin_layout Standard
31568 A more convenient way to typeset chemical formulas is to use the command
31576 \begin_inset Index idx
31579 \begin_layout Plain Layout
31587 that is available when the \SpecialChar LaTeX
31593 \begin_inset Index idx
31596 \begin_layout Plain Layout
31609 to a formula a new blue box appears where chemical formulas can be inserted
31610 in an intuitive way.
31613 \begin_layout Standard
31615 \begin_inset Tabular
31616 <lyxtabular version="3" rows="10" columns="2">
31617 <features booktabs="true" tabularvalignment="middle">
31618 <column alignment="center" valignment="top" width="0pt">
31619 <column alignment="center" valignment="top">
31621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31624 \begin_layout Plain Layout
31630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31633 \begin_layout Plain Layout
31641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31644 \begin_layout Plain Layout
31648 \begin_inset space \textvisiblespace{}
31656 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31659 \begin_layout Plain Layout
31660 \begin_inset Formula $\ce{H2CO3}$
31669 <row topspace="1.5mm">
31670 <cell alignment="center" valignment="top" usebox="none">
31673 \begin_layout Plain Layout
31677 \begin_inset space \textvisiblespace{}
31685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31688 \begin_layout Plain Layout
31689 \begin_inset Formula $\ce{SO4^{2-}}$
31698 <row topspace="1.5mm">
31699 <cell alignment="center" valignment="top" usebox="none">
31702 \begin_layout Plain Layout
31706 \begin_inset space \textvisiblespace{}
31714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31717 \begin_layout Plain Layout
31718 \begin_inset Formula $\ce{(NH4)2S}$
31727 <row topspace="1.5mm">
31728 <cell alignment="center" valignment="top" usebox="none">
31731 \begin_layout Plain Layout
31735 \begin_inset space \textvisiblespace{}
31743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31746 \begin_layout Plain Layout
31747 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31756 <row topspace="1.5mm">
31757 <cell alignment="center" valignment="top" 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 $\ce{A-B\dbond C\tbond D}$
31797 <row topspace="1.5mm">
31798 <cell alignment="center" valignment="top" usebox="none">
31801 \begin_layout Plain Layout
31805 \begin_inset space \textvisiblespace{}
31809 \begin_inset Formula $\downarrow$
31813 \begin_inset Formula $\to$
31821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31824 \begin_layout Plain Layout
31825 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31835 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31838 \begin_layout Plain Layout
31842 \begin_inset space \textvisiblespace{}
31848 \begin_inset space \textvisiblespace{}
31854 \begin_inset space \textvisiblespace{}
31862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31865 \begin_layout Plain Layout
31866 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31879 \begin_layout Plain Layout
31883 \begin_inset space \textvisiblespace{}
31887 \begin_inset space \textvisiblespace{}
31891 \begin_inset space \textvisiblespace{}
31895 \begin_inset space \textvisiblespace{}
31899 \begin_inset space \textvisiblespace{}
31907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31910 \begin_layout Plain Layout
31911 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31920 <row topspace="1.5mm">
31921 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31924 \begin_layout Plain Layout
31928 \begin_inset space \textvisiblespace{}
31932 \begin_inset space \textvisiblespace{}
31936 \begin_inset space \textvisiblespace{}
31940 \begin_inset space \textvisiblespace{}
31948 \begin_inset space \textvisiblespace{}
31956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31959 \begin_layout Plain Layout
31960 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31976 \begin_layout Standard
31977 \begin_inset Note Greyedout
31980 \begin_layout Plain Layout
31985 It is not possible in \SpecialChar LyX
31986 to use the character ^ to get an up-arrow as described
31992 One instead uses a negative thin space followed by the command
31999 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32010 \begin_layout Standard
32017 the command for equation
32018 \begin_inset space ~
32022 \begin_inset CommandInset ref
32024 reference "eq:chem-reaction"
32029 \begin_inset Newline newline
32037 \begin_inset space \textvisiblespace{}
32041 \begin_inset space \textvisiblespace{}
32045 \begin_inset space \textvisiblespace{}
32049 \begin_inset space \textvisiblespace{}
32053 \begin_inset space \textvisiblespace{}
32057 \begin_inset space \textvisiblespace{}
32063 \begin_layout Standard
32064 To create multiline chemical equations first a multiline formula is created
32066 \begin_inset CommandInset ref
32068 reference "sec:Multiline-Formulas"
32073 Afterwards the command
32079 is used in every small blue box of the formula.
32081 \begin_inset CommandInset ref
32083 reference "eq:TEOS-reaction-1"
32088 \begin_inset CommandInset ref
32090 reference "eq:TEOS-reaction-2"
32094 are an example of a multi-stage chemical reaction where every equation
32095 has its own number.
32096 \begin_inset Formula
32098 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32099 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32107 \begin_layout Standard
32118 package provides the command
32125 \begin_inset Index idx
32128 \begin_layout Plain Layout
32136 that has to be used for special cases.
32137 For more information about
32143 and more examples have a look at the documentation of
32148 \begin_inset CommandInset citation
32158 \begin_layout Section
32162 \begin_layout Standard
32164 supports two types of commutative diagrams:
32172 that are explained in the following.
32175 \begin_layout Subsection
32177 \begin_inset Index idx
32180 \begin_layout Plain Layout
32189 \begin_layout Standard
32190 Diagrams of this type visualize relations by vertical and horizontal lines
32192 \begin_inset Formula
32194 \begin{CD}A@>>>B@>>>C\\
32205 \begin_layout Standard
32206 To get them, the command
32211 \begin_inset Index idx
32214 \begin_layout Plain Layout
32224 is inserted to a formula.
32225 A blue box appears with two dashed lines where further commands can be
32230 arg "newline-insert newline"
32233 a new line is created.
32234 Horizontal relations are inserted in odd, vertical in even formula lines.
32237 \begin_layout Standard
32238 To create the relations there are the following commands:
32241 \begin_layout Itemize
32246 creates a left arrow,
32257 \begin_layout Itemize
32262 creates an up arrow,
32270 a vertical equal sign
32273 \begin_layout Itemize
32279 is a placeholder for non-existent relations
32282 \begin_layout Standard
32283 All arrows can be labeled as follows:
32286 \begin_layout Itemize
32287 If text inserted between the first and second < or >, resp., it is placed
32289 When it is inserted between the second and third one, it appears under
32293 \begin_layout Itemize
32294 When text for vertical arrows is inserted between the first and second A
32295 or V, resp., it is placed left beside the arrow.
32296 When it is inserted between the second and third one, it appears right
32298 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32302 \begin_layout Standard
32303 As example a diagram with all possible relations:
32306 \begin_layout Standard
32307 \begin_inset Formula
32309 \begin{CD}A@>j>>B@>>k>C@=F\\
32320 \begin_layout Standard
32321 The command for this is:
32322 \begin_inset Newline newline
32330 \begin_inset space \textvisiblespace{}
32333 A@>j>>B@>>k>C@=F Ctrl+Return
32334 \begin_inset Newline newline
32338 \begin_inset Phantom HPhantom
32341 \begin_layout Plain Layout
32347 \begin_inset space \textvisiblespace{}
32360 \begin_inset Formula $\to$
32366 \begin_inset Newline newline
32370 \begin_inset Phantom HPhantom
32373 \begin_layout Plain Layout
32379 \begin_inset space \textvisiblespace{}
32390 \begin_layout Subsection
32392 \begin_inset Index idx
32395 \begin_layout Plain Layout
32396 Diagrams ! xymatrix
32404 \begin_layout Standard
32405 To be able to use xymatrices, the \SpecialChar LaTeX
32411 A xymatrix is created by inserting the command
32418 Then you are able to add new matrix columns and rows like for normal matrices,
32420 \begin_inset CommandInset ref
32422 reference "sec:Matrices"
32429 \begin_layout Standard
32430 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32432 All possibilities to create commutative diagrams and decorations are explained
32437 that you find in the menu
32439 Help\SpecialChar menuseparator
32441 \begin_inset space ~
32449 \begin_layout Subsection
32455 \begin_inset Index idx
32458 \begin_layout Plain Layout
32467 \begin_layout Standard
32472 -diagrams, the \SpecialChar LaTeX
32482 -diagram is created by inserting the command
32489 Then you are able to add new matrix columns and rows like for normal matrices,
32491 \begin_inset CommandInset ref
32493 reference "sec:Matrices"
32500 \begin_layout Standard
32501 Examples how to create
32505 diagrams in \SpecialChar LyX
32508 Feynman-diagram manual
32510 that you find in the menu
32512 Help\SpecialChar menuseparator
32514 \begin_inset space ~
32522 \begin_layout Section
32523 User-defined Commands
32524 \begin_inset Index idx
32527 \begin_layout Plain Layout
32528 User-defined commands
32536 \begin_layout Standard
32537 \begin_inset Note Greyedout
32540 \begin_layout Plain Layout
32545 The names of user-defined commands and macros may only consist of Latin
32554 \begin_layout Subsection
32558 \begin_inset CommandInset label
32560 name "subsec:The-Command-newcommand"
32565 \begin_inset Index idx
32568 \begin_layout Plain Layout
32569 User-defined commands !
32577 \begin_inset Index idx
32580 \begin_layout Plain Layout
32591 \begin_layout Standard
32592 Many \SpecialChar LaTeX
32593 -commands are too long to be used frequently.
32594 But it is possible to define with the command
32600 new shorter commands.
32603 \begin_layout Standard
32604 The command scheme of
32613 \begin_layout Standard
32618 newcommand{new command name}[number of arguments][optional
32623 \begin_inset Newline newline
32627 \begin_inset Phantom HPhantom
32630 \begin_layout Plain Layout
32640 {command definition}
32643 \begin_layout Standard
32644 \begin_inset Note Greyedout
32647 \begin_layout Plain Layout
32652 Assure that the name of the new command is not already used in your document
32653 or by \SpecialChar LaTeX
32654 -packages that you use.
32655 When you for example define the command
32667 , you get an error message because
32673 is already defined as command for
32674 \begin_inset Quotes eld
32678 \begin_inset Formula $\le$
32682 \begin_inset Quotes erd
32693 \begin_layout Standard
32694 The number of arguments is an integer in the range 0
32695 \begin_inset space \thinspace{}
32699 \begin_inset space \thinspace{}
32702 9 and specifies how many arguments the new command should have.
32703 With the optional value a value for an optional argument can be predefined.
32704 When this is done, the
32712 rgument of the new command is automatically an optional one.
32715 \begin_layout Standard
32716 Here are some examples:
32719 \begin_layout Itemize
32720 To define the command
32732 , the \SpecialChar LaTeX
32734 \begin_inset VSpace medskip
32738 \begin_inset Newline newline
32752 \begin_layout Itemize
32753 To define the command
32765 , the argument (that should be underlined) must be taken into account.
32766 For this the preamble line is:
32767 \begin_inset VSpace medskip
32771 \begin_inset Newline newline
32785 \begin_inset VSpace medskip
32789 \begin_inset Newline newline
32796 acts as argument placeholder, the
32800 behind it denotes that it is the placeholder for the first argument.
32803 \begin_layout Itemize
32811 \begin_inset space \thinspace{}
32815 \begin_inset space \space{}
32825 \begin_inset VSpace medskip
32829 \begin_inset Newline newline
32840 framebox#1#2{$#3$}}
32843 \begin_inset VSpace medskip
32847 \begin_inset Newline newline
32850 The two Dollar signs creates the extra formula needed for
32857 \begin_inset CommandInset ref
32859 reference "subsec:Boxes-with-Frame"
32866 \begin_layout Itemize
32867 To create a new command for
32873 where the color for the box need not be specified, the argument for the
32874 color is defined optional:
32875 \begin_inset VSpace medskip
32879 \begin_inset Newline newline
32890 fcolorbox{#2}{#1}{$#3$}}
32893 \begin_inset VSpace medskip
32897 \begin_inset Newline newline
32900 When the color is not specified when using
32906 , the predefined color
32913 \begin_layout Standard
32914 A test of the new defined commands:
32917 \begin_layout Standard
32919 \begin_inset Tabular
32920 <lyxtabular version="3" rows="6" columns="2">
32921 <features booktabs="true" tabularvalignment="middle">
32922 <column alignment="center" valignment="top" width="0pt">
32923 <column alignment="center" valignment="top">
32925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32928 \begin_layout Plain Layout
32934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32937 \begin_layout Plain Layout
32945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32948 \begin_layout Plain Layout
32952 \begin_inset space \textvisiblespace{}
32960 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32963 \begin_layout Plain Layout
32964 \begin_inset Formula $A\gr B$
32974 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32977 \begin_layout Plain Layout
32985 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32988 \begin_layout Plain Layout
32989 \begin_inset Formula $\us{ABcd}$
32998 <row topspace="1mm">
32999 <cell alignment="center" valignment="top" usebox="none">
33002 \begin_layout Plain Layout
33006 \begin_inset Formula $\to$
33012 \begin_inset Formula $\to$
33020 \begin_inset space \textvisiblespace{}
33028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33031 \begin_layout Plain Layout
33032 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33041 <row topspace="1.5mm">
33042 <cell alignment="center" valignment="top" usebox="none">
33045 \begin_layout Plain Layout
33049 \begin_inset Formula $\to$
33057 \begin_inset space \textvisiblespace{}
33065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33068 \begin_layout Plain Layout
33069 \begin_inset Formula $\cb{red}{\int A=B}$
33078 <row topspace="1.5mm" bottomspace="1mm">
33079 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33082 \begin_layout Plain Layout
33088 \begin_inset Formula $\to$
33096 \begin_inset space \textvisiblespace{}
33104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33107 \begin_layout Plain Layout
33108 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33124 \begin_layout Subsection
33126 \begin_inset Index idx
33129 \begin_layout Plain Layout
33130 User-defined commands! Math macros
33136 \begin_inset Index idx
33139 \begin_layout Plain Layout
33148 \begin_layout Standard
33149 User-defined commands are especially convenient for complex expressions.
33150 When you are for example dealing with a document that has quadratic equations,
33151 the same solution type occurs several times.
33152 The general form of a quadratic equation is
33153 \begin_inset Formula
33155 0=\lambda^{2}+p\lambda+q
33160 The general form of the solution is
33161 \begin_inset Formula
33163 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33171 \begin_layout Standard
33172 To define a command for the solution formula where only the three parameters
33174 \begin_inset Formula $\lambda$
33178 \begin_inset Formula $p$
33182 \begin_inset Formula $q$
33185 need to be specified and the index of
33186 \begin_inset Formula $\lambda$
33189 can be given optionally, the \SpecialChar LaTeX
33191 \begin_inset Newline newline
33207 \begin_inset Newline newline
33211 \begin_inset Phantom HPhantom
33214 \begin_layout Plain Layout
33228 frac{#3^{2}}{4}-#4}}
33231 \begin_layout Standard
33232 To create with this the solution formula, the command
33233 \begin_inset Newline newline
33243 \begin_inset Formula $\to$
33249 \begin_inset Formula $\to$
33256 is inserted to a formula
33261 \begin_layout Standard
33262 The definition of the new command is unintuitive because one has to know
33263 the schemes of all used \SpecialChar LaTeX
33265 \begin_inset space \thinspace{}
33269 \begin_inset space \space{}
33272 that a fraction is inserted in \SpecialChar LaTeX
33277 frac{numerator}{denominator}
33280 Furthermore one can easily forget a brace in the definition and cannot
33281 see in \SpecialChar LyX
33282 what the new command is doing.
33283 To avoid these problems \SpecialChar LyX
33284 offers the possibility to use math macros instead
33294 \begin_layout Standard
33295 A math macro is created by using the menu
33297 Insert\SpecialChar menuseparator
33298 Math\SpecialChar menuseparator
33301 or the toolbar button
33304 arg "math-macro newmacroname_newcommand"
33308 The math macro toolbar appears together with the following box where the
33310 \begin_inset Newline newline
33314 \begin_inset space \hspace*{\fill}
33318 \begin_inset Graphics
33319 filename clipart/macrobox.png
33325 \begin_inset space \hspace*{\fill}
33329 \begin_inset Newline newline
33333 \begin_inset FormulaMacro
33334 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33339 newmacroname is the default name of the macro that should be changed to
33340 something sensible.
33341 The wanted formula is inserted in the first blue box.
33342 An argument placeholder is inserted with the command
33349 \begin_inset space \thinspace{}
33353 \begin_inset space \space{}
33362 or by using the macro toolbar button
33365 arg "math-macro-add-param"
33369 Argument placeholders are displayed red.
33371 \begin_inset space ~
33374 arguments are possible.
33375 Optional arguments are created with the toolbar button
33378 arg "math-macro-add-optional-param"
33382 The first non-optional argument can be transformed to an optional one with
33386 arg "math-macro-make-optional"
33390 In the second blue box the appearance of the macro in \SpecialChar LyX
33392 Normally you want to see it as it is defined, so the box is kept empty.
33393 But when you have created a macro that needs lot of space on the screen,
33394 you can insert in the box for example
33395 \begin_inset Newline newline
33425 \begin_inset Newline newline
33430 For the macro only the arguments with the macro name in front of them will
33431 then be displayed in \SpecialChar LyX
33432 , leading to a better overview.
33433 The formula appears in the output as defined in the first box.
33434 \begin_inset Newline newline
33437 The appearance of macros in formulas can furthermore be changed for single
33438 macros by setting the cursor in the macro and using the menu
33440 View\SpecialChar menuseparator
33442 \begin_inset space ~
33446 \begin_inset space ~
33454 \begin_layout Standard
33455 To use a macro, the macro name is inserted as command to a formula, in our
33463 Our macro looks in \SpecialChar LyX
33465 \begin_inset Newline newline
33469 \begin_inset space \hspace*{\fill}
33473 \begin_inset Graphics
33474 filename clipart/macrouse.png
33480 \begin_inset space \hspace*{\fill}
33484 \begin_inset Newline newline
33487 Here is our macro example with the arguments
33488 \begin_inset Formula $x$
33492 \begin_inset Formula $\ln(x)$
33496 \begin_inset Formula $B$
33502 \begin_layout Standard
33503 \begin_inset Formula
33513 \begin_layout Standard
33517 Tools\SpecialChar menuseparator
33518 Preferences\SpecialChar menuseparator
33519 Editing\SpecialChar menuseparator
33522 different styles to edit macros.
33523 To find the style that suits you the most, choose a style and set the cursor
33524 in a macro formula to see the difference.
33527 \begin_layout Standard
33528 A math macro is transformed internally to a
33534 command when exporting the document.
33541 command is not placed in the \SpecialChar LaTeX
33542 -preamble, therefore macros can only be used
33543 in formulas that are in the document below the macro definition box.
33546 \begin_layout Standard
33547 Math macros can also be directly created from a
33554 When writing for example the command
33557 \begin_inset Newline newline
33566 xleftarrow[#2]{#1}}
33567 \begin_inset Newline newline
33572 in \SpecialChar LyX
33573 as normal text, highlighting it completely and using then the shortcut
33578 , the command will be transformed to a math macro.
33579 Using this method you need to be careful that the
33585 command is typed correctly, otherwise you get a faulty macro leading to
33590 \begin_layout Standard
33591 Math macros currently have the problem that further formulas in macro definition
33592 s are handled wrongly.
33593 Therefore the example
33600 \begin_inset CommandInset ref
33602 reference "subsec:The-Command-newcommand"
33606 cannot be created as macro.
33609 \begin_layout Standard
33610 When the cursor is in a macro definition box, you will see the macro toolbar
33611 in \SpecialChar LyX
33615 \begin_layout Standard
33616 \begin_inset VSpace defskip
33622 \begin_layout Standard
33623 \begin_inset Graphics
33624 filename clipart/MacroToolbar.png
33629 \begin_inset Index idx
33632 \begin_layout Plain Layout
33641 \begin_layout Standard
33642 \begin_inset VSpace defskip
33648 \begin_layout Standard
33649 The macro toolbar contains from left to right the following buttons:
33652 \begin_layout Standard
33653 \begin_inset VSpace defskip
33659 \begin_layout Standard
33660 \begin_inset Tabular
33661 <lyxtabular version="3" rows="9" columns="2">
33662 <features islongtable="true" longtabularalignment="center">
33663 <column alignment="left" valignment="top">
33664 <column alignment="left" valignment="top" width="85col%">
33665 <row interlinespace="2.5mm">
33666 <cell alignment="center" valignment="top" usebox="none">
33669 \begin_layout Plain Layout
33672 arg "math-macro-remove-param"
33680 <cell alignment="center" valignment="top" usebox="none">
33683 \begin_layout Plain Layout
33686 Edit\SpecialChar menuseparator
33687 Math\SpecialChar menuseparator
33689 \begin_inset space ~
33692 Definition\SpecialChar menuseparator
33693 Remove Last Argument
33699 <row interlinespace="2.5mm">
33700 <cell alignment="center" valignment="top" usebox="none">
33703 \begin_layout Plain Layout
33706 arg "math-macro-add-param"
33714 <cell alignment="center" valignment="top" usebox="none">
33717 \begin_layout Plain Layout
33720 Edit\SpecialChar menuseparator
33721 Math\SpecialChar menuseparator
33723 \begin_inset space ~
33726 Definition\SpecialChar menuseparator
33733 <row interlinespace="2.5mm">
33734 <cell alignment="center" valignment="top" usebox="none">
33737 \begin_layout Plain Layout
33740 arg "math-macro-make-optional"
33748 <cell alignment="center" valignment="top" usebox="none">
33751 \begin_layout Plain Layout
33754 Edit\SpecialChar menuseparator
33755 Math\SpecialChar menuseparator
33757 \begin_inset space ~
33760 Definition\SpecialChar menuseparator
33761 Transform First Non-Optional to
33762 \begin_inset Newline newline
33766 \begin_inset Phantom HPhantom
33769 \begin_layout Plain Layout
33772 Edit\SpecialChar menuseparator
33773 Math\SpecialChar menuseparator
33775 \begin_inset space ~
33778 Definition\SpecialChar menuseparator
33790 <row interlinespace="2.5mm">
33791 <cell alignment="center" valignment="top" usebox="none">
33794 \begin_layout Plain Layout
33797 arg "math-macro-make-nonoptional"
33805 <cell alignment="center" valignment="top" usebox="none">
33808 \begin_layout Plain Layout
33811 Edit\SpecialChar menuseparator
33812 Math\SpecialChar menuseparator
33814 \begin_inset space ~
33817 Definition\SpecialChar menuseparator
33818 Transform Last Optional to
33819 \begin_inset Newline newline
33823 \begin_inset Phantom HPhantom
33826 \begin_layout Plain Layout
33829 Edit\SpecialChar menuseparator
33830 Math\SpecialChar menuseparator
33832 \begin_inset space ~
33835 Definition\SpecialChar menuseparator
33841 Non-Optional Argument
33847 <row interlinespace="2.5mm">
33848 <cell alignment="center" valignment="top" usebox="none">
33851 \begin_layout Plain Layout
33854 arg "math-macro-remove-optional-param"
33862 <cell alignment="center" valignment="top" usebox="none">
33865 \begin_layout Plain Layout
33868 Edit\SpecialChar menuseparator
33869 Math\SpecialChar menuseparator
33871 \begin_inset space ~
33874 Definition\SpecialChar menuseparator
33875 Remove Optional Argument
33881 <row interlinespace="2.5mm">
33882 <cell alignment="center" valignment="top" usebox="none">
33885 \begin_layout Plain Layout
33888 arg "math-macro-add-optional-param"
33896 <cell alignment="center" valignment="top" usebox="none">
33899 \begin_layout Plain Layout
33902 Edit\SpecialChar menuseparator
33903 Math\SpecialChar menuseparator
33905 \begin_inset space ~
33908 Definition\SpecialChar menuseparator
33909 Insert Optional Argument
33915 <row interlinespace="2.5mm">
33916 <cell alignment="center" valignment="top" usebox="none">
33919 \begin_layout Plain Layout
33922 arg "math-macro-remove-greedy-param"
33930 <cell alignment="center" valignment="top" usebox="none">
33933 \begin_layout Plain Layout
33936 Edit\SpecialChar menuseparator
33937 Math\SpecialChar menuseparator
33939 \begin_inset space ~
33942 Definition\SpecialChar menuseparator
33943 Remove Last Argument
33944 \begin_inset Newline newline
33948 \begin_inset Phantom HPhantom
33951 \begin_layout Plain Layout
33954 Edit\SpecialChar menuseparator
33955 Math\SpecialChar menuseparator
33957 \begin_inset space ~
33960 Definition\SpecialChar menuseparator
33966 Spitting Out To The Right
33972 <row interlinespace="2.5mm">
33973 <cell alignment="center" valignment="top" usebox="none">
33976 \begin_layout Plain Layout
33979 arg "math-macro-append-greedy-param"
33987 <cell alignment="center" valignment="top" usebox="none">
33990 \begin_layout Plain Layout
33993 Edit\SpecialChar menuseparator
33994 Math\SpecialChar menuseparator
33996 \begin_inset space ~
33999 Definition\SpecialChar menuseparator
34001 \begin_inset Newline newline
34005 \begin_inset Phantom HPhantom
34008 \begin_layout Plain Layout
34011 Edit\SpecialChar menuseparator
34012 Math\SpecialChar menuseparator
34014 \begin_inset space ~
34017 Definition\SpecialChar menuseparator
34023 Eating From The Right
34029 <row interlinespace="2.5mm">
34030 <cell alignment="center" valignment="top" usebox="none">
34033 \begin_layout Plain Layout
34036 arg "math-macro-add-greedy-optional-param"
34044 <cell alignment="center" valignment="top" usebox="none">
34047 \begin_layout Plain Layout
34050 Edit\SpecialChar menuseparator
34051 Math\SpecialChar menuseparator
34053 \begin_inset space ~
34056 Definition\SpecialChar menuseparator
34057 Append Optional Argument
34058 \begin_inset Newline newline
34062 \begin_inset Phantom HPhantom
34065 \begin_layout Plain Layout
34068 Edit\SpecialChar menuseparator
34069 Math\SpecialChar menuseparator
34071 \begin_inset space ~
34074 Definition\SpecialChar menuseparator
34080 Eating From The Right
34093 \begin_layout Section
34094 Computer Algebra Systems
34097 \begin_layout Standard
34099 offers the exchange between mathematical expressions written in \SpecialChar LyX
34101 editor and external applications or user defined scripts.
34102 Currently supported applications are
34119 Note that the set of supported mathematical constructs is limited only
34120 to very simple cases.
34123 \begin_layout Subsection
34127 \begin_layout Standard
34128 Write some expression in a formula, go to the
34130 Edit\SpecialChar menuseparator
34131 Math\SpecialChar menuseparator
34132 Use Computer Algebra System
34134 menu and choose the application you have installed on the computer.
34135 After that the result of computation should show on the right side of the
34136 expression together with the
34137 \begin_inset Quotes eld
34141 \begin_inset Quotes erd
34147 \begin_layout Standard
34148 Here are few simple examples (with results from
34152 ) to show what kind of computations can be performed:
34155 \begin_layout Itemize
34156 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34162 \begin_layout Itemize
34163 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34169 \begin_layout Itemize
34170 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34176 \begin_layout Itemize
34177 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34181 \begin_inset Newline newline
34185 \begin_inset Note Greyedout
34188 \begin_layout Plain Layout
34193 One needs to use proper delimiter insets
34194 \begin_inset Formula $\left(\right)$
34197 instead of simple '(' ')' characters.
34205 \begin_layout Itemize
34206 \begin_inset Formula $\det\left[\begin{array}{ccc}
34210 \end{array}\right]=-56$
34216 \begin_layout Itemize
34217 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34223 \begin_layout Itemize
34224 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34230 \begin_layout Itemize
34231 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34237 \begin_layout Subsection
34241 \begin_layout Standard
34242 Currently there is no keyboard shortcut for calling the algebra applications.
34243 One can easily bind a shortcut to the
34257 \begin_inset space \thinspace{}
34261 \begin_inset space \space{}
34268 key inside the math editor.
34273 one would use this shortcut definition command:
34276 \begin_layout Standard
34279 command-alternatives paragraph-break;math-extern maxima
34282 \begin_layout Section
34284 \begin_inset Index idx
34287 \begin_layout Plain Layout
34296 \begin_layout Subsection
34298 \begin_inset Index idx
34301 \begin_layout Plain Layout
34310 \begin_layout Standard
34311 Negative numbers often look ugly in formulas because the minus sign before
34312 the number is set with the same length as the minus operator sign.
34313 When writing the negative number in normal text, the minus sign appears
34317 \begin_layout Standard
34318 Thus, the problem disappears when converting the minus sign to mathematical
34322 \begin_layout Standard
34323 An example to visualize the problem:
34326 \begin_layout Standard
34328 \begin_inset Tabular
34329 <lyxtabular version="3" rows="3" columns="2">
34330 <features booktabs="true" tabularvalignment="middle">
34331 <column alignment="right" valignment="top" width="0pt">
34332 <column alignment="left" valignment="top">
34334 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34337 \begin_layout Plain Layout
34343 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34346 \begin_layout Plain Layout
34354 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34357 \begin_layout Plain Layout
34363 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34366 \begin_layout Plain Layout
34367 \begin_inset Formula $x=-2$
34377 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34380 \begin_layout Plain Layout
34386 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34389 \begin_layout Plain Layout
34390 \begin_inset Formula $x=\textrm{-}2$
34406 \begin_layout Subsection
34407 Comma as decimal Separator
34408 \begin_inset Index idx
34411 \begin_layout Plain Layout
34420 \begin_layout Standard
34421 In \SpecialChar LaTeX
34422 a comma inside a formula is used, according to the English convention,
34423 as number group separator.
34424 So there will be space added behind all commas in formulas.
34427 \begin_layout Standard
34428 To avoid this, the comma is highlighted and changed to mathematical text
34438 \begin_layout Standard
34439 To use all formula commas in the document as decimal separator, the file
34448 \begin_layout Plain Layout
34453 is part of the \SpecialChar LaTeX
34459 \begin_inset Index idx
34462 \begin_layout Plain Layout
34467 \begin_layout Plain Layout
34487 \begin_inset Index idx
34490 \begin_layout Plain Layout
34496 is loaded with the \SpecialChar LaTeX
34500 \begin_layout Standard
34508 \begin_layout Subsection
34510 \begin_inset CommandInset label
34512 name "subsec:Physical-Vectors"
34517 \begin_inset Index idx
34520 \begin_layout Plain Layout
34529 \begin_layout Standard
34530 Predefined vectors are offered by the \SpecialChar LaTeX
34536 \begin_inset Index idx
34539 \begin_layout Plain Layout
34545 that is loaded with the \SpecialChar LaTeX
34549 \begin_layout Standard
34557 \begin_layout Standard
34561 \begin_layout Plain Layout
34571 \begin_inset Note Note
34574 \begin_layout Plain Layout
34575 The following table will only be displayed when the \SpecialChar LaTeX
34588 \begin_layout Standard
34589 The following commands are defined:
34592 \begin_layout Standard
34594 \begin_inset Tabular
34595 <lyxtabular version="3" rows="4" columns="2">
34596 <features booktabs="true" tabularvalignment="middle">
34597 <column alignment="center" valignment="top" width="0pt">
34598 <column alignment="center" valignment="top">
34600 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34603 \begin_layout Plain Layout
34609 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34612 \begin_layout Plain Layout
34620 <cell alignment="center" valignment="top" usebox="none">
34623 \begin_layout Plain Layout
34633 <cell alignment="center" valignment="top" usebox="none">
34636 \begin_layout Plain Layout
34637 \begin_inset Formula $\Bra{\psi}$
34647 <cell alignment="center" valignment="top" usebox="none">
34650 \begin_layout Plain Layout
34660 <cell alignment="center" valignment="top" usebox="none">
34663 \begin_layout Plain Layout
34664 \begin_inset Formula $\Ket{\psi}$
34674 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34677 \begin_layout Plain Layout
34689 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34692 \begin_layout Plain Layout
34693 \begin_inset Formula $\Braket{\psi|\phi}$
34709 \begin_layout Standard
34716 assures that all vertical bars are set in the size of the surrounding brackets:
34717 \begin_inset Formula
34719 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34728 \begin_layout Plain Layout
34738 \begin_inset Note Note
34741 \begin_layout Plain Layout
34742 The following will be displayed when the \SpecialChar LaTeX
34755 \begin_layout Standard
34756 You need to install the \SpecialChar LaTeX
34761 to see the rest of this subsection in the output.
34764 \begin_layout Standard
34768 \begin_layout Plain Layout
34780 \begin_layout Standard
34787 can also be achieved using the command
34793 , that is described in
34794 \begin_inset CommandInset ref
34796 reference "subsec:Automatic-Bracket-Size"
34803 \begin_layout Subsection
34804 Self-defined Fractions
34805 \begin_inset CommandInset label
34807 name "subsec:Self-defined-Fractions"
34812 \begin_inset Index idx
34815 \begin_layout Plain Layout
34816 Fractions ! self-defined
34824 \begin_layout Standard
34825 To define custom commands for fractions, the command
34832 \begin_inset Index idx
34835 \begin_layout Plain Layout
34842 \begin_layout Plain Layout
34856 is used in the following scheme:
34859 \begin_layout Standard
34872 bracket}{fraction bar thickness}{style}
34873 \begin_inset Newline newline
34877 \begin_inset Phantom HPhantom
34880 \begin_layout Plain Layout
34890 {numerator}{denominator}
34893 \begin_layout Standard
34894 The style is a number in the range of 0
34895 \begin_inset space \thinspace{}
34899 \begin_inset space \thinspace{}
34905 \begin_layout Standard
34907 \begin_inset Tabular
34908 <lyxtabular version="3" rows="5" columns="2">
34909 <features booktabs="true" tabularvalignment="middle">
34910 <column alignment="center" valignment="top" width="0pt">
34911 <column alignment="center" valignment="top">
34913 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34916 \begin_layout Plain Layout
34922 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34925 \begin_layout Plain Layout
34933 <cell alignment="center" valignment="top" usebox="none">
34936 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" usebox="none">
34945 \begin_layout Plain Layout
34946 display style formula
34953 <cell alignment="center" valignment="top" usebox="none">
34956 \begin_layout Plain Layout
34962 <cell alignment="center" valignment="top" usebox="none">
34965 \begin_layout Plain Layout
34973 <cell alignment="center" valignment="top" usebox="none">
34976 \begin_layout Plain Layout
34982 <cell alignment="center" valignment="top" usebox="none">
34985 \begin_layout Plain Layout
34993 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34996 \begin_layout Plain Layout
35002 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35005 \begin_layout Plain Layout
35019 \begin_layout Standard
35020 When no style is given, the size is adjusted to the surrounding environment
35021 like for the command
35030 \begin_layout Standard
35031 When no fraction bar thickness is given, the predefined value of 0.4
35032 \begin_inset space \thinspace{}
35038 \begin_layout Standard
35039 \begin_inset VSpace medskip
35042 For example, the commands
35055 \begin_inset CommandInset ref
35057 reference "subsec:Fractions"
35061 are defined with the commands
35064 \begin_layout Standard
35073 genfrac{}{}{}{0}{#1}{#2}}
35076 \begin_layout Standard
35080 \begin_layout Standard
35089 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35092 \begin_layout Standard
35093 \begin_inset VSpace medskip
35096 To define a fraction where the fraction bar thickness can be given as optional
35097 argument, the following line is inserted to the \SpecialChar LaTeX
35101 \begin_layout Standard
35110 genfrac{}{}{#1}{}{#2}{#3}}
35113 \begin_layout Standard
35115 \begin_inset Formula
35117 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35118 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35123 As one can see, the distance of the numerator and the denominator to the
35124 fraction bar is round about three times the bar thickness.
35127 \begin_layout Subsection
35129 \begin_inset Index idx
35132 \begin_layout Plain Layout
35141 \begin_layout Standard
35142 There are four ways to cancel formulas or parts of formulas:
35145 \begin_layout Standard
35149 \begin_layout Plain Layout
35159 \begin_inset Note Note
35162 \begin_layout Plain Layout
35163 The following table will only be displayed when the \SpecialChar LaTeX
35176 \begin_layout Standard
35178 \begin_inset Tabular
35179 <lyxtabular version="3" rows="5" columns="2">
35180 <features booktabs="true" tabularvalignment="middle">
35181 <column alignment="center" valignment="top" width="0pt">
35182 <column alignment="center" valignment="top">
35184 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35187 \begin_layout Plain Layout
35193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35196 \begin_layout Plain Layout
35204 <cell alignment="center" valignment="top" usebox="none">
35207 \begin_layout Plain Layout
35211 \begin_inset space \textvisiblespace{}
35217 \begin_inset space \textvisiblespace{}
35225 <cell alignment="center" valignment="top" usebox="none">
35228 \begin_layout Plain Layout
35229 \begin_inset Formula $\cancel{\int A=B}$
35238 <row topspace="1.5mm">
35239 <cell alignment="center" valignment="top" usebox="none">
35242 \begin_layout Plain Layout
35246 \begin_inset space \textvisiblespace{}
35252 \begin_inset space \textvisiblespace{}
35260 <cell alignment="center" valignment="top" usebox="none">
35263 \begin_layout Plain Layout
35264 \begin_inset Formula $\bcancel{\int A=B}$
35273 <row topspace="1.5mm">
35274 <cell alignment="center" valignment="top" usebox="none">
35277 \begin_layout Plain Layout
35281 \begin_inset space \textvisiblespace{}
35287 \begin_inset space \textvisiblespace{}
35295 <cell alignment="center" valignment="top" usebox="none">
35298 \begin_layout Plain Layout
35299 \begin_inset Formula $\xcancel{\int A=B}$
35309 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35312 \begin_layout Plain Layout
35316 \begin_inset space \textvisiblespace{}
35322 \begin_inset space \textvisiblespace{}
35326 \begin_inset Formula $\to$
35334 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35337 \begin_layout Plain Layout
35338 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35354 \begin_layout Standard
35361 is especially suitable to visualize the reduction of fractions within formulas:
35362 \begin_inset Formula
35364 \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}}}
35372 \begin_layout Standard
35373 To change the size of
35380 \begin_inset Quotes eld
35384 \begin_inset Quotes erd
35387 value one can add the \SpecialChar LaTeX
35391 \begin_layout Standard
35396 PassOptionsToPackage{option}{cancel}
35399 \begin_layout Standard
35408 which leads to the same size as for the canceled value, or
35412 which makes is it a bit smaller than normal.
35415 \begin_layout Standard
35416 To color the cancellation bar one adds this command as \SpecialChar TeX
35420 \begin_layout Standard
35432 \begin_layout Standard
35437 can be replaced by a color of your choice.
35440 \begin_layout Standard
35444 \begin_layout Plain Layout
35460 \begin_layout Standard
35461 \begin_inset Formula
35463 \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}}}
35471 \begin_layout Standard
35475 \begin_layout Plain Layout
35489 \begin_inset Note Note
35492 \begin_layout Plain Layout
35501 \begin_layout Standard
35502 For further customizations, see the documentation of the package
35507 \begin_inset CommandInset citation
35515 \begin_inset Index idx
35518 \begin_layout Plain Layout
35527 \begin_layout Standard
35531 \begin_layout Plain Layout
35541 \begin_inset Note Note
35544 \begin_layout Plain Layout
35545 The following will be displayed when the \SpecialChar LaTeX
35558 \begin_layout Standard
35559 You need to install the \SpecialChar LaTeX
35564 to see the rest of this subsection in the output.
35567 \begin_layout Standard
35571 \begin_layout Plain Layout
35583 \begin_layout Subsection
35584 Formulas in Section Headings
35585 \begin_inset CommandInset label
35587 name "subsec:Formulas-in-Section"
35592 \begin_inset Index idx
35595 \begin_layout Plain Layout
35596 Formula ! in section headings
35604 \begin_layout Standard
35605 When formulas are used in section headings, the following has to be taken
35609 \begin_layout Standard
35610 \begin_inset Note Greyedout
35613 \begin_layout Plain Layout
35619 \begin_inset Index idx
35622 \begin_layout Plain Layout
35623 Packages ! hyperref
35628 support is enabled in the document settings dialog under
35631 \begin_inset space ~
35636 , PDF-bookmarks are created for every section heading in the table of contents.
35637 If a section heading contains formulas, they are incorrectly displayed
35638 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35647 \begin_layout Standard
35648 Both problems can be solved by inserting at the end of the section heading
35649 a short title with the menu
35651 Insert\SpecialChar menuseparator
35653 \begin_inset space ~
35659 Short titles are used as alternative for multiline section headings to
35660 keep the table of contents clearly arranged.
35661 Only the short title appears in the table of contents and therefore also
35662 in the PDF-bookmark.
35665 \begin_layout Standard
35666 When formulas should be used in the table of contents but
35670 is used, one can use the following command in \SpecialChar TeX
35674 \begin_layout Standard
35679 texorpdfstring{part}{alternative}
35680 \begin_inset Index idx
35683 \begin_layout Plain Layout
35694 \begin_layout Standard
35695 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35696 This can be characters, formulas, footnotes, but also cross-references.
35697 The alternative is used instead of the part for the bookmark.
35700 \begin_layout Standard
35701 Here are two example headings:
35702 \begin_inset VSpace -3mm
35709 \begin_layout Plain Layout
35721 \begin_layout Subsubsection
35722 Heading without formula in table of contents
35723 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35727 \begin_inset Argument 1
35730 \begin_layout Plain Layout
35731 Heading without formula in table of contents
35739 \begin_layout Subsubsection
35740 Heading with formula in table of contents
35744 \begin_layout Plain Layout
35754 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35761 \begin_layout Plain Layout
35771 \begin_layout Standard
35775 \begin_layout Plain Layout
35784 In the first heading a short title was used, in the second one
35793 \begin_layout Standard
35794 To get the same formatting as for the other headings, the complete heading
35803 \begin_layout Plain Layout
35805 \begin_inset CommandInset ref
35807 reference "subsec:Bold-Formulas"
35819 \begin_layout Subsection
35820 Formulas in multi-column Text
35821 \begin_inset Index idx
35824 \begin_layout Plain Layout
35825 Formula ! in multi-column text
35833 \begin_layout Standard
35834 Formulas in multi-column text are often too wide to fit into a column and
35835 thus need to be set over the whole page width.
35836 This is done by using the \SpecialChar LaTeX
35845 \begin_layout Plain Layout
35850 is part of every \SpecialChar LaTeX
35851 standard installation.
35857 \begin_inset Index idx
35860 \begin_layout Plain Layout
35861 Packages ! multicol
35866 , that is loaded with the \SpecialChar LaTeX
35870 \begin_layout Standard
35875 usepackage{multicol}
35878 \begin_layout Standard
35879 \begin_inset Note Greyedout
35882 \begin_layout Plain Layout
35883 Note that in this case the setting
35886 \begin_inset space ~
35893 Document\SpecialChar menuseparator
35899 \begin_inset space ~
35919 \begin_layout Standard
35920 Before the multi-column text the command
35923 \begin_layout Standard
35928 begin{multicols}{column number}
35931 \begin_layout Standard
35932 is written in \SpecialChar TeX
35934 The column number is a number in the range of 2
35935 \begin_inset space \thinspace{}
35939 \begin_inset space \thinspace{}
35943 Before the formula the multi-column text is ended by inserting the command
35946 \begin_layout Standard
35954 \begin_layout Standard
35955 in \SpecialChar TeX
35959 \begin_layout Standard
35960 Due to the command some space is automatically added before the formula.
35962 \begin_inset space \thinspace{}
35965 mm vertical space is inserted before the formula.
35966 When the formula style
35972 \begin_layout Plain Layout
35974 \begin_inset CommandInset ref
35976 reference "sec:Formula-Styles"
35988 \begin_inset space \thinspace{}
35991 mm space is inserted instead.
35994 \begin_layout Standard
35995 As example a multi-column text with a displayed formula:
35998 \begin_layout Standard
36004 \begin_layout Plain Layout
36008 begin{multicols}{2}
36013 Das Spektrum wird fouriertransformiert.
36014 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36015 , Lösungsmittel) zu trennen.
36016 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36017 nun das Aussehen des Ausgangssignals.
36018 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36019 über alle Phasen integrieren muss.
36021 \begin_inset Formula $S$
36024 unser normiertes Ausgangssignal und
36025 \begin_inset Formula $P$
36028 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36032 \begin_layout Plain Layout
36042 \begin_inset VSpace -6mm
36046 \begin_inset Formula
36048 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36057 \begin_layout Plain Layout
36061 begin{multicols}{2}
36067 \begin_inset Formula $S_{0}$
36070 das Signal ohne Gradient ist und die Normierungsbedingung
36071 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36075 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36077 \begin_inset Formula $\nicefrac{\pi}{2}$
36081 \begin_inset space \thinspace{}
36084 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36085 das Signal zusätzlich abschwächt.
36086 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36088 \begin_inset Formula $T_{2}$
36094 \begin_layout Standard
36100 \begin_layout Plain Layout
36112 \begin_layout Subsection
36113 Formulas with Description of Variables
36114 \begin_inset Index idx
36117 \begin_layout Plain Layout
36118 Formula ! with description of variables
36126 \begin_layout Standard
36127 To describe variables within a formula, like in formula
36128 \begin_inset CommandInset ref
36130 reference "eq:within"
36139 \begin_inset Formula $n$
36143 \begin_inset space ~
36146 matrix is used with left aligned columns for the
36147 \begin_inset Formula $n$
36154 \begin_layout Plain Layout
36156 \begin_inset CommandInset ref
36158 reference "sec:Matrices"
36167 To set the description in a smaller size, before the matrix e.
36168 \begin_inset space \thinspace{}
36172 \begin_inset space \space{}
36185 \begin_layout Plain Layout
36187 \begin_inset CommandInset ref
36189 reference "subsec:Font-Sizes"
36201 \begin_layout Standard
36202 When the formula style
36208 \begin_layout Plain Layout
36210 \begin_inset CommandInset ref
36212 reference "sec:Formula-Styles"
36233 \begin_layout Plain Layout
36240 only works in formulas with the style
36245 \begin_inset CommandInset ref
36247 reference "subsec:Variable-Space"
36256 is inserted before and after the matrix to have the same separation of
36257 the matrix from the equation and the side margin.
36260 \begin_layout Standard
36261 When the formula style
36265 is used, the method described in
36266 \begin_inset CommandInset ref
36268 reference "subsec:Flalign-Environment"
36272 is used to indent formulas.
36274 \begin_inset CommandInset ref
36276 reference "eq:within"
36280 consists of five columns where in the first two columns contain the equation,
36281 the third the matrix and the last one an empty \SpecialChar TeX
36283 \begin_inset Formula
36285 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36286 \rho & \textrm{density}\\
36287 V & \textrm{volume}\\
36288 g & \textrm{gravitational acceleration}
36289 \end{array} & & {}\label{eq:within}
36297 \begin_layout Subsection
36298 Upright small Greek Letters
36299 \begin_inset CommandInset label
36301 name "subsec:Upright-small-Greek"
36306 \begin_inset Index idx
36309 \begin_layout Plain Layout
36310 Greek letters ! upright
36318 \begin_layout Standard
36319 Most of the math fonts only provide italic small Greek letters.
36320 But for symbols of elementary particles like pions and neutrinos, upright
36321 Greek letters are needed.
36330 \begin_layout Plain Layout
36335 is part of the \SpecialChar LaTeX
36341 \begin_inset Index idx
36344 \begin_layout Plain Layout
36349 \begin_layout Plain Layout
36369 \begin_inset Index idx
36372 \begin_layout Plain Layout
36378 that is loaded with the \SpecialChar LaTeX
36382 \begin_layout Standard
36387 usepackage{upgreek}
36390 \begin_layout Standard
36396 \begin_layout Plain Layout
36406 \begin_inset Note Note
36409 \begin_layout Plain Layout
36410 The following table will only be displayed when the \SpecialChar LaTeX
36420 They are created when the command for a small Greek letter is started with
36426 For example the command
36433 \begin_inset Formula $\uptau$
36439 \begin_layout Standard
36440 With these commands reactions of elementary particles can be typeset:
36441 \begin_inset Formula
36443 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36451 \begin_layout Standard
36452 The upright letters are more bold and wider than the italic ones.
36453 They should therefore not be used for units like
36454 \begin_inset Quotes eld
36458 \begin_inset Quotes erd
36464 \begin_layout Standard
36468 \begin_layout Plain Layout
36478 \begin_inset Note Note
36481 \begin_layout Plain Layout
36482 The following will be displayed when the \SpecialChar LaTeX
36495 \begin_layout Standard
36496 You need to install the \SpecialChar LaTeX
36501 to see the rest of this subsection in the output.
36504 \begin_layout Standard
36508 \begin_layout Plain Layout
36520 \begin_layout Subsection
36521 Text Characters in Formulas
36522 \begin_inset Index idx
36525 \begin_layout Plain Layout
36534 \begin_layout Standard
36535 In some cases you might want to insert text characters directly into formulas.
36536 When for example the centered dot · is often used in formulas like
36537 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36540 , one would have to insert the command
36550 \begin_layout Plain Layout
36552 \begin_inset CommandInset ref
36554 reference "subsec:Binary-Operators"
36563 all the time, because this character is defined in all encodings as text
36565 But the encoding can be changed by this \SpecialChar LaTeX
36569 \begin_layout Standard
36574 Declare Inputtext{183}{
36584 f\SpecialChar ligaturebreak
36588 \begin_layout Standard
36589 The character encoding (menu
36591 Document\SpecialChar menuseparator
36592 Settings\SpecialChar menuseparator
36595 ) specifies what character appears when a keyboard key is pressed.
36596 When the key for the character '·' is pressed, internally the command
36603 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36605 With the changed encoding the right command is chosen automatically, depending
36606 on if the character was inserted into a formula or not.
36609 \begin_layout Standard
36610 The encoding of several characters is saved in definition files.
36611 For example the encoding
36615 is defined in the file
36619 which is in the installation folder of \SpecialChar LaTeX
36621 Encodings should only be changed via the \SpecialChar LaTeX
36622 -preamble and not in the definition
36624 Otherwise documents could not be edited by other \SpecialChar LyX
36625 users working on other
36629 \begin_layout Standard
36630 \begin_inset VSpace medskip
36633 Besides the centered dot, in this document the degree sign ° is defined
36634 with the following \SpecialChar LaTeX
36635 -preamble line so that it can be directly inserted into
36639 \begin_layout Standard
36644 DeclareInputtext{176}{
36654 f\SpecialChar ligaturebreak
36658 \begin_layout Subsection
36660 -comments in formulas
36661 \begin_inset Index idx
36664 \begin_layout Plain Layout
36674 \begin_layout Standard
36675 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36677 code of your file with the menu
36679 Insert\SpecialChar menuseparator
36680 Note\SpecialChar menuseparator
36684 This is not possible in a formula but you can insert \SpecialChar LaTeX
36689 \begin_layout Standard
36697 \begin_layout Standard
36698 This creates a box in which you can write your comment.
36699 Due to a bug in \SpecialChar LyX
36704 \begin_layout Plain Layout
36705 \begin_inset CommandInset href
36707 name "LyX-bug #9002"
36708 target "https://www.lyx.org/trac/ticket/9002"
36718 you cannot write normal text inside the comment, even when you use mathematical
36719 text, you will see its \SpecialChar LaTeX
36720 -commands in the \SpecialChar LaTeX
36722 \begin_inset Newline newline
36725 This a formula with a \SpecialChar LaTeX
36727 \begin_inset Formula
36729 A=B%\text{This is the comment}
36737 \begin_layout Standard
36738 \begin_inset Newpage newpage
36744 \begin_layout Section
36747 \begin_inset Index idx
36750 \begin_layout Plain Layout
36759 \begin_layout Standard
36760 This section is a summary of the most important typographic rules, listed
36765 \begin_layout Plain Layout
36766 This collection was partly taken from the German semi-official dictionary
36768 \begin_inset Quotes eld
36772 \begin_inset Quotes erd
36776 \begin_inset CommandInset citation
36783 that lists some of the ISO rules.
36784 More rules are listed in
36785 \begin_inset CommandInset citation
36800 \begin_layout Itemize
36809 \begin_layout Plain Layout
36810 done with font styles, see
36811 \begin_inset CommandInset ref
36813 reference "subsec:Font-Styles"
36822 , no matter if they appear in italic text: 30
36823 \begin_inset space \thinspace{}
36827 \begin_inset Newline newline
36830 Between the value and the unit is the smallest space, see
36831 \begin_inset CommandInset ref
36833 reference "subsec:Predefined-Space"
36838 \begin_inset Newline newline
36841 This convention is automatically fulfilled when the command
36848 When it is entered to a formula, two boxes appear.
36849 In the first one the value is inserted, in the second one the unit, and
36851 \begin_inset Formula $\unit[30]{km/h}$
36855 \begin_inset space \thinspace{}
36865 is not a real \SpecialChar LaTeX
36866 command but the command
36872 , therefore you cannot use it in \SpecialChar TeX
36876 \begin_layout Itemize
36877 Percent and perthousand signs are set like physical units:
36878 \begin_inset Newline newline
36882 \begin_inset space \thinspace{}
36888 \begin_layout Itemize
36889 The degree sign follows directly on the value: 15°, but not when it is used
36891 \begin_inset space \thinspace{}
36897 \begin_layout Itemize
36898 In numbers with more than four digits the smallest space is inserted before
36899 every third digit to group them:
36909 \begin_inset space \thinspace{}
36913 \begin_inset space \thinspace{}
36919 \begin_layout Itemize
36920 For dimensions like 120×90×40
36921 \begin_inset space \thinspace{}
36924 cm the multiplication sign
36925 \begin_inset Quotes eld
36929 \begin_inset Quotes erd
36933 It is available either via the command
36941 Insert\SpecialChar menuseparator
36942 Special Character\SpecialChar menuseparator
36948 \begin_layout Itemize
36949 Functions with names consisting of several letters are set upright to avoid
36951 \begin_inset CommandInset ref
36953 reference "subsec:Predefined-Functions"
36960 \begin_layout Itemize
36961 Indices consisting of several letters, are set upright:
36962 \begin_inset Formula $E_{\mathrm{kin}}$
36966 \begin_inset Newline newline
36969 Components of matrices are set italic:
36970 \begin_inset Formula $\hat{H}_{kl}$
36976 \begin_layout Itemize
36977 The differentiation/integration operator 'd', the Euler's number 'e' and
36978 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36982 \begin_layout Itemize
36983 The character that denotes a
36987 transformation is inserted either by the command
36992 \begin_inset space \textvisiblespace{}
36999 Insert\SpecialChar menuseparator
37000 Special Character\SpecialChar menuseparator
37001 Symbols\SpecialChar menuseparator
37003 \begin_inset space ~
37009 \begin_inset Formula $\mathscr{F}$
37015 \begin_layout Standard
37016 \begin_inset Newpage newpage
37022 \begin_layout Section
37024 \begin_inset Index idx
37027 \begin_layout Plain Layout
37036 \begin_layout Standard
37037 Some characters and symbols can be created with several commands.
37038 Here is a list of the synonym commands:
37041 \begin_layout Standard
37042 \begin_inset VSpace bigskip
37046 \begin_inset space \hfill{}
37050 \begin_inset Tabular
37051 <lyxtabular version="3" rows="12" columns="2">
37052 <features booktabs="true" tabularvalignment="middle">
37053 <column alignment="center" valignment="top" width="0pt">
37054 <column alignment="center" valignment="top" width="0pt">
37056 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37059 \begin_layout Plain Layout
37065 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37068 \begin_layout Plain Layout
37076 <cell alignment="center" valignment="top" usebox="none">
37079 \begin_layout Plain Layout
37087 <cell alignment="center" valignment="top" usebox="none">
37090 \begin_layout Plain Layout
37098 <cell alignment="center" valignment="top" usebox="none">
37101 \begin_layout Plain Layout
37109 <cell alignment="center" valignment="top" usebox="none">
37112 \begin_layout Plain Layout
37122 <cell alignment="center" valignment="top" usebox="none">
37125 \begin_layout Plain Layout
37133 <cell alignment="center" valignment="top" usebox="none">
37136 \begin_layout Plain Layout
37146 <cell alignment="center" valignment="top" usebox="none">
37149 \begin_layout Plain Layout
37157 <cell alignment="center" valignment="top" usebox="none">
37160 \begin_layout Plain Layout
37168 <cell alignment="center" valignment="top" usebox="none">
37171 \begin_layout Plain Layout
37179 <cell alignment="center" valignment="top" usebox="none">
37182 \begin_layout Plain Layout
37190 <cell alignment="center" valignment="top" usebox="none">
37193 \begin_layout Plain Layout
37201 <cell alignment="center" valignment="top" usebox="none">
37204 \begin_layout Plain Layout
37214 <cell alignment="center" valignment="top" usebox="none">
37217 \begin_layout Plain Layout
37225 <cell alignment="center" valignment="top" usebox="none">
37228 \begin_layout Plain Layout
37238 <cell alignment="center" valignment="top" usebox="none">
37241 \begin_layout Plain Layout
37249 <cell alignment="center" valignment="top" usebox="none">
37252 \begin_layout Plain Layout
37262 <cell alignment="center" valignment="top" usebox="none">
37265 \begin_layout Plain Layout
37273 <cell alignment="center" valignment="top" usebox="none">
37276 \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
37308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37311 \begin_layout Plain Layout
37319 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37322 \begin_layout Plain Layout
37334 \begin_inset space \hfill{}
37338 \begin_inset Tabular
37339 <lyxtabular version="3" rows="12" columns="2">
37340 <features booktabs="true" tabularvalignment="middle">
37341 <column alignment="center" valignment="top" width="0pt">
37342 <column alignment="center" valignment="top" width="0pt">
37344 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37347 \begin_layout Plain Layout
37353 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37356 \begin_layout Plain Layout
37364 <cell alignment="center" valignment="top" usebox="none">
37367 \begin_layout Plain Layout
37375 <cell alignment="center" valignment="top" usebox="none">
37378 \begin_layout Plain Layout
37390 <cell alignment="center" valignment="top" usebox="none">
37393 \begin_layout Plain Layout
37401 <cell alignment="center" valignment="top" usebox="none">
37404 \begin_layout Plain Layout
37414 <cell alignment="center" valignment="top" usebox="none">
37417 \begin_layout Plain Layout
37425 <cell alignment="center" valignment="top" usebox="none">
37428 \begin_layout Plain Layout
37438 <cell alignment="center" valignment="top" usebox="none">
37441 \begin_layout Plain Layout
37449 <cell alignment="center" valignment="top" usebox="none">
37452 \begin_layout Plain Layout
37460 <cell alignment="center" valignment="top" usebox="none">
37463 \begin_layout Plain Layout
37471 <cell alignment="center" valignment="top" usebox="none">
37474 \begin_layout Plain Layout
37482 <cell alignment="center" valignment="top" usebox="none">
37485 \begin_layout Plain Layout
37493 <cell alignment="center" valignment="top" usebox="none">
37496 \begin_layout Plain Layout
37506 <cell alignment="center" valignment="top" usebox="none">
37509 \begin_layout Plain Layout
37517 <cell alignment="center" valignment="top" usebox="none">
37520 \begin_layout Plain Layout
37530 <cell alignment="center" valignment="top" usebox="none">
37533 \begin_layout Plain Layout
37541 <cell alignment="center" valignment="top" usebox="none">
37544 \begin_layout Plain Layout
37554 <cell alignment="center" valignment="top" usebox="none">
37557 \begin_layout Plain Layout
37565 <cell alignment="center" valignment="top" usebox="none">
37568 \begin_layout Plain Layout
37578 <cell alignment="center" valignment="top" usebox="none">
37581 \begin_layout Plain Layout
37589 <cell alignment="center" valignment="top" usebox="none">
37592 \begin_layout Plain Layout
37602 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37605 \begin_layout Plain Layout
37613 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37616 \begin_layout Plain Layout
37630 \begin_inset space \hfill{}
37634 \begin_inset CommandInset href
37637 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37645 \begin_layout Standard
37646 \begin_inset Newpage newpage
37652 \begin_layout Bibliography
37653 \begin_inset CommandInset bibitem
37654 LatexCommand bibitem
37668 The \SpecialChar LaTeX
37672 Addison Wesley, 2004
37675 \begin_layout Bibliography
37676 \begin_inset CommandInset bibitem
37677 LatexCommand bibitem
37684 \begin_inset CommandInset href
37687 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37692 of \SpecialChar LaTeX
37696 \begin_layout Bibliography
37697 \begin_inset CommandInset bibitem
37698 LatexCommand bibitem
37705 \begin_inset CommandInset href
37708 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
37717 \begin_layout Plain Layout
37726 -\SpecialChar LaTeX
37730 \begin_layout Bibliography
37731 \begin_inset CommandInset bibitem
37732 LatexCommand bibitem
37739 \begin_inset CommandInset href
37742 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37747 of all symbols available with \SpecialChar LaTeX
37751 \begin_layout Bibliography
37752 \begin_inset CommandInset bibitem
37753 LatexCommand bibitem
37760 \begin_inset CommandInset href
37762 name "Documentation"
37763 target "https://www.ctan.org/tex-archive/macros/latex/contrib/cancel/cancel.pdf"
37768 of the \SpecialChar LaTeX
37774 \begin_inset Index idx
37777 \begin_layout Plain Layout
37786 \begin_layout Bibliography
37787 \begin_inset CommandInset bibitem
37788 LatexCommand bibitem
37795 \begin_inset CommandInset href
37797 name "Documentation"
37798 target "https://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/doc/manual.pdf"
37803 of the \SpecialChar LaTeX
37809 \begin_inset Index idx
37812 \begin_layout Plain Layout
37813 Packages ! hyperref
37821 \begin_layout Bibliography
37822 \begin_inset CommandInset bibitem
37823 LatexCommand bibitem
37830 \begin_inset CommandInset href
37832 name "Documentation"
37833 target "https://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37838 of the \SpecialChar LaTeX
37844 \begin_inset Index idx
37847 \begin_layout Plain Layout
37856 \begin_layout Bibliography
37857 \begin_inset CommandInset bibitem
37858 LatexCommand bibitem
37867 \begin_inset space ~
37874 \begin_inset space ~
37877 Auflage, Dudenverlag, 2000
37880 \begin_layout Bibliography
37881 \begin_inset CommandInset bibitem
37882 LatexCommand bibitem
37889 \begin_inset CommandInset href
37892 target "https://www.nist.gov/physical-measurement-laboratory/special-publication-811"
37897 for reviewing manuscripts
37900 \begin_layout Standard
37901 \begin_inset CommandInset index_print
37902 LatexCommand printindex