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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32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
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54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
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126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children no
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
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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 makeindex
165 \float_placement class
166 \float_alignment class
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
186 \use_package amsmath 2
187 \use_package amssymb 2
188 \use_package cancel 1
190 \use_package mathdots 1
191 \use_package mathtools 2
192 \use_package mhchem 1
193 \use_package stackrel 1
194 \use_package stmaryrd 1
195 \use_package undertilde 0
197 \cite_engine_type default
201 \paperorientation portrait
207 \notefontcolor #0000ff
214 \paragraph_separation skip
217 \math_numbering_side default
218 \quotes_style english
222 \paperpagestyle plain
227 \tracking_changes true
228 \output_changes false
230 \postpone_fragile_content false
233 \html_be_strict false
234 \docbook_table_output 0
235 \author -563046850 "Jean-Marc LASGOUTTES"
236 \author 47243155 "Jean-Marc"
243 's detailed Math manual
247 by the \SpecialChar LyX
252 \begin_layout Plain Layout
254 If you have comments or error corrections, please send them to the \SpecialChar LyX
259 \begin_inset CommandInset href
261 name "lyx-docs@lists.lyx.org"
262 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
274 \begin_inset Note Note
277 \begin_layout Plain Layout
284 \begin_inset Newline newline
288 \begin_inset Newline newline
294 \change_inserted 47243155 1563226038
296 \change_deleted 47243155 1563226038
302 \begin_layout Standard
303 \begin_inset CommandInset toc
304 LatexCommand tableofcontents
311 \begin_layout Standard
312 \begin_inset Note Note
315 \begin_layout Plain Layout
316 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
319 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
326 If they are not installed the document can be exported anyway but the sections
327 where the packages are required will not appear in the output.
332 ; if it is not installed, this file cannot be exported.
335 \begin_layout Plain Layout
336 The latest PDF-version of this document can be found here:
337 \begin_inset Newline newline
342 https://wiki.lyx.org/LyX/Manuals#Math
350 \begin_layout Standard
351 \begin_inset Newpage newpage
357 \begin_layout Section
361 \begin_layout Standard
362 This document explains \SpecialChar LyX
363 's math features and is furthermore a collection
364 of \SpecialChar LaTeX
365 -commands used for mathematical characters and constructs.
366 The explanations are designed for the usage of commands.
367 It is therefore required that you have read the section
378 \begin_layout Standard
379 Most of the characters and many constructs explained in this manual are
380 also accessible via the menu
384 \SpecialChar menuseparator
400 But everybody who has to write lots of formulas will notice that it is
401 much faster to use commands instead of the math toolbar.
402 Therefore this manual is focused on commands but also mentions the correspondin
403 g toolbar buttons when available.
406 \begin_layout Standard
407 If not specially mentioned the commands are only available within formulas.
408 To be able to use all commands explained in this document, the option
412 must be checked in the document settings (menu
414 Document\SpecialChar menuseparator
415 Settings\SpecialChar menuseparator
426 \begin_layout Plain Layout
429 Use AMS math package automatically
435 \begin_layout Plain Layout
444 -math when math constructs are found that are supported by \SpecialChar LyX
453 \begin_layout Standard
454 This document doesn't list all
458 \begin_layout Plain Layout
471 \begin_layout Plain Layout
476 \begin_layout Plain Layout
485 -math commands is in the file
488 \begin_inset CommandInset href
491 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
498 , which is part of every \SpecialChar LaTeX
499 standard installation.
504 for lucidity reasons.
507 \begin_layout Section
511 \begin_layout Standard
512 To create an inline formula
513 \begin_inset Index idx
516 \begin_layout Plain Layout
522 that is embedded into a text line, use one of the shortcuts
528 or the toolbar button
535 \begin_inset Newline newline
538 To create a display style formula
539 \begin_inset Index idx
542 \begin_layout Plain Layout
543 Formula ! display style
548 which will appear bigger, has a different format, and will be in a separate
549 paragraph, use one of these shortcuts:
558 \begin_layout Standard
559 To change a display style formula to an inline formula, set the cursor into
560 the formula and use one of the shortcuts
568 Edit\SpecialChar menuseparator
569 Math\SpecialChar menuseparator
573 The same way is used to change an inline formula to a display style formula.
576 \begin_layout Standard
577 To display parts of an inline formula in the size of a display style formula,
585 \begin_inset Index idx
588 \begin_layout Plain Layout
597 Then a new blue box appears in which the desired formula part is inserted.
600 \begin_layout Standard
601 Only inline formulas are allowed inside tables.
604 \begin_layout Standard
609 can be turned on in the menu
611 View\SpecialChar menuseparator
615 When you click there on
616 \begin_inset Quotes eld
620 \begin_inset Quotes erd
623 the toolbar will be shown permanently at the bottom; this state is visualized
628 menu with a checkmark.
629 When you click in this state again on
630 \begin_inset Quotes eld
634 \begin_inset Quotes erd
645 is only shown when the cursor is within a formula; this state is visualized
646 by the renaming of the menu entry from
647 \begin_inset Quotes eld
651 \begin_inset Quotes erd
655 \begin_inset Quotes eld
663 \begin_inset Quotes erd
669 \begin_layout Standard
672 \begin_inset Index idx
675 \begin_layout Plain Layout
682 is invoked by pressing the toolbar button
690 Insert\SpecialChar menuseparator
702 \begin_layout Standard
703 To change the \SpecialChar LaTeX
705 \begin_inset Index idx
708 \begin_layout Plain Layout
717 Document\SpecialChar menuseparator
718 Settings\SpecialChar menuseparator
728 \begin_layout Standard
729 To edit matrices, case differentiations and multiline formulas subsequently,
732 Edit\SpecialChar menuseparator
737 Edit\SpecialChar menuseparator
739 \begin_inset space \thinspace{}
743 \begin_inset space \thinspace{}
753 When lines and columns are swapped via the menu, the column or line where
754 the cursor is in is exchanged with the column to the right or the line
756 Is the cursor in the last column or row, the exchange is done with the
757 column to the left or the line above.
760 \begin_layout Standard
761 To write text in formulas
765 \begin_layout Plain Layout
766 For multiline formulas the command
773 \begin_inset CommandInset ref
775 reference "subsec:Text-in-multiline"
789 \begin_inset Index idx
792 \begin_layout Plain Layout
799 \begin_inset Index idx
802 \begin_layout Plain Layout
809 This mode is invoked with the shortcut
815 or by the insertion of the command
822 \begin_inset Index idx
825 \begin_layout Plain Layout
834 The text appears black in \SpecialChar LyX
835 and can therefore be distinguished from the
836 other formula parts which appear blue.
837 In the output mathematical text is set upright, in contrary to other formula
841 \begin_layout Subsection*
845 \begin_layout Standard
846 Most of the \SpecialChar LaTeX
847 -commands for math constructs have the following scheme:
850 \begin_layout Standard
866 \begin_layout Standard
867 A command always starts with a backslash
868 \begin_inset Quotes gld
878 \begin_inset Quotes grd
882 To omit optional arguments, also omit the associated brackets.
883 The braces around the required arguments are named in this document as
886 \begin_inset Index idx
889 \begin_layout Plain Layout
897 If you add in a formula a left brace to a command name, \SpecialChar LyX
899 creates a \SpecialChar TeX
901 In all other cases \SpecialChar TeX
902 braces are created in formulas with the command
910 braces appear red in \SpecialChar LyX
911 , in contrary to normal braces which appear blue.
913 mode no command is needed to get \SpecialChar TeX
916 braces don't appear in the output.
919 \begin_layout Standard
920 When commands without arguments, like commands for symbols are entered in
922 mode, a space character must
926 be behind the command to end it.
927 This space doesn't appear in the output.
928 When the space should appear in the output, the space must be followed
929 by a protected space in normal text.
932 \begin_layout Standard
933 A protected space is inserted with
936 arg "command-alternatives space-insert protected ; math-space"
942 \begin_layout Subsection*
943 \begin_inset Newpage newpage
949 \begin_layout Itemize
951 \begin_inset space \textvisiblespace{}
954 denotes a space character to be input.
957 \begin_layout Itemize
959 \begin_inset Formula $\to$
962 denotes the usage of the corresponding arrow key on the keyboard.
967 key can often be used instead of
968 \begin_inset Formula $\to$
972 \begin_inset Formula $\downarrow$
980 \begin_inset Formula $\leftarrow$
984 \begin_inset Formula $\uparrow$
990 \begin_layout Subsection*
994 \begin_layout Standard
996 \begin_inset Float table
1003 \begin_layout Plain Layout
1005 \begin_inset Caption Standard
1007 \begin_layout Plain Layout
1008 \begin_inset CommandInset label
1010 name "tab:Available-units"
1022 \begin_layout Plain Layout
1024 \begin_inset Tabular
1025 <lyxtabular version="3" rows="13" columns="2">
1026 <features booktabs="true" tabularvalignment="middle">
1027 <column alignment="center" valignment="top">
1028 <column alignment="center" valignment="top" width="0pt">
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1033 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1042 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1053 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1062 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1104 \begin_inset space \thinspace{}
1108 \begin_inset space \thinspace{}
1118 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1121 \begin_layout Plain Layout
1127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1130 \begin_layout Plain Layout
1132 \begin_inset space \thinspace{}
1136 \begin_inset space \thinspace{}
1146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1149 \begin_layout Plain Layout
1155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1158 \begin_layout Plain Layout
1160 \begin_inset space \thinspace{}
1164 \begin_inset space \thinspace{}
1174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1177 \begin_layout Plain Layout
1183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1186 \begin_layout Plain Layout
1188 \begin_inset space \thinspace{}
1192 \begin_inset space \thinspace{}
1202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1205 \begin_layout Plain Layout
1211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1214 \begin_layout Plain Layout
1216 \begin_inset space \thinspace{}
1220 \begin_inset space \thinspace{}
1230 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1233 \begin_layout Plain Layout
1239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1242 \begin_layout Plain Layout
1244 \begin_inset space \thinspace{}
1248 \begin_inset Formula $\approx$
1252 \begin_inset space \thinspace{}
1262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1265 \begin_layout Plain Layout
1271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1274 \begin_layout Plain Layout
1276 \begin_inset space \thinspace{}
1280 \begin_inset space \thinspace{}
1290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1293 \begin_layout Plain Layout
1299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1302 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1312 \begin_inset Quotes erd
1322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1325 \begin_layout Plain Layout
1331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1334 \begin_layout Plain Layout
1336 \begin_inset Quotes eld
1344 \begin_inset Quotes erd
1354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1357 \begin_layout Plain Layout
1363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1366 \begin_layout Plain Layout
1368 \begin_inset space \thinspace{}
1372 \begin_inset Formula $\nicefrac{1}{18}$
1376 \begin_inset space \thinspace{}
1397 \begin_layout Standard
1398 \begin_inset Newpage newpage
1404 \begin_layout Section
1408 \begin_layout Subsection
1410 \begin_inset Index idx
1413 \begin_layout Plain Layout
1420 \begin_inset Index idx
1423 \begin_layout Plain Layout
1430 \begin_inset Index idx
1433 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1462 \begin_inset Index idx
1465 \begin_layout Plain Layout
1470 \begin_layout Plain Layout
1481 \begin_layout Plain Layout
1496 \begin_layout Standard
1497 Indices are created with an underscore
1498 \begin_inset Quotes eld
1502 \begin_inset Quotes erd
1505 or via the math toolbar button
1508 arg "math-subscript"
1511 , exponents with a caret
1512 \begin_inset Quotes eld
1516 \begin_inset Quotes erd
1519 or via the math toolbar button
1522 arg "math-superscript"
1528 \begin_layout Standard
1530 \begin_inset Tabular
1531 <lyxtabular version="3" rows="4" columns="2">
1532 <features booktabs="true" tabularvalignment="middle">
1533 <column alignment="center" valignment="top" width="0pt">
1534 <column alignment="center" valignment="top" width="0pt">
1536 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1539 \begin_layout Plain Layout
1545 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1548 \begin_layout Plain Layout
1556 <cell alignment="center" valignment="top" usebox="none">
1559 \begin_layout Plain Layout
1565 <cell alignment="center" valignment="top" usebox="none">
1568 \begin_layout Plain Layout
1569 \begin_inset Formula $B_{V}$
1578 <row topspace="1.5mm">
1579 <cell alignment="center" valignment="top" usebox="none">
1582 \begin_layout Plain Layout
1588 <cell alignment="center" valignment="top" usebox="none">
1591 \begin_layout Plain Layout
1592 \begin_inset Formula $B^{V}$
1601 <row topspace="1.5mm">
1602 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1605 \begin_layout Plain Layout
1607 \begin_inset space \textvisiblespace{}
1615 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1618 \begin_layout Plain Layout
1619 \begin_inset Formula $B^{A}$
1635 \begin_layout Standard
1636 As the caret is in some languages an accent, vowels will be accentuated
1637 in this case and not set as exponents
1641 \begin_layout Plain Layout
1642 Depending on the used keyboard settings this can also happen for characters
1649 To get exponents in this case, press
1653 after the caret as in the last example.
1656 \begin_layout Subsection
1658 \begin_inset CommandInset label
1660 name "subsec:Fractions"
1665 \begin_inset Index idx
1668 \begin_layout Plain Layout
1677 \begin_layout Standard
1678 Fractions are generated with the command
1685 \begin_inset Index idx
1688 \begin_layout Plain Layout
1696 or via the math toolbar button
1699 arg "math-insert \\frac"
1703 The font size is adjusted automatically, depending on whether the fraction
1704 is in an inline or display style formula.
1705 With the math toolbar button
1708 arg "math-insert \\frac-square"
1711 you can select different fraction types.
1714 \begin_layout Standard
1722 \begin_inset Index idx
1725 \begin_layout Plain Layout
1733 a fraction can be created that always has the size of a display style formula.
1741 \begin_inset Index idx
1744 \begin_layout Plain Layout
1752 the fraction appears always with the size of an inline formula.
1756 \begin_layout Standard
1757 A line with the fraction
1758 \begin_inset Formula $\frac{1}{2}$
1761 that was created with the command
1770 \begin_layout Standard
1771 A line with the fraction
1772 \begin_inset Formula $\dfrac{1}{2}$
1775 that was created with the command
1784 \begin_layout Standard
1786 \begin_inset Tabular
1787 <lyxtabular version="3" rows="4" columns="2">
1788 <features booktabs="true" tabularvalignment="middle">
1789 <column alignment="center" valignment="top" width="0pt">
1790 <column alignment="center" valignment="top" width="0pt">
1792 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1795 \begin_layout Plain Layout
1801 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1804 \begin_layout Plain Layout
1811 <row topspace="1.5mm">
1812 <cell alignment="center" valignment="top" usebox="none">
1815 \begin_layout Plain Layout
1819 \begin_inset space \textvisiblespace{}
1823 \begin_inset Formula $\downarrow$
1831 <cell alignment="center" valignment="top" usebox="none">
1834 \begin_layout Plain Layout
1835 \begin_inset Formula $\frac{A}{B}$
1844 <row topspace="2mm">
1845 <cell alignment="center" valignment="top" usebox="none">
1848 \begin_layout Plain Layout
1852 \begin_inset space \textvisiblespace{}
1856 \begin_inset Formula $\downarrow$
1864 <cell alignment="center" valignment="top" usebox="none">
1867 \begin_layout Plain Layout
1868 \begin_inset Formula $\dfrac{A}{B}$
1877 <row topspace="2mm" bottomspace="1mm">
1878 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1881 \begin_layout Plain Layout
1885 \begin_inset space \textvisiblespace{}
1891 \begin_inset space \textvisiblespace{}
1895 \begin_inset Formula $\downarrow$
1899 \begin_inset Formula $\downarrow\downarrow$
1907 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1910 \begin_layout Plain Layout
1911 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1927 \begin_layout Standard
1928 \begin_inset VSpace bigskip
1932 \begin_inset Newpage newpage
1935 For nested fractions the command
1942 \begin_inset Index idx
1945 \begin_layout Plain Layout
1955 \begin_inset VSpace -3mm
1961 \begin_layout Standard
1962 \begin_inset Formula
1964 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1965 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1973 \begin_layout Standard
1974 The command for the example above is:
1977 \begin_layout Standard
1983 \begin_inset space \textvisiblespace{}
1987 \begin_inset Formula $\downarrow$
1993 \begin_inset space \textvisiblespace{}
1999 \begin_inset space \textvisiblespace{}
2003 \begin_inset Formula $\downarrow$
2007 \begin_inset Formula $\downarrow$
2013 \begin_layout Standard
2014 \begin_inset VSpace medskip
2020 \begin_layout Standard
2027 sets the fraction always in the size of a displayed formula, also when
2028 it is part of another fraction.
2031 \begin_layout Standard
2032 It is possible to specify the alignment of the numerator.
2039 is used to left align it, the command
2052 centers the numerator.
2053 These fractions demonstrate the different alignments:
2056 \begin_layout Standard
2059 \begin_inset Formula
2061 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2069 \begin_layout Standard
2070 \begin_inset Note Greyedout
2073 \begin_layout Plain Layout
2090 are no real \SpecialChar LaTeX
2091 commands but represent the command
2095 cfrac[alignment]{numerator}{denominator}
2098 Therefore you cannot use them in \SpecialChar TeX
2107 \begin_layout Standard
2108 \begin_inset VSpace medskip
2111 It is often advantageous to combine
2124 \begin_inset Formula
2126 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2134 \begin_layout Standard
2135 For inline fractions with a sloped fraction stroke you can use the command
2143 \begin_inset Index idx
2146 \begin_layout Plain Layout
2155 \begin_inset Formula $\nicefrac{5}{31}$
2165 \begin_inset Index idx
2168 \begin_layout Plain Layout
2177 \begin_inset Formula $\unitfrac{5}{31}$
2180 There is furthermore the command
2186 that offers to write a fraction in combination with a number:
2187 \begin_inset Formula $\unitfrac[2]{1}{3}$
2193 \begin_layout Standard
2194 \begin_inset Note Greyedout
2197 \begin_layout Plain Layout
2208 is not a real \SpecialChar LaTeX
2209 command but the command
2210 \begin_inset Newline newline
2217 unitfrac[number]{numerator}{denominator}
2220 Therefore you cannot use it in \SpecialChar TeX
2229 \begin_layout Standard
2230 How to define own fractions where the fraction stroke can be changed, is
2232 \begin_inset CommandInset ref
2234 reference "subsec:Self-defined-Fractions"
2241 \begin_layout Standard
2242 Multiline fractions are explained in
2243 \begin_inset CommandInset ref
2245 reference "subsec:Multiline-Fractions"
2252 \begin_layout Subsection
2254 \begin_inset Index idx
2257 \begin_layout Plain Layout
2266 \begin_layout Standard
2267 Square roots are created with
2274 \begin_inset Index idx
2277 \begin_layout Plain Layout
2285 or the math toolbar button
2288 arg "math-insert \\sqrt"
2291 , all other roots with the command
2298 \begin_inset Index idx
2301 \begin_layout Plain Layout
2309 or with the math toolbar button
2312 arg "math-insert \\root"
2318 \begin_layout Standard
2320 \begin_inset Tabular
2321 <lyxtabular version="3" rows="3" columns="2">
2322 <features booktabs="true" tabularvalignment="middle">
2323 <column alignment="center" valignment="top" width="0pt">
2324 <column alignment="center" valignment="top" width="0pt">
2326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2329 \begin_layout Plain Layout
2335 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2338 \begin_layout Plain Layout
2345 <row topspace="1mm">
2346 <cell alignment="center" valignment="top" usebox="none">
2349 \begin_layout Plain Layout
2353 \begin_inset space \textvisiblespace{}
2361 <cell alignment="center" valignment="top" usebox="none">
2364 \begin_layout Plain Layout
2365 \begin_inset Formula $\sqrt{A-B}$
2374 <row topspace="1mm">
2375 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2378 \begin_layout Plain Layout
2382 \begin_inset space \textvisiblespace{}
2386 \begin_inset Formula $\downarrow$
2394 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2397 \begin_layout Plain Layout
2398 \begin_inset Formula $\sqrt[3]{A-B}$
2414 \begin_layout Standard
2415 A square root can also be created with
2421 when the root index field is left empty.
2424 \begin_layout Standard
2425 With certain indices the distance to the root is too small, like in this
2427 \begin_inset Formula $\sqrt[\beta]{B}$
2431 \begin_inset Newline newline
2435 \begin_inset Formula $\beta$
2439 To avoid this, the commands
2446 \begin_inset Index idx
2449 \begin_layout Plain Layout
2464 \begin_inset Index idx
2467 \begin_layout Plain Layout
2475 are used with the following scheme:
2478 \begin_layout Standard
2492 \begin_layout Standard
2493 Distance is the number of Big Points (unit bp;
2494 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2497 ), that the index should be moved to the left or top, resp..
2498 The commands are written to the index.
2499 This way the command
2500 \begin_inset Newline newline
2510 \begin_inset Formula $\to$
2516 \begin_inset Formula $\to$
2522 \begin_inset space \textvisiblespace{}
2526 \begin_inset Formula $\to$
2530 \begin_inset Newline newline
2535 produces a correct typeset formula:
2536 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2542 \begin_layout Subsection
2543 Binomial Coefficients
2544 \begin_inset Index idx
2547 \begin_layout Plain Layout
2548 Binomial coefficients
2556 \begin_layout Standard
2557 Binomial coefficients are inserted with the command
2564 \begin_inset Index idx
2567 \begin_layout Plain Layout
2575 or with the submenu of the math toolbar button
2578 arg "math-insert \\frac-square"
2594 there are the commands
2601 \begin_inset Index idx
2604 \begin_layout Plain Layout
2619 \begin_inset Index idx
2622 \begin_layout Plain Layout
2631 For other brackets around binomial coefficients there are the commands
2639 \begin_inset Index idx
2642 \begin_layout Plain Layout
2657 \begin_inset Index idx
2660 \begin_layout Plain Layout
2671 \begin_layout Standard
2673 \begin_inset Tabular
2674 <lyxtabular version="3" rows="6" columns="2">
2675 <features booktabs="true" tabularvalignment="middle">
2676 <column alignment="center" valignment="top" width="0pt">
2677 <column alignment="center" valignment="top" width="0pt">
2679 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2682 \begin_layout Plain Layout
2688 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2691 \begin_layout Plain Layout
2698 <row topspace="1mm">
2699 <cell alignment="center" valignment="top" usebox="none">
2702 \begin_layout Plain Layout
2706 \begin_inset space \textvisiblespace{}
2710 \begin_inset Formula $\downarrow$
2718 <cell alignment="center" valignment="top" usebox="none">
2721 \begin_layout Plain Layout
2722 \begin_inset Formula $\binom{A}{B}$
2731 <row topspace="2mm">
2732 <cell alignment="center" valignment="top" usebox="none">
2735 \begin_layout Plain Layout
2739 \begin_inset space \textvisiblespace{}
2743 \begin_inset Formula $\downarrow$
2751 <cell alignment="center" valignment="top" usebox="none">
2754 \begin_layout Plain Layout
2755 \begin_inset Formula $\dbinom{A}{B}$
2764 <row topspace="2mm" bottomspace="0.5mm">
2765 <cell alignment="center" valignment="top" usebox="none">
2768 \begin_layout Plain Layout
2772 \begin_inset space \textvisiblespace{}
2776 \begin_inset Formula $\downarrow$
2784 <cell alignment="center" valignment="top" usebox="none">
2787 \begin_layout Plain Layout
2788 \begin_inset Formula $\tbinom{A}{B}$
2797 <row topspace="1mm">
2798 <cell alignment="center" valignment="top" topline="true" usebox="none">
2801 \begin_layout Plain Layout
2805 \begin_inset space \textvisiblespace{}
2809 \begin_inset Formula $\downarrow$
2817 <cell alignment="center" valignment="top" topline="true" usebox="none">
2820 \begin_layout Plain Layout
2821 \begin_inset Formula ${A \brack B}$
2830 <row topspace="2mm" bottomspace="0.5mm">
2831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2834 \begin_layout Plain Layout
2838 \begin_inset space \textvisiblespace{}
2842 \begin_inset Formula $\downarrow$
2850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2853 \begin_layout Plain Layout
2854 \begin_inset Formula ${A \brace B}$
2870 \begin_layout Subsection
2871 Case Differentiations
2872 \begin_inset Index idx
2875 \begin_layout Plain Layout
2876 Case differentiations
2884 \begin_layout Standard
2886 \begin_inset Tabular
2887 <lyxtabular version="3" rows="3" columns="2">
2888 <features booktabs="true" tabularvalignment="middle">
2889 <column alignment="center" valignment="top" width="0pt">
2890 <column alignment="center" valignment="top" width="0pt">
2892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2895 \begin_layout Plain Layout
2901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2904 \begin_layout Plain Layout
2912 <cell alignment="center" valignment="top" usebox="none">
2915 \begin_layout Plain Layout
2919 \begin_inset space \textvisiblespace{}
2923 \begin_inset Formula $\to$
2927 \begin_inset Index idx
2930 \begin_layout Plain Layout
2943 <cell alignment="center" valignment="top" usebox="none">
2946 \begin_layout Plain Layout
2947 \begin_inset Formula $\begin{cases}
2957 <row topspace="1.5mm">
2958 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2961 \begin_layout Plain Layout
2965 \begin_inset space \textvisiblespace{}
2971 arg "newline-insert newline"
2979 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2982 \begin_layout Plain Layout
2983 \begin_inset Formula $\begin{cases}
2984 A & \textrm{for }x>0\\
2985 B & \textrm{for }x=0
3002 \begin_layout Standard
3009 or pressing the math toolbar button
3012 arg "math-insert \\cases"
3015 you can create new lines with the shortcut
3018 arg "newline-insert newline"
3021 or the table toolbar button
3024 arg "tabular-feature append-row"
3030 \begin_layout Standard
3037 is also available via the menu
3039 Insert\SpecialChar menuseparator
3040 Math\SpecialChar menuseparator
3046 \begin_layout Subsection
3048 \begin_inset Index idx
3051 \begin_layout Plain Layout
3060 \begin_layout Standard
3068 \begin_inset Index idx
3071 \begin_layout Plain Layout
3079 every character can be displayed canceled.
3080 The characters are quasi accentuated by a slash.
3083 \begin_layout Standard
3085 \begin_inset Tabular
3086 <lyxtabular version="3" rows="4" columns="2">
3087 <features booktabs="true" tabularvalignment="middle">
3088 <column alignment="center" valignment="top" width="0pt">
3089 <column alignment="center" valignment="top" width="0pt">
3091 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3094 \begin_layout Plain Layout
3100 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3103 \begin_layout Plain Layout
3111 <cell alignment="center" valignment="top" usebox="none">
3114 \begin_layout Plain Layout
3122 <cell alignment="center" valignment="top" usebox="none">
3125 \begin_layout Plain Layout
3126 \begin_inset Formula $\not=$
3136 <cell alignment="center" valignment="top" usebox="none">
3139 \begin_layout Plain Layout
3149 <cell alignment="center" valignment="top" usebox="none">
3152 \begin_layout Plain Layout
3153 \begin_inset Formula $\not\le$
3163 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3166 \begin_layout Plain Layout
3176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3179 \begin_layout Plain Layout
3180 \begin_inset Formula $\not\parallel$
3196 \begin_layout Standard
3197 The last example shows that not all negations look good.
3198 Therefore there are special commands for some negations (see
3199 \begin_inset CommandInset ref
3201 reference "subsec:Mathematical-Symbols"
3206 \begin_inset CommandInset ref
3208 reference "sec:Relations"
3215 \begin_layout Subsection
3217 \begin_inset CommandInset label
3219 name "subsec:Placeholders"
3224 \begin_inset Index idx
3227 \begin_layout Plain Layout
3234 \begin_inset Index idx
3237 \begin_layout Plain Layout
3238 Chemical characters ! Isotopes
3244 \begin_inset Index idx
3247 \begin_layout Plain Layout
3252 \begin_layout Plain Layout
3263 \begin_layout Plain Layout
3278 \begin_layout Standard
3280 \begin_inset space \thinspace{}
3284 \begin_inset space \space{}
3291 \begin_layout Plain Layout
3292 Typesetting isotopes and chemical symbols is described in
3293 \begin_inset CommandInset ref
3295 reference "subsec:Chemical-Symbols-and"
3304 the following problem occurs:
3307 \begin_layout Standard
3309 \begin_inset Tabular
3310 <lyxtabular version="3" rows="2" columns="2">
3311 <features booktabs="true" tabularvalignment="middle">
3312 <column alignment="center" valignment="top" width="0pt">
3313 <column alignment="center" valignment="top" width="0pt">
3315 <cell alignment="center" valignment="top" usebox="none">
3318 \begin_layout Plain Layout
3319 Indices created with sub- and superscripts:
3324 <cell alignment="center" valignment="top" usebox="none">
3327 \begin_layout Plain Layout
3328 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3337 <row topspace="1.5mm">
3338 <cell alignment="center" valignment="top" usebox="none">
3341 \begin_layout Plain Layout
3347 <cell alignment="center" valignment="top" usebox="none">
3350 \begin_layout Plain Layout
3351 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3367 \begin_layout Standard
3368 The shorter index is by default placed below or above the first character
3369 of the longer index.
3370 To avoid this there is the command
3377 \begin_inset Index idx
3380 \begin_layout Plain Layout
3388 or the math toolbar button
3389 \begin_inset space \thinspace{}
3396 \begin_layout Plain Layout
3397 can be found in the submenu of the toolbar button
3400 arg "math-insert \\space"
3414 that creates one or more phantom characters.
3421 a small blue box appears that is superposed with two red arrows.
3422 The arrows indicate that the complete width and height of the box content
3423 will be created as placeholder.
3424 Phantom characters are accordingly placeholders with the size of the characters.
3427 \begin_layout Standard
3429 \begin_inset Tabular
3430 <lyxtabular version="3" rows="4" columns="2">
3431 <features booktabs="true" tabularvalignment="middle">
3432 <column alignment="center" valignment="top" width="0pt">
3433 <column alignment="center" valignment="top" width="0pt">
3435 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3438 \begin_layout Plain Layout
3444 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3447 \begin_layout Plain Layout
3454 <row topspace="1.5mm">
3455 <cell alignment="center" valignment="top" usebox="none">
3458 \begin_layout Plain Layout
3460 \begin_inset space \textvisiblespace{}
3466 \begin_inset space \textvisiblespace{}
3470 \begin_inset Formula $\to$
3474 \begin_inset space \textvisiblespace{}
3482 <cell alignment="center" valignment="top" usebox="none">
3485 \begin_layout Plain Layout
3486 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3495 <row topspace="1.5mm" bottomspace="0.5mm">
3496 <cell alignment="center" valignment="top" usebox="none">
3499 \begin_layout Plain Layout
3501 \begin_inset space \textvisiblespace{}
3507 \begin_inset space \textvisiblespace{}
3511 \begin_inset Formula $\to$
3515 \begin_inset space \textvisiblespace{}
3523 <cell alignment="center" valignment="top" usebox="none">
3526 \begin_layout Plain Layout
3527 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3536 <row topspace="1.5mm" bottomspace="0.5mm">
3537 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3540 \begin_layout Plain Layout
3544 \begin_inset space \textvisiblespace{}
3550 \begin_inset space \textvisiblespace{}
3554 \begin_inset Formula $\to$
3558 \begin_inset space \textvisiblespace{}
3566 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3569 \begin_layout Plain Layout
3570 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3586 \begin_layout Standard
3587 Furthermore there are the commands
3594 \begin_inset Index idx
3597 \begin_layout Plain Layout
3618 \begin_inset Index idx
3621 \begin_layout Plain Layout
3642 creates only space for the maximal height of the characters in the box
3643 but not for its width.
3650 creates only space for the width of the box content.
3651 Therefore the boxes of both commands have only one red arrow.
3654 \begin_layout Standard
3655 For example the command
3660 \begin_inset space \textvisiblespace{}
3667 creates space for the height of the integral sign,
3671 \begin_layout Plain Layout
3678 creates an integral sign, see
3679 \begin_inset CommandInset ref
3681 reference "subsec:Big-Operators"
3690 because this is the larger character.
3691 An example application is in
3692 \begin_inset CommandInset ref
3694 reference "subsec:Multiline-Brackets"
3701 \begin_layout Standard
3702 Placeholders can also be used for text when they are inserted via the menu
3705 Insert\SpecialChar menuseparator
3706 Formatting\SpecialChar menuseparator
3712 \begin_layout Standard
3714 \begin_inset Newline newline
3718 \begin_inset Phantom Phantom
3721 \begin_layout Plain Layout
3730 \begin_layout Subsection
3732 \begin_inset Index idx
3735 \begin_layout Plain Layout
3742 \begin_inset Index idx
3745 \begin_layout Plain Layout
3746 Formula ! underlined
3754 \begin_layout Standard
3756 \begin_inset Tabular
3757 <lyxtabular version="3" rows="4" columns="2">
3758 <features booktabs="true" tabularvalignment="middle">
3759 <column alignment="center" valignment="top" width="0pt">
3760 <column alignment="center" valignment="top" width="0pt">
3762 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3765 \begin_layout Plain Layout
3771 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3774 \begin_layout Plain Layout
3781 <row topspace="2mm">
3782 <cell alignment="center" valignment="top" usebox="none">
3785 \begin_layout Plain Layout
3789 \begin_inset space \textvisiblespace{}
3793 \begin_inset Index idx
3796 \begin_layout Plain Layout
3809 <cell alignment="center" valignment="top" usebox="none">
3812 \begin_layout Plain Layout
3813 \begin_inset Formula $\overline{A+B}$
3822 <row bottomspace="1mm">
3823 <cell alignment="center" valignment="top" usebox="none">
3826 \begin_layout Plain Layout
3830 \begin_inset space \textvisiblespace{}
3834 \begin_inset Index idx
3837 \begin_layout Plain Layout
3850 <cell alignment="center" valignment="top" usebox="none">
3853 \begin_layout Plain Layout
3854 \begin_inset Formula $\underline{A+B}$
3863 <row topspace="2mm" bottomspace="1mm">
3864 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3867 \begin_layout Plain Layout
3871 \begin_inset space \textvisiblespace{}
3877 \begin_inset space \textvisiblespace{}
3885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3888 \begin_layout Plain Layout
3889 \begin_inset Formula $\overline{\underline{A+B}}$
3905 \begin_layout Standard
3906 In the last example it doesn't matter if first
3921 \begin_layout Standard
3922 To double underline use
3931 \begin_layout Standard
3932 It is possible to place up to 6 lines above or below characters.
3935 \begin_layout Standard
3936 \begin_inset VSpace bigskip
3939 Custom lines can be created using the command
3946 \begin_inset Index idx
3949 \begin_layout Plain Layout
3957 which has the following scheme:
3960 \begin_layout Standard
3965 rule[vertical offset]{length}{thickness}
3968 \begin_layout Standard
3969 The optional vertical offset shifts the line upwards (or downwards, when
3970 the value is negative).
3972 \begin_inset CommandInset ref
3974 reference "tab:Available-units"
3978 can be used for the values.
3979 Here are two example lines created with the commands
3980 \begin_inset Newline newline
3987 rule[-2ex]{3cm}{2pt}
3998 \begin_layout Standard
4000 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4006 \begin_layout Standard
4013 can also be used for text when a line is inserted via the menu
4015 Insert\SpecialChar menuseparator
4016 Formatting\SpecialChar menuseparator
4018 \begin_inset space ~
4026 \begin_layout Standard
4028 \begin_inset CommandInset line
4039 \begin_layout Subsection
4041 \begin_inset CommandInset label
4043 name "subsec:Ellipses"
4048 \begin_inset Index idx
4051 \begin_layout Plain Layout
4060 \begin_layout Standard
4061 There are different types of ellipses available.
4065 \begin_layout Plain Layout
4066 In the math toolbar in the submenu of the button
4069 arg "math-insert \\ldots"
4077 For listings dots at the baseline are used (
4084 \begin_inset Index idx
4087 \begin_layout Plain Layout
4095 ), while for operations dots are needed that are on the same height as the
4103 \begin_inset Index idx
4106 \begin_layout Plain Layout
4115 When using the command
4122 \begin_inset Index idx
4125 \begin_layout Plain Layout
4133 , \SpecialChar LaTeX
4134 decides on the basis of the next character what type is used.
4137 \begin_layout Standard
4139 \begin_inset Tabular
4140 <lyxtabular version="3" rows="9" columns="2">
4141 <features booktabs="true" tabularvalignment="middle">
4142 <column alignment="center" valignment="top" width="0pt">
4143 <column alignment="center" valignment="top" width="0pt">
4145 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4148 \begin_layout Plain Layout
4154 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4157 \begin_layout Plain Layout
4165 <cell alignment="center" valignment="top" usebox="none">
4168 \begin_layout Plain Layout
4170 \begin_inset space \textvisiblespace{}
4176 \begin_inset space \textvisiblespace{}
4184 <cell alignment="center" valignment="top" usebox="none">
4187 \begin_layout Plain Layout
4188 \begin_inset Formula $A_{1},\dots,A_{n}$
4198 <cell alignment="center" valignment="top" usebox="none">
4201 \begin_layout Plain Layout
4203 \begin_inset space \textvisiblespace{}
4209 \begin_inset space \textvisiblespace{}
4217 <cell alignment="center" valignment="top" usebox="none">
4220 \begin_layout Plain Layout
4221 \begin_inset Formula $A_{1}+\dots+A_{n}$
4231 <cell alignment="center" valignment="top" usebox="none">
4234 \begin_layout Plain Layout
4236 \begin_inset space \textvisiblespace{}
4242 \begin_inset space \textvisiblespace{}
4250 <cell alignment="center" valignment="top" usebox="none">
4253 \begin_layout Plain Layout
4254 \begin_inset Formula $A_{1},\ldots,A_{n}$
4264 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4267 \begin_layout Plain Layout
4269 \begin_inset space \textvisiblespace{}
4275 \begin_inset space \textvisiblespace{}
4283 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4286 \begin_layout Plain Layout
4287 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4297 <cell alignment="center" valignment="top" usebox="none">
4300 \begin_layout Plain Layout
4308 <cell alignment="center" valignment="top" usebox="none">
4311 \begin_layout Plain Layout
4312 \begin_inset Formula $\vdots$
4322 <cell alignment="center" valignment="top" usebox="none">
4325 \begin_layout Plain Layout
4333 <cell alignment="center" valignment="top" usebox="none">
4336 \begin_layout Plain Layout
4337 \begin_inset Formula $\ddots$
4347 <cell alignment="center" valignment="top" usebox="none">
4350 \begin_layout Plain Layout
4358 <cell alignment="center" valignment="top" usebox="none">
4361 \begin_layout Plain Layout
4362 \begin_inset Formula $\iddots$
4372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4375 \begin_layout Plain Layout
4377 \begin_inset space \thinspace{}
4380 matrix with the different dots
4385 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4388 \begin_layout Plain Layout
4389 \begin_inset Formula $\begin{array}{ccc}
4390 A_{11} & \cdots & A_{1m}\\
4391 \vdots & \ddots & \vdots\\
4392 A_{n1} & \cdots & A_{nm}
4409 \begin_layout Standard
4410 The ellipses available in menu
4412 Insert\SpecialChar menuseparator
4414 \begin_inset space ~
4428 \begin_layout Standard
4429 \begin_inset VSpace medskip
4438 , one of the options
4440 Use mathdots package (automatically)
4442 must be set in the document settings under
4445 \begin_inset space ~
4451 \begin_inset Newline newline
4456 Use mathdots package
4458 will improve the appearance of all dots in the documents if their font
4459 style or size is not the default.
4462 \begin_layout Standard
4463 \begin_inset VSpace medskip
4466 Specially for matrices there are ellipses that span over several columns.
4467 They are created with the command
4474 \begin_inset Index idx
4477 \begin_layout Plain Layout
4485 , that has the following scheme:
4488 \begin_layout Standard
4493 hdotsfor[distance]{number of columns}
4496 \begin_layout Standard
4497 The number of columns specifies how many columns should be spanned.
4498 Distance is a factor for the distance between the dots.
4501 \begin_layout Standard
4502 In the following matrix the command
4508 was inserted in the first box of the second line, to get an ellipsis with
4509 a dot distance twice as long as with the command
4516 \begin_inset Formula
4518 \left(\begin{array}{cccc}
4527 Note that the matrix fields that should be spanned must be empty, otherwise
4528 you get \SpecialChar LaTeX
4532 \begin_layout Standard
4533 \begin_inset VSpace bigskip
4536 Furthermore you can fill with the command
4543 \begin_inset Index idx
4546 \begin_layout Plain Layout
4554 the rest of a line with dots.
4555 The effect of these commands is the same as with
4562 \begin_inset CommandInset ref
4564 reference "subsec:Variable-Space"
4571 \begin_layout Standard
4572 For example the command
4577 \begin_inset space \textvisiblespace{}
4585 \begin_layout Standard
4586 \begin_inset Formula $A\dotfill B$
4592 \begin_layout Standard
4599 there is for a line the command
4606 \begin_inset Index idx
4609 \begin_layout Plain Layout
4620 \begin_layout Standard
4621 \begin_inset Formula $A\hrulefill B$
4627 \begin_layout Standard
4628 To use the commands for text, they have to be inserted in \SpecialChar TeX
4632 \begin_layout Section
4634 \begin_inset CommandInset label
4641 \begin_inset Index idx
4644 \begin_layout Plain Layout
4653 \begin_layout Standard
4654 Matrices can be inserted via the math toolbar button
4657 arg "dialog-show mathmatrix"
4662 Insert\SpecialChar menuseparator
4663 Math\SpecialChar menuseparator
4667 In the matrix dialog you can specify the number of columns and rows, the
4668 alignment and the decoration.
4669 The vertical alignment is only of importance for matrices in inline formulas:
4672 \begin_layout Standard
4673 The first matrix is top
4674 \begin_inset Formula $\begin{array}[t]{cccc}
4682 \begin_inset Formula $\begin{array}{cccc}
4689 and the third bottom
4690 \begin_inset Formula $\begin{array}[b]{cccc}
4700 \begin_layout Standard
4701 The horizontal alignment specifies how the column entries should be aligned.
4702 It is set by entering a letter for every column.
4707 denotes left aligned,
4716 To create for example a 4
4721 \begin_inset space ~
4724 matrix where the first column is left aligned, the second and third are
4725 centered and the last one is right aligned, one enters for the horizontal
4731 Normally in a matrix all columns are centered, therefore the default for
4739 \begin_layout Standard
4740 Horizontal alignment:
4743 \begin_layout Standard
4749 \begin_inset Formula $\begin{array}{lll}
4761 \begin_inset Formula $\begin{array}{ccc}
4773 \begin_inset Formula $\begin{array}{rrr}
4783 \begin_layout Standard
4784 To add or delete rows and columns subsequently, the math toolbar buttons
4788 arg "tabular-feature append-row"
4794 arg "tabular-feature delete-row"
4798 \begin_inset space \thinspace{}
4803 Edit\SpecialChar menuseparator
4807 New rows can also be created with
4810 arg "newline-insert newline"
4816 \begin_layout Standard
4817 \begin_inset VSpace bigskip
4821 \change_deleted 47243155 1563226130
4823 \change_deleted -563046850 1563190969
4827 \change_inserted -563046850 1563190971
4833 \change_deleted -563046850 1563192602
4835 \change_inserted -563046850 1563192607
4838 parentheses in the selected style around the matrix
4839 \change_inserted -563046850 1563192780
4844 style, suitable for an inline matrix like this one
4845 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
4847 \end{smallmatrix}\bigr)$
4854 \change_inserted -563046850 1563192943
4855 Here the parentheses have been added manually using commands
4868 \begin_layout Standard
4870 \change_deleted -563046850 1563192735
4873 Alternatively, parentheses can can
4874 \change_deleted -563046850 1563192971
4877 be created with the commands
4884 \begin_inset Index idx
4887 \begin_layout Plain Layout
4902 \begin_inset Index idx
4905 \begin_layout Plain Layout
4916 \begin_inset space ~
4922 \begin_inset CommandInset ref
4924 reference "subsec:Automatic-Bracket-Size"
4928 , or by using the following commands:
4929 \begin_inset VSpace medskip
4935 \begin_layout Standard
4936 \begin_inset space \hfill{}
4940 \begin_inset Tabular
4941 <lyxtabular version="3" rows="4" columns="2">
4942 <features booktabs="true" tabularvalignment="middle">
4943 <column alignment="center" valignment="top" width="0pt">
4944 <column alignment="center" valignment="top">
4946 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4949 \begin_layout Plain Layout
4955 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4958 \begin_layout Plain Layout
4965 <row topspace="1.5mm">
4966 <cell alignment="center" valignment="top" usebox="none">
4969 \begin_layout Plain Layout
4973 \begin_inset space \textvisiblespace{}
4981 \begin_inset space \thinspace{}
4989 <cell alignment="center" valignment="top" usebox="none">
4992 \begin_layout Plain Layout
4993 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4994 0 & \textrm{-}\mathrm{i}\\
4996 \end{array}\end{bmatrix}$
5005 <row topspace="1.5mm" bottomspace="0.5mm">
5006 <cell alignment="center" valignment="top" usebox="none">
5009 \begin_layout Plain Layout
5013 \begin_inset space \textvisiblespace{}
5021 \begin_inset space \thinspace{}
5029 <cell alignment="center" valignment="top" usebox="none">
5032 \begin_layout Plain Layout
5033 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5034 0 & \textrm{-}\mathrm{i}\\
5036 \end{array}\end{Bmatrix}$
5046 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5049 \begin_layout Plain Layout
5053 \begin_inset space \textvisiblespace{}
5061 \begin_inset space \thinspace{}
5069 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5072 \begin_layout Plain Layout
5073 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5074 0 & \textrm{-}\mathrm{i}\\
5076 \end{array}\end{pmatrix}$
5090 \begin_inset space \hfill{}
5094 \begin_inset Tabular
5095 <lyxtabular version="3" rows="4" columns="2">
5096 <features booktabs="true" tabularvalignment="middle">
5097 <column alignment="center" valignment="top" width="0pt">
5098 <column alignment="center" valignment="top">
5100 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5103 \begin_layout Plain Layout
5109 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5112 \begin_layout Plain Layout
5119 <row topspace="1.5mm">
5120 <cell alignment="center" valignment="top" usebox="none">
5123 \begin_layout Plain Layout
5127 \begin_inset space \textvisiblespace{}
5135 \begin_inset space \thinspace{}
5143 <cell alignment="center" valignment="top" usebox="none">
5146 \begin_layout Plain Layout
5147 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5148 0 & \textrm{-}\mathrm{i}\\
5150 \end{array}\end{vmatrix}$
5159 <row topspace="1.5mm" bottomspace="0.5mm">
5160 <cell alignment="center" valignment="top" usebox="none">
5163 \begin_layout Plain Layout
5167 \begin_inset space \textvisiblespace{}
5175 \begin_inset space \thinspace{}
5183 <cell alignment="center" valignment="top" usebox="none">
5186 \begin_layout Plain Layout
5187 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5188 0 & \textrm{-}\mathrm{i}\\
5190 \end{array}\end{Vmatrix}$
5200 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5203 \begin_layout Plain Layout
5207 \begin_inset space \textvisiblespace{}
5215 \begin_inset space \thinspace{}
5223 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5226 \begin_layout Plain Layout
5227 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5228 0 & \textrm{-}\mathrm{i}\\
5230 \end{array}\end{matrix}$
5244 \begin_inset space \hfill{}
5250 \begin_layout Standard
5251 \begin_inset VSpace medskip
5255 \begin_inset space \thinspace{}
5259 \begin_inset space \space{}
5268 is inserted, a blue box appears between two vertical lines where the matrix
5270 \begin_inset Newline newline
5273 Note that decorated matrices ignore the vertical alignment.
5276 \begin_layout Standard
5277 \begin_inset VSpace bigskip
5280 As all multiline formulas are matrices, the length
5287 \begin_inset Index idx
5290 \begin_layout Plain Layout
5298 that is described in
5299 \begin_inset CommandInset ref
5301 reference "subsec:Column-Separation"
5305 can also be used to change the column separation of matrices.
5308 \begin_layout Standard
5309 To change the row separation, the command
5316 \begin_inset Index idx
5319 \begin_layout Plain Layout
5328 It is used as follows:
5331 \begin_layout Standard
5338 arraystretch}{stretch factor}
5339 \begin_inset Index idx
5342 \begin_layout Plain Layout
5353 \begin_layout Standard
5360 assigns the stretch factor to the predefined command
5368 \begin_inset space \thinspace{}
5372 \begin_inset space \space{}
5375 the row separation, use the factor 2.
5376 This is then used for all following matrices.
5377 To go back to the original separation, assign the factor 1 to
5386 \begin_layout Standard
5388 \change_inserted 47243155 1563226178
5389 Small inline matrices can also be obtained using
5390 \change_deleted 47243155 1563226182
5391 To set matrices into a text line,
5400 \begin_inset Index idx
5403 \begin_layout Plain Layout
5412 \change_deleted 47243155 1563226186
5416 When it is inserted a blue box with two dashed lines appears.
5417 In this box the matrix is inserted.
5420 \begin_layout Standard
5422 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5424 \end{smallmatrix}\right)$
5428 \change_inserted 47243155 1563226243
5429 with automatic delimiters around it
5434 \begin_layout Section
5435 Brackets and Delimiters
5436 \begin_inset Index idx
5439 \begin_layout Plain Layout
5446 \begin_inset Index idx
5449 \begin_layout Plain Layout
5458 \begin_layout Subsection
5459 Vertical Brackets and Delimiters
5460 \begin_inset Index idx
5463 \begin_layout Plain Layout
5472 \begin_layout Standard
5473 \begin_inset space \hfill{}
5477 \begin_inset Tabular
5478 <lyxtabular version="3" rows="9" columns="2">
5479 <features booktabs="true" tabularvalignment="middle">
5480 <column alignment="center" valignment="top" width="0pt">
5481 <column alignment="center" valignment="top" width="0pt">
5483 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5486 \begin_layout Plain Layout
5492 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5495 \begin_layout Plain Layout
5503 <cell alignment="center" valignment="top" usebox="none">
5506 \begin_layout Plain Layout
5512 <cell alignment="center" valignment="top" usebox="none">
5515 \begin_layout Plain Layout
5516 \begin_inset Formula $($
5526 <cell alignment="center" valignment="top" usebox="none">
5529 \begin_layout Plain Layout
5535 <cell alignment="center" valignment="top" usebox="none">
5538 \begin_layout Plain Layout
5539 \begin_inset Formula $\{$
5549 <cell alignment="center" valignment="top" usebox="none">
5552 \begin_layout Plain Layout
5558 <cell alignment="center" valignment="top" usebox="none">
5561 \begin_layout Plain Layout
5562 \begin_inset Formula $[$
5572 <cell alignment="center" valignment="top" usebox="none">
5575 \begin_layout Plain Layout
5583 <cell alignment="center" valignment="top" usebox="none">
5586 \begin_layout Plain Layout
5587 \begin_inset Formula $\langle$
5597 <cell alignment="center" valignment="top" usebox="none">
5600 \begin_layout Plain Layout
5608 <cell alignment="center" valignment="top" usebox="none">
5611 \begin_layout Plain Layout
5612 \begin_inset Formula $\lceil$
5622 <cell alignment="center" valignment="top" usebox="none">
5625 \begin_layout Plain Layout
5633 <cell alignment="center" valignment="top" usebox="none">
5636 \begin_layout Plain Layout
5637 \begin_inset Formula $\lfloor$
5647 <cell alignment="center" valignment="top" usebox="none">
5650 \begin_layout Plain Layout
5656 <cell alignment="center" valignment="top" usebox="none">
5659 \begin_layout Plain Layout
5660 \begin_inset Formula $/$
5670 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5673 \begin_layout Plain Layout
5679 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5682 \begin_layout Plain Layout
5683 \begin_inset Formula $|$
5697 \begin_inset space \hfill{}
5701 \begin_inset Tabular
5702 <lyxtabular version="3" rows="9" columns="2">
5703 <features booktabs="true" tabularvalignment="middle">
5704 <column alignment="center" valignment="top" width="0pt">
5705 <column alignment="center" valignment="top" width="0pt">
5707 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5710 \begin_layout Plain Layout
5716 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5719 \begin_layout Plain Layout
5727 <cell alignment="center" valignment="top" usebox="none">
5730 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $)$
5750 <cell alignment="center" valignment="top" usebox="none">
5753 \begin_layout Plain Layout
5759 <cell alignment="center" valignment="top" usebox="none">
5762 \begin_layout Plain Layout
5763 \begin_inset Formula $\}$
5773 <cell alignment="center" valignment="top" usebox="none">
5776 \begin_layout Plain Layout
5782 <cell alignment="center" valignment="top" usebox="none">
5785 \begin_layout Plain Layout
5786 \begin_inset Formula $]$
5796 <cell alignment="center" valignment="top" usebox="none">
5799 \begin_layout Plain Layout
5807 <cell alignment="center" valignment="top" usebox="none">
5810 \begin_layout Plain Layout
5811 \begin_inset Formula $\rangle$
5821 <cell alignment="center" valignment="top" usebox="none">
5824 \begin_layout Plain Layout
5832 <cell alignment="center" valignment="top" usebox="none">
5835 \begin_layout Plain Layout
5836 \begin_inset Formula $\rceil$
5846 <cell alignment="center" valignment="top" usebox="none">
5849 \begin_layout Plain Layout
5857 <cell alignment="center" valignment="top" usebox="none">
5860 \begin_layout Plain Layout
5861 \begin_inset Formula $\rfloor$
5871 <cell alignment="center" valignment="top" usebox="none">
5874 \begin_layout Plain Layout
5884 <cell alignment="center" valignment="top" usebox="none">
5887 \begin_layout Plain Layout
5888 \begin_inset Formula $\backslash$
5898 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5901 \begin_layout Plain Layout
5909 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5912 \begin_layout Plain Layout
5913 \begin_inset Formula $\|$
5927 \begin_inset space \hfill{}
5933 \begin_layout Standard
5936 \begin_inset Note Greyedout
5939 \begin_layout Plain Layout
5952 \begin_inset Index idx
5955 \begin_layout Plain Layout
5963 must be used for the backslash, because the command
5971 produces a line break there.
5979 \begin_layout Standard
5980 For all characters listed above the size can be adjusted with the commands
5981 described in the following two subsections.
5982 When using these commands, the characters < and > can directly be used
5983 instead of the commands
5998 \begin_layout Subsubsection
6000 \begin_inset CommandInset label
6002 name "subsec:Manual-Bracket-Size"
6007 \begin_inset Index idx
6010 \begin_layout Plain Layout
6011 Bracket size ! manual
6019 \begin_layout Standard
6020 The bracket size can be specified manually by the \SpecialChar LaTeX
6028 \begin_inset Index idx
6031 \begin_layout Plain Layout
6064 denotes the smallest and
6070 the largest bracket size.
6073 \begin_layout Standard
6074 These commands are used to emphasize levels of brackets:
6077 \begin_layout Standard
6079 \begin_inset Tabular
6080 <lyxtabular version="3" rows="2" columns="2">
6081 <features booktabs="true" tabularvalignment="middle">
6082 <column alignment="center" valignment="top" width="0pt">
6083 <column alignment="center" valignment="top" width="0pt">
6085 <cell alignment="center" valignment="top" usebox="none">
6088 \begin_layout Plain Layout
6089 all brackets in the same size:
6094 <cell alignment="center" valignment="top" usebox="none">
6097 \begin_layout Plain Layout
6098 \begin_inset Formula $((A+B)(A-B))^{C}$
6107 <row topspace="2mm">
6108 <cell alignment="center" valignment="top" usebox="none">
6111 \begin_layout Plain Layout
6117 <cell alignment="center" valignment="top" usebox="none">
6120 \begin_layout Plain Layout
6121 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6137 \begin_layout Standard
6138 For the second formula the command
6145 \begin_inset space \textvisiblespace{}
6153 \begin_layout Standard
6154 Here is an overview about all bracket sizes:
6157 \begin_layout Standard
6174 \begin_inset space \textvisiblespace{}
6182 \begin_inset space \textvisiblespace{}
6186 \begin_inset space \textvisiblespace{}
6196 \begin_layout Standard
6198 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6204 \begin_layout Standard
6211 -commands there is the variant
6218 \begin_inset Index idx
6221 \begin_layout Plain Layout
6229 that adds a bit more space between the bracket and its content, and the
6243 \begin_inset Index idx
6246 \begin_layout Plain Layout
6256 , that don't add additional space.
6261 at the end of the command
6267 is for a left bracket; for a right bracket this will be replaced by an
6273 A left or right bracket can each be an opening or closing bracket.
6276 \begin_layout Standard
6277 In the following table is a comparison of the variants:
6280 \begin_layout Standard
6282 \begin_inset Tabular
6283 <lyxtabular version="3" rows="5" columns="2">
6284 <features booktabs="true" tabularvalignment="middle">
6285 <column alignment="center" valignment="top" width="0pt">
6286 <column alignment="center" valignment="middle">
6288 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6291 \begin_layout Plain Layout
6297 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6300 \begin_layout Plain Layout
6307 <row topspace="2mm">
6308 <cell alignment="center" valignment="top" usebox="none">
6311 \begin_layout Plain Layout
6321 \begin_inset space \textvisiblespace{}
6331 <cell alignment="center" valignment="top" usebox="none">
6334 \begin_layout Plain Layout
6335 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6344 <row topspace="2mm">
6345 <cell alignment="center" valignment="top" usebox="none">
6348 \begin_layout Plain Layout
6358 \begin_inset space \textvisiblespace{}
6368 <cell alignment="center" valignment="top" usebox="none">
6371 \begin_layout Plain Layout
6372 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6381 <row topspace="2mm" bottomspace="0.5mm">
6382 <cell alignment="center" valignment="top" usebox="none">
6385 \begin_layout Plain Layout
6395 \begin_inset space \textvisiblespace{}
6405 <cell alignment="center" valignment="top" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6418 <row topspace="1.5mm" bottomspace="0.5mm">
6419 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6422 \begin_layout Plain Layout
6434 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6437 \begin_layout Plain Layout
6438 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6454 \begin_layout Subsubsection
6455 Automatic Bracket Size
6456 \begin_inset CommandInset label
6458 name "subsec:Automatic-Bracket-Size"
6463 \begin_inset Index idx
6466 \begin_layout Plain Layout
6467 Bracket size ! automatic
6475 \begin_layout Standard
6476 Brackets with variable size can be inserted with the commands
6483 \begin_inset Index idx
6486 \begin_layout Plain Layout
6501 \begin_inset Index idx
6504 \begin_layout Plain Layout
6512 or via the math toolbar button
6515 arg "dialog-show mathdelimiter"
6531 the wanted bracket must be inserted.
6532 The bracket size will then automatically be calculated for the output.
6535 \begin_layout Standard
6537 normal bracket: The command
6544 \begin_inset space \textvisiblespace{}
6548 \begin_inset Formula $\downarrow$
6552 \begin_inset space \textvisiblespace{}
6558 \begin_inset Formula
6568 \begin_layout Standard
6570 multiline bracket: The command
6579 \begin_inset space \textvisiblespace{}
6583 \begin_inset Formula $\downarrow$
6587 \begin_inset space \textvisiblespace{}
6595 \begin_inset Formula
6597 \ln\left(\frac{A}{C}\right)
6605 \begin_layout Standard
6621 \begin_inset space ~
6627 This has the advantage that you can see in \SpecialChar LyX
6628 immediately the real bracket
6629 size and that the matching right bracket will be created too.
6630 \begin_inset Newline newline
6633 The command for the last example would then be:
6644 \begin_inset space \textvisiblespace{}
6648 \begin_inset Formula $\downarrow$
6654 \begin_layout Standard
6655 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6656 For example the command
6663 \begin_inset space \textvisiblespace{}
6667 \begin_inset Formula $\downarrow$
6671 \begin_inset space \textvisiblespace{}
6681 \begin_inset Formula
6683 \left.\frac{A}{B}\right\}
6702 will be converted by \SpecialChar LyX
6703 to brackets in the right size when the document is
6704 reloaded and an omitted bracket will appear as dashed line.
6707 \begin_layout Standard
6708 \begin_inset VSpace bigskip
6711 Because all popular \SpecialChar LaTeX
6712 distributions use e\SpecialChar TeX
6713 , an extension to \SpecialChar LaTeX
6722 \begin_inset Index idx
6725 \begin_layout Plain Layout
6733 is additionally available for all brackets and limits.
6734 With this command the height of the following character is adapted to the
6735 one of the surrounding brackets, what is e.
6736 \begin_inset space \thinspace{}
6740 \begin_inset space \space{}
6743 needed for physical vectors:
6744 \begin_inset Formula
6746 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6751 For physical vectors there is a special \SpecialChar LaTeX
6752 -package, described in
6753 \begin_inset CommandInset ref
6755 reference "subsec:Physical-Vectors"
6762 \begin_layout Subsection
6764 \begin_inset Index idx
6767 \begin_layout Plain Layout
6768 Brackets ! horizontal
6776 \begin_layout Standard
6778 \begin_inset Tabular
6779 <lyxtabular version="3" rows="4" columns="2">
6780 <features booktabs="true" tabularvalignment="middle">
6781 <column alignment="center" valignment="top" width="0pt">
6782 <column alignment="center" valignment="top" width="0pt">
6784 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6787 \begin_layout Plain Layout
6793 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6796 \begin_layout Plain Layout
6804 <cell alignment="center" valignment="top" usebox="none">
6807 \begin_layout Plain Layout
6811 \begin_inset space \textvisiblespace{}
6815 \begin_inset space \textvisiblespace{}
6819 \begin_inset Index idx
6822 \begin_layout Plain Layout
6835 <cell alignment="center" valignment="top" usebox="none">
6838 \begin_layout Plain Layout
6839 \begin_inset Formula $\overbrace{A+B}^{3}$
6848 <row topspace="2mm">
6849 <cell alignment="center" valignment="top" usebox="none">
6852 \begin_layout Plain Layout
6856 \begin_inset space \textvisiblespace{}
6860 \begin_inset space \textvisiblespace{}
6864 \begin_inset Index idx
6867 \begin_layout Plain Layout
6880 <cell alignment="center" valignment="top" usebox="none">
6883 \begin_layout Plain Layout
6884 \begin_inset Formula $\underbrace{A+B}_{5}$
6894 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6897 \begin_layout Plain Layout
6901 \begin_inset space \textvisiblespace{}
6907 \begin_inset space \textvisiblespace{}
6911 \begin_inset space \textvisiblespace{}
6915 \begin_inset space \textvisiblespace{}
6919 \begin_inset space \textvisiblespace{}
6923 \begin_inset space \textvisiblespace{}
6927 \begin_inset space \textvisiblespace{}
6935 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6938 \begin_layout Plain Layout
6939 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6955 \begin_layout Standard
6956 In the last example it doesn't matter if
6968 is inserted at first.
6971 \begin_layout Standard
6972 \begin_inset VSpace medskip
6978 \begin_layout Standard
6979 If you set in the document settings under
6982 \begin_inset space ~
6992 \begin_inset Index idx
6995 \begin_layout Plain Layout
6996 Packages ! mathtools
7004 \begin_inset space ~
7009 , you have access to square brackets:
7012 \begin_layout Standard
7014 \begin_inset Tabular
7015 <lyxtabular version="3" rows="4" columns="2">
7016 <features booktabs="true" tabularvalignment="middle">
7017 <column alignment="center" valignment="top" width="0pt">
7018 <column alignment="center" valignment="top" width="0pt">
7020 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7023 \begin_layout Plain Layout
7029 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7032 \begin_layout Plain Layout
7040 <cell alignment="center" valignment="top" usebox="none">
7043 \begin_layout Plain Layout
7071 \begin_inset space \textvisiblespace{}
7075 \begin_inset Index idx
7078 \begin_layout Plain Layout
7091 <cell alignment="center" valignment="top" usebox="none">
7094 \begin_layout Plain Layout
7095 \begin_inset Formula $\overbracket{A+B}^{3}$
7104 <row topspace="2mm">
7105 <cell alignment="center" valignment="top" usebox="none">
7108 \begin_layout Plain Layout
7136 \begin_inset space \textvisiblespace{}
7140 \begin_inset Index idx
7143 \begin_layout Plain Layout
7168 <cell alignment="center" valignment="top" usebox="none">
7171 \begin_layout Plain Layout
7172 \begin_inset Formula $\underbracket{A+B}_{5}$
7182 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7185 \begin_layout Plain Layout
7191 \begin_inset space \textvisiblespace{}
7195 \begin_inset space \textvisiblespace{}
7199 \begin_inset space \textvisiblespace{}
7203 \begin_inset space \textvisiblespace{}
7207 \begin_inset space \textvisiblespace{}
7215 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7218 \begin_layout Plain Layout
7219 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7235 \begin_layout Standard
7248 you can change the thickness of the bracket's stroke by specifying the
7249 desired thickness in square brackets behind the command:
7252 \begin_layout Standard
7254 \begin_inset Tabular
7255 <lyxtabular version="3" rows="3" columns="2">
7256 <features booktabs="true" tabularvalignment="middle">
7257 <column alignment="center" valignment="top" width="0pt">
7258 <column alignment="center" valignment="top" width="0pt">
7260 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7263 \begin_layout Plain Layout
7269 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7272 \begin_layout Plain Layout
7280 <cell alignment="center" valignment="top" usebox="none">
7283 \begin_layout Plain Layout
7313 \begin_inset space \textvisiblespace{}
7321 <cell alignment="center" valignment="top" usebox="none">
7324 \begin_layout Plain Layout
7325 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7334 <row topspace="2mm">
7335 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7338 \begin_layout Plain Layout
7368 \begin_inset space \textvisiblespace{}
7376 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7379 \begin_layout Plain Layout
7380 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7396 \begin_layout Standard
7397 \begin_inset VSpace bigskip
7400 When brackets should overlap each other, multiline formulas, as described
7402 \begin_inset CommandInset ref
7404 reference "sec:Multiline-Formulas"
7409 \begin_inset Formula
7411 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7412 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7417 In the first row the formula is inserted together with the first brace.
7418 It is hereby important that the space command
7422 \begin_layout Plain Layout
7423 Space commands are explained in
7424 \begin_inset CommandInset ref
7426 reference "subsec:Predefined-Space"
7441 is inserted before the first
7442 \begin_inset Formula $d$
7445 , because the brace that ends behind the
7446 \begin_inset Formula $q$
7449 prevents that the following
7450 \begin_inset Quotes eld
7454 \begin_inset Quotes erd
7457 is surrounded by space.
7461 \begin_layout Plain Layout
7462 because a bracket is not handled as a character, see
7463 \begin_inset CommandInset ref
7465 reference "subsec:Binary-Operators"
7474 In the second row the second brace is inserted.
7475 As it should begin before the
7476 \begin_inset Formula $b$
7491 \begin_layout Plain Layout
7499 \begin_inset CommandInset ref
7501 reference "subsec:Placeholders"
7510 This space is needed because the
7511 \begin_inset Quotes eld
7515 \begin_inset Quotes erd
7518 is also surrounded by space in the formula.
7519 The brace is placed under the command
7528 \begin_layout Standard
7529 It gets more complicated when brackets overlap each other above and under
7530 the formula, like in the following example:
7534 \begin_layout Plain Layout
7546 \begin_inset Formula
7548 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7549 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7558 \begin_layout Plain Layout
7569 The first formula row is the same as the second row of the previous example,
7570 with the difference that the brace is above.
7571 The second row contains the formula together with the second brace.
7572 To avoid that there is space between the upper brace in the first row and
7573 the formula, the row spacing needs to be reduced.
7574 This is not easily possible due to a bug in \SpecialChar LyX
7579 \begin_layout Plain Layout
7580 \begin_inset CommandInset href
7582 name "LyX-bug #1505"
7583 target "https://www.lyx.org/trac/ticket/1505"
7593 As a solution for the problem, the global formula row separation
7600 \begin_inset Index idx
7603 \begin_layout Plain Layout
7611 must be changed to -6
7612 \begin_inset space \thinspace{}
7615 pt before the formula with the command
7631 is set back after the formula to the standard value of 3
7632 \begin_inset space \thinspace{}
7635 pt using the same command.
7636 More about the row separation in formulas is explained in
7637 \begin_inset CommandInset ref
7639 reference "subsec:Line-Separation"
7646 \begin_layout Section
7648 \begin_inset Index idx
7651 \begin_layout Plain Layout
7660 \begin_layout Standard
7661 Arrows can be inserted via the math toolbar button
7664 arg "math-insert \\leftarrow"
7667 or the commands listed in the following subsections.
7670 \begin_layout Subsection
7672 \begin_inset Index idx
7675 \begin_layout Plain Layout
7684 \begin_layout Standard
7685 \begin_inset space \hfill{}
7689 \begin_inset Tabular
7690 <lyxtabular version="3" rows="8" columns="2">
7691 <features booktabs="true" tabularvalignment="middle">
7692 <column alignment="center" valignment="top" width="0pt">
7693 <column alignment="center" valignment="top" width="0pt">
7695 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7698 \begin_layout Plain Layout
7704 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7707 \begin_layout Plain Layout
7715 <cell alignment="center" valignment="top" usebox="none">
7718 \begin_layout Plain Layout
7726 <cell alignment="center" valignment="top" usebox="none">
7729 \begin_layout Plain Layout
7730 \begin_inset Formula $\gets$
7740 <cell alignment="center" valignment="top" usebox="none">
7743 \begin_layout Plain Layout
7751 <cell alignment="center" valignment="top" usebox="none">
7754 \begin_layout Plain Layout
7755 \begin_inset Formula $\Leftarrow$
7765 <cell alignment="center" valignment="top" usebox="none">
7768 \begin_layout Plain Layout
7776 <cell alignment="center" valignment="top" usebox="none">
7779 \begin_layout Plain Layout
7780 \begin_inset Formula $\longleftarrow$
7790 <cell alignment="center" valignment="top" usebox="none">
7793 \begin_layout Plain Layout
7801 <cell alignment="center" valignment="top" usebox="none">
7804 \begin_layout Plain Layout
7805 \begin_inset Formula $\Longleftarrow$
7815 <cell alignment="center" valignment="top" usebox="none">
7818 \begin_layout Plain Layout
7826 <cell alignment="center" valignment="top" usebox="none">
7829 \begin_layout Plain Layout
7830 \begin_inset Formula $\leftharpoonup$
7840 <cell alignment="center" valignment="top" usebox="none">
7843 \begin_layout Plain Layout
7851 <cell alignment="center" valignment="top" usebox="none">
7854 \begin_layout Plain Layout
7855 \begin_inset Formula $\leftharpoondown$
7865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7868 \begin_layout Plain Layout
7876 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7879 \begin_layout Plain Layout
7880 \begin_inset Formula $\hookleftarrow$
7894 \begin_inset space \hfill{}
7898 \begin_inset Tabular
7899 <lyxtabular version="3" rows="8" columns="2">
7900 <features booktabs="true" tabularvalignment="middle">
7901 <column alignment="center" valignment="top" width="0pt">
7902 <column alignment="center" valignment="top" width="0pt">
7904 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7907 \begin_layout Plain Layout
7913 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7916 \begin_layout Plain Layout
7924 <cell alignment="center" valignment="top" usebox="none">
7927 \begin_layout Plain Layout
7935 <cell alignment="center" valignment="top" usebox="none">
7938 \begin_layout Plain Layout
7939 \begin_inset Formula $\to$
7949 <cell alignment="center" valignment="top" usebox="none">
7952 \begin_layout Plain Layout
7960 <cell alignment="center" valignment="top" usebox="none">
7963 \begin_layout Plain Layout
7964 \begin_inset Formula $\Rightarrow$
7974 <cell alignment="center" valignment="top" usebox="none">
7977 \begin_layout Plain Layout
7985 <cell alignment="center" valignment="top" usebox="none">
7988 \begin_layout Plain Layout
7989 \begin_inset Formula $\longrightarrow$
7999 <cell alignment="center" valignment="top" usebox="none">
8002 \begin_layout Plain Layout
8010 <cell alignment="center" valignment="top" usebox="none">
8013 \begin_layout Plain Layout
8014 \begin_inset Formula $\Longrightarrow$
8024 <cell alignment="center" valignment="top" usebox="none">
8027 \begin_layout Plain Layout
8035 <cell alignment="center" valignment="top" usebox="none">
8038 \begin_layout Plain Layout
8039 \begin_inset Formula $\rightharpoonup$
8049 <cell alignment="center" valignment="top" usebox="none">
8052 \begin_layout Plain Layout
8060 <cell alignment="center" valignment="top" usebox="none">
8063 \begin_layout Plain Layout
8064 \begin_inset Formula $\rightharpoondown$
8074 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8077 \begin_layout Plain Layout
8085 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8088 \begin_layout Plain Layout
8089 \begin_inset Formula $\hookrightarrow$
8103 \begin_inset space \hfill{}
8109 \begin_layout Standard
8110 \begin_inset space \hfill{}
8114 \begin_inset Tabular
8115 <lyxtabular version="3" rows="6" columns="2">
8116 <features booktabs="true" tabularvalignment="middle">
8117 <column alignment="center" valignment="top" width="0pt">
8118 <column alignment="center" valignment="top" width="0pt">
8120 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8123 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8132 \begin_layout Plain Layout
8140 <cell alignment="center" valignment="top" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\leftrightarrow$
8165 <cell alignment="center" valignment="top" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\Leftrightarrow$
8190 <cell alignment="center" valignment="top" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\longleftrightarrow$
8215 <cell alignment="center" valignment="top" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\Longleftrightarrow$
8240 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\rightleftharpoons$
8269 \begin_inset space \hspace{}
8274 \begin_inset space \hfill{}
8278 \begin_inset Tabular
8279 <lyxtabular version="3" rows="5" columns="2">
8280 <features booktabs="true" tabularvalignment="middle">
8281 <column alignment="center" valignment="top" width="0pt">
8282 <column alignment="center" valignment="top" width="0pt">
8284 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8287 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" usebox="none">
8307 \begin_layout Plain Layout
8315 <cell alignment="center" valignment="top" usebox="none">
8318 \begin_layout Plain Layout
8319 \begin_inset Formula $\mapsto$
8329 <cell alignment="center" valignment="top" usebox="none">
8332 \begin_layout Plain Layout
8340 <cell alignment="center" valignment="top" usebox="none">
8343 \begin_layout Plain Layout
8344 \begin_inset Formula $\longmapsto$
8354 <cell alignment="center" valignment="top" usebox="none">
8357 \begin_layout Plain Layout
8365 <cell alignment="center" valignment="top" usebox="none">
8368 \begin_layout Plain Layout
8369 \begin_inset Formula $\leadsto$
8379 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8382 \begin_layout Plain Layout
8390 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8393 \begin_layout Plain Layout
8394 \begin_inset Formula $\dasharrow$
8408 \begin_inset space \hfill{}
8414 \begin_layout Standard
8415 \begin_inset VSpace medskip
8418 Arrows used as accents like e.
8419 \begin_inset space \thinspace{}
8423 \begin_inset space \space{}
8426 vector arrows are listed in
8427 \begin_inset CommandInset ref
8429 reference "sec:Accents"
8436 \begin_layout Standard
8437 \begin_inset VSpace bigskip
8440 Furthermore there are the labeled arrows
8441 \begin_inset Index idx
8444 \begin_layout Plain Layout
8457 \begin_inset Index idx
8460 \begin_layout Plain Layout
8475 \begin_inset Index idx
8478 \begin_layout Plain Layout
8485 \begin_layout Plain Layout
8500 When inserting one of these commands in a formula, an arrow with two blue
8501 boxes appear where the label can be inserted.
8502 The length of the arrow adapts to the label width.
8505 \begin_layout Standard
8507 \begin_inset Tabular
8508 <lyxtabular version="3" rows="3" columns="2">
8509 <features booktabs="true" tabularvalignment="middle">
8510 <column alignment="center" valignment="top" width="0pt">
8511 <column alignment="center" valignment="top" width="0pt">
8513 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8516 \begin_layout Plain Layout
8522 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8525 \begin_layout Plain Layout
8533 <cell alignment="center" valignment="top" usebox="none">
8536 \begin_layout Plain Layout
8540 \begin_inset space \textvisiblespace{}
8544 \begin_inset Formula $\downarrow$
8548 \begin_inset Formula $\to$
8556 <cell alignment="center" valignment="top" usebox="none">
8559 \begin_layout Plain Layout
8560 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8569 <row topspace="2mm">
8570 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8573 \begin_layout Plain Layout
8577 \begin_inset space \textvisiblespace{}
8581 \begin_inset Formula $\downarrow$
8585 \begin_inset Formula $\to$
8593 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8596 \begin_layout Plain Layout
8597 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8613 \begin_layout Standard
8614 \begin_inset VSpace medskip
8620 \begin_layout Standard
8621 If you set in the document settings under
8624 \begin_inset space ~
8634 \begin_inset Index idx
8637 \begin_layout Plain Layout
8638 Packages ! mathtools
8646 \begin_inset space ~
8651 , you have access to the following labeled arrows:
8654 \begin_layout Standard
8655 \begin_inset Newpage newpage
8661 \begin_layout Standard
8663 \begin_inset space \hspace*{\fill}
8667 \begin_inset Tabular
8668 <lyxtabular version="3" rows="7" columns="2">
8669 <features booktabs="true" tabularvalignment="middle">
8670 <column alignment="center" valignment="top" width="0pt">
8671 <column alignment="center" valignment="top" width="0pt">
8673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8676 \begin_layout Plain Layout
8682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8685 \begin_layout Plain Layout
8693 <cell alignment="center" valignment="top" usebox="none">
8696 \begin_layout Plain Layout
8716 <cell alignment="center" valignment="top" usebox="none">
8719 \begin_layout Plain Layout
8720 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8729 <row topspace="2mm">
8730 <cell alignment="center" valignment="top" usebox="none">
8733 \begin_layout Plain Layout
8753 <cell alignment="center" valignment="top" usebox="none">
8756 \begin_layout Plain Layout
8757 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8766 <row topspace="2mm">
8767 <cell alignment="center" valignment="top" usebox="none">
8770 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" usebox="none">
8793 \begin_layout Plain Layout
8794 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8803 <row topspace="2mm">
8804 <cell alignment="center" valignment="top" usebox="none">
8807 \begin_layout Plain Layout
8827 <cell alignment="center" valignment="top" usebox="none">
8830 \begin_layout Plain Layout
8831 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8840 <row topspace="2mm">
8841 <cell alignment="center" valignment="top" usebox="none">
8844 \begin_layout Plain Layout
8864 <cell alignment="center" valignment="top" usebox="none">
8867 \begin_layout Plain Layout
8868 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8877 <row topspace="2mm">
8878 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8881 \begin_layout Plain Layout
8901 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8904 \begin_layout Plain Layout
8905 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8919 \begin_inset space \hspace*{\fill}
8923 \begin_inset Tabular
8924 <lyxtabular version="3" rows="7" columns="2">
8925 <features booktabs="true" tabularvalignment="middle">
8926 <column alignment="center" valignment="top" width="0pt">
8927 <column alignment="center" valignment="top" width="0pt">
8929 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8932 \begin_layout Plain Layout
8938 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8941 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8972 <cell alignment="center" valignment="top" usebox="none">
8975 \begin_layout Plain Layout
8976 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8985 <row topspace="2mm">
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
9009 <cell alignment="center" valignment="top" usebox="none">
9012 \begin_layout Plain Layout
9013 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9022 <row topspace="2mm">
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9059 <row topspace="2mm">
9060 <cell alignment="center" valignment="top" usebox="none">
9063 \begin_layout Plain Layout
9083 <cell alignment="center" valignment="top" usebox="none">
9086 \begin_layout Plain Layout
9087 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9096 <row topspace="2mm">
9097 <cell alignment="center" valignment="top" usebox="none">
9100 \begin_layout Plain Layout
9120 <cell alignment="center" valignment="top" usebox="none">
9123 \begin_layout Plain Layout
9124 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9133 <row topspace="2mm">
9134 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9137 \begin_layout Plain Layout
9157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9160 \begin_layout Plain Layout
9161 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9175 \begin_inset space \hspace*{\fill}
9181 \begin_layout Standard
9182 The command scheme is for all these arrows:
9185 \begin_layout Standard
9187 \begin_inset Tabular
9188 <lyxtabular version="3" rows="2" columns="2">
9189 <features booktabs="true" tabularvalignment="middle">
9190 <column alignment="center" valignment="top" width="0pt">
9191 <column alignment="center" valignment="top" width="0pt">
9193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9196 \begin_layout Plain Layout
9202 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9205 \begin_layout Plain Layout
9212 <row bottomspace="0.5mm">
9213 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9216 \begin_layout Plain Layout
9219 xleftrightarrow[x=a]
9222 \begin_inset Formula $\to$
9230 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9233 \begin_layout Plain Layout
9234 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9250 \begin_layout Subsection
9251 Vertical and diagonal Arrows
9252 \begin_inset Index idx
9255 \begin_layout Plain Layout
9262 \begin_inset Index idx
9265 \begin_layout Plain Layout
9274 \begin_layout Standard
9275 \begin_inset space \hfill{}
9279 \begin_inset Tabular
9280 <lyxtabular version="3" rows="7" columns="2">
9281 <features booktabs="true" tabularvalignment="middle">
9282 <column alignment="center" valignment="top" width="0pt">
9283 <column alignment="center" valignment="top" width="0pt">
9285 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9288 \begin_layout Plain Layout
9294 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9297 \begin_layout Plain Layout
9305 <cell alignment="center" valignment="top" usebox="none">
9308 \begin_layout Plain Layout
9316 <cell alignment="center" valignment="top" usebox="none">
9319 \begin_layout Plain Layout
9320 \begin_inset Formula $\uparrow$
9330 <cell alignment="center" valignment="top" usebox="none">
9333 \begin_layout Plain Layout
9341 <cell alignment="center" valignment="top" usebox="none">
9344 \begin_layout Plain Layout
9345 \begin_inset Formula $\Uparrow$
9355 <cell alignment="center" valignment="top" usebox="none">
9358 \begin_layout Plain Layout
9366 <cell alignment="center" valignment="top" usebox="none">
9369 \begin_layout Plain Layout
9370 \begin_inset Formula $\updownarrow$
9380 <cell alignment="center" valignment="top" usebox="none">
9383 \begin_layout Plain Layout
9391 <cell alignment="center" valignment="top" usebox="none">
9394 \begin_layout Plain Layout
9395 \begin_inset Formula $\Updownarrow$
9405 <cell alignment="center" valignment="top" usebox="none">
9408 \begin_layout Plain Layout
9416 <cell alignment="center" valignment="top" usebox="none">
9419 \begin_layout Plain Layout
9420 \begin_inset Formula $\Downarrow$
9430 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9433 \begin_layout Plain Layout
9441 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9444 \begin_layout Plain Layout
9445 \begin_inset Formula $\downarrow$
9459 \begin_inset space \hfill{}
9463 \begin_inset Tabular
9464 <lyxtabular version="3" rows="5" columns="2">
9465 <features booktabs="true" tabularvalignment="middle">
9466 <column alignment="center" valignment="top" width="0pt">
9467 <column alignment="center" valignment="top" width="0pt">
9469 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9472 \begin_layout Plain Layout
9478 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9481 \begin_layout Plain Layout
9489 <cell alignment="center" valignment="top" usebox="none">
9492 \begin_layout Plain Layout
9500 <cell alignment="center" valignment="top" usebox="none">
9503 \begin_layout Plain Layout
9504 \begin_inset Formula $\nearrow$
9514 <cell alignment="center" valignment="top" usebox="none">
9517 \begin_layout Plain Layout
9525 <cell alignment="center" valignment="top" usebox="none">
9528 \begin_layout Plain Layout
9529 \begin_inset Formula $\searrow$
9539 <cell alignment="center" valignment="top" usebox="none">
9542 \begin_layout Plain Layout
9550 <cell alignment="center" valignment="top" usebox="none">
9553 \begin_layout Plain Layout
9554 \begin_inset Formula $\swarrow$
9564 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9567 \begin_layout Plain Layout
9575 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9578 \begin_layout Plain Layout
9579 \begin_inset Formula $\nwarrow$
9593 \begin_inset space \hfill{}
9599 \begin_layout Standard
9600 \begin_inset VSpace medskip
9603 Vertical arrows can be used also as delimiters together with the commands
9605 \begin_inset CommandInset ref
9607 reference "subsec:Manual-Bracket-Size"
9612 \begin_inset CommandInset ref
9614 reference "subsec:Automatic-Bracket-Size"
9621 \begin_layout Section
9623 \begin_inset CommandInset label
9630 \begin_inset Index idx
9633 \begin_layout Plain Layout
9642 \begin_layout Standard
9643 Accents can be inserted via the math toolbar button
9646 arg "math-insert \\hat"
9649 or the commands listed in the following subsections.
9652 \begin_layout Subsection
9653 Accents for one Character
9657 \begin_layout Plain Layout
9670 \begin_layout Plain Layout
9672 \begin_inset CommandInset ref
9674 reference "subsec:Accents-in-Text"
9687 \begin_layout Plain Layout
9695 \begin_inset Note Note
9698 \begin_layout Plain Layout
9705 is used to avoid that the footnote appears in the PDF-bookmark.
9708 \begin_layout Plain Layout
9716 \begin_inset CommandInset ref
9718 reference "subsec:Formulas-in-Section"
9728 \begin_inset CommandInset label
9730 name "subsec:Accents-for-one"
9735 \begin_inset Index idx
9738 \begin_layout Plain Layout
9739 Accents ! for one character
9747 \begin_layout Standard
9748 \begin_inset space \hfill{}
9752 \begin_inset Tabular
9753 <lyxtabular version="3" rows="8" columns="2">
9754 <features booktabs="true" tabularvalignment="middle">
9755 <column alignment="center" valignment="top" width="0pt">
9756 <column alignment="center" valignment="top" width="0pt">
9758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9761 \begin_layout Plain Layout
9767 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9770 \begin_layout Plain Layout
9777 <row topspace="1.5mm">
9778 <cell alignment="center" valignment="top" usebox="none">
9781 \begin_layout Plain Layout
9785 \begin_inset space \textvisiblespace{}
9793 <cell alignment="center" valignment="top" usebox="none">
9796 \begin_layout Plain Layout
9797 \begin_inset Formula $\dot{A}$
9806 <row topspace="1.5mm">
9807 <cell alignment="center" valignment="top" usebox="none">
9810 \begin_layout Plain Layout
9814 \begin_inset space \textvisiblespace{}
9822 <cell alignment="center" valignment="top" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\ddot{A}$
9835 <row topspace="1.5mm">
9836 <cell alignment="center" valignment="top" usebox="none">
9839 \begin_layout Plain Layout
9843 \begin_inset space \textvisiblespace{}
9851 <cell alignment="center" valignment="top" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\dddot{A}$
9864 <row topspace="1.5mm">
9865 <cell alignment="center" valignment="top" usebox="none">
9868 \begin_layout Plain Layout
9872 \begin_inset space \textvisiblespace{}
9880 <cell alignment="center" valignment="top" usebox="none">
9883 \begin_layout Plain Layout
9884 \begin_inset Formula $\ddddot{A}$
9893 <row topspace="1.5mm">
9894 <cell alignment="center" valignment="top" usebox="none">
9897 \begin_layout Plain Layout
9901 \begin_inset space \textvisiblespace{}
9905 \begin_inset Index idx
9908 \begin_layout Plain Layout
9919 <cell alignment="center" valignment="top" usebox="none">
9922 \begin_layout Plain Layout
9923 \begin_inset Formula $\vec{A}$
9932 <row topspace="1.5mm">
9933 <cell alignment="center" valignment="top" usebox="none">
9936 \begin_layout Plain Layout
9940 \begin_inset space \textvisiblespace{}
9948 <cell alignment="center" valignment="top" usebox="none">
9951 \begin_layout Plain Layout
9952 \begin_inset Formula $\bar{A}$
9961 <row topspace="1.5mm">
9962 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9965 \begin_layout Plain Layout
9969 \begin_inset space \textvisiblespace{}
9977 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9980 \begin_layout Plain Layout
9981 \begin_inset Formula $\mathring{A}$
9995 \begin_inset space \hfill{}
9999 \begin_inset Tabular
10000 <lyxtabular version="3" rows="7" columns="2">
10001 <features booktabs="true" tabularvalignment="middle">
10002 <column alignment="center" valignment="top" width="0pt">
10003 <column alignment="center" valignment="top" width="0pt">
10005 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10008 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10017 \begin_layout Plain Layout
10024 <row topspace="1.5mm">
10025 <cell alignment="center" valignment="top" usebox="none">
10028 \begin_layout Plain Layout
10032 \begin_inset space \textvisiblespace{}
10040 <cell alignment="center" valignment="top" usebox="none">
10043 \begin_layout Plain Layout
10044 \begin_inset Formula $\tilde{A}$
10053 <row topspace="1.5mm">
10054 <cell alignment="center" valignment="top" usebox="none">
10057 \begin_layout Plain Layout
10061 \begin_inset space \textvisiblespace{}
10069 <cell alignment="center" valignment="top" usebox="none">
10072 \begin_layout Plain Layout
10073 \begin_inset Formula $\hat{A}$
10082 <row topspace="1.5mm">
10083 <cell alignment="center" valignment="top" usebox="none">
10086 \begin_layout Plain Layout
10090 \begin_inset space \textvisiblespace{}
10098 <cell alignment="center" valignment="top" usebox="none">
10101 \begin_layout Plain Layout
10102 \begin_inset Formula $\check{A}$
10111 <row topspace="1.5mm">
10112 <cell alignment="center" valignment="top" usebox="none">
10115 \begin_layout Plain Layout
10119 \begin_inset space \textvisiblespace{}
10127 <cell alignment="center" valignment="top" usebox="none">
10130 \begin_layout Plain Layout
10131 \begin_inset Formula $\acute{A}$
10140 <row topspace="1.5mm">
10141 <cell alignment="center" valignment="top" usebox="none">
10144 \begin_layout Plain Layout
10148 \begin_inset space \textvisiblespace{}
10156 <cell alignment="center" valignment="top" usebox="none">
10159 \begin_layout Plain Layout
10160 \begin_inset Formula $\grave{A}$
10169 <row topspace="1.5mm">
10170 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10173 \begin_layout Plain Layout
10177 \begin_inset space \textvisiblespace{}
10185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10188 \begin_layout Plain Layout
10189 \begin_inset Formula $\breve{A}$
10203 \begin_inset space \hfill{}
10209 \begin_layout Standard
10210 \begin_inset VSpace bigskip
10216 \begin_layout Standard
10217 You can directly insert accents like é to formulas.
10219 will transform them to the corresponding accent command.
10221 \begin_inset Index idx
10224 \begin_layout Plain Layout
10230 it is better to insert a quotation mark before the vowel.
10231 These two characters are then treated by \SpecialChar LaTeX
10236 character when the formula part with the umlaut is marked as German.
10244 \begin_inset Quotes eld
10248 \begin_inset Quotes erd
10251 umlauts are created as demonstrated in the following example:
10254 \begin_layout Standard
10255 \begin_inset VSpace -2mm
10261 \begin_layout Standard
10263 \begin_inset Tabular
10264 <lyxtabular version="3" rows="3" columns="2">
10265 <features booktabs="true" tabularvalignment="middle">
10266 <column alignment="center" valignment="top" width="0pt">
10267 <column alignment="center" valignment="top">
10269 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10272 \begin_layout Plain Layout
10278 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10281 \begin_layout Plain Layout
10289 <cell alignment="center" valignment="top" usebox="none">
10292 \begin_layout Plain Layout
10293 \begin_inset Quotes grd
10301 <cell alignment="center" valignment="top" usebox="none">
10304 \begin_layout Plain Layout
10305 \begin_inset space \hspace{}
10312 \begin_inset Formula $"i$
10321 <row topspace="1.5mm">
10322 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10325 \begin_layout Plain Layout
10329 \begin_inset space \textvisiblespace{}
10337 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10340 \begin_layout Plain Layout
10341 \begin_inset Formula $\ddot{i}$
10357 \begin_layout Standard
10358 Another advantage to
10364 is that umlauts can directly be converted to mathematical text because
10365 the accent commands above are
10371 in mathematical text
10374 To convert an accented character to mathematical text, only the character
10375 under the accent may be converted.
10376 This applies also for all other conversions, e.
10377 \begin_inset space \thinspace{}
10381 \begin_inset space \space{}
10387 \begin_layout Standard
10388 In mathematical text, umlauts and other accented characters can directly
10392 \begin_layout Standard
10393 \begin_inset VSpace bigskip
10399 \begin_layout Standard
10401 also supports a tilde under the character if the \SpecialChar LaTeX
10407 \begin_inset Index idx
10410 \begin_layout Plain Layout
10411 Packages ! undertilde
10416 is installed on your system:
10419 \begin_layout Standard
10423 \begin_layout Plain Layout
10433 \begin_inset Note Note
10436 \begin_layout Plain Layout
10437 The following table will only be displayed when the \SpecialChar LaTeX
10450 \begin_layout Standard
10453 \begin_inset Tabular
10454 <lyxtabular version="3" rows="2" columns="2">
10455 <features booktabs="true" tabularvalignment="middle">
10456 <column alignment="center" valignment="top" width="0pt">
10457 <column alignment="center" valignment="top" width="0pt">
10459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10462 \begin_layout Plain Layout
10468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10471 \begin_layout Plain Layout
10479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10482 \begin_layout Plain Layout
10486 \begin_inset space \textvisiblespace{}
10494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10497 \begin_layout Plain Layout
10498 \begin_inset Formula $\utilde{A}$
10514 \begin_layout Standard
10518 \begin_layout Plain Layout
10528 \begin_inset Note Note
10531 \begin_layout Plain Layout
10532 The following will be displayed when the \SpecialChar LaTeX
10545 \begin_layout Standard
10546 You need to install the \SpecialChar LaTeX
10551 to see the rest of this subsection in the output.
10554 \begin_layout Standard
10558 \begin_layout Plain Layout
10570 \begin_layout Standard
10571 \begin_inset Newpage newpage
10577 \begin_layout Subsection
10578 Accents for several Characters
10579 \begin_inset Index idx
10582 \begin_layout Plain Layout
10583 Accents ! for several characters
10591 \begin_layout Standard
10592 \begin_inset space \hfill{}
10596 \begin_inset Tabular
10597 <lyxtabular version="3" rows="5" columns="2">
10598 <features booktabs="true" tabularvalignment="middle">
10599 <column alignment="center" valignment="top" width="0pt">
10600 <column alignment="center" valignment="top" width="0pt">
10602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10605 \begin_layout Plain Layout
10611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10614 \begin_layout Plain Layout
10621 <row topspace="1.5mm">
10622 <cell alignment="center" valignment="top" usebox="none">
10625 \begin_layout Plain Layout
10629 \begin_inset space \textvisiblespace{}
10637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10640 \begin_layout Plain Layout
10641 \begin_inset Formula $\overleftarrow{A=B}$
10650 <row topspace="1.5mm">
10651 <cell alignment="center" valignment="top" usebox="none">
10654 \begin_layout Plain Layout
10658 \begin_inset space \textvisiblespace{}
10666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10669 \begin_layout Plain Layout
10670 \begin_inset Formula $\underleftarrow{A=B}$
10679 <row topspace="1.5mm">
10680 <cell alignment="center" valignment="top" usebox="none">
10683 \begin_layout Plain Layout
10687 \begin_inset space \textvisiblespace{}
10695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10698 \begin_layout Plain Layout
10699 \begin_inset Formula $\overleftrightarrow{A=B}$
10708 <row topspace="1.5mm" bottomspace="1mm">
10709 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10712 \begin_layout Plain Layout
10715 underleftrightarrow
10716 \begin_inset space \textvisiblespace{}
10724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10727 \begin_layout Plain Layout
10728 \begin_inset Formula $\underleftrightarrow{A=B}$
10742 \begin_inset space \hfill{}
10746 \begin_inset Tabular
10747 <lyxtabular version="3" rows="5" columns="2">
10748 <features booktabs="true" tabularvalignment="middle">
10749 <column alignment="center" valignment="top" width="0pt">
10750 <column alignment="center" valignment="top" width="0pt">
10752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10755 \begin_layout Plain Layout
10761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10764 \begin_layout Plain Layout
10771 <row topspace="1.5mm">
10772 <cell alignment="center" valignment="top" usebox="none">
10775 \begin_layout Plain Layout
10779 \begin_inset space \textvisiblespace{}
10787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10790 \begin_layout Plain Layout
10791 \begin_inset Formula $\overrightarrow{A=B}$
10800 <row topspace="1.5mm">
10801 <cell alignment="center" valignment="top" usebox="none">
10804 \begin_layout Plain Layout
10808 \begin_inset space \textvisiblespace{}
10816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10819 \begin_layout Plain Layout
10820 \begin_inset Formula $\underrightarrow{A=B}$
10829 <row topspace="1.5mm">
10830 <cell alignment="center" valignment="top" usebox="none">
10833 \begin_layout Plain Layout
10837 \begin_inset space \textvisiblespace{}
10845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10848 \begin_layout Plain Layout
10849 \begin_inset Formula $\widetilde{A=B}$
10858 <row topspace="1.5mm" bottomspace="1mm">
10859 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10862 \begin_layout Plain Layout
10866 \begin_inset space \textvisiblespace{}
10874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10877 \begin_layout Plain Layout
10878 \begin_inset Formula $\widehat{A=B}$
10892 \begin_inset space \hfill{}
10898 \begin_layout Standard
10899 \begin_inset VSpace medskip
10902 With these commands as many characters as you like can be accented.
10915 will only be set in the output with a length of three characters, as shown
10916 in the following example:
10917 \begin_inset Formula
10919 \widetilde{A+B=C-D}
10927 \begin_layout Standard
10935 \begin_inset Index idx
10938 \begin_layout Plain Layout
10953 \begin_inset Index idx
10956 \begin_layout Plain Layout
10964 described in the previous subsection it is also possible to accent several
10971 \begin_inset space \textvisiblespace{}
10975 \begin_inset Formula $\downarrow$
10981 \begin_inset Formula
10983 \underset{***}{A=B}
10991 \begin_layout Section
10993 \begin_inset CommandInset label
10995 name "subsec:Space"
11000 \begin_inset Index idx
11003 \begin_layout Plain Layout
11012 \begin_layout Subsection
11014 \begin_inset CommandInset label
11016 name "subsec:Predefined-Space"
11021 \begin_inset Index idx
11024 \begin_layout Plain Layout
11025 Space ! horizontal ! predefined
11033 \begin_layout Standard
11034 Sometimes it is necessary to insert horizontal space into a formula.
11035 This is done by inserting a protected space (shortcut
11038 arg "command-alternatives space-insert protected ; math-space"
11043 \begin_inset Quotes eld
11049 \begin_inset space \textvisiblespace{}
11055 \begin_inset Quotes erd
11058 appears and by pressing
11062 several times one can select one of eight different space sizes.
11063 The spaces can also be inserted using the math toolbar button
11066 arg "math-insert \\space"
11069 or special commands.
11070 Independent from the inserted command, one can select the size again by
11078 \begin_layout Standard
11081 \begin_inset Tabular
11082 <lyxtabular version="3" rows="6" columns="3">
11083 <features booktabs="true" tabularvalignment="middle">
11084 <column alignment="center" valignment="top">
11085 <column alignment="center" valignment="top" width="15col%">
11086 <column alignment="center" valignment="top">
11088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11100 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11113 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11144 \begin_layout Plain Layout
11145 \begin_inset Formula $A\,B$
11155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11158 \begin_layout Plain Layout
11166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11178 \begin_layout Plain Layout
11179 \begin_inset Formula $A\:B$
11189 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11192 \begin_layout Plain Layout
11200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11203 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11212 \begin_layout Plain Layout
11213 \begin_inset Formula $A\;B$
11223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11226 \begin_layout Plain Layout
11234 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11246 \begin_layout Plain Layout
11247 \begin_inset Formula $A\quad B$
11257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11260 \begin_layout Plain Layout
11268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11280 \begin_layout Plain Layout
11281 \begin_inset Formula $A\qquad B$
11295 \begin_inset space \hfill{}
11299 \begin_inset Tabular
11300 <lyxtabular version="3" rows="6" columns="3">
11301 <features booktabs="true" tabularvalignment="middle">
11302 <column alignment="center" valignment="top">
11303 <column alignment="center" valignment="top" width="15col%">
11304 <column alignment="center" valignment="top">
11306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11309 \begin_layout Plain Layout
11315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11318 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11331 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11342 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11362 \begin_layout Plain Layout
11363 \begin_inset Formula $A\hfill B$
11373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11376 \begin_layout Plain Layout
11384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11396 \begin_layout Plain Layout
11397 \begin_inset Formula $A\hspace*{1em}B$
11407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11410 \begin_layout Plain Layout
11418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11430 \begin_layout Plain Layout
11431 \begin_inset Formula $A\hspace{1em}B$
11441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11444 \begin_layout Plain Layout
11448 \begin_inset space \textvisiblespace{}
11456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11459 \begin_layout Plain Layout
11465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11468 \begin_layout Plain Layout
11469 \begin_inset Formula $A\ B$
11479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11482 \begin_layout Plain Layout
11490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11493 \begin_layout Plain Layout
11499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11502 \begin_layout Plain Layout
11503 \begin_inset Formula $A\!B$
11519 \begin_layout Standard
11521 \begin_inset space ~
11525 \begin_inset space \thinspace{}
11529 \begin_inset space \thinspace{}
11532 7 are variable spaces which are explained in
11533 \begin_inset CommandInset ref
11535 reference "subsec:Variable-Space"
11541 \begin_inset space ~
11544 9 seems to produce no space.
11545 It is displayed red in \SpecialChar LyX
11546 contrary to the other sizes, because it is a negative
11548 There are two more negative spaces:
11551 \begin_layout Standard
11553 \begin_inset Tabular
11554 <lyxtabular version="3" rows="3" columns="3">
11555 <features booktabs="true" tabularvalignment="middle">
11556 <column alignment="center" valignment="middle" width="6.8cm">
11557 <column alignment="center" valignment="top" width="0pt">
11558 <column alignment="center" valignment="top" width="0pt">
11560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11563 \begin_layout Plain Layout
11569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11572 \begin_layout Plain Layout
11580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11583 \begin_layout Plain Layout
11593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11596 \begin_layout Plain Layout
11601 keystrokes after inserting the protected space
11606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11609 \begin_layout Plain Layout
11615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11618 \begin_layout Plain Layout
11626 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11629 \begin_layout Plain Layout
11635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11638 \begin_layout Plain Layout
11639 \begin_inset Formula $A\negmedspace B$
11647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11650 \begin_layout Plain Layout
11651 \begin_inset Formula $A\negthickspace B$
11667 \begin_layout Standard
11668 Negative spaces can lead to characters overlapping each other.
11669 Thus they can be used to enforce ligatures, which are e.
11670 \begin_inset space \thinspace{}
11674 \begin_inset space \space{}
11677 useful for summation operators:
11680 \begin_layout Standard
11682 \begin_inset Tabular
11683 <lyxtabular version="3" rows="3" columns="2">
11684 <features booktabs="true" tabularvalignment="middle">
11685 <column alignment="center" valignment="top" width="0pt">
11686 <column alignment="center" valignment="top">
11688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11691 \begin_layout Plain Layout
11697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11700 \begin_layout Plain Layout
11708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11711 \begin_layout Plain Layout
11717 \begin_inset space \textvisiblespace{}
11725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11728 \begin_layout Plain Layout
11729 \begin_inset Formula $\sum\sum f_{kl}$
11739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11742 \begin_layout Plain Layout
11750 \begin_inset space \textvisiblespace{}
11758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11761 \begin_layout Plain Layout
11762 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11778 \begin_layout Standard
11780 \begin_inset VSpace medskip
11786 \begin_layout Standard
11788 Relations like for example equal signs, are always surrounded by space.
11789 To suppress this, the equal sign is placed into a \SpecialChar TeX
11791 The following example demonstrates this:
11794 \begin_layout Standard
11796 \begin_inset Tabular
11797 <lyxtabular version="3" rows="2" columns="2">
11798 <features tabularvalignment="middle">
11799 <column alignment="center" valignment="top" width="0pt">
11800 <column alignment="center" valignment="top" width="0pt">
11802 <cell alignment="center" valignment="top" usebox="none">
11805 \begin_layout Plain Layout
11811 <cell alignment="center" valignment="top" usebox="none">
11814 \begin_layout Plain Layout
11815 \begin_inset Formula $A=B$
11825 <cell alignment="center" valignment="top" usebox="none">
11828 \begin_layout Plain Layout
11829 equation without space
11834 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11837 \begin_layout Plain Layout
11838 \begin_inset Formula $A{=}B$
11854 \begin_layout Standard
11856 The command for the last formula is:
11861 \begin_inset Formula $\to$
11867 \begin_layout Standard
11868 \begin_inset VSpace bigskip
11874 \begin_layout Standard
11875 Spaces are needed for physical units, because the space between the value
11876 and the unit is the smallest one and not a normal space.
11877 For units in text, the smallest space is inserted via the menu
11879 Insert\SpecialChar menuseparator
11880 Formatting\SpecialChar menuseparator
11882 \begin_inset space ~
11890 arg "space-insert thin"
11896 \begin_layout Standard
11897 An example to visualize the difference:
11900 \begin_layout Standard
11901 \begin_inset Tabular
11902 <lyxtabular version="3" rows="2" columns="2">
11903 <features tabularvalignment="middle">
11904 <column alignment="left" valignment="top">
11905 <column alignment="left" valignment="top">
11907 <cell alignment="center" valignment="top" usebox="none">
11910 \begin_layout Plain Layout
11912 \begin_inset Formula $\cdot$
11920 <cell alignment="center" valignment="top" usebox="none">
11923 \begin_layout Plain Layout
11924 space between value and unit
11931 <cell alignment="center" valignment="top" usebox="none">
11934 \begin_layout Plain Layout
11936 \begin_inset space \thinspace{}
11940 \begin_inset Formula $\cdot$
11948 <cell alignment="center" valignment="top" usebox="none">
11951 \begin_layout Plain Layout
11952 smallest space between value and unit
11965 \begin_layout Subsection
11970 \begin_layout Plain Layout
11983 \begin_layout Plain Layout
11984 for vertical space in formulas see
11985 \begin_inset CommandInset ref
11987 reference "subsec:Line-Separation"
12000 \begin_layout Plain Layout
12008 \begin_inset Note Note
12011 \begin_layout Plain Layout
12014 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12017 \begin_layout Plain Layout
12020 texorpdfstring is in section
12021 \begin_inset CommandInset ref
12023 reference "subsec:Formulas-in-Section"
12033 \begin_inset CommandInset label
12035 name "subsec:Variable-Space"
12040 \begin_inset Index idx
12043 \begin_layout Plain Layout
12044 Space ! horizontal ! variable
12052 \begin_layout Standard
12053 Space with a defined length can be inserted with the command
12060 \begin_inset Index idx
12063 \begin_layout Plain Layout
12073 \begin_inset Quotes eld
12079 \begin_inset space \textvisiblespace{}
12085 \begin_inset Quotes erd
12089 The length can be specified by left-clicking on the
12090 \begin_inset Quotes eld
12096 \begin_inset space \textvisiblespace{}
12102 \begin_inset Quotes erd
12106 The length may also be negative.
12107 When a space would be the first character in a line it would be omitted.
12108 To force its output use the command
12120 or left-click on the
12121 \begin_inset Quotes eld
12127 \begin_inset space \textvisiblespace{}
12133 \begin_inset Quotes erd
12136 and check the option
12141 \begin_inset Newline newline
12144 To insert as much space as is available, the command
12151 \begin_inset Index idx
12154 \begin_layout Plain Layout
12165 \begin_layout Standard
12167 \begin_inset Tabular
12168 <lyxtabular version="3" rows="4" columns="2">
12169 <features booktabs="true" tabularvalignment="middle">
12170 <column alignment="center" valignment="top" width="0pt">
12171 <column alignment="center" valignment="top">
12173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12176 \begin_layout Plain Layout
12184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12187 \begin_layout Plain Layout
12195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12198 \begin_layout Plain Layout
12202 \begin_inset space \textvisiblespace{}
12208 \begin_inset space \thinspace{}
12216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12219 \begin_layout Plain Layout
12220 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12230 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12233 \begin_layout Plain Layout
12237 \begin_inset space \textvisiblespace{}
12243 \begin_inset space \thinspace{}
12251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12254 \begin_layout Plain Layout
12255 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12268 \begin_layout Plain Layout
12272 \begin_inset space \textvisiblespace{}
12280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12283 \begin_layout Plain Layout
12284 \begin_inset Formula $A=A\hfill B=B$
12300 \begin_layout Standard
12301 In the last example the available space is given by the longest column entry
12303 In an inline formula the space depends on the length of the line in which
12311 Thus, when the line uses the full width, no space will be created.
12318 only has an effect on displayed formulas when the formula style
12323 (Formula styles are explained in
12324 \begin_inset CommandInset ref
12326 reference "sec:Formula-Styles"
12333 \begin_layout Standard
12340 , there are the commands
12352 that fill the space with a pattern, see
12353 \begin_inset CommandInset ref
12355 reference "subsec:Ellipses"
12362 \begin_layout Standard
12363 For text, variable space can be inserted via the menu
12365 Insert\SpecialChar menuseparator
12366 Formatting\SpecialChar menuseparator
12368 \begin_inset space ~
12376 \begin_layout Standard
12377 This is a line with
12378 \begin_inset space \hspace{}
12383 \begin_inset space \thinspace{}
12389 \begin_layout Standard
12390 This is a line with
12391 \begin_inset space \hfill{}
12397 \begin_layout Subsection
12398 Space besides inline Formulas
12399 \begin_inset Index idx
12402 \begin_layout Plain Layout
12403 Space ! besides inline formulas
12411 \begin_layout Standard
12412 The space that surrounds inline formulas can be adjusted with the length
12420 \begin_inset Index idx
12423 \begin_layout Plain Layout
12432 The value of a length is set with the command
12439 \begin_inset Index idx
12442 \begin_layout Plain Layout
12450 which has the following scheme:
12453 \begin_layout Standard
12458 setlength{length name}{value}
12461 \begin_layout Standard
12469 \begin_inset space \thinspace{}
12475 \begin_layout Standard
12485 \begin_layout Standard
12486 is inserted in \SpecialChar TeX
12489 \begin_inset space \thinspace{}
12492 mm space will now be set around all inline formulas:
12496 \begin_layout Plain Layout
12510 \begin_layout Standard
12511 This is a line with an inline formula
12512 \begin_inset Formula $A=B$
12516 \begin_inset space \thinspace{}
12519 mm surrounding space.
12523 \begin_layout Plain Layout
12537 \begin_layout Standard
12538 To return to the predefined value,
12544 is set to the value 0
12545 \begin_inset space \thinspace{}
12551 \begin_layout Standard
12552 \begin_inset Newpage newpage
12558 \begin_layout Section
12560 \begin_inset Index idx
12563 \begin_layout Plain Layout
12570 \begin_inset Index idx
12573 \begin_layout Plain Layout
12578 \begin_layout Plain Layout
12589 \begin_layout Plain Layout
12604 \begin_layout Standard
12605 Boxes for text are described in chapter
12612 \begin_inset space ~
12620 \begin_layout Subsection
12622 \begin_inset CommandInset label
12624 name "subsec:Boxes-with-Frame"
12629 \begin_inset Index idx
12632 \begin_layout Plain Layout
12641 \begin_layout Standard
12642 It is possible to frame a formula or part of one with the commands
12649 \begin_inset Index idx
12652 \begin_layout Plain Layout
12667 \begin_inset Index idx
12670 \begin_layout Plain Layout
12681 \begin_layout Standard
12682 When one of these commands is inserted in a formula, a blue box appears
12683 within a frame to enter formula parts.
12690 an additional formula has to be created by
12694 within this box, because the box content will otherwise be treated as mathemati
12702 is used, a new formula is automatically created inside the frame.
12705 \begin_layout Standard
12712 is not suitable to frame displayed formulas because the formula will always
12713 be set in the size of the text.
12720 is in contrary not suitable to frame inline formulas, because the formula
12721 will always be set in the size of a displayed formula.
12724 \begin_layout Standard
12738 \begin_inset Index idx
12741 \begin_layout Plain Layout
12749 where additionally the frame width and the alignment can be specified.
12756 is used in the following scheme:
12759 \begin_layout Standard
12764 framebox[frame width][position]{box content}
12767 \begin_layout Standard
12768 The position can either be
12785 right aligns the formula in the box.
12786 When no position is given, the formula will be centered.
12787 \begin_inset Newline newline
12790 If no width is given, also no position can be given.
12791 In this case the frame width is adjusted to the box content like for
12800 \begin_layout Standard
12807 is inserted, a box appears containing three blue boxes.
12808 The first two boxes are surrounded by brackets and denote the two optional
12810 The third box is for formula parts like for
12819 \begin_layout Standard
12821 \begin_inset Tabular
12822 <lyxtabular version="3" rows="5" columns="2">
12823 <features booktabs="true" tabularvalignment="middle">
12824 <column alignment="center" valignment="top" width="0pt">
12825 <column alignment="center" valignment="top">
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12830 \begin_layout Plain Layout
12836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12839 \begin_layout Plain Layout
12846 <row topspace="1.5mm">
12847 <cell alignment="center" valignment="top" usebox="none">
12850 \begin_layout Plain Layout
12854 \begin_inset space \textvisiblespace{}
12864 \begin_inset space \textvisiblespace{}
12872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12875 \begin_layout Plain Layout
12876 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12885 <row topspace="1.5mm">
12886 <cell alignment="center" valignment="top" usebox="none">
12889 \begin_layout Plain Layout
12893 \begin_inset space \textvisiblespace{}
12899 \begin_inset space \textvisiblespace{}
12907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12910 \begin_layout Plain Layout
12911 \begin_inset Formula $\boxed{\int A=B}$
12920 <row topspace="1.5mm">
12921 <cell alignment="center" valignment="top" usebox="none">
12924 \begin_layout Plain Layout
12928 \begin_inset space \textvisiblespace{}
12936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12939 \begin_layout Plain Layout
12940 \begin_inset Formula $A+\fbox{B}$
12949 <row topspace="1.5mm" bottomspace="1mm">
12950 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12953 \begin_layout Plain Layout
12957 \begin_inset space \textvisiblespace{}
12961 \begin_inset Formula $\to$
12965 \begin_inset Formula $\to$
12975 \begin_inset space \textvisiblespace{}
12979 \begin_inset Formula $\downarrow$
12987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12990 \begin_layout Plain Layout
12991 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13007 \begin_layout Standard
13008 The frame thickness can also be adjusted.
13009 To do this the following commands have to be inserted in \SpecialChar TeX
13014 \begin_layout Standard
13024 \begin_inset Quotes eld
13028 \begin_inset Quotes erd
13042 \begin_inset Quotes eld
13046 \begin_inset Quotes erd
13052 \begin_layout Standard
13053 \begin_inset Quotes eld
13057 \begin_inset Quotes erd
13060 specifies the minimal distance between the frame and the first character
13062 An example for this is the following framed formula:
13066 \begin_layout Plain Layout
13078 \begin_inset Formula
13085 Before this formula the commands
13088 \begin_layout Standard
13110 \begin_layout Standard
13111 were inserted in \SpecialChar TeX
13113 The given values are used for all following boxes.
13116 \begin_layout Standard
13117 To return to the standard frame size, the command
13120 \begin_layout Standard
13145 \begin_layout Plain Layout
13159 \begin_layout Standard
13160 is inserted in \SpecialChar TeX
13161 mode before the next formula.
13164 \begin_layout Subsection
13165 Boxes without Frame
13166 \begin_inset CommandInset label
13168 name "subsec:Boxes-without-Frame"
13173 \begin_inset Index idx
13176 \begin_layout Plain Layout
13177 Boxes ! without frame
13185 \begin_layout Standard
13186 For boxes without a frame there are the following box commands:
13193 \begin_inset Index idx
13196 \begin_layout Plain Layout
13211 \begin_inset Index idx
13214 \begin_layout Plain Layout
13229 \begin_inset Index idx
13232 \begin_layout Plain Layout
13243 \begin_layout Standard
13250 a box can be super- or subscripted.
13251 But in contrary to normal super- and subscripting, the characters in the
13252 box keep their font size.
13259 is used in the following scheme:
13262 \begin_layout Standard
13267 raisebox{height}{box content}
13270 \begin_layout Standard
13271 When the box should contain a formula, an extra formula is needed like for
13282 \begin_inset Note Greyedout
13285 \begin_layout Plain Layout
13296 this extra formula is created by pressing
13300 twice instead of once because \SpecialChar LyX
13301 doesn't yet support
13315 \begin_layout Standard
13317 \begin_inset Tabular
13318 <lyxtabular version="3" rows="4" columns="2">
13319 <features booktabs="true" tabularvalignment="middle">
13320 <column alignment="center" valignment="top" width="0pt">
13321 <column alignment="center" valignment="top">
13323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13326 \begin_layout Plain Layout
13332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13335 \begin_layout Plain Layout
13343 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13346 \begin_layout Plain Layout
13350 \begin_inset Formula $\to$
13356 \begin_inset Formula $\to$
13364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13367 \begin_layout Plain Layout
13368 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13381 \begin_layout Plain Layout
13385 \begin_inset Formula $\to$
13391 \begin_inset Formula $\to$
13399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13402 \begin_layout Plain Layout
13403 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13416 \begin_layout Plain Layout
13420 \begin_inset Formula $\to$
13436 \begin_inset space \textvisiblespace{}
13444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13447 \begin_layout Plain Layout
13448 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13464 \begin_layout Standard
13489 , with the difference that there is no frame.
13492 \begin_layout Subsection
13494 \begin_inset CommandInset label
13496 name "subsec:Colored-Boxes"
13501 \begin_inset Index idx
13504 \begin_layout Plain Layout
13513 \begin_layout Standard
13514 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13523 \begin_layout Plain Layout
13524 The \SpecialChar LaTeX
13529 is part of every \SpecialChar LaTeX
13530 standard installation.
13536 \begin_inset Index idx
13539 \begin_layout Plain Layout
13545 has to be loaded in the \SpecialChar LaTeX
13546 -preamble with the line
13550 \begin_layout Plain Layout
13551 When text is colored somewhere in the document with a predefined color,
13553 loads the \SpecialChar LaTeX
13559 Thus it is possible that the package is loaded twice, but this does not
13566 \begin_inset Note Note
13569 \begin_layout Plain Layout
13570 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13579 \begin_layout Standard
13587 \begin_layout Standard
13588 \begin_inset VSpace medskip
13591 To color boxes, the command
13598 \begin_inset Index idx
13601 \begin_layout Plain Layout
13609 is used in the following scheme:
13612 \begin_layout Standard
13617 colorbox{color}{box content}
13620 \begin_layout Standard
13621 The box content can also be a box and a
13627 can also be part of another box (see the 2nd and 3rd example).
13628 When the box should contain a formula, an extra formula has to be created,
13629 the same way as for
13639 \begin_layout Plain Layout
13640 This also applies for the command
13654 \begin_layout Standard
13655 One of the following predefined colors can be chosen:
13658 \begin_layout Standard
13692 \begin_layout Standard
13694 \begin_inset Tabular
13695 <lyxtabular version="3" rows="4" columns="2">
13696 <features booktabs="true" tabularvalignment="middle">
13697 <column alignment="center" valignment="top" width="0pt">
13698 <column alignment="center" valignment="top">
13700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13703 \begin_layout Plain Layout
13709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13712 \begin_layout Plain Layout
13720 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13723 \begin_layout Plain Layout
13727 \begin_inset Formula $\to$
13737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13740 \begin_layout Plain Layout
13741 \begin_inset Formula $\colorbox{yellow}{A=B}$
13750 <row topspace="1.5mm">
13751 <cell alignment="center" valignment="top" usebox="none">
13754 \begin_layout Plain Layout
13758 \begin_inset Formula $\to$
13766 \begin_inset space \textvisiblespace{}
13774 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13777 \begin_layout Plain Layout
13778 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13787 <row topspace="1.5mm" bottomspace="1mm">
13788 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13791 \begin_layout Plain Layout
13795 \begin_inset space \textvisiblespace{}
13801 \begin_inset Formula $\to$
13817 \begin_inset space \textvisiblespace{}
13825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13828 \begin_layout Plain Layout
13829 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13845 \begin_layout Standard
13852 only colors the box but not the characters in the box.
13853 To color all characters, the whole formula is highlighted and the desired
13854 color is chosen in the
13857 \begin_inset space ~
13863 The dialog can be called with the toolbar button
13866 arg "dialog-show character"
13871 Edit\SpecialChar menuseparator
13873 \begin_inset space ~
13876 Style\SpecialChar menuseparator
13880 The formula number then has the same color as the formula.
13881 When the formula number should get another color than the formula characters,
13882 the color must be changed within the formula.
13885 \begin_layout Standard
13889 \begin_layout Standard
13892 \begin_inset Formula
13894 \int A=B\label{eq:red}
13902 \begin_inset Formula
13904 \textcolor{red}{\int A=B}\label{eq:redgreen}
13912 \begin_layout Standard
13914 \begin_inset CommandInset ref
13920 is completely colored red.
13921 \begin_inset Newline newline
13925 \begin_inset CommandInset ref
13927 reference "eq:redgreen"
13931 was first completely colored green to set the color for the formula number.
13932 Subsequently the formula characters were colored red.
13935 \begin_layout Standard
13936 \begin_inset VSpace bigskip
13939 To color the frame different than the rest of the box, the command
13946 \begin_inset Index idx
13949 \begin_layout Plain Layout
13957 is used in the following scheme:
13960 \begin_layout Standard
13965 fcolorbox{frame color}{color}{box content}
13968 \begin_layout Standard
13975 is an extension of the command
13982 The frame width is set, like for
14005 \begin_layout Plain Layout
14017 \begin_inset Formula
14019 \fcolorbox{cyan}{magenta}{A=B}
14028 \begin_layout Plain Layout
14042 \begin_layout Standard
14043 This formula was created with the command
14044 \begin_inset Newline newline
14052 \begin_inset Formula $\to$
14058 \begin_inset Formula $\to$
14068 \begin_layout Standard
14069 \begin_inset VSpace bigskip
14072 To use other colors than the predefined ones, they have to be defined first.
14075 \begin_layout Standard
14076 One can for example define the color
14077 \begin_inset Quotes eld
14085 \begin_inset Quotes erd
14088 with the \SpecialChar LaTeX
14092 \begin_layout Standard
14097 definecolor{darkgreen}{cmyk}{0.5,
14112 \begin_inset Index idx
14115 \begin_layout Plain Layout
14126 \begin_layout Standard
14131 is the color space that denotes the colors
14148 The four comma separated numbers are the portion factor for the corresponding
14149 colors of the color space.
14150 The factors can be in the range of 0
14151 \begin_inset space \thinspace{}
14155 \begin_inset space \thinspace{}
14163 also the color space
14167 can be used for definitions.
14184 , so that there are in this case three portion factors for the corresponding
14186 Furthermore there is the color space
14190 with one portion factor for the gray value.
14193 \begin_layout Standard
14194 As example a framed box with the new defined color
14198 where the characters have been colored
14203 \begin_inset Formula
14205 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14213 \begin_layout Standard
14214 Self-defined colors can also be used for text with the help of the command
14222 \begin_inset Index idx
14225 \begin_layout Plain Layout
14234 \begin_layout Standard
14238 \begin_layout Plain Layout
14242 textcolor{darkgreen}{
14248 \begin_inset Quotes eld
14252 \begin_inset Quotes erd
14259 \begin_layout Plain Layout
14269 \begin_layout Standard
14277 \begin_inset Index idx
14280 \begin_layout Plain Layout
14288 is used in the scheme
14292 textcolor{color}{characters to color}
14297 \begin_layout Subsection
14299 \begin_inset CommandInset label
14301 name "subsec:Paragraph-Boxes"
14306 \begin_inset Index idx
14309 \begin_layout Plain Layout
14310 Boxes ! as paragraph
14318 \begin_layout Standard
14319 A box that can contain several lines and paragraphs, a so-called paragraph
14320 box (parbox), can be created with the menu
14322 Insert\SpecialChar menuseparator
14325 or the toolbar button
14334 \begin_layout Standard
14335 The following example shows a framed parbox in a line:
14338 \begin_layout Standard
14339 \begin_inset VSpace medskip
14343 \begin_inset Box Boxed
14353 height_special "totalheight"
14358 backgroundcolor "none"
14361 \begin_layout Plain Layout
14362 This is a paragraph box.
14364 \begin_inset space \thinspace{}
14367 cm long and can also contain formulas:
14368 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14379 \begin_layout Standard
14380 \begin_inset VSpace medskip
14386 \begin_layout Standard
14387 Such a box is created by right-clicking on the gray box inset.
14388 A dialog pops up showing the box properties.
14402 \begin_inset space \thinspace{}
14407 Vertical Box Alignment
14412 \begin_layout Standard
14413 \begin_inset VSpace medskip
14416 In \SpecialChar LaTeX
14417 a parbox is created with the command
14424 \begin_inset Index idx
14427 \begin_layout Plain Layout
14435 which has the following scheme:
14438 \begin_layout Standard
14443 parbox[position]{width}{box content}
14446 \begin_layout Standard
14461 \begin_inset Quotes eld
14465 \begin_inset Quotes erd
14468 means that the box is aligned within the surrounding text with its last
14475 \begin_inset Quotes eld
14479 \begin_inset Quotes erd
14482 this is done with the first line.
14483 When no position is given, the box will be vertically centered, see section
14491 \begin_inset space ~
14496 manual for examples.
14499 \begin_layout Standard
14500 \begin_inset VSpace bigskip
14503 To frame formulas completely, including the formula number, the formula
14504 must be set into a parbox.
14505 To do this, the command
14519 is inserted in \SpecialChar TeX
14520 mode before the formula.
14528 \begin_inset Index idx
14531 \begin_layout Plain Layout
14539 is hereby the line width set for the document.
14540 Because the frame is outside the parbox, 2
14541 \begin_inset space \thinspace{}
14544 times the frame separation and the frame thickness must be subtracted from
14546 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14555 \begin_layout Plain Layout
14560 is part of every \SpecialChar LaTeX
14561 standard installation.
14567 \begin_inset Index idx
14570 \begin_layout Plain Layout
14576 must be loaded in the \SpecialChar LaTeX
14577 -preamble with the line
14580 \begin_layout Standard
14588 \begin_layout Standard
14589 Behind the formula both boxes are closed by entering
14593 in \SpecialChar TeX
14595 Here is an example:
14599 \begin_layout Plain Layout
14613 \begin_layout Standard
14617 \begin_layout Plain Layout
14635 \begin_inset Formula
14637 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14646 \begin_layout Plain Layout
14657 \begin_layout Plain Layout
14671 \begin_layout Standard
14672 \begin_inset VSpace medskip
14675 As a parbox is used as the argument of
14681 , there is in this case no difference between
14696 \begin_layout Standard
14697 \begin_inset VSpace bigskip
14700 Paragraph boxes are very useful to comment formulas directly.
14707 is used in combination with the command
14721 \begin_inset CommandInset ref
14723 reference "subsec:User-defined-Numbering"
14730 \begin_layout Standard
14731 An example of a formula commented with
14740 \begin_layout Standard
14744 \begin_layout Plain Layout
14757 This is a description.
14758 It is distinctly separated from the formula and multiline.
14762 \begin_layout Plain Layout
14774 \begin_layout Standard
14775 Such a formula must be inserted completely in \SpecialChar TeX
14776 mode because \SpecialChar LyX
14778 support the command
14785 The formula is created with the following command sequence:
14788 \begin_layout Standard
14801 is inserted in \SpecialChar TeX
14806 \begin_layout Plain Layout
14807 When the formula style
14819 can also be replaced by
14826 (formula styles see
14827 \begin_inset CommandInset ref
14829 reference "sec:Formula-Styles"
14838 Then the description follows as normal text and finally
14844 is inserted in \SpecialChar TeX
14858 hereby create a displayed formula.
14861 \begin_layout Standard
14868 can be seen in this example that was
14869 \begin_inset Quotes eld
14873 \begin_inset Quotes erd
14876 using the mathematical textmode:
14877 \begin_inset Formula
14879 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14887 \begin_layout Section
14889 \begin_inset Index idx
14892 \begin_layout Plain Layout
14901 \begin_layout Subsection
14903 \begin_inset CommandInset label
14905 name "subsec:Big-Operators"
14910 \begin_inset Index idx
14913 \begin_layout Plain Layout
14920 \begin_inset Index idx
14923 \begin_layout Plain Layout
14930 \begin_inset Index idx
14933 \begin_layout Plain Layout
14942 \begin_layout Standard
14943 To be able to use all integral operators listed here, the option
14945 Use esint package automatically
14947 must be set in the document settings under
14950 \begin_inset space ~
14958 \begin_layout Standard
14959 \begin_inset space \hfill{}
14963 \begin_inset Tabular
14964 <lyxtabular version="3" rows="11" columns="2">
14965 <features booktabs="true" tabularvalignment="middle">
14966 <column alignment="center" valignment="top" width="0pt">
14967 <column alignment="center" valignment="top" width="0pt">
14969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14972 \begin_layout Plain Layout
14978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14981 \begin_layout Plain Layout
14989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14992 \begin_layout Plain Layout
14996 \begin_inset Index idx
14999 \begin_layout Plain Layout
15012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15015 \begin_layout Plain Layout
15016 \begin_inset Formula $\int$
15026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15029 \begin_layout Plain Layout
15037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15040 \begin_layout Plain Layout
15041 \begin_inset Formula $\oint$
15051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15054 \begin_layout Plain Layout
15062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15065 \begin_layout Plain Layout
15066 \begin_inset Formula $\ointctrclockwise$
15076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15079 \begin_layout Plain Layout
15087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15090 \begin_layout Plain Layout
15091 \begin_inset Formula $\ointclockwise$
15101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15104 \begin_layout Plain Layout
15112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15115 \begin_layout Plain Layout
15116 \begin_inset Formula $\sqint$
15126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15129 \begin_layout Plain Layout
15137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15140 \begin_layout Plain Layout
15142 \begin_inset Formula $\fint$
15152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15155 \begin_layout Plain Layout
15163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15166 \begin_layout Plain Layout
15168 \begin_inset Formula $\landupint$
15178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15181 \begin_layout Plain Layout
15189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15192 \begin_layout Plain Layout
15194 \begin_inset Formula $\landdownint$
15204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15207 \begin_layout Plain Layout
15215 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15218 \begin_layout Plain Layout
15219 \begin_inset Formula $\bigcap$
15229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15232 \begin_layout Plain Layout
15240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15243 \begin_layout Plain Layout
15244 \begin_inset Formula $\bigcup$
15258 \begin_inset space \hfill{}
15262 \begin_inset Tabular
15263 <lyxtabular version="3" rows="11" columns="2">
15264 <features booktabs="true" tabularvalignment="middle">
15265 <column alignment="center" valignment="top" width="0pt">
15266 <column alignment="center" valignment="top" width="0pt">
15268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15271 \begin_layout Plain Layout
15277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15280 \begin_layout Plain Layout
15288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15291 \begin_layout Plain Layout
15295 \begin_inset Index idx
15298 \begin_layout Plain Layout
15311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15314 \begin_layout Plain Layout
15315 \begin_inset Formula $\sum$
15325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15328 \begin_layout Plain Layout
15332 \begin_inset Index idx
15335 \begin_layout Plain Layout
15342 \begin_layout Plain Layout
15361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15364 \begin_layout Plain Layout
15365 \begin_inset Formula $\prod$
15375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15378 \begin_layout Plain Layout
15386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15389 \begin_layout Plain Layout
15390 \begin_inset Formula $\coprod$
15400 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15403 \begin_layout Plain Layout
15411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15414 \begin_layout Plain Layout
15415 \begin_inset Formula $\bigodot$
15425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15428 \begin_layout Plain Layout
15436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15439 \begin_layout Plain Layout
15440 \begin_inset Formula $\bigotimes$
15450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15453 \begin_layout Plain Layout
15461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15464 \begin_layout Plain Layout
15465 \begin_inset Formula $\bigoplus$
15475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15478 \begin_layout Plain Layout
15486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15489 \begin_layout Plain Layout
15490 \begin_inset Formula $\bigwedge$
15500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15503 \begin_layout Plain Layout
15511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15514 \begin_layout Plain Layout
15515 \begin_inset Formula $\bigvee$
15525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15528 \begin_layout Plain Layout
15536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15539 \begin_layout Plain Layout
15540 \begin_inset Formula $\bigsqcup$
15550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15553 \begin_layout Plain Layout
15561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15564 \begin_layout Plain Layout
15565 \begin_inset Formula $\biguplus$
15579 \begin_inset space \hfill{}
15585 \begin_layout Standard
15586 All big operators can also be inserted via the math toolbar button
15589 arg "math-insert \\intop"
15595 \begin_layout Standard
15596 The operators are called big because they are bigger than the sometimes
15597 equal looking binary operators.
15598 All big operators can have limits as described in the next subsection.
15601 \begin_layout Standard
15602 For all integral operators there is a second version available, ending in
15620 These operators are different from
15627 \begin_inset space \space{}
15630 in the style the operator limits are displayed, see
15631 \begin_inset CommandInset ref
15633 reference "subsec:Operator-Limits"
15641 \begin_layout Subsubsection*
15642 Advice for Integrals
15645 \begin_layout Standard
15650 in an integral is an operator, that therefore has to be set upright.
15651 This is done by highlighting the
15655 and using the keyboard shortcut
15665 \begin_layout Plain Layout
15671 \begin_inset CommandInset ref
15673 reference "subsec:Font-Styles"
15683 Finally the smallest space is inserted before the
15687 , as this is usual for operators.
15691 \begin_layout Standard
15693 \begin_inset Formula $\int A(x)dx$
15697 \begin_inset Newline newline
15701 \begin_inset Phantom HPhantom
15704 \begin_layout Plain Layout
15711 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15717 \begin_layout Standard
15718 For multiple integrals there are the following commands:
15719 \begin_inset VSpace medskip
15725 \begin_layout Standard
15726 \begin_inset space \hfill{}
15730 \begin_inset Tabular
15731 <lyxtabular version="3" rows="4" columns="2">
15732 <features booktabs="true" tabularvalignment="middle">
15733 <column alignment="center" valignment="top" width="0pt">
15734 <column alignment="center" valignment="top" width="0pt">
15736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15739 \begin_layout Plain Layout
15745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15748 \begin_layout Plain Layout
15755 <row bottomspace="1mm">
15756 <cell alignment="center" valignment="top" usebox="none">
15759 \begin_layout Plain Layout
15767 <cell alignment="center" valignment="top" usebox="none">
15770 \begin_layout Plain Layout
15771 \begin_inset Formula $\iint$
15780 <row bottomspace="1mm">
15781 <cell alignment="center" valignment="top" usebox="none">
15784 \begin_layout Plain Layout
15792 <cell alignment="center" valignment="top" usebox="none">
15795 \begin_layout Plain Layout
15796 \begin_inset Formula $\oiint$
15805 <row bottomspace="1mm">
15806 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15809 \begin_layout Plain Layout
15817 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15820 \begin_layout Plain Layout
15821 \begin_inset Formula $\sqiint$
15835 \begin_inset space \hfill{}
15839 \begin_inset Tabular
15840 <lyxtabular version="3" rows="4" columns="2">
15841 <features booktabs="true" tabularvalignment="middle">
15842 <column alignment="center" valignment="top" width="0pt">
15843 <column alignment="center" valignment="top" width="0pt">
15845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15848 \begin_layout Plain Layout
15854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15857 \begin_layout Plain Layout
15864 <row bottomspace="1mm">
15865 <cell alignment="center" valignment="top" usebox="none">
15868 \begin_layout Plain Layout
15876 <cell alignment="center" valignment="top" usebox="none">
15879 \begin_layout Plain Layout
15880 \begin_inset Formula $\iiint$
15889 <row bottomspace="1mm">
15890 <cell alignment="center" valignment="top" usebox="none">
15893 \begin_layout Plain Layout
15901 <cell alignment="center" valignment="top" usebox="none">
15904 \begin_layout Plain Layout
15905 \begin_inset Formula $\iiiint$
15914 <row bottomspace="1mm">
15915 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15918 \begin_layout Plain Layout
15926 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15929 \begin_layout Plain Layout
15930 \begin_inset Formula $\dotsint$
15944 \begin_inset space \hfill{}
15950 \begin_layout Subsection
15952 \begin_inset CommandInset label
15954 name "subsec:Operator-Limits"
15959 \begin_inset Index idx
15962 \begin_layout Plain Layout
15971 \begin_layout Standard
15972 Limits are created by super- and subscripts:
15975 \begin_layout Standard
15977 \begin_inset Tabular
15978 <lyxtabular version="3" rows="2" columns="2">
15979 <features booktabs="true" tabularvalignment="middle">
15980 <column alignment="center" valignment="top" width="0pt">
15981 <column alignment="center" valignment="top" width="0pt">
15983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15986 \begin_layout Plain Layout
15992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15995 \begin_layout Plain Layout
16003 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16006 \begin_layout Plain Layout
16012 \begin_inset space \textvisiblespace{}
16016 \begin_inset Formula $\to$
16020 \begin_inset Formula $\to$
16028 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16031 \begin_layout Plain Layout
16032 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16048 \begin_layout Standard
16049 Limits of inline formulas are set right beside the operator.
16050 Limits in displayed formulas are set above or below the operator, except
16051 for integral limits.
16054 \begin_layout Standard
16055 To force that the limits are set beside the operator, the cursor is set
16056 directly behind the operator and the limits type is changed with the menu
16059 Edit\SpecialChar menuseparator
16060 Math\SpecialChar menuseparator
16079 \begin_layout Standard
16080 The default limits type is this:
16081 \begin_inset Formula
16083 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16088 This is how it looks when the limits type was changed to
16095 \begin_inset Formula
16097 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16102 For integrals, except those ending with
16118 etc., the limits are by default set beside the operator.
16119 But for multiple integrals the limits are often set below the operator.
16120 In the following example the limits type was therefore set to
16124 and so set below the integrals:
16125 \begin_inset Formula
16127 \iiint_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16135 \begin_layout Standard
16136 \begin_inset VSpace medskip
16139 To specify conditions for limits, the commands
16146 \begin_inset Index idx
16149 \begin_layout Plain Layout
16164 \begin_inset Index idx
16167 \begin_layout Plain Layout
16176 To create for example this expression
16177 \begin_inset Formula
16179 \sum_{\begin{subarray}{c}
16183 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16191 \begin_layout Standard
16192 the following has to be done:
16193 \begin_inset Newline newline
16205 \begin_inset space \textvisiblespace{}
16211 One is now in a blue box under the summation operator and insert there
16217 \begin_inset space \textvisiblespace{}
16223 The blue box is now within a purple box and now several lines can be written
16225 A new line is created by inserting a line break (
16228 arg "newline-insert newline"
16233 \begin_inset Newline newline
16238 0<k<1000 Ctrl+Return
16239 \begin_inset Newline newline
16244 is typed in, a new box appears below for the new line.
16247 \begin_layout Standard
16248 The alignment of the lines can be changed to left aligned with the
16258 Edit\SpecialChar menuseparator
16262 To get right alignment,
16267 \begin_inset space \textvisiblespace{}
16272 is inserted at the beginning of the line.
16275 \begin_layout Standard
16288 with the difference that the lines are always centered.
16291 \begin_layout Standard
16292 \begin_inset VSpace bigskip
16296 \begin_inset CommandInset ref
16298 reference "eq:substack"
16302 there can be too much space beside an operator, because the characters
16303 following the operator are set beside the limits.
16304 To avoid this the command
16311 \begin_inset Index idx
16314 \begin_layout Plain Layout
16323 To activate it, set in the document settings under
16326 \begin_inset space ~
16336 \begin_inset Index idx
16339 \begin_layout Plain Layout
16340 Packages ! mathtools
16348 \begin_inset space ~
16360 sets the space besides the operator to 0
16361 \begin_inset space \thinspace{}
16365 \begin_inset Newline newline
16369 \begin_inset CommandInset ref
16371 reference "eq:substack"
16375 , one uses the command
16378 \begin_layout Standard
16386 \begin_layout Standard
16387 and inserts the operator with its limits into the braces.
16388 Behind the brace one continues the formula:
16389 \begin_inset Formula
16391 \smashoperator{\sum_{\begin{subarray}{c}
16395 \end{subarray}}^{n}}k^{-2}
16403 \begin_layout Standard
16404 It is possible to set the space of only one side of the operator to 0
16405 \begin_inset space \thinspace{}
16409 To do this write either
16428 stands for the left and
16432 for the right side of the operator.
16433 Here is an example of the possible
16442 \begin_layout Standard
16443 \begin_inset Formula
16445 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}
16453 \begin_layout Standard
16454 \begin_inset VSpace bigskip
16460 \begin_layout Standard
16461 When several consecutive operators have limits the typesetting of the limits
16462 looks often imperfect in the output, see this example:
16463 \begin_inset Formula
16465 \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}
16470 To improve the typesetting set in the document settings under
16473 \begin_inset space ~
16483 \begin_inset Index idx
16486 \begin_layout Plain Layout
16487 Packages ! mathtools
16495 \begin_inset space ~
16501 Then insert into your formula the command
16508 \begin_inset Index idx
16511 \begin_layout Plain Layout
16519 directly before the first operator.
16520 The example will then look like this:
16521 \begin_inset Formula
16523 \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}
16531 \begin_layout Standard
16532 \begin_inset VSpace bigskip
16535 How to use one limit for several operators is described in
16536 \begin_inset CommandInset ref
16538 reference "subsec:Self-defined-Operators"
16545 \begin_layout Subsection
16546 Decoration for Operators
16547 \begin_inset Index idx
16550 \begin_layout Plain Layout
16551 Operators ! Decoration
16559 \begin_layout Standard
16567 \begin_inset Index idx
16570 \begin_layout Plain Layout
16585 \begin_inset Index idx
16588 \begin_layout Plain Layout
16596 characters can be placed above or below an operator, respectively.
16604 \begin_inset Index idx
16607 \begin_layout Plain Layout
16615 characters can be set before and behind a big operator.
16618 \begin_layout Standard
16620 \begin_inset space ~
16632 \begin_layout Itemize
16639 is used to set characters at the corners of the operator
16642 \begin_layout Itemize
16649 is used to set characters before and/or behind the operator (this variant
16650 represents \SpecialChar LaTeX
16660 \begin_layout Itemize
16667 is used to set characters at the left corners and/or behind the operator
16670 \begin_layout Itemize
16677 is used to set characters at the right corners and/or before the operator
16680 \begin_layout Standard
16681 For example the command
16686 \begin_inset space \textvisiblespace{}
16692 \begin_inset space \textvisiblespace{}
16696 \begin_inset Formula $\to$
16700 \begin_inset Formula $\to$
16704 \begin_inset space \textvisiblespace{}
16714 \begin_inset Formula
16716 \sideset{}{'}\sum_{k=1}^{n}
16724 \begin_layout Standard
16725 \begin_inset Note Greyedout
16728 \begin_layout Plain Layout
16735 can only be used to decorate big operators, binary operators are not allowed.
16743 \begin_layout Standard
16756 can also be used to decorate symbols and characters.
16757 For example, the command
16762 \begin_inset space \textvisiblespace{}
16768 \begin_inset space \textvisiblespace{}
16774 \begin_inset Formula $\uparrow$
16782 \begin_inset Formula
16784 \overset{a}{\maltese}
16792 \begin_layout Subsection
16794 \begin_inset CommandInset label
16796 name "subsec:Binary-Operators"
16801 \begin_inset Index idx
16804 \begin_layout Plain Layout
16813 \begin_layout Standard
16814 Binary operators are surrounded by space when there is a character before
16816 \begin_inset VSpace medskip
16822 \begin_layout Standard
16823 \begin_inset Tabular
16824 <lyxtabular version="3" rows="13" columns="2">
16825 <features booktabs="true" tabularvalignment="middle">
16826 <column alignment="center" valignment="top" width="0pt">
16827 <column alignment="center" valignment="top" width="0pt">
16829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16832 \begin_layout Plain Layout
16834 \begin_inset Note Note
16837 \begin_layout Plain Layout
16844 is only used as spacer.
16854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16868 \begin_layout Plain Layout
16874 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16877 \begin_layout Plain Layout
16878 \begin_inset Formula $+$
16888 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16891 \begin_layout Plain Layout
16897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16900 \begin_layout Plain Layout
16901 \begin_inset Formula $-$
16911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16914 \begin_layout Plain Layout
16922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16925 \begin_layout Plain Layout
16926 \begin_inset Formula $\pm$
16936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16939 \begin_layout Plain Layout
16947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16950 \begin_layout Plain Layout
16951 \begin_inset Formula $\mp$
16961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16964 \begin_layout Plain Layout
16972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16975 \begin_layout Plain Layout
16976 \begin_inset Formula $\cdot$
16986 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16989 \begin_layout Plain Layout
16997 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17000 \begin_layout Plain Layout
17001 \begin_inset Formula $\times$
17011 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17014 \begin_layout Plain Layout
17022 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17025 \begin_layout Plain Layout
17026 \begin_inset Formula $\div$
17036 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17039 \begin_layout Plain Layout
17043 \begin_layout Plain Layout
17056 \begin_layout Plain Layout
17068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17071 \begin_layout Plain Layout
17072 \begin_inset Formula $*$
17082 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17085 \begin_layout Plain Layout
17093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17096 \begin_layout Plain Layout
17097 \begin_inset Formula $\star$
17107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17121 \begin_layout Plain Layout
17122 \begin_inset Formula $\circ$
17132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\diamond$
17157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17171 \begin_layout Plain Layout
17172 \begin_inset Formula $\bullet$
17186 \begin_inset space \hfill{}
17190 \begin_inset Tabular
17191 <lyxtabular version="3" rows="13" columns="2">
17192 <features booktabs="true" tabularvalignment="middle">
17193 <column alignment="center" valignment="top" width="0pt">
17194 <column alignment="center" valignment="top" width="0pt">
17196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17199 \begin_layout Plain Layout
17205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17208 \begin_layout Plain Layout
17216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17219 \begin_layout Plain Layout
17227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17230 \begin_layout Plain Layout
17231 \begin_inset Formula $\nabla$
17241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17244 \begin_layout Plain Layout
17252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17255 \begin_layout Plain Layout
17256 \begin_inset Formula $\bigtriangledown$
17266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17269 \begin_layout Plain Layout
17277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17280 \begin_layout Plain Layout
17281 \begin_inset Formula $\bigtriangleup$
17291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17294 \begin_layout Plain Layout
17302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17305 \begin_layout Plain Layout
17306 \begin_inset Formula $\Box$
17316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17319 \begin_layout Plain Layout
17327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17330 \begin_layout Plain Layout
17331 \begin_inset Formula $\cap$
17341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17344 \begin_layout Plain Layout
17352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17355 \begin_layout Plain Layout
17356 \begin_inset Formula $\cup$
17366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17369 \begin_layout Plain Layout
17377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17380 \begin_layout Plain Layout
17381 \begin_inset Formula $\dagger$
17391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17394 \begin_layout Plain Layout
17402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17405 \begin_layout Plain Layout
17406 \begin_inset Formula $\ddagger$
17416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17419 \begin_layout Plain Layout
17427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17430 \begin_layout Plain Layout
17431 \begin_inset Formula $\wr$
17441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17455 \begin_layout Plain Layout
17456 \begin_inset Formula $\bigcirc$
17466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17469 \begin_layout Plain Layout
17477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17480 \begin_layout Plain Layout
17481 \begin_inset Formula $\wedge$
17491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17494 \begin_layout Plain Layout
17502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17505 \begin_layout Plain Layout
17506 \begin_inset Formula $\vee$
17520 \begin_inset space \hfill{}
17524 \begin_inset Tabular
17525 <lyxtabular version="3" rows="13" columns="2">
17526 <features booktabs="true" tabularvalignment="middle">
17527 <column alignment="center" valignment="top" width="0pt">
17528 <column alignment="center" valignment="top" width="0pt">
17530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17533 \begin_layout Plain Layout
17539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17542 \begin_layout Plain Layout
17550 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17553 \begin_layout Plain Layout
17561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17564 \begin_layout Plain Layout
17565 \begin_inset Formula $\oplus$
17575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17578 \begin_layout Plain Layout
17586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17589 \begin_layout Plain Layout
17590 \begin_inset Formula $\ominus$
17600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17603 \begin_layout Plain Layout
17611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17614 \begin_layout Plain Layout
17615 \begin_inset Formula $\otimes$
17625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17628 \begin_layout Plain Layout
17636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17639 \begin_layout Plain Layout
17640 \begin_inset Formula $\oslash$
17650 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17653 \begin_layout Plain Layout
17661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17664 \begin_layout Plain Layout
17665 \begin_inset Formula $\odot$
17675 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17678 \begin_layout Plain Layout
17686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17689 \begin_layout Plain Layout
17690 \begin_inset Formula $\amalg$
17700 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17703 \begin_layout Plain Layout
17711 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17714 \begin_layout Plain Layout
17715 \begin_inset Formula $\uplus$
17725 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17728 \begin_layout Plain Layout
17736 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17739 \begin_layout Plain Layout
17740 \begin_inset Formula $\setminus$
17750 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17753 \begin_layout Plain Layout
17761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17764 \begin_layout Plain Layout
17765 \begin_inset Formula $\sqcap$
17775 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17778 \begin_layout Plain Layout
17786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17789 \begin_layout Plain Layout
17790 \begin_inset Formula $\sqcup$
17800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17803 \begin_layout Plain Layout
17811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17814 \begin_layout Plain Layout
17815 \begin_inset Formula $\triangleleft$
17825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17828 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17839 \begin_layout Plain Layout
17840 \begin_inset Formula $\triangleright$
17856 \begin_layout Standard
17857 All binary operators can also be inserted via the math toolbar button
17860 arg "math-insert \\pm"
17866 \begin_layout Standard
17867 To typeset the Laplace operator also
17884 \begin_inset Formula $\nabla^{2}$
17887 ) can be used instead of
17896 \begin_layout Standard
17903 Insert\SpecialChar menuseparator
17915 \begin_layout Subsection
17916 Self-defined Operators
17917 \begin_inset CommandInset label
17919 name "subsec:Self-defined-Operators"
17924 \begin_inset Index idx
17927 \begin_layout Plain Layout
17928 Operators ! self-defined
17936 \begin_layout Standard
17937 With the help of the command
17941 DeclareMathOperator
17944 \begin_inset Index idx
17947 \begin_layout Plain Layout
17952 DeclareMathOperator
17957 custom operators can be defined in the \SpecialChar LaTeX
17959 Its command scheme is:
17962 \begin_layout Standard
17967 DeclareMathOperator{new command}{display}
17970 \begin_layout Standard
17971 Display can be characters or symbols that define how the operator looks
17973 To define a big operator a * is set behind the command.
17974 All self-defined big operators can have limits as described in
17975 \begin_inset CommandInset ref
17977 reference "subsec:Operator-Limits"
17984 \begin_layout Standard
17985 For example the \SpecialChar LaTeX
17989 \begin_layout Standard
17994 DeclareMathOperator*{
18001 \begin_layout Standard
18002 defines the command
18008 , that inserts a big operator consisting of the lozenge symbol from
18009 \begin_inset CommandInset ref
18011 reference "subsec:Miscellaneous-Symbols"
18016 \begin_inset Formula
18018 \Lozenge_{n=1}^{\infty}
18023 The command for this formula is:
18034 \begin_inset Formula $\to$
18040 \begin_layout Standard
18041 \begin_inset VSpace bigskip
18044 When self-defined operators are not used several times in the document,
18045 they can also be defined with the commands
18052 \begin_inset Index idx
18055 \begin_layout Plain Layout
18070 \begin_inset Index idx
18073 \begin_layout Plain Layout
18081 , which have the following scheme:
18084 \begin_layout Standard
18098 \begin_layout Standard
18105 defines big operators,
18114 \begin_layout Standard
18122 \begin_inset space \thinspace{}
18126 \begin_inset space \space{}
18129 be used to use one limit for several operators:
18132 \begin_layout Standard
18133 \begin_inset Formula
18135 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18143 \begin_layout Standard
18144 The command for the formula above is:
18145 \begin_inset Newline newline
18161 \begin_inset space \textvisiblespace{}
18167 \begin_inset Formula $\to$
18173 \begin_inset space \textvisiblespace{}
18181 \begin_layout Section
18183 \begin_inset Index idx
18186 \begin_layout Plain Layout
18195 \begin_layout Subsection
18197 \begin_inset CommandInset label
18199 name "subsec:Font-Styles"
18204 \begin_inset Index idx
18207 \begin_layout Plain Layout
18216 \begin_layout Standard
18217 Latin letters in formulas can be set in one of the following font styles:
18220 \begin_layout Standard
18222 \begin_inset Tabular
18223 <lyxtabular version="3" rows="6" columns="3">
18224 <features booktabs="true" tabularvalignment="middle">
18225 <column alignment="center" valignment="top" width="0pt">
18226 <column alignment="center" valignment="top">
18227 <column alignment="center" valignment="top">
18229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18232 \begin_layout Plain Layout
18238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18241 \begin_layout Plain Layout
18247 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18250 \begin_layout Plain Layout
18258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18261 \begin_layout Plain Layout
18267 \begin_inset space \textvisiblespace{}
18277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\mathbb{ABC}$
18289 <cell alignment="center" valignment="top" usebox="none">
18292 \begin_layout Plain Layout
18300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18303 \begin_layout Plain Layout
18309 \begin_inset space \textvisiblespace{}
18319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18322 \begin_layout Plain Layout
18323 \begin_inset Formula $\mathbf{AbC}$
18331 <cell alignment="center" valignment="top" usebox="none">
18334 \begin_layout Plain Layout
18347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18350 \begin_layout Plain Layout
18356 \begin_inset space \textvisiblespace{}
18366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18369 \begin_layout Plain Layout
18370 \begin_inset Formula $\boldsymbol{AbC}$
18378 <cell alignment="center" valignment="top" usebox="none">
18381 \begin_layout Plain Layout
18384 arg "font-boldsymbol"
18394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18397 \begin_layout Plain Layout
18403 \begin_inset space \textvisiblespace{}
18413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18416 \begin_layout Plain Layout
18417 \begin_inset Formula $\mathcal{ABC}$
18425 <cell alignment="center" valignment="top" usebox="none">
18428 \begin_layout Plain Layout
18436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18439 \begin_layout Plain Layout
18445 \begin_inset space \textvisiblespace{}
18455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18458 \begin_layout Plain Layout
18459 \begin_inset Formula $\mathfrak{AbC}$
18467 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18470 \begin_layout Plain Layout
18484 \begin_layout Standard
18486 \begin_inset Tabular
18487 <lyxtabular version="3" rows="6" columns="3">
18488 <features booktabs="true" tabularvalignment="middle">
18489 <column alignment="center" valignment="top" width="0pt">
18490 <column alignment="center" valignment="top">
18491 <column alignment="center" valignment="top">
18493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18496 \begin_layout Plain Layout
18502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18505 \begin_layout Plain Layout
18511 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18514 \begin_layout Plain Layout
18522 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18525 \begin_layout Plain Layout
18531 \begin_inset space \textvisiblespace{}
18541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18544 \begin_layout Plain Layout
18545 \begin_inset Formula $\mathit{AbC}$
18553 <cell alignment="center" valignment="top" usebox="none">
18556 \begin_layout Plain Layout
18564 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18567 \begin_layout Plain Layout
18573 \begin_inset space \textvisiblespace{}
18583 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18586 \begin_layout Plain Layout
18587 \begin_inset Formula $\mathrm{AbC}$
18595 <cell alignment="center" valignment="top" usebox="none">
18598 \begin_layout Plain Layout
18611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18614 \begin_layout Plain Layout
18620 \begin_inset space \textvisiblespace{}
18630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18633 \begin_layout Plain Layout
18634 \begin_inset Formula $\mathsf{AbC}$
18642 <cell alignment="center" valignment="top" usebox="none">
18645 \begin_layout Plain Layout
18658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18661 \begin_layout Plain Layout
18667 \begin_inset space \textvisiblespace{}
18677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18680 \begin_layout Plain Layout
18681 \begin_inset Formula $\mathtt{AbC}$
18689 <cell alignment="center" valignment="top" usebox="none">
18692 \begin_layout Plain Layout
18695 arg "font-typewriter"
18705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18708 \begin_layout Plain Layout
18714 \begin_inset space \textvisiblespace{}
18724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18727 \begin_layout Plain Layout
18728 \begin_inset Formula $\mathscr{ABC}$
18736 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18739 \begin_layout Plain Layout
18753 \begin_layout Standard
18754 \begin_inset Note Greyedout
18757 \begin_layout Plain Layout
18780 can only be used for big letters.
18788 \begin_layout Standard
18789 Predefined is the style
18798 \begin_layout Standard
18799 The style commands work also for letters in mathematical constructs:
18800 \begin_inset Formula
18802 \mathfrak{A=\frac{b}{C}}
18810 \begin_layout Standard
18811 Characters in mathematical text don't appear in a math font style but in
18812 the text font style
18819 That their style can't be set correctly via the text style dialog is a
18820 bug in \SpecialChar LyX
18825 \begin_layout Plain Layout
18826 \begin_inset CommandInset href
18828 name "LyX-bug #4629"
18829 target "https://www.lyx.org/trac/ticket/4629"
18842 \begin_layout Standard
18843 Instead of the style commands the dialog
18845 Edit\SpecialChar menuseparator
18846 Math\SpecialChar menuseparator
18849 or the toolbar button
18852 arg "math-insert \\font"
18858 \begin_layout Subsection
18860 \begin_inset CommandInset label
18862 name "subsec:Bold-Formulas"
18867 \begin_inset Index idx
18870 \begin_layout Plain Layout
18879 \begin_layout Standard
18880 To make a complete formula bold, the command
18886 from the previous subsection cannot be used, because it doesn't work for
18887 small Greek letters.
18888 Furthermore it prints Latin letters always upright, like in the following
18892 \begin_layout Standard
18893 \begin_inset Formula
18895 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18903 \begin_layout Standard
18904 To display the formula correctly, the command
18911 \begin_inset Formula
18913 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18918 It is also possible to set the formula in a
18920 boldmath environment
18923 This environment is created by inserting the command
18930 \begin_inset Index idx
18933 \begin_layout Plain Layout
18941 in \SpecialChar TeX
18943 To end the environment, the command
18950 \begin_inset Index idx
18953 \begin_layout Plain Layout
18961 is inserted in \SpecialChar TeX
18966 \begin_layout Plain Layout
18976 \begin_inset Formula
18978 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18987 \begin_layout Plain Layout
18999 \begin_layout Subsection
19001 \begin_inset Index idx
19004 \begin_layout Plain Layout
19013 \begin_layout Standard
19014 Formulas can be colored like normal text: Highlight a formula or a formula
19020 Here is a formula in magenta:
19021 \begin_inset Formula
19023 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19031 \begin_layout Standard
19032 You can also define your own colors as described in
19033 \begin_inset CommandInset ref
19035 reference "subsec:Colored-Boxes"
19040 They can be used with the \SpecialChar TeX
19048 \begin_inset Index idx
19051 \begin_layout Plain Layout
19062 \begin_layout Standard
19067 textcolor{color}{characters or formula}
19070 \begin_layout Standard
19071 The following example was colored completely dark green and partly red:
19074 \begin_layout Standard
19078 \begin_layout Plain Layout
19082 textcolor{darkgreen}{
19088 \begin_inset Formula
19090 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19099 \begin_layout Plain Layout
19109 \begin_layout Standard
19110 Due to a bug in \SpecialChar LyX
19111 only complete formulas can be colored with self-defined
19116 \begin_layout Plain Layout
19117 \begin_inset CommandInset href
19119 name "LyX-bug #5269"
19120 target "https://www.lyx.org/trac/ticket/5269"
19133 \begin_layout Subsection
19135 \begin_inset CommandInset label
19137 name "subsec:Font-Sizes"
19142 \begin_inset Index idx
19145 \begin_layout Plain Layout
19154 \begin_layout Standard
19155 For characters in formulas there are, analog to characters in text, the
19156 following size commands:
19159 \begin_layout Standard
19203 \begin_inset Newline newline
19225 \begin_layout Standard
19226 The size produced by the commands depends on the document font size, which
19227 corresponds to the command
19234 The other commands produce smaller or larger sizes than
19241 The font size can however not exceed a certain value.
19242 Is for example the document font size 12
19243 \begin_inset space \thinspace{}
19252 switches to the same size as
19262 \begin_layout Standard
19263 A size command is inserted in \SpecialChar TeX
19264 mode before the formula and sets the size
19265 for all following formula and text characters.
19266 To switch back to the initial size, the command
19272 is inserted behind the formula in \SpecialChar TeX
19276 \begin_layout Standard
19277 Within a formula the size can be changed using the following size commands
19278 or the toolbar button
19281 arg "math-insert \\style"
19287 \begin_layout Standard
19290 \begin_inset Tabular
19291 <lyxtabular version="3" rows="5" columns="2">
19292 <features booktabs="true" tabularvalignment="middle">
19293 <column alignment="center" valignment="top" width="0pt">
19294 <column alignment="center" valignment="top">
19296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19299 \begin_layout Plain Layout
19305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19308 \begin_layout Plain Layout
19316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19319 \begin_layout Plain Layout
19323 \begin_inset Index idx
19326 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19343 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19352 <row topspace="1mm">
19353 <cell alignment="center" valignment="top" usebox="none">
19356 \begin_layout Plain Layout
19364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19367 \begin_layout Plain Layout
19368 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19381 \begin_layout Plain Layout
19389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19392 \begin_layout Plain Layout
19393 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19406 \begin_layout Plain Layout
19414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19417 \begin_layout Plain Layout
19418 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19434 \begin_layout Standard
19435 After entering these commands, a blue box appears in which the formula parts
19439 \begin_layout Standard
19440 There is a further method to change the font size, that though only works
19441 for symbols or letters in mathematical text.
19442 To use it, one of the above text size commands is inserted in mathematical
19444 All following characters until the end of the mathematical text or until
19445 another size command will have the selected size.
19447 \begin_inset VSpace -2mm
19453 \begin_layout Standard
19457 \begin_layout Plain Layout
19467 \begin_inset Formula
19469 A=\frac{B}{c}\cdot\maltese
19475 \begin_inset Formula
19477 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19486 \begin_layout Plain Layout
19498 \begin_layout Standard
19499 \begin_inset VSpace medskip
19502 Before both formulas the command
19509 The command for the second formula is:
19510 \begin_inset Newline newline
19518 \begin_inset space \textvisiblespace{}
19524 \begin_inset space \textvisiblespace{}
19530 \begin_inset space \textvisiblespace{}
19536 \begin_inset space \textvisiblespace{}
19540 \begin_inset Formula $\to$
19544 \begin_inset Formula $\to$
19548 \begin_inset Newline newline
19552 \begin_inset space \hspace*{}
19563 \begin_inset space \textvisiblespace{}
19569 \begin_inset space \textvisiblespace{}
19575 \begin_inset space \textvisiblespace{}
19581 \begin_layout Standard
19582 If a symbol cannot be displayed in different sizes, it will always be displayed
19583 in the default size.
19586 \begin_layout Section
19588 \begin_inset Index idx
19591 \begin_layout Plain Layout
19600 \begin_layout Standard
19601 Greek letters can also be inserted via the toolbar button
19604 arg "math-insert \\alpha"
19608 All international typesetting norms purport that Greek letters in math
19609 have to be typeset italic/slanted.
19610 In some languages, like French or Russian, they are nevertheless sometimes
19614 \begin_layout Subsection
19616 \begin_inset Index idx
19619 \begin_layout Plain Layout
19620 Greek letters ! small
19628 \begin_layout Standard
19629 \begin_inset space \hfill{}
19633 \begin_inset Tabular
19634 <lyxtabular version="3" rows="11" columns="2">
19635 <features booktabs="true" tabularvalignment="middle">
19636 <column alignment="center" valignment="top" width="0pt">
19637 <column alignment="center" valignment="top" width="0pt">
19639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19642 \begin_layout Plain Layout
19648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19651 \begin_layout Plain Layout
19659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19662 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19673 \begin_layout Plain Layout
19674 \begin_inset Formula $\alpha$
19684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19687 \begin_layout Plain Layout
19695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19698 \begin_layout Plain Layout
19699 \begin_inset Formula $\beta$
19709 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19712 \begin_layout Plain Layout
19720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19723 \begin_layout Plain Layout
19724 \begin_inset Formula $\gamma$
19734 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19737 \begin_layout Plain Layout
19745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19748 \begin_layout Plain Layout
19749 \begin_inset Formula $\delta$
19759 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19762 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19774 \begin_inset Formula $\epsilon$
19784 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19787 \begin_layout Plain Layout
19795 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19798 \begin_layout Plain Layout
19799 \begin_inset Formula $\varepsilon$
19809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19812 \begin_layout Plain Layout
19820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19823 \begin_layout Plain Layout
19824 \begin_inset Formula $\zeta$
19834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19837 \begin_layout Plain Layout
19845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19848 \begin_layout Plain Layout
19849 \begin_inset Formula $\eta$
19859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19862 \begin_layout Plain Layout
19870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19873 \begin_layout Plain Layout
19874 \begin_inset Formula $\theta$
19884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19887 \begin_layout Plain Layout
19895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19898 \begin_layout Plain Layout
19899 \begin_inset Formula $\vartheta$
19913 \begin_inset space \hfill{}
19917 \begin_inset Tabular
19918 <lyxtabular version="3" rows="12" columns="2">
19919 <features booktabs="true" tabularvalignment="middle">
19920 <column alignment="center" valignment="top" width="0pt">
19921 <column alignment="center" valignment="top" width="0pt">
19923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19926 \begin_layout Plain Layout
19932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19935 \begin_layout Plain Layout
19943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19946 \begin_layout Plain Layout
19954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19957 \begin_layout Plain Layout
19958 \begin_inset Formula $\iota$
19968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19971 \begin_layout Plain Layout
19979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19982 \begin_layout Plain Layout
19983 \begin_inset Formula $\kappa$
19993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19996 \begin_layout Plain Layout
20004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20007 \begin_layout Plain Layout
20008 \begin_inset Formula $\varkappa$
20018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20021 \begin_layout Plain Layout
20029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20032 \begin_layout Plain Layout
20033 \begin_inset Formula $\lambda$
20043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20046 \begin_layout Plain Layout
20054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20057 \begin_layout Plain Layout
20058 \begin_inset Formula $\mu$
20068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20071 \begin_layout Plain Layout
20079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20082 \begin_layout Plain Layout
20083 \begin_inset Formula $\nu$
20093 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20096 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Plain Layout
20108 \begin_inset Formula $\xi$
20118 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20121 \begin_layout Plain Layout
20127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20130 \begin_layout Plain Layout
20131 \begin_inset Formula $o$
20141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20144 \begin_layout Plain Layout
20152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20155 \begin_layout Plain Layout
20156 \begin_inset Formula $\pi$
20166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20169 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20180 \begin_layout Plain Layout
20181 \begin_inset Formula $\varpi$
20191 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20194 \begin_layout Plain Layout
20202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20205 \begin_layout Plain Layout
20206 \begin_inset Formula $\rho$
20220 \begin_inset space \hfill{}
20224 \begin_inset Tabular
20225 <lyxtabular version="3" rows="11" columns="2">
20226 <features booktabs="true" tabularvalignment="middle">
20227 <column alignment="center" valignment="top" width="0pt">
20228 <column alignment="center" valignment="top" width="0pt">
20230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20233 \begin_layout Plain Layout
20239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20242 \begin_layout Plain Layout
20250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20253 \begin_layout Plain Layout
20261 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20264 \begin_layout Plain Layout
20265 \begin_inset Formula $\varrho$
20275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20278 \begin_layout Plain Layout
20286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20289 \begin_layout Plain Layout
20290 \begin_inset Formula $\sigma$
20300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20303 \begin_layout Plain Layout
20311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20314 \begin_layout Plain Layout
20315 \begin_inset Formula $\varsigma$
20325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20328 \begin_layout Plain Layout
20336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20339 \begin_layout Plain Layout
20340 \begin_inset Formula $\tau$
20350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20353 \begin_layout Plain Layout
20361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20364 \begin_layout Plain Layout
20365 \begin_inset Formula $\upsilon$
20375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20378 \begin_layout Plain Layout
20386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20389 \begin_layout Plain Layout
20390 \begin_inset Formula $\phi$
20400 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20403 \begin_layout Plain Layout
20411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20414 \begin_layout Plain Layout
20415 \begin_inset Formula $\varphi$
20425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20428 \begin_layout Plain Layout
20436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20439 \begin_layout Plain Layout
20440 \begin_inset Formula $\chi$
20450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20453 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20464 \begin_layout Plain Layout
20465 \begin_inset Formula $\psi$
20475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20490 \begin_inset Formula $\omega$
20504 \begin_inset space \hfill{}
20510 \begin_layout Standard
20511 \begin_inset VSpace medskip
20517 \begin_layout Standard
20518 How to create special upright Greek letters is explained in
20519 \begin_inset CommandInset ref
20521 reference "subsec:Upright-small-Greek"
20528 \begin_layout Subsection
20530 \begin_inset Index idx
20533 \begin_layout Plain Layout
20534 Greek letters ! big
20542 \begin_layout Standard
20543 \begin_inset space \hfill{}
20547 \begin_inset Tabular
20548 <lyxtabular version="3" rows="7" columns="2">
20549 <features booktabs="true" tabularvalignment="middle">
20550 <column alignment="center" valignment="top" width="0pt">
20551 <column alignment="center" valignment="top" width="0pt">
20553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20556 \begin_layout Plain Layout
20562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20565 \begin_layout Plain Layout
20573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20576 \begin_layout Plain Layout
20584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20587 \begin_layout Plain Layout
20588 \begin_inset Formula $\Gamma$
20598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20601 \begin_layout Plain Layout
20609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20612 \begin_layout Plain Layout
20613 \begin_inset Formula $\Delta$
20623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20626 \begin_layout Plain Layout
20634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20637 \begin_layout Plain Layout
20638 \begin_inset Formula $\Theta$
20648 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20662 \begin_layout Plain Layout
20663 \begin_inset Formula $\Lambda$
20673 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20676 \begin_layout Plain Layout
20684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20687 \begin_layout Plain Layout
20688 \begin_inset Formula $\Xi$
20698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20701 \begin_layout Plain Layout
20709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Plain Layout
20713 \begin_inset Formula $\Pi$
20727 \begin_inset space \hfill{}
20731 \begin_inset Tabular
20732 <lyxtabular version="3" rows="6" columns="2">
20733 <features booktabs="true" tabularvalignment="middle">
20734 <column alignment="center" valignment="top" width="0pt">
20735 <column alignment="center" valignment="top" width="0pt">
20737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20740 \begin_layout Plain Layout
20746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20749 \begin_layout Plain Layout
20757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20760 \begin_layout Plain Layout
20768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20771 \begin_layout Plain Layout
20772 \begin_inset Formula $\Sigma$
20782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20785 \begin_layout Plain Layout
20793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20796 \begin_layout Plain Layout
20797 \begin_inset Formula $\Upsilon$
20807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20810 \begin_layout Plain Layout
20818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20821 \begin_layout Plain Layout
20822 \begin_inset Formula $\Phi$
20832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20835 \begin_layout Plain Layout
20843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20846 \begin_layout Plain Layout
20847 \begin_inset Formula $\Psi$
20857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20860 \begin_layout Plain Layout
20868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20871 \begin_layout Plain Layout
20872 \begin_inset Formula $\Omega$
20886 \begin_inset space \hfill{}
20892 \begin_layout Standard
20893 \begin_inset VSpace medskip
20896 That the big Greek letters appear upright is caused by a design bug when
20899 To get correct italic big letters, begin every command with
20904 For example the command
20911 \begin_inset Formula $\varGamma$
20915 Another way is to load the package
20923 \begin_layout Plain Layout
20928 is part of the \SpecialChar LaTeX
20934 \begin_inset Index idx
20937 \begin_layout Plain Layout
20942 \begin_layout Plain Layout
20962 \begin_inset Index idx
20965 \begin_layout Plain Layout
20971 with the \SpecialChar LaTeX
20975 \begin_layout Standard
20980 usepackage{fixmath}
20983 \begin_layout Standard
20984 Then all big Greek letters in a document will automatically be typeset italic.
20987 \begin_layout Subsection
20989 \begin_inset Index idx
20992 \begin_layout Plain Layout
20993 Greek letters ! bold
21001 \begin_layout Standard
21002 Greek letters cannot be set with different font styles like Latin letters.
21003 They can only be made bold with the command
21010 \begin_inset Index idx
21013 \begin_layout Plain Layout
21024 \begin_layout Standard
21026 \begin_inset Tabular
21027 <lyxtabular version="3" rows="3" columns="2">
21028 <features booktabs="true" tabularvalignment="middle">
21029 <column alignment="center" valignment="top" width="0pt">
21030 <column alignment="center" valignment="top">
21032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21035 \begin_layout Plain Layout
21041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21044 \begin_layout Plain Layout
21052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21055 \begin_layout Plain Layout
21067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21070 \begin_layout Plain Layout
21071 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21084 \begin_layout Plain Layout
21096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21099 \begin_layout Plain Layout
21100 \begin_inset Formula $\theta\boldsymbol{\theta}$
21116 \begin_layout Section
21121 \begin_layout Plain Layout
21134 \begin_layout Plain Layout
21135 A list with all symbols of most of the \SpecialChar LaTeX
21136 -packages can be found in
21137 \begin_inset CommandInset citation
21153 \begin_layout Plain Layout
21161 \begin_inset Note Note
21164 \begin_layout Plain Layout
21167 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21170 \begin_layout Plain Layout
21173 texorpdfstring is in section
21174 \begin_inset CommandInset ref
21176 reference "subsec:Formulas-in-Section"
21186 \begin_inset Index idx
21189 \begin_layout Plain Layout
21198 \begin_layout Standard
21199 Many of the symbols listed in this section can also be inserted via the
21203 arg "math-insert \\nabla"
21209 arg "math-insert \\digamma"
21215 \begin_layout Subsection
21216 Mathematical Symbols
21217 \begin_inset CommandInset label
21219 name "subsec:Mathematical-Symbols"
21224 \begin_inset Index idx
21227 \begin_layout Plain Layout
21228 Symbols ! mathematical
21236 \begin_layout Standard
21237 \begin_inset Tabular
21238 <lyxtabular version="3" rows="10" columns="2">
21239 <features booktabs="true" tabularvalignment="middle">
21240 <column alignment="center" valignment="top" width="0pt">
21241 <column alignment="center" valignment="top" width="0pt">
21243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21246 \begin_layout Plain Layout
21252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21255 \begin_layout Plain Layout
21263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21266 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21278 \begin_inset Formula $\neg$
21288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\Im$
21313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\Re$
21338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\aleph$
21363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\partial$
21388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\infty$
21413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21427 \begin_layout Plain Layout
21428 \begin_inset Formula $\wp$
21438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $\imath$
21463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\jmath$
21492 \begin_inset space \hfill{}
21496 \begin_inset Tabular
21497 <lyxtabular version="3" rows="10" columns="2">
21498 <features booktabs="true" tabularvalignment="middle">
21499 <column alignment="center" valignment="top" width="0pt">
21500 <column alignment="center" valignment="top" width="0pt">
21502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21505 \begin_layout Plain Layout
21511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Plain Layout
21516 \begin_inset Note Note
21519 \begin_layout Plain Layout
21526 is only used as spacer.
21538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $\forall$
21563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\exists$
21588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21603 \begin_inset Formula $\nexists$
21613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21616 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21628 \begin_inset Formula $\emptyset$
21638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21653 \begin_inset Formula $\varnothing$
21663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21666 \begin_layout Plain Layout
21674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21677 \begin_layout Plain Layout
21678 \begin_inset Formula $\dag$
21688 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21691 \begin_layout Plain Layout
21699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21702 \begin_layout Plain Layout
21703 \begin_inset Formula $\ddag$
21713 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21716 \begin_layout Plain Layout
21724 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21727 \begin_layout Plain Layout
21731 \begin_layout Plain Layout
21741 \begin_inset Formula $\complement$
21748 \begin_layout Plain Layout
21762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\Bbbk$
21791 \begin_inset space \hfill{}
21795 \begin_inset Tabular
21796 <lyxtabular version="3" rows="10" columns="2">
21797 <features booktabs="true" tabularvalignment="middle">
21798 <column alignment="center" valignment="top" width="0pt">
21799 <column alignment="center" valignment="top" width="0pt">
21801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21804 \begin_layout Plain Layout
21810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\prime$
21846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\backprime$
21871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\mho$
21896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\triangle$
21921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\angle$
21946 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\measuredangle$
21971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\sphericalangle$
21996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\top$
22021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\bot$
22052 \begin_layout Subsection
22053 Miscellaneous Symbols
22054 \begin_inset CommandInset label
22056 name "subsec:Miscellaneous-Symbols"
22061 \begin_inset Index idx
22064 \begin_layout Plain Layout
22065 Symbols ! miscellaneous
22073 \begin_layout Standard
22076 \begin_inset Tabular
22077 <lyxtabular version="3" rows="10" columns="2">
22078 <features booktabs="true" tabularvalignment="middle">
22079 <column alignment="center" valignment="top" width="0pt">
22080 <column alignment="center" valignment="top" width="0pt">
22082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22085 \begin_layout Plain Layout
22091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\flat$
22127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\natural$
22152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\sharp$
22177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22180 \begin_layout Plain Layout
22188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22192 \begin_inset Formula $\surd$
22202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22216 \begin_layout Plain Layout
22217 \begin_inset Formula $\checkmark$
22227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Plain Layout
22242 \begin_inset Formula $\yen$
22252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22255 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22267 \begin_inset Formula $\pounds$
22277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22289 \begin_layout Plain Layout
22290 \begin_inset Formula $\$$
22300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22312 \begin_layout Plain Layout
22313 \begin_inset Formula $§$
22327 \begin_inset space \hfill{}
22331 \begin_inset Tabular
22332 <lyxtabular version="3" rows="10" columns="2">
22333 <features booktabs="true" tabularvalignment="middle">
22334 <column alignment="center" valignment="top" width="0pt">
22335 <column alignment="center" valignment="top">
22337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22340 \begin_layout Plain Layout
22346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22349 \begin_layout Plain Layout
22357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\hbar$
22382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\hslash$
22407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\clubsuit$
22432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\spadesuit$
22457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\bigstar$
22482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\blacklozenge$
22507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\blacktriangle$
22532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\blacktriangledown$
22557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\bullet$
22586 \begin_inset space \hfill{}
22590 \begin_inset Tabular
22591 <lyxtabular version="3" rows="10" columns="2">
22592 <features booktabs="true" tabularvalignment="middle">
22593 <column alignment="center" valignment="top" width="0pt">
22594 <column alignment="center" valignment="top" width="0pt">
22596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22608 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22619 \begin_layout Plain Layout
22627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22630 \begin_layout Plain Layout
22631 \begin_inset Formula $\diamondsuit$
22641 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22644 \begin_layout Plain Layout
22652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22655 \begin_layout Plain Layout
22656 \begin_inset Formula $\Diamond$
22666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22669 \begin_layout Plain Layout
22677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22680 \begin_layout Plain Layout
22681 \begin_inset Formula $\heartsuit$
22691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22694 \begin_layout Plain Layout
22702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22705 \begin_layout Plain Layout
22706 \begin_inset Formula $\P$
22716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22719 \begin_layout Plain Layout
22727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22730 \begin_layout Plain Layout
22731 \begin_inset Formula $\copyright$
22741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22744 \begin_layout Plain Layout
22752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22755 \begin_layout Plain Layout
22756 \begin_inset Formula $\circledR$
22766 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22769 \begin_layout Plain Layout
22777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22780 \begin_layout Plain Layout
22781 \begin_inset Formula $\maltese$
22791 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22794 \begin_layout Plain Layout
22802 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22805 \begin_layout Plain Layout
22806 \begin_inset Formula $\diagup$
22816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22819 \begin_layout Plain Layout
22827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22830 \begin_layout Plain Layout
22831 \begin_inset Formula $\diagdown$
22847 \begin_layout Standard
22848 \begin_inset VSpace medskip
22854 \begin_layout Standard
22855 Some symbols can be displayed in different sizes, see
22856 \begin_inset CommandInset ref
22858 reference "subsec:Font-Sizes"
22865 \begin_layout Subsection
22867 \begin_inset Index idx
22870 \begin_layout Plain Layout
22871 Symbols ! Euro-symbol
22877 \begin_inset Index idx
22880 \begin_layout Plain Layout
22887 \begin_layout Plain Layout
22904 \begin_layout Standard
22905 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22911 \begin_inset Index idx
22914 \begin_layout Plain Layout
22920 must be installed and loaded with the \SpecialChar LaTeX
22924 \begin_layout Standard
22929 usepackage[gennarrow]{eurosym}
22932 \begin_layout Standard
22933 The Euro symbol can now be inserted with the command
22940 \begin_inset Index idx
22943 \begin_layout Plain Layout
22954 \begin_layout Standard
22955 The Euro symbol can directly be inserted with the € key in mathematical
22956 text, without having
22971 can also be inserted in \SpecialChar TeX
22973 The official currency symbol can then be inserted with the command
22980 \begin_inset Index idx
22983 \begin_layout Plain Layout
22991 , that is only available in \SpecialChar TeX
22995 \begin_layout Standard
22999 \begin_layout Plain Layout
23009 \begin_inset Note Note
23012 \begin_layout Plain Layout
23013 The following table will only be displayed when the \SpecialChar LaTeX
23026 \begin_layout Standard
23027 An overview about the different Euro symbols:
23030 \begin_layout Standard
23032 \begin_inset Tabular
23033 <lyxtabular version="3" rows="4" columns="3">
23034 <features booktabs="true" tabularvalignment="middle">
23035 <column alignment="center" valignment="top" width="0pt">
23036 <column alignment="center" valignment="top" width="0pt">
23037 <column alignment="center" valignment="top" width="0pt">
23039 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23042 \begin_layout Plain Layout
23046 \begin_layout Plain Layout
23050 cmidrule[0.08em]{2-3}
23060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23063 \begin_layout Plain Layout
23069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23072 \begin_layout Plain Layout
23080 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23083 \begin_layout Plain Layout
23089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23092 \begin_layout Plain Layout
23100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23103 \begin_layout Plain Layout
23104 \begin_inset Formula $\euro$
23114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23117 \begin_layout Plain Layout
23123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23126 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\mbox{€}$
23146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23174 \begin_layout Plain Layout
23194 \begin_inset Note Note
23197 \begin_layout Plain Layout
23204 is used here only for table borders.
23214 manual for details.
23222 \begin_layout Standard
23226 \begin_layout Plain Layout
23236 \begin_inset Note Note
23239 \begin_layout Plain Layout
23240 The following will be displayed when the \SpecialChar LaTeX
23253 \begin_layout Standard
23254 You need to install the \SpecialChar LaTeX
23259 to see the rest of this subsection in the output.
23262 \begin_layout Standard
23266 \begin_layout Plain Layout
23278 \begin_layout Section
23280 \begin_inset CommandInset label
23282 name "sec:Relations"
23287 \begin_inset Index idx
23290 \begin_layout Plain Layout
23297 \begin_inset Index idx
23300 \begin_layout Plain Layout
23305 \begin_layout Plain Layout
23316 \begin_layout Plain Layout
23331 \begin_layout Standard
23332 All following relations can also be inserted via the toolbar button
23335 arg "math-insert \\leq"
23341 \begin_layout Standard
23342 \begin_inset Tabular
23343 <lyxtabular version="3" rows="17" columns="2">
23344 <features booktabs="true" tabularvalignment="middle">
23345 <column alignment="center" valignment="top" width="0pt">
23346 <column alignment="center" valignment="top" width="0pt">
23348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23351 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23371 \begin_layout Plain Layout
23377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23380 \begin_layout Plain Layout
23381 \begin_inset Formula $<$
23391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23394 \begin_layout Plain Layout
23402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23405 \begin_layout Plain Layout
23406 \begin_inset Formula $\le$
23416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23419 \begin_layout Plain Layout
23427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23430 \begin_layout Plain Layout
23431 \begin_inset Formula $\ll$
23441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23444 \begin_layout Plain Layout
23452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23455 \begin_layout Plain Layout
23456 \begin_inset Formula $\prec$
23466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23469 \begin_layout Plain Layout
23477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23480 \begin_layout Plain Layout
23481 \begin_inset Formula $\preceq$
23491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23494 \begin_layout Plain Layout
23502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23505 \begin_layout Plain Layout
23506 \begin_inset Formula $\subset$
23516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23519 \begin_layout Plain Layout
23527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23530 \begin_layout Plain Layout
23531 \begin_inset Formula $\subseteq$
23541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23544 \begin_layout Plain Layout
23552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23555 \begin_layout Plain Layout
23556 \begin_inset Formula $\sqsubseteq$
23566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23569 \begin_layout Plain Layout
23577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23580 \begin_layout Plain Layout
23581 \begin_inset Formula $\in$
23591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23605 \begin_layout Plain Layout
23606 \begin_inset Formula $\vdash$
23616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23619 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23631 \begin_inset Formula $\smile$
23641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\lhd$
23666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23669 \begin_layout Plain Layout
23677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23680 \begin_layout Plain Layout
23681 \begin_inset Formula $\unlhd$
23691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23694 \begin_layout Plain Layout
23702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23705 \begin_layout Plain Layout
23706 \begin_inset Formula $\gtrless$
23716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23730 \begin_layout Plain Layout
23731 \begin_inset Formula $\mid$
23741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23744 \begin_layout Plain Layout
23752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23755 \begin_layout Plain Layout
23756 \begin_inset Formula $\nmid$
23770 \begin_inset space \hfill{}
23774 \begin_inset Tabular
23775 <lyxtabular version="3" rows="17" columns="2">
23776 <features booktabs="true" tabularvalignment="middle">
23777 <column alignment="center" valignment="top" width="0pt">
23778 <column alignment="center" valignment="top" width="0pt">
23780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23783 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23792 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23803 \begin_layout Plain Layout
23809 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23812 \begin_layout Plain Layout
23813 \begin_inset Formula $=$
23823 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23826 \begin_layout Plain Layout
23834 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Plain Layout
23838 \begin_inset Formula $\not=$
23848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23863 \begin_inset Formula $\equiv$
23873 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23876 \begin_layout Plain Layout
23884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23887 \begin_layout Plain Layout
23888 \begin_inset Formula $\sim$
23898 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23913 \begin_inset Formula $\simeq$
23923 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23926 \begin_layout Plain Layout
23934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23937 \begin_layout Plain Layout
23938 \begin_inset Formula $\approx$
23948 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23951 \begin_layout Plain Layout
23959 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23962 \begin_layout Plain Layout
23963 \begin_inset Formula $\cong$
23973 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23976 \begin_layout Plain Layout
23984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23987 \begin_layout Plain Layout
23988 \begin_inset Formula $\bowtie$
23998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24001 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $\notin$
24023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24037 \begin_layout Plain Layout
24038 \begin_inset Formula $\perp$
24048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24062 \begin_layout Plain Layout
24063 \begin_inset Formula $\propto$
24073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24088 \begin_inset Formula $\asymp$
24098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24101 \begin_layout Plain Layout
24109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24112 \begin_layout Plain Layout
24113 \begin_inset Formula $\doteq$
24123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24126 \begin_layout Plain Layout
24134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24137 \begin_layout Plain Layout
24138 \begin_inset Formula $\circeq$
24148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24162 \begin_layout Plain Layout
24163 \begin_inset Formula $\models$
24173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24176 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24187 \begin_layout Plain Layout
24188 \begin_inset Formula $\widehat{=}$
24202 \begin_inset space \hfill{}
24206 \begin_inset Tabular
24207 <lyxtabular version="3" rows="17" columns="2">
24208 <features booktabs="true" tabularvalignment="middle">
24209 <column alignment="center" valignment="top" width="0pt">
24210 <column alignment="center" valignment="top" width="0pt">
24212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24215 \begin_layout Plain Layout
24221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24224 \begin_layout Plain Layout
24232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24235 \begin_layout Plain Layout
24241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24244 \begin_layout Plain Layout
24245 \begin_inset Formula $>$
24255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24269 \begin_layout Plain Layout
24270 \begin_inset Formula $\ge$
24280 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24283 \begin_layout Plain Layout
24291 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24294 \begin_layout Plain Layout
24295 \begin_inset Formula $\gg$
24305 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24308 \begin_layout Plain Layout
24316 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24319 \begin_layout Plain Layout
24320 \begin_inset Formula $\succ$
24330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24333 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24344 \begin_layout Plain Layout
24345 \begin_inset Formula $\succeq$
24355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24369 \begin_layout Plain Layout
24370 \begin_inset Formula $\supset$
24380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24394 \begin_layout Plain Layout
24395 \begin_inset Formula $\supseteq$
24405 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $\sqsupseteq$
24430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24444 \begin_layout Plain Layout
24445 \begin_inset Formula $\ni$
24455 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24469 \begin_layout Plain Layout
24470 \begin_inset Formula $\dashv$
24480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24483 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24495 \begin_inset Formula $\frown$
24505 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24508 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24519 \begin_layout Plain Layout
24520 \begin_inset Formula $\rhd$
24530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24533 \begin_layout Plain Layout
24541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24544 \begin_layout Plain Layout
24545 \begin_inset Formula $\unrhd$
24555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24558 \begin_layout Plain Layout
24566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24569 \begin_layout Plain Layout
24570 \begin_inset Formula $\lessgtr$
24580 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Plain Layout
24595 \begin_inset Formula $\parallel$
24605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24608 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24619 \begin_layout Plain Layout
24620 \begin_inset Formula $\nparallel$
24636 \begin_layout Standard
24637 \begin_inset VSpace medskip
24652 are bigger than the equal looking operators
24667 \begin_layout Standard
24669 supports also many special relations.
24670 Use the toolbar button
24673 arg "math-insert \\leqq"
24676 to see a list of these relations.
24679 \begin_layout Standard
24680 Relations are, in contrary to symbols, always surrounded by space.
24683 \begin_layout Standard
24684 Relations with labels can be created with the command
24691 \begin_inset Index idx
24694 \begin_layout Plain Layout
24705 \begin_layout Standard
24707 \begin_inset Tabular
24708 <lyxtabular version="3" rows="2" columns="2">
24709 <features booktabs="true" tabularvalignment="middle">
24710 <column alignment="center" valignment="top" width="0pt">
24711 <column alignment="center" valignment="top">
24713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24716 \begin_layout Plain Layout
24722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24725 \begin_layout Plain Layout
24732 <row topspace="1.5mm">
24733 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24736 \begin_layout Plain Layout
24740 \begin_inset space \textvisiblespace{}
24748 \begin_inset space \textvisiblespace{}
24752 \begin_inset Formula $\downarrow$
24758 \begin_inset space \textvisiblespace{}
24762 \begin_inset space \textvisiblespace{}
24770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24773 \begin_layout Plain Layout
24774 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24790 \begin_layout Section
24794 \begin_layout Subsection
24795 Predefined Functions
24796 \begin_inset CommandInset label
24798 name "subsec:Predefined-Functions"
24803 \begin_inset Index idx
24806 \begin_layout Plain Layout
24807 Functions ! predefined
24815 \begin_layout Standard
24816 In general, variables are set
24820 in mathematical expressions, but not function names, because
24821 \begin_inset Formula $sin$
24824 could be misunderstood as
24825 \begin_inset Formula $s\cdot i\cdot n$
24829 Therefore there are predefined functions which are additionally a bit separated
24831 They are inserted as commands starting with a backslash before their name.
24834 \begin_layout Standard
24836 \begin_inset Tabular
24837 <lyxtabular version="3" rows="2" columns="2">
24838 <features booktabs="true" tabularvalignment="middle">
24839 <column alignment="center" valignment="top" width="0pt">
24840 <column alignment="center" valignment="top" width="0pt">
24842 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24845 \begin_layout Plain Layout
24851 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24854 \begin_layout Plain Layout
24862 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24865 \begin_layout Plain Layout
24871 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24874 \begin_layout Plain Layout
24875 \begin_inset Formula $Asin(x)+B$
24889 \begin_inset space \quad{}
24893 \begin_inset Tabular
24894 <lyxtabular version="3" rows="2" columns="2">
24895 <features booktabs="true" tabularvalignment="middle">
24896 <column alignment="center" valignment="top" width="0pt">
24897 <column alignment="center" valignment="top" width="0pt">
24899 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24902 \begin_layout Plain Layout
24908 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24911 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24922 \begin_layout Plain Layout
24930 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24933 \begin_layout Plain Layout
24934 \begin_inset Formula $A\sin(x)+B$
24950 \begin_layout Standard
24951 The following functions are predefined:
24954 \begin_layout Standard
24955 \begin_inset VSpace -2mm
24961 \begin_layout Standard
24963 \begin_inset Tabular
24964 <lyxtabular version="3" rows="9" columns="4">
24965 <features booktabs="true" tabularvalignment="middle">
24966 <column alignment="center" valignment="top" width="0pt">
24967 <column alignment="center" valignment="top" width="0pt">
24968 <column alignment="center" valignment="top" width="0pt">
24969 <column alignment="center" valignment="top" width="0pt">
24971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24983 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24992 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25001 \begin_layout Plain Layout
25009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25012 \begin_layout Plain Layout
25020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25023 \begin_layout Plain Layout
25031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25034 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25045 \begin_layout Plain Layout
25055 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25058 \begin_layout Plain Layout
25066 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25069 \begin_layout Plain Layout
25077 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25080 \begin_layout Plain Layout
25088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25091 \begin_layout Plain Layout
25101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25104 \begin_layout Plain Layout
25112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25115 \begin_layout Plain Layout
25123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25126 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25137 \begin_layout Plain Layout
25147 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25150 \begin_layout Plain Layout
25158 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25172 \begin_layout Plain Layout
25180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25183 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25196 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25207 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25218 \begin_layout Plain Layout
25226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25229 \begin_layout Plain Layout
25239 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25242 \begin_layout Plain Layout
25250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25253 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25264 \begin_layout Plain Layout
25272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25275 \begin_layout Plain Layout
25285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25288 \begin_layout Plain Layout
25296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25310 \begin_layout Plain Layout
25318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25321 \begin_layout Plain Layout
25331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25334 \begin_layout Plain Layout
25342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25345 \begin_layout Plain Layout
25353 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25356 \begin_layout Plain Layout
25364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25367 \begin_layout Plain Layout
25383 \begin_layout Standard
25384 They can also be inserted with the math toolbar button
25387 arg "math-insert \\functions"
25393 \begin_layout Subsection
25394 Self-defined Functions
25395 \begin_inset Index idx
25398 \begin_layout Plain Layout
25399 Functions ! self-defined
25407 \begin_layout Standard
25408 To use a function that is not predefined, like for example the sign function
25409 sgn(x), there are two possibilities:
25412 \begin_layout Itemize
25413 Define the function by inserting the following line to the \SpecialChar LaTeX
25418 \begin_layout Plain Layout
25423 DeclareMathOperator
25426 \begin_inset CommandInset ref
25428 reference "subsec:Self-defined-Operators"
25438 \begin_inset Newline newline
25442 \begin_inset VSpace -3mm
25446 \begin_inset Newline newline
25453 DeclareMathOperator{
25458 \begin_inset Index idx
25461 \begin_layout Plain Layout
25466 DeclareMathOperator
25472 \begin_inset Newline newline
25476 \begin_inset VSpace -2mm
25480 \begin_inset Newline newline
25483 Now the new defined function can be called with the command
25492 \begin_layout Itemize
25493 Write the formula as usual, mark the formula name, in our example the letters
25498 , and change it to mathematical text.
25499 Finally, a space is inserted between prefactor and function.
25502 \begin_layout Standard
25503 The result is the same with both methods as with a predefined function
25507 \begin_layout Plain Layout
25508 In \SpecialChar LyX
25509 self-defined functions are displayed red, predefined ones black.
25517 \begin_layout Standard
25519 \begin_inset Tabular
25520 <lyxtabular version="3" rows="3" columns="2">
25521 <features booktabs="true" tabularvalignment="middle">
25522 <column alignment="center" valignment="top" width="0pt">
25523 <column alignment="center" valignment="top" width="0pt">
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25528 \begin_layout Plain Layout
25534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25537 \begin_layout Plain Layout
25545 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25548 \begin_layout Plain Layout
25556 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25559 \begin_layout Plain Layout
25560 \begin_inset Formula $A\sgn(x)+B$
25570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25573 \begin_layout Plain Layout
25577 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25588 \begin_layout Plain Layout
25589 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25605 \begin_layout Standard
25606 The first method is more suitable when the self-defined function should
25607 be used several times.
25610 \begin_layout Subsection
25612 \begin_inset Index idx
25615 \begin_layout Plain Layout
25624 \begin_layout Standard
25625 For limits, in addition to the commands
25632 \begin_inset Index idx
25635 \begin_layout Plain Layout
25655 the following functions are defined:
25658 \begin_layout Standard
25660 \begin_inset Tabular
25661 <lyxtabular version="3" rows="5" columns="2">
25662 <features booktabs="true" tabularvalignment="middle">
25663 <column alignment="center" valignment="top" width="0pt">
25664 <column alignment="center" valignment="top" width="0pt">
25666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25669 \begin_layout Plain Layout
25675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25678 \begin_layout Plain Layout
25686 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25689 \begin_layout Plain Layout
25697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25700 \begin_layout Plain Layout
25701 \begin_inset Formula $\varliminf$
25710 <row topspace="1.5mm">
25711 <cell alignment="center" valignment="top" usebox="none">
25714 \begin_layout Plain Layout
25722 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25725 \begin_layout Plain Layout
25726 \begin_inset Formula $\varlimsup$
25735 <row topspace="1.5mm">
25736 <cell alignment="center" valignment="top" usebox="none">
25739 \begin_layout Plain Layout
25747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25750 \begin_layout Plain Layout
25751 \begin_inset Formula $\varprojlim$
25760 <row topspace="1.5mm" bottomspace="1mm">
25761 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25764 \begin_layout Plain Layout
25772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25775 \begin_layout Plain Layout
25776 \begin_inset Formula $\varinjlim$
25792 \begin_layout Standard
25793 \begin_inset VSpace medskip
25796 The limit is created by inserting a subscript.
25797 It is set right beside the function in an inline formula:
25800 \begin_layout Standard
25802 \begin_inset Tabular
25803 <lyxtabular version="3" rows="2" columns="2">
25804 <features booktabs="true" tabularvalignment="middle">
25805 <column alignment="center" valignment="top" width="0pt">
25806 <column alignment="center" valignment="top" width="0pt">
25808 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25811 \begin_layout Plain Layout
25817 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25820 \begin_layout Plain Layout
25828 <cell alignment="center" valignment="top" usebox="none">
25831 \begin_layout Plain Layout
25837 \begin_inset space \textvisiblespace{}
25841 \begin_inset space \textvisiblespace{}
25849 <cell alignment="center" valignment="top" usebox="none">
25852 \begin_layout Plain Layout
25853 \begin_inset Formula $\lim_{x\to A}x=B$
25869 \begin_layout Standard
25870 In a displayed formula the limit is set below the formula, as usual:
25871 \begin_inset Formula
25881 \begin_layout Standard
25882 \begin_inset VSpace medskip
25888 \begin_layout Standard
25889 How to adjust the typesetting of the limits see
25890 \begin_inset CommandInset ref
25892 reference "subsec:Operator-Limits"
25899 \begin_layout Subsection
25901 \begin_inset Index idx
25904 \begin_layout Plain Layout
25905 Functions ! modulo-
25913 \begin_layout Standard
25914 The modulo-function is special, because it exists in four variants.
25915 The variants in a displayed formula are:
25916 \begin_inset Formula
25918 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25919 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25920 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25921 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25922 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25930 \begin_layout Standard
25931 In an inline formula less space is set before the function names for all
25933 By default the modulo-functions take only the first following character
25935 To use more than one character, one has to put them into \SpecialChar TeX
25937 \begin_inset Formula
25939 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25940 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25941 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25949 \begin_layout Section
25951 \begin_inset Index idx
25954 \begin_layout Plain Layout
25963 \begin_layout Standard
25964 The characters ^ and _ would normally create a superscript and subscript,
25966 To get these characters you have to insert them with a leading
25971 \begin_layout Standard
25974 \begin_inset Tabular
25975 <lyxtabular version="3" rows="3" columns="2">
25976 <features booktabs="true" tabularvalignment="middle">
25977 <column alignment="left" valignment="top" width="0pt">
25978 <column alignment="block" valignment="top">
25980 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25983 \begin_layout Plain Layout
25989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25992 \begin_layout Plain Layout
26000 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26003 \begin_layout Plain Layout
26007 \begin_inset space \textvisiblespace{}
26015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26018 \begin_layout Plain Layout
26019 \begin_inset Formula $\mathcircumflex$
26029 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26032 \begin_layout Plain Layout
26040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26043 \begin_layout Plain Layout
26044 \begin_inset Formula $\_$
26060 \begin_layout Subsection
26061 Special Characters in Mathematical Text
26064 \begin_layout Standard
26065 The following commands can only be used in mathematical text or in \SpecialChar TeX
26069 \begin_layout Standard
26070 \begin_inset space \hfill{}
26074 \begin_inset Tabular
26075 <lyxtabular version="3" rows="8" columns="2">
26076 <features booktabs="true" tabularvalignment="middle">
26077 <column alignment="left" valignment="top" width="0pt">
26078 <column alignment="block" valignment="top">
26080 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26083 \begin_layout Plain Layout
26089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26092 \begin_layout Plain Layout
26100 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26103 \begin_layout Plain Layout
26111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26114 \begin_layout Plain Layout
26115 \begin_inset Formula $\textrm{œ}$
26125 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26128 \begin_layout Plain Layout
26136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26139 \begin_layout Plain Layout
26140 \begin_inset Formula $\textrm{Œ}$
26150 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26153 \begin_layout Plain Layout
26161 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26164 \begin_layout Plain Layout
26165 \begin_inset Formula $\textrm{æ}$
26175 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26178 \begin_layout Plain Layout
26186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26189 \begin_layout Plain Layout
26190 \begin_inset Formula $\textrm{Æ}$
26200 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26203 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26214 \begin_layout Plain Layout
26215 \begin_inset Formula $\textrm{å}$
26225 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26239 \begin_layout Plain Layout
26240 \begin_inset Formula $\textrm{Å}$
26250 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26253 \begin_layout Plain Layout
26261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26264 \begin_layout Plain Layout
26265 \begin_inset Formula $\textrm{ı}$
26279 \begin_inset space \hfill{}
26283 \begin_inset Tabular
26284 <lyxtabular version="3" rows="8" columns="2">
26285 <features booktabs="true" tabularvalignment="middle">
26286 <column alignment="left" valignment="top" width="0pt">
26287 <column alignment="center" valignment="top">
26289 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26292 \begin_layout Plain Layout
26294 \begin_inset Note Note
26297 \begin_layout Plain Layout
26299 \begin_inset space \thinspace{}
26302 mm is used for separation, because otherwise the output will be ¡ and ¿
26313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26316 \begin_layout Plain Layout
26324 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26339 \begin_inset Formula $\textrm{ø}$
26349 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26364 \begin_inset Formula $\textrm{Ø}$
26374 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26377 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26389 \begin_inset Formula $\textrm{ł}$
26399 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26413 \begin_layout Plain Layout
26414 \begin_inset Formula $\textrm{Ł}$
26424 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26427 \begin_layout Plain Layout
26429 \begin_inset space \hspace{}
26434 \begin_inset space \textvisiblespace{}
26442 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26445 \begin_layout Plain Layout
26446 \begin_inset Formula $\textrm{!`}$
26456 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26459 \begin_layout Plain Layout
26461 \begin_inset space \hspace{}
26466 \begin_inset space \textvisiblespace{}
26474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26477 \begin_layout Plain Layout
26478 \begin_inset Formula $\textrm{?`}$
26488 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26491 \begin_layout Plain Layout
26499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26502 \begin_layout Plain Layout
26503 \begin_inset Formula $\textrm{ȷ}$
26517 \begin_inset space \hfill{}
26523 \begin_layout Standard
26525 \begin_inset Formula $\textrm{Å}$
26529 \begin_inset Formula $\textrm{Ø}$
26532 can also be inserted via the math toolbar button
26535 arg "math-insert \\digamma"
26541 \begin_layout Standard
26542 An exception are the commands
26545 \begin_inset space \hspace{}
26554 \begin_inset space \hspace{}
26560 , because they can be inserted in \SpecialChar LyX
26564 \begin_layout Subsection
26566 \begin_inset CommandInset label
26568 name "subsec:Accents-in-Text"
26573 \begin_inset Index idx
26576 \begin_layout Plain Layout
26585 \begin_layout Standard
26586 With the following commands all letters can be accented.
26587 The commands must be inserted in \SpecialChar TeX
26591 \begin_layout Standard
26592 \begin_inset space \hfill{}
26596 \begin_inset Tabular
26597 <lyxtabular version="3" rows="8" columns="2">
26598 <features booktabs="true" tabularvalignment="middle">
26599 <column alignment="left" valignment="top" width="0pt">
26600 <column alignment="block" valignment="top">
26602 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26605 \begin_layout Plain Layout
26611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26614 \begin_layout Plain Layout
26622 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26625 \begin_layout Plain Layout
26629 \begin_inset Quotes grd
26637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26640 \begin_layout Plain Layout
26644 \begin_layout Plain Layout
26660 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26663 \begin_layout Plain Layout
26671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26674 \begin_layout Plain Layout
26678 \begin_layout Plain Layout
26694 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26697 \begin_layout Plain Layout
26701 \begin_inset space \textvisiblespace{}
26709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26712 \begin_layout Plain Layout
26716 \begin_layout Plain Layout
26732 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26735 \begin_layout Plain Layout
26743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26746 \begin_layout Plain Layout
26750 \begin_layout Plain Layout
26766 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26769 \begin_layout Plain Layout
26773 \begin_inset space \textvisiblespace{}
26781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26784 \begin_layout Plain Layout
26788 \begin_layout Plain Layout
26804 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26807 \begin_layout Plain Layout
26811 \begin_inset space \textvisiblespace{}
26819 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26822 \begin_layout Plain Layout
26826 \begin_layout Plain Layout
26842 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26845 \begin_layout Plain Layout
26849 \begin_inset space \textvisiblespace{}
26857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26860 \begin_layout Plain Layout
26864 \begin_layout Plain Layout
26884 \begin_inset space \hfill{}
26888 \begin_inset Tabular
26889 <lyxtabular version="3" rows="8" columns="2">
26890 <features booktabs="true" tabularvalignment="middle">
26891 <column alignment="left" valignment="top" width="0pt">
26892 <column alignment="center" valignment="top">
26894 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26897 \begin_layout Plain Layout
26903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26906 \begin_layout Plain Layout
26914 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26917 \begin_layout Plain Layout
26921 \begin_inset space \textvisiblespace{}
26929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26932 \begin_layout Plain Layout
26936 \begin_layout Plain Layout
26952 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26955 \begin_layout Plain Layout
26963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26966 \begin_layout Plain Layout
26970 \begin_layout Plain Layout
26986 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26989 \begin_layout Plain Layout
26993 \begin_inset Index idx
26996 \begin_layout Plain Layout
27007 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27010 \begin_layout Plain Layout
27014 \begin_layout Plain Layout
27030 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27033 \begin_layout Plain Layout
27041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27044 \begin_layout Plain Layout
27048 \begin_layout Plain Layout
27064 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27067 \begin_layout Plain Layout
27071 \begin_inset space \textvisiblespace{}
27079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27082 \begin_layout Plain Layout
27086 \begin_layout Plain Layout
27102 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27105 \begin_layout Plain Layout
27109 \begin_inset space \textvisiblespace{}
27117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27120 \begin_layout Plain Layout
27124 \begin_layout Plain Layout
27140 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27143 \begin_layout Plain Layout
27147 \begin_inset space \textvisiblespace{}
27155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27158 \begin_layout Plain Layout
27162 \begin_layout Plain Layout
27182 \begin_inset space \hfill{}
27188 \begin_layout Standard
27189 \begin_inset VSpace medskip
27198 also two different characters can be accented.
27204 \begin_inset space \textvisiblespace{}
27213 \begin_layout Plain Layout
27225 \begin_layout Standard
27238 can in combination with vowels directly be inserted with the keyboard without
27239 using \SpecialChar TeX
27241 The same applies for the tilde
27245 \begin_layout Plain Layout
27246 This only applies for keyboards where the tilde is defined as accent.
27255 in combination with
27270 \begin_layout Standard
27313 and accents that are inserted directly with the keyboard are also available
27314 in mathematical text.
27315 For the other accents there are special math commands to be used in formulas,
27317 \begin_inset CommandInset ref
27319 reference "subsec:Accents-for-one"
27326 \begin_layout Standard
27327 \begin_inset VSpace bigskip
27330 Furthermore, with the command
27337 \begin_inset Index idx
27340 \begin_layout Plain Layout
27348 all numbers and letters can be set into a circle, quasi accented with a
27349 circle, similar to the copyright symbol.
27352 \begin_layout Standard
27354 \begin_inset Tabular
27355 <lyxtabular version="3" rows="3" columns="2">
27356 <features booktabs="true" tabularvalignment="middle">
27357 <column alignment="center" valignment="top" width="0pt">
27358 <column alignment="center" valignment="top">
27360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27363 \begin_layout Plain Layout
27369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27372 \begin_layout Plain Layout
27380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27383 \begin_layout Plain Layout
27391 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27394 \begin_layout Plain Layout
27398 \begin_layout Plain Layout
27413 <row topspace="1mm">
27414 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27417 \begin_layout Plain Layout
27428 raisebox{-1.5pt}{W}}
27433 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27436 \begin_layout Plain Layout
27440 \begin_layout Plain Layout
27470 \begin_layout Standard
27471 One has to take care that the character fits in the circle.
27482 \begin_layout Plain Layout
27484 \begin_inset CommandInset ref
27486 reference "subsec:Font-Sizes"
27495 specifies thereby the size of the circle.
27506 \begin_layout Plain Layout
27508 \begin_inset CommandInset ref
27510 reference "subsec:Boxes-without-Frame"
27519 the character can be centered.
27522 \begin_layout Subsection
27524 \begin_inset Index idx
27527 \begin_layout Plain Layout
27536 \begin_layout Standard
27537 Old-style figures (also known as old-style numerals) are created with the
27545 \begin_inset Index idx
27548 \begin_layout Plain Layout
27557 The command can be used in formulas and in \SpecialChar TeX
27559 The command scheme is:
27562 \begin_layout Standard
27567 oldstylenums{number}
27570 \begin_layout Standard
27575 oldstylenums{0123456789}
27578 \begin_inset Formula $\oldstylenums{0123456789}$
27584 \begin_layout Section
27586 \begin_inset CommandInset label
27588 name "sec:Formula-Styles"
27593 \begin_inset Index idx
27596 \begin_layout Plain Layout
27605 \begin_layout Itemize
27606 There are two different alignment styles:
27610 \begin_layout Description
27611 Centered is the predefined standard.
27614 \begin_layout Description
27615 Indented this can be set using the menu
27617 Document\SpecialChar menuseparator
27623 \begin_inset space ~
27629 \begin_layout Standard
27634 is used, the indentation can be adjusted.
27635 The default value depends on the used document class.
27639 \begin_layout Itemize
27640 And two different numbering styles that can be set in the menu
27642 Document\SpecialChar menuseparator
27648 \begin_inset space ~
27657 \begin_layout Description
27658 Right is in most cases the default.
27661 \begin_layout Description
27666 \begin_layout Standard
27667 The chosen styles are used for all displayed formulas of the document.
27668 When both, centered and indented formulas should be created in a document,
27674 The indented formulas are then set in a flalign environment, see
27675 \begin_inset CommandInset ref
27677 reference "subsec:Flalign-Environment"
27684 \begin_layout Section
27686 \begin_inset CommandInset label
27688 name "sec:Multiline-Formulas"
27693 \begin_inset Index idx
27696 \begin_layout Plain Layout
27697 Formula ! multiline
27705 \begin_layout Subsection
27709 \begin_layout Standard
27710 In \SpecialChar LyX
27711 multiline formulas are created by pressing
27714 arg "newline-insert newline"
27718 This creates either an
27722 that is described in
27723 \begin_inset CommandInset ref
27725 reference "subsec:Standard-align-Environment"
27729 or, when automatically loading the package
27733 is disabled in the document settings, an
27735 eqnarray environment
27737 that is described in
27738 \begin_inset CommandInset ref
27740 reference "subsec:Eqnarray-Environment"
27745 The align environment is recommended because it provides in any case a
27746 typographically correct output.
27749 \begin_layout Standard
27750 There are other multiline formula environments that can be created via the
27753 Insert\SpecialChar menuseparator
27757 These environments are described in the following sections.
27760 \begin_layout Standard
27761 In all multiline formula environments a new line is created by pressing
27765 arg "newline-insert newline"
27769 To add or delete lines, the math toolbar buttons
27772 arg "tabular-feature append-row"
27778 arg "tabular-feature delete-row"
27781 , respectively, or the menu
27783 Edit\SpecialChar menuseparator
27789 \begin_layout Subsubsection
27791 \begin_inset CommandInset label
27793 name "subsec:Line-Separation"
27798 \begin_inset Index idx
27801 \begin_layout Plain Layout
27802 Formula ! multiline ! Line separation
27810 \begin_layout Standard
27811 There is sometimes not enough space in multiline formulas between the lines:
27812 \begin_inset Formula
27814 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}\\
27815 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
27823 \begin_layout Standard
27824 In \SpecialChar LaTeX
27825 additional line space is specified as optional argument of the new line
27827 This is not yet possible in \SpecialChar LyX
27832 \begin_layout Plain Layout
27834 \begin_inset CommandInset href
27836 name "LyX-bug #1505"
27837 target "https://www.lyx.org/trac/ticket/1505"
27847 , therefore the whole formula must be inserted in \SpecialChar TeX
27849 To add in our example space, the command
27857 is inserted at the end of the first line.
27862 \begin_layout Plain Layout
27869 \begin_layout Plain Layout
27871 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27874 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27881 \begin_layout Plain Layout
27885 left(B^{2}+x_{0}^{2}
27893 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27898 \begin_layout Plain Layout
27910 \begin_layout Standard
27911 \begin_inset VSpace bigskip
27914 To set the line separation for all lines in a formula, the length
27921 \begin_inset Index idx
27924 \begin_layout Plain Layout
27934 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27945 \begin_inset space \thinspace{}
27950 \begin_inset space \thinspace{}
27953 mm additional line separation as in the previous example, the command
27956 \begin_layout Standard
27966 \begin_layout Standard
27967 is inserted in \SpecialChar TeX
27968 mode before the formula.
27969 This requires that the \SpecialChar LaTeX
27978 \begin_layout Plain Layout
27983 is part of every \SpecialChar LaTeX
27984 standard installation.
27990 \begin_inset Index idx
27993 \begin_layout Plain Layout
27999 was loaded in \SpecialChar LaTeX
28000 -preamble with the line
28003 \begin_layout Standard
28011 \begin_layout Standard
28016 \begin_layout Plain Layout
28028 \begin_inset Formula
28030 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}\\
28031 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
28039 \begin_layout Standard
28043 \begin_layout Plain Layout
28054 To get back to the predefined distance,
28060 is set to the value 3
28061 \begin_inset space \thinspace{}
28067 \begin_layout Subsubsection
28069 \begin_inset CommandInset label
28071 name "subsec:Column-Separation"
28076 \begin_inset Index idx
28079 \begin_layout Plain Layout
28080 Formula ! multiline ! Column separation
28088 \begin_layout Standard
28089 Multiline formulas form a matrix.
28090 A formula in the eqnarray environment is for example a matrix with three
28092 By changing the column separation in this environment, the space beside
28093 the relation sign can be changed.
28096 \begin_layout Standard
28097 The column separation is specified with the length
28104 \begin_inset Index idx
28107 \begin_layout Plain Layout
28116 \begin_inset Newline newline
28119 column separation = 2
28120 \begin_inset space \thinspace{}
28130 \begin_inset Newline newline
28136 \begin_layout Standard
28146 \begin_layout Standard
28147 inserted in \SpecialChar TeX
28148 mode, sets for all following formulas a column separation of
28150 \begin_inset space \thinspace{}
28154 To get back to the predefined distance,
28161 \begin_inset space \thinspace{}
28167 \begin_layout Standard
28169 \begin_inset space \thinspace{}
28172 cm column separation:
28176 \begin_layout Plain Layout
28188 \begin_inset Formula
28196 A formula with the predefined column separation for matrices of 10
28197 \begin_inset space \thinspace{}
28204 \begin_layout Plain Layout
28216 \begin_inset Formula
28227 \begin_layout Standard
28228 \begin_inset Newpage newpage
28234 \begin_layout Subsubsection
28236 \begin_inset Index idx
28239 \begin_layout Plain Layout
28248 \begin_layout Standard
28249 Long formulas can be typeset using these methods:
28252 \begin_layout Itemize
28253 When one side of the equation is much shorter than the line width, this
28254 one is chosen for the left side and the right side is typeset over two
28256 \begin_inset Formula
28258 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 \\
28259 & & -\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}
28264 The minus sign at the beginning of the second line does normally not appear
28265 as an operator because it is the first character of the line.
28266 Thus it would not be surrounded by space and could not be distinguished
28267 from the fraction bar.
28269 \begin_inset space \thinspace{}
28272 pt space was inserted behind the minus sign with the command
28282 \begin_layout Plain Layout
28290 \begin_inset CommandInset ref
28292 reference "subsec:Variable-Space"
28302 \begin_inset Index idx
28305 \begin_layout Plain Layout
28316 \begin_layout Itemize
28317 When both sides of the equation are too long, the command
28324 \begin_inset Index idx
28327 \begin_layout Plain Layout
28336 It is inserted in the first column of the first line and causes all further
28337 insertions to overwrite the following columns:
28338 \begin_inset Formula
28340 \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 \\
28341 & & -\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 \\
28342 & & =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}
28347 After the insertion of
28353 , the cursor is in a purple box that is a bit shifted to the left from the
28355 In this the formula is inserted.
28356 \begin_inset Newline newline
28359 The content of the further lines is inserted to the second or another formula
28361 The greater the column number where it was inserted, the larger the indentation.
28362 \begin_inset VSpace medskip
28366 \begin_inset Newline newline
28370 \begin_inset Note Greyedout
28373 \begin_layout Plain Layout
28374 Note the following when using
28383 \begin_layout Itemize
28384 The formula doesn't use the full page width.
28386 \begin_inset space \thinspace{}
28390 \begin_inset space \space{}
28394 \begin_inset Formula $-B^{2}$
28397 is added to the first line in the above example, it would have been outside
28399 To better use the width, negative space can be inserted at the beginning
28403 \begin_layout Itemize
28404 Due to a bug in \SpecialChar LyX
28405 the cursor cannot be set with the mouse into the first
28410 \begin_layout Plain Layout
28411 \begin_inset CommandInset href
28413 name "LyX-bug #1429"
28414 target "https://www.lyx.org/trac/ticket/1429"
28424 One can only set the cursor at the beginning of the line and move it with
28433 \begin_layout Itemize
28434 Other methods to set long formulas are offered by the environments described
28436 \begin_inset CommandInset ref
28438 reference "subsec:Multline-Environment"
28443 \begin_inset CommandInset ref
28445 reference "subsec:Multiline-Formula-Parts"
28452 \begin_layout Subsubsection
28453 Multiline Fractions
28454 \begin_inset CommandInset label
28456 name "subsec:Multiline-Fractions"
28461 \begin_inset Index idx
28464 \begin_layout Plain Layout
28465 Fractions ! multiline
28473 \begin_layout Standard
28474 There are cases where the denominator and/or the numerator of a fraction
28475 is so long that the fraction does not fit into one line.
28476 It is then necessary to add a line break within the fraction.
28477 This can be done using the command
28484 \begin_inset Index idx
28487 \begin_layout Plain Layout
28496 To activate it, set in the document settings under
28499 \begin_inset space ~
28509 \begin_inset Index idx
28512 \begin_layout Plain Layout
28513 Packages ! mathtools
28521 \begin_inset space ~
28536 \begin_layout Standard
28541 splitfrac{first line}{second line}
28544 \begin_layout Standard
28545 and is used as denominator and/or numerator:
28548 \begin_layout Standard
28549 \begin_inset Formula
28551 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}
28556 The command for the first numerator above is:
28559 \begin_layout Standard
28564 splitfrac{xy+xy+xy+xy+xy
28565 \begin_inset space \textvisiblespace{}
28573 \begin_layout Subsubsection
28575 \begin_inset CommandInset label
28577 name "subsec:Multiline-Brackets"
28582 \begin_inset Index idx
28585 \begin_layout Plain Layout
28586 Brackets ! for multiline expressions
28594 \begin_layout Standard
28595 For brackets spanning multiple lines the following problem occurs:
28596 \begin_inset Formula
28598 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28599 & & \left.\cdots+B-D\right]
28607 \begin_layout Standard
28608 The closing bracket is smaller than the opening bracket because brackets
28609 with variable size may not span multiple lines.
28612 \begin_layout Standard
28613 To set the bracket size for the second line correctly, the first line is
28621 \begin_inset Index idx
28624 \begin_layout Plain Layout
28632 and the second line with
28640 \begin_layout Plain Layout
28654 \begin_inset CommandInset ref
28656 reference "subsec:Automatic-Bracket-Size"
28668 \begin_inset Index idx
28671 \begin_layout Plain Layout
28694 \begin_inset space \textvisiblespace{}
28704 \begin_inset space \textvisiblespace{}
28714 \begin_inset space \textvisiblespace{}
28720 \begin_inset Formula $\downarrow$
28726 \begin_inset Index idx
28729 \begin_layout Plain Layout
28737 is inserted, because the multiplication operator with its limits is the
28738 largest symbol in the first line and this should be the size for the bracket
28739 in the second line.
28742 \begin_layout Standard
28743 The result is this:
28744 \begin_inset Formula
28746 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28747 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28755 \begin_layout Subsection
28759 \begin_layout Standard
28760 Align environments can be used for every kind of multiline formulas.
28761 They are especially useful to set several formulas side by side.
28764 \begin_layout Standard
28765 Align environments consist of columns.
28766 The odd columns are right aligned, the even ones left aligned.
28767 Every line in an Align environment can be numbered.
28770 \begin_layout Standard
28771 Align environments are created via the menu
28773 Insert\SpecialChar menuseparator
28779 Edit\SpecialChar menuseparator
28780 Math\SpecialChar menuseparator
28781 Change Formula Type
28783 already existing formulas can be converted to Align environments.
28786 \begin_layout Standard
28787 To add or delete columns, the math toolbar buttons
28790 arg "tabular-feature append-column"
28796 arg "tabular-feature delete-column"
28799 , respectively, or the menu
28801 Edit\SpecialChar menuseparator
28807 \begin_layout Subsubsection
28808 Standard align Environment
28809 \begin_inset CommandInset label
28811 name "subsec:Standard-align-Environment"
28816 \begin_inset Index idx
28819 \begin_layout Plain Layout
28820 Formula ! multiline ! align environment
28828 \begin_layout Standard
28829 This Align environment is created by pressing
28832 arg "newline-insert newline"
28835 in a formula or by the menu
28837 Insert\SpecialChar menuseparator
28838 Math\SpecialChar menuseparator
28839 AMS align Environment
28844 \begin_layout Standard
28845 An example for two formulas set side by side, that are created with a four
28846 column align environment:
28847 \begin_inset Formula
28849 A & =\sin(B) & C & =D\\
28850 C & \ne A & B & \ne D
28855 As it can be seen, the formulas in this environment are placed so as if
28864 \begin_layout Plain Layout
28872 \begin_inset CommandInset ref
28874 reference "subsec:Variable-Space"
28885 before the first and after every even column.
28886 When the formula style
28892 \begin_layout Plain Layout
28894 \begin_inset CommandInset ref
28896 reference "sec:Formula-Styles"
28907 is used, the formula is set without the
28913 before the first column.
28916 \begin_layout Subsubsection
28917 Alignat Environment
28918 \begin_inset Index idx
28921 \begin_layout Plain Layout
28922 Formula ! multiline ! alignat environment
28930 \begin_layout Standard
28931 The alignat environment has no predefined column separation.
28932 It can be inserted manually with the spaces that are described
28933 \begin_inset CommandInset ref
28935 reference "subsec:Space"
28942 \begin_layout Standard
28943 The above example in the alignat environment where 1
28944 \begin_inset space \thinspace{}
28947 cm space was inserted at the beginning of the second formula:
28948 \begin_inset Formula
28949 \begin{alignat*}{2}
28950 A & =\sin(B) & \hspace{1cm}C & =D\\
28951 C & \ne A & B & \ne D
28956 Because the column separation can be set separately for every column, this
28957 environment is especially suitable to set three and more formulas side
28961 \begin_layout Subsubsection
28962 Flalign Environment
28963 \begin_inset CommandInset label
28965 name "subsec:Flalign-Environment"
28970 \begin_inset Index idx
28973 \begin_layout Plain Layout
28974 Formula ! multiline ! flalign environment
28982 \begin_layout Standard
28983 In this environment the first two columns are always set as much as possible
28984 to the left and the last two ones to the right.
28986 \begin_inset Formula
28988 A & =1 & B & =2 & C & =3\\
28989 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28997 \begin_layout Standard
28998 By creating a flalign environment with an odd number of columns where an
28999 empty \SpecialChar TeX
29000 brace is inserted to the last column, several formulas in a document
29001 can be set to the left, although the formula style
29006 As example the indented formula
29007 \begin_inset CommandInset ref
29009 reference "eq:VolInt"
29014 \begin_inset Formula
29016 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
29021 The first two columns contain the formula.
29022 To indent it as with the formula style
29027 \begin_inset space \thinspace{}
29030 pt space was inserted at the beginning of the first column.
29033 \begin_layout Subsection
29034 Eqnarray Environment
29035 \begin_inset CommandInset label
29037 name "subsec:Eqnarray-Environment"
29042 \begin_inset Index idx
29045 \begin_layout Plain Layout
29046 Formula ! multiline ! eqnarray environment
29054 \begin_layout Standard
29055 When this environment has been created, three blue boxes appear.
29056 The content of the first box is right aligned, the content of the last
29058 The content of the middle box appears centered and a bit smaller, because
29059 it is designed to insert there only relation characters.
29060 \begin_inset Formula
29062 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29072 \begin_layout Subsection
29074 \begin_inset Index idx
29077 \begin_layout Plain Layout
29078 Formula ! multiline ! gather environment
29086 \begin_layout Standard
29087 This environment consists of only one centered column.
29088 Every line can be numbered.
29089 \begin_inset Formula
29100 \begin_layout Subsection
29101 Multline Environment
29102 \begin_inset CommandInset label
29104 name "subsec:Multline-Environment"
29109 \begin_inset Index idx
29112 \begin_layout Plain Layout
29113 Formula ! multiline ! multline environment
29121 \begin_layout Standard
29122 The multline environment consists, like the gather environment, of only
29124 But the first line is left aligned, the last one right aligned.
29125 All other lines are centered.
29126 Therefore this environment is suitable for long formulas.
29128 \begin_inset CommandInset ref
29130 reference "eq:lefteqn"
29134 in the multline environment:
29135 \begin_inset Formula
29137 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}\\
29138 -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}\\
29139 =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}}
29147 \begin_layout Standard
29148 In the output only the last (first) line of a multline environment appears
29149 numbered when the document numbering is right (left).
29153 \begin_layout Plain Layout
29154 numbering styles see
29155 \begin_inset CommandInset ref
29157 reference "sec:Formula-Styles"
29169 \begin_layout Standard
29177 \begin_inset Index idx
29180 \begin_layout Plain Layout
29195 \begin_inset Index idx
29198 \begin_layout Plain Layout
29206 a centered line can be right or left aligned, respectively.
29207 The commands are used as follows:
29210 \begin_layout Standard
29215 shoveright{line content}
29221 shoveleft{line content}
29224 \begin_layout Standard
29225 \begin_inset VSpace medskip
29235 \begin_inset Index idx
29238 \begin_layout Plain Layout
29246 specifies the distance of the first line from the left page margin.
29247 Predefined is the length 0
29248 \begin_inset space \thinspace{}
29254 \begin_layout Standard
29255 As example the above formula where the command
29258 \begin_layout Standard
29268 \begin_layout Standard
29269 was inserted in \SpecialChar TeX
29274 \begin_layout Plain Layout
29286 \begin_inset Formula
29288 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}\\
29289 \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}}\\
29290 =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}}
29299 \begin_layout Plain Layout
29310 The second line was left aligned using
29319 \begin_layout Subsection
29320 Multiline Formula Parts
29321 \begin_inset CommandInset label
29323 name "subsec:Multiline-Formula-Parts"
29328 \begin_inset Index idx
29331 \begin_layout Plain Layout
29332 Formula ! multiline ! formula parts
29340 \begin_layout Standard
29341 To display only parts of a formula with multiple lines, one of the following
29342 environments is used:
29359 They can be inserted via the menu
29361 Insert\SpecialChar menuseparator
29364 or by using the commands described in this section.
29367 \begin_layout Standard
29368 The first three have the same properties as the corresponding multiline
29369 formula environments, but it is possible to set further formula parts beside
29372 \begin_inset Formula
29374 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29375 \Delta E\Delta t & \ge\frac{\hbar}{2}
29377 \right\} \textrm{Uncertainty relations}
29385 \begin_layout Standard
29386 To get this formula, a displayed formula is created where the command
29393 \begin_inset Index idx
29396 \begin_layout Plain Layout
29405 A purple box appears around the blue formula box where now columns and
29406 lines can be added.
29407 Outside the multiline environment other formula parts can be set, like
29411 \begin_layout Standard
29412 The aligned environment is also suitable for long formulas whose lines are
29413 horizontally aligned.
29414 Using aligned in a displayed formula has the advantage that the formula
29415 number is vertically centered behind the lines.
29417 \begin_inset CommandInset ref
29419 reference "eq:shortlong"
29423 in the aligned environment:
29424 \begin_inset Formula
29426 \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}|}\\
29427 & -\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}|}
29436 \begin_layout Standard
29437 To use the environments
29456 \begin_inset Index idx
29459 \begin_layout Plain Layout
29474 \begin_inset Index idx
29477 \begin_layout Plain Layout
29492 \begin_inset Index idx
29495 \begin_layout Plain Layout
29503 are inserted, respectively.
29504 The split environment has the same properties as the aligned environment
29505 but it can only have two columns.
29508 \begin_layout Subsection
29509 Text in multiline Formulas
29510 \begin_inset CommandInset label
29512 name "subsec:Text-in-multiline"
29517 \begin_inset Index idx
29520 \begin_layout Plain Layout
29527 \begin_inset Index idx
29530 \begin_layout Plain Layout
29531 Formula ! multiline ! text
29539 \begin_layout Standard
29540 In the Align environments, and the multline and gather environment, text
29541 can be inserted that will appear in a separate line and doesn't affect
29542 the column alignment.
29543 To do this, the command
29550 \begin_inset Index idx
29553 \begin_layout Plain Layout
29561 is used in the following scheme:
29564 \begin_layout Standard
29572 \begin_layout Standard
29573 The text should not be longer than a line because it cannot be hyphenated.
29574 As \SpecialChar LyX
29575 doesn't yet support
29581 directly, the text is written as mathematical text.
29588 must hereby be at the beginning of a line and appears in the output above
29590 An example where the text was inserted at the beginning of the second line:
29591 \begin_inset Formula
29593 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29594 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29602 \begin_layout Standard
29609 always creates some vertical space between the text and the formula lines.
29610 To avoid this space, set in the document settings under
29613 \begin_inset space ~
29623 \begin_inset Index idx
29626 \begin_layout Plain Layout
29627 Packages ! mathtools
29635 \begin_inset space ~
29641 Then you can use the command
29648 \begin_inset Index idx
29651 \begin_layout Plain Layout
29668 \begin_layout Standard
29669 \begin_inset Formula
29671 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29672 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29680 \begin_layout Section
29682 \begin_inset Index idx
29685 \begin_layout Plain Layout
29692 \begin_inset Index idx
29695 \begin_layout Plain Layout
29696 Formula ! numbering|see
29700 \begin_layout Plain Layout
29711 \begin_layout Plain Layout
29726 \begin_layout Subsection
29730 \begin_layout Standard
29731 Numbered formulas can be created with the menu
29733 Insert\SpecialChar menuseparator
29734 Math\SpecialChar menuseparator
29736 \begin_inset space ~
29744 arg "command-sequence math-display; math-number-toggle;"
29748 Existing formulas can be numbered with the menu
29750 Edit\SpecialChar menuseparator
29751 Math\SpecialChar menuseparator
29753 \begin_inset space ~
29761 arg "math-number-toggle"
29765 The formula number is displayed in \SpecialChar LyX
29766 behind the formula as a number sign
29768 The number sign is replaced in the output by the formula number.
29771 \begin_layout Standard
29772 When numbering is turned on in multiline formulas, all lines will be numbered.
29773 But the numbering can be controlled with the menu
29775 Edit\SpecialChar menuseparator
29776 Math\SpecialChar menuseparator
29778 \begin_inset space ~
29782 \begin_inset space ~
29786 \begin_inset space ~
29794 arg "math-number-line-toggle"
29800 \begin_layout Standard
29801 Except for inline formulas, all formulas can be numbered with two different
29803 \begin_inset CommandInset ref
29805 reference "sec:Formula-Styles"
29812 \begin_layout Subsection
29814 \begin_inset Index idx
29817 \begin_layout Plain Layout
29818 Cross-references ! to formulas
29826 \begin_layout Standard
29827 All labeled formulas can be cross-referenced.
29828 A label is added by the menu
29830 Insert\SpecialChar menuseparator
29833 or the toolbar button
29840 The cursor must hereby be inside a displayed formula.
29841 Alternatively you can right-click on the formula and choose
29846 A dialog pops up displaying the prefix
29851 The label is inserted there behind the prefix.
29852 The predefined prefix means
29853 \begin_inset Quotes eld
29857 \begin_inset Quotes erd
29860 and makes it easier to find labels in large documents because it marks
29861 it as formula label to divide it from e.
29862 \begin_inset space \thinspace{}
29866 \begin_inset space \space{}
29870 To change a label, the menu
29872 Insert\SpecialChar menuseparator
29875 is used again or you right-click on a formula and then on
29882 \begin_layout Standard
29883 The name of the label is displayed in \SpecialChar LyX
29884 within two parentheses behind formula.
29885 A formula with a label is always numbered.
29888 \begin_layout Standard
29889 Cross-references are inserted via the menu
29891 Insert\SpecialChar menuseparator
29894 or with the toolbar button
29897 arg "dialog-show-new-inset ref"
29901 A formula cross-reference appears in the output as formula number.
29902 When in the cross-reference dialog window the format
29906 is chosen, the cross-reference appears in the output as formula number
29908 \begin_inset Newline newline
29911 By right-clicking on a cross-reference in \SpecialChar LyX
29912 , one jumps to the formula that
29916 \begin_layout Standard
29917 Here are as examples cross-references to formulas of the following subsections:
29918 \begin_inset Note Note
29921 \begin_layout Plain Layout
29922 Note the different cross-reference types.
29930 \begin_layout Standard
29932 \begin_inset CommandInset ref
29939 \begin_inset CommandInset ref
29947 \begin_inset CommandInset ref
29953 ) big Latin letters are used for the numbering in contrary to (
29954 \begin_inset CommandInset ref
29963 \begin_layout Standard
29964 \begin_inset VSpace medskip
29967 When the argument of
29975 \begin_layout Plain Layout
29983 \begin_inset CommandInset ref
29985 reference "subsec:User-defined-Numbering"
29996 contains a box like in
29997 \begin_inset CommandInset ref
29999 reference "subsec:Paragraph-Boxes"
30003 , the formula cannot be referenced.
30006 \begin_layout Subsection
30008 \begin_inset Index idx
30011 \begin_layout Plain Layout
30012 Formula numbering ! subnumbering
30020 \begin_layout Standard
30021 Formulas can be numbered as subequations.
30022 To activate this feature, add the module
30026 to the document in the menu
30028 Document\SpecialChar menuseparator
30029 Settings\SpecialChar menuseparator
30033 To insert subequations use the menu
30035 Insert\SpecialChar menuseparator
30036 Custom Insets\SpecialChar menuseparator
30042 \begin_layout Standard
30043 The equations to be subnumbered are put into the
30049 \begin_inset Formula
30057 \begin_inset VSpace -5mm
30061 \begin_inset Flex Subequations
30064 \begin_layout Plain Layout
30065 \begin_inset Formula
30073 \begin_inset Formula
30088 \begin_layout Standard
30089 Every formula in the
30093 inset will be subnumbered with a, b, c, \SpecialChar ldots
30095 For multiline formulas every line will be subnumbered.
30098 \begin_layout Standard
30099 Referencing subequations work like for normal equations:
30100 \begin_inset CommandInset ref
30107 \begin_inset CommandInset ref
30114 If you want to reference the subequations collectively, insert a label
30115 as first thing in the
30121 \begin_inset CommandInset ref
30123 reference "eq:Here-is-an"
30133 \begin_layout Standard
30134 By inserting subequations vertical space is added before it.
30135 To remove this, insert -5
30136 \begin_inset space \thinspace{}
30139 mm vertical space right before the
30144 If the formula style
30150 \begin_layout Plain Layout
30152 \begin_inset CommandInset ref
30154 reference "sec:Formula-Styles"
30166 \begin_inset space \thinspace{}
30172 \begin_layout Standard
30173 To get another subnumber instead of small Latin letters, insert this command
30174 as \SpecialChar TeX
30175 code before the equations in the
30182 \begin_layout Standard
30191 theparentequation -
30196 \begin_layout Standard
30203 creates hereby the parent number and
30209 adds a small Roman number as subnumber.
30210 For more information about the customization of the numbering, see
30211 \begin_inset CommandInset ref
30213 reference "subsec:Numbering-with-Roman"
30220 \begin_layout Standard
30221 Here is an example for a multiline formula where the numbering is customized
30222 and turned off for the second line:
30223 \begin_inset Flex Subequations
30226 \begin_layout Plain Layout
30227 \begin_inset CommandInset label
30229 name "eq:Here-is-an"
30237 \begin_layout Plain Layout
30245 theparentequation -
30253 \begin_inset Formula
30255 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30256 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30257 & = & B^{2}-2BZ+Z^{2}
30270 \begin_layout Subsection
30271 Numbering with Roman Numbers and Letters
30272 \begin_inset CommandInset label
30274 name "subsec:Numbering-with-Roman"
30279 \begin_inset Index idx
30282 \begin_layout Plain Layout
30283 Formula numbering ! with letters
30289 \begin_inset Index idx
30292 \begin_layout Plain Layout
30293 Formula numbering ! with Roman numbers
30301 \begin_layout Standard
30302 Formulas can also be numbered with Roman numbers and Latin letters.
30303 To number for example with small Roman numbers, the command
30306 \begin_layout Standard
30318 \begin_layout Standard
30319 is inserted before the formula in \SpecialChar TeX
30328 \begin_inset Index idx
30331 \begin_layout Plain Layout
30339 redefines the predefined command
30355 \begin_layout Plain Layout
30362 has the same scheme like the command
30368 that is described in
30369 \begin_inset CommandInset ref
30371 reference "subsec:The-Command-newcommand"
30384 is the formula counter.
30391 is used as prefix for a counter, the value of the counter is output as
30393 When a formula is numbered, \SpecialChar LaTeX
30394 sets internally the command
30400 behind the formula.
30406 \begin_inset Index idx
30409 \begin_layout Plain Layout
30419 outputs the counter as small Roman number.
30422 \begin_layout Standard
30423 All formulas behind the command
30433 are now numbered Roman.
30434 To switch to numbering with big Roman numbers, the command is inserted
30448 \begin_inset Index idx
30451 \begin_layout Plain Layout
30463 \begin_inset Quotes eld
30467 \begin_inset Quotes erd
30470 with small Latin letters there is the command
30477 \begin_inset Index idx
30480 \begin_layout Plain Layout
30488 , for big ones there is the command
30495 \begin_inset Index idx
30498 \begin_layout Plain Layout
30511 \begin_layout Standard
30512 \begin_inset Note Greyedout
30515 \begin_layout Plain Layout
30521 \begin_inset space ~
30524 formulas can be numbered with Latin letters in one document.
30532 \begin_layout Standard
30536 \begin_layout Plain Layout
30552 \begin_layout Standard
30553 \begin_inset Formula
30555 A=\textrm{small roman}
30564 \begin_layout Plain Layout
30578 \begin_inset Formula
30580 B=\textrm{big Roman}\label{eq:Rom}
30589 \begin_layout Plain Layout
30603 \begin_inset Formula
30605 C=\textrm{small Latin}
30614 \begin_layout Plain Layout
30628 \begin_inset Formula
30630 D=\textrm{big Latin}\label{eq:Lat}
30638 \begin_layout Standard
30639 To switch back to the default numbering, insert the command:
30642 \begin_layout Standard
30652 \begin_inset Index idx
30655 \begin_layout Plain Layout
30666 \begin_layout Standard
30670 \begin_layout Plain Layout
30684 \begin_inset Formula
30694 \begin_layout Standard
30695 \begin_inset VSpace medskip
30698 As you see, formulas are numbered serially independent from the numbering
30700 When then numbering should start with
30701 \begin_inset Quotes eld
30705 \begin_inset Quotes erd
30708 when the style is changed, new equation counters have to be defined.
30709 A description about this can be found in the file
30710 \begin_inset CommandInset href
30712 name "Formula-numbering.lyx"
30713 target "run:Formula-numbering.lyx"
30721 \begin_layout Subsection
30722 User-defined Numbering
30723 \begin_inset CommandInset label
30725 name "subsec:User-defined-Numbering"
30730 \begin_inset Index idx
30733 \begin_layout Plain Layout
30734 Formula numbering ! user-defined
30742 \begin_layout Standard
30743 \begin_inset Note Greyedout
30746 \begin_layout Plain Layout
30751 If the document language is a right-to-left language such as Arabic, you
30752 must add this to the to the \SpecialChar LaTeX
30753 -preamble to be able to use the commands described
30755 \begin_inset Newline newline
30763 \begin_inset Newline newline
30767 \begin_inset Phantom HPhantom
30770 \begin_layout Plain Layout
30773 \begin_inset space ~
30799 \begin_layout Standard
30800 \begin_inset Index idx
30803 \begin_layout Plain Layout
30804 Formula numbering ! self-defined delimiters
30809 With the standard numbering parentheses are set around the formula number.
30810 To replace the parentheses for example by vertical bars, the following
30811 line is added to the \SpecialChar LaTeX
30815 \begin_layout Standard
30821 \begin_inset Newline newline
30825 \begin_inset Phantom HPhantom
30828 \begin_layout Plain Layout
30831 \begin_inset space ~
30845 maketag@@@{|#1|}} }
30848 \begin_inset Note Note
30851 \begin_layout Plain Layout
30852 This macro is already declared in the \SpecialChar LaTeX
30853 -preamble for testing.
30854 To activate it, remove the percent signs at the beginning.
30862 \begin_layout Standard
30863 To use other characters, the vertical bars besides the
30867 are replaced by one ore more characters.
30868 To get only the formula number the vertical bars are omitted.
30871 \begin_layout Standard
30872 \begin_inset VSpace bigskip
30875 When there should be an expression of your choice instead of the consecutive
30876 formula number in parentheses behind the formula, the command
30883 \begin_inset Index idx
30886 \begin_layout Plain Layout
30895 \begin_inset Formula
30897 A+B=C\tag{something}\label{eq:tag}
30902 In this example the command
30907 \begin_inset space \textvisiblespace{}
30912 was inserted in the formula.
30915 \begin_layout Standard
30921 \begin_inset space \textvisiblespace{}
30926 is inserted instead, the star prevents the parentheses around the expression:
30927 \begin_inset Formula
30929 A+B=C\tag*{something}
30937 \begin_layout Standard
30938 \begin_inset VSpace bigskip
30941 To restart the formula numbering with new document parts or sections, the
30942 following command is used:
30945 \begin_layout Standard
30950 @addtoreset{equation}{part}
30953 \begin_inset Index idx
30956 \begin_layout Plain Layout
30961 \begin_layout Plain Layout
30972 \begin_layout Plain Layout
30985 \begin_layout Plain Layout
30996 \begin_layout Plain Layout
31009 \begin_inset Newline newline
31013 \begin_inset Newline newline
31020 @addtoreset{equation}{section}
31023 \begin_layout Standard
31024 To be able to use these commands in \SpecialChar TeX
31026 \begin_inset Quotes eld
31030 \begin_inset Quotes erd
31033 character has to be made
31034 \begin_inset Quotes eld
31038 \begin_inset Quotes erd
31041 for \SpecialChar LaTeX
31056 So the command sequence in \SpecialChar TeX
31060 \begin_layout Standard
31066 \begin_inset Newline newline
31071 @addtoreset{equation}{section}
31072 \begin_inset Newline newline
31080 \begin_layout Standard
31081 In the \SpecialChar LaTeX
31094 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31098 \begin_layout Standard
31113 \begin_layout Plain Layout
31118 is part of the \SpecialChar LaTeX
31124 \begin_inset Index idx
31127 \begin_layout Plain Layout
31128 Packages ! carlisle
31133 that is part of every \SpecialChar LaTeX
31134 standard installation.
31140 \begin_inset Index idx
31143 \begin_layout Plain Layout
31144 Packages ! remreset
31149 has to be loaded in the \SpecialChar LaTeX
31150 -preamble with the line
31153 \begin_layout Standard
31158 usepackage{remreset}
31161 \begin_layout Standard
31169 \begin_inset Index idx
31172 \begin_layout Plain Layout
31177 \begin_layout Plain Layout
31188 \begin_layout Plain Layout
31201 \begin_layout Plain Layout
31212 \begin_layout Plain Layout
31224 can be used with the same scheme as
31233 \begin_layout Standard
31234 \begin_inset VSpace bigskip
31237 Sometimes formulas should be numbered in the following form:
31240 \begin_layout Standard
31243 (section number.formula number)
31246 \begin_layout Standard
31247 The formula number should start with every section with
31248 \begin_inset Quotes eld
31252 \begin_inset Quotes erd
31258 \begin_layout Standard
31259 For this case there is the command
31266 \begin_inset Index idx
31269 \begin_layout Plain Layout
31277 , which is used with the following scheme:
31280 \begin_layout Standard
31285 numberwithin{counter}{sectioning}
31288 \begin_layout Standard
31289 Counter denotes what kind of numbering is affected, sectioning denotes what
31290 number is before the dot.
31293 \begin_layout Standard
31294 Thus in our case the following \SpecialChar LaTeX
31295 preamble or \SpecialChar TeX
31299 \begin_layout Standard
31304 numberwithin{equation}{section}
31307 \begin_layout Standard
31308 This is the result:
31312 \begin_layout Plain Layout
31316 numberwithin{equation}{section}
31322 \begin_inset Formula
31332 \begin_layout Standard
31334 \begin_inset space \thinspace{}
31338 \begin_inset space \space{}
31341 tables so that the number of the part is the sectioning,
31342 \begin_inset Newline newline
31349 numberwithin{table}{part}
31354 \begin_layout Standard
31355 To go back to the standard numbering or to prevent this kind of numbering
31356 when it is defined by the document class, the following command is inserted
31357 as \SpecialChar TeX
31358 code or to the \SpecialChar LaTeX
31362 \begin_layout Standard
31372 \begin_inset Index idx
31375 \begin_layout Plain Layout
31389 \begin_layout Plain Layout
31405 \begin_inset Newline newline
31413 \begin_inset Newline newline
31425 \begin_layout Standard
31432 uses internally the command
31438 , described above, that also needs to be reverted.
31442 \begin_layout Plain Layout
31449 \begin_layout Plain Layout
31453 @removefromreset{equation}{section}
31456 \begin_layout Plain Layout
31468 \begin_layout Section
31469 Chemical Symbols and Equations
31470 \begin_inset CommandInset label
31472 name "subsec:Chemical-Symbols-and"
31477 \begin_inset Index idx
31480 \begin_layout Plain Layout
31481 Chemical characters ! Symbols
31487 \begin_inset Index idx
31490 \begin_layout Plain Layout
31497 \begin_inset Index idx
31500 \begin_layout Plain Layout
31509 \begin_layout Standard
31510 An example text from chemistry:
31513 \begin_layout Quote
31515 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31518 -ion reacts with two
31519 \begin_inset Formula $\mathrm{Na^{+}}$
31522 -ions to sodium sulfate
31523 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31527 The chemical equation for this is:
31528 \begin_inset Formula
31530 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31538 \begin_layout Standard
31539 This chemical equation can directly be created as formula.
31540 To avoid that the symbols appear italic, everything is highlighted and
31541 changed by the shortcut
31547 to the upright font style.
31551 \begin_layout Plain Layout
31557 \begin_inset CommandInset ref
31559 reference "subsec:Font-Styles"
31571 \begin_layout Standard
31572 A more convenient way to typeset chemical formulas is to use the command
31580 \begin_inset Index idx
31583 \begin_layout Plain Layout
31591 that is available when the \SpecialChar LaTeX
31597 \begin_inset Index idx
31600 \begin_layout Plain Layout
31613 to a formula a new blue box appears where chemical formulas can be inserted
31614 in an intuitive way.
31617 \begin_layout Standard
31619 \begin_inset Tabular
31620 <lyxtabular version="3" rows="10" columns="2">
31621 <features booktabs="true" tabularvalignment="middle">
31622 <column alignment="center" valignment="top" width="0pt">
31623 <column alignment="center" valignment="top">
31625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31628 \begin_layout Plain Layout
31634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31637 \begin_layout Plain Layout
31645 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31648 \begin_layout Plain Layout
31652 \begin_inset space \textvisiblespace{}
31660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31663 \begin_layout Plain Layout
31664 \begin_inset Formula $\ce{H2CO3}$
31673 <row topspace="1.5mm">
31674 <cell alignment="center" valignment="top" usebox="none">
31677 \begin_layout Plain Layout
31681 \begin_inset space \textvisiblespace{}
31689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31692 \begin_layout Plain Layout
31693 \begin_inset Formula $\ce{SO4^{2-}}$
31702 <row topspace="1.5mm">
31703 <cell alignment="center" valignment="top" usebox="none">
31706 \begin_layout Plain Layout
31710 \begin_inset space \textvisiblespace{}
31718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31721 \begin_layout Plain Layout
31722 \begin_inset Formula $\ce{(NH4)2S}$
31731 <row topspace="1.5mm">
31732 <cell alignment="center" valignment="top" usebox="none">
31735 \begin_layout Plain Layout
31739 \begin_inset space \textvisiblespace{}
31747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31750 \begin_layout Plain Layout
31751 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31760 <row topspace="1.5mm">
31761 <cell alignment="center" valignment="top" usebox="none">
31764 \begin_layout Plain Layout
31768 \begin_inset space \textvisiblespace{}
31774 \begin_inset space \textvisiblespace{}
31780 \begin_inset space \textvisiblespace{}
31788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31791 \begin_layout Plain Layout
31792 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31801 <row topspace="1.5mm">
31802 <cell alignment="center" valignment="top" usebox="none">
31805 \begin_layout Plain Layout
31809 \begin_inset space \textvisiblespace{}
31813 \begin_inset Formula $\downarrow$
31817 \begin_inset Formula $\to$
31825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31828 \begin_layout Plain Layout
31829 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31842 \begin_layout Plain Layout
31846 \begin_inset space \textvisiblespace{}
31852 \begin_inset space \textvisiblespace{}
31858 \begin_inset space \textvisiblespace{}
31866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31869 \begin_layout Plain Layout
31870 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31883 \begin_layout Plain Layout
31887 \begin_inset space \textvisiblespace{}
31891 \begin_inset space \textvisiblespace{}
31895 \begin_inset space \textvisiblespace{}
31899 \begin_inset space \textvisiblespace{}
31903 \begin_inset space \textvisiblespace{}
31911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31914 \begin_layout Plain Layout
31915 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31924 <row topspace="1.5mm">
31925 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31928 \begin_layout Plain Layout
31932 \begin_inset space \textvisiblespace{}
31936 \begin_inset space \textvisiblespace{}
31940 \begin_inset space \textvisiblespace{}
31944 \begin_inset space \textvisiblespace{}
31952 \begin_inset space \textvisiblespace{}
31960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31963 \begin_layout Plain Layout
31964 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31980 \begin_layout Standard
31981 \begin_inset Note Greyedout
31984 \begin_layout Plain Layout
31989 It is not possible in \SpecialChar LyX
31990 to use the character ^ to get an up-arrow as described
31996 One instead uses a negative thin space followed by the command
32003 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32014 \begin_layout Standard
32021 the command for equation
32022 \begin_inset space ~
32026 \begin_inset CommandInset ref
32028 reference "eq:chem-reaction"
32033 \begin_inset Newline newline
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{}
32061 \begin_inset space \textvisiblespace{}
32067 \begin_layout Standard
32068 To create multiline chemical equations first a multiline formula is created
32070 \begin_inset CommandInset ref
32072 reference "sec:Multiline-Formulas"
32077 Afterwards the command
32083 is used in every small blue box of the formula.
32085 \begin_inset CommandInset ref
32087 reference "eq:TEOS-reaction-1"
32092 \begin_inset CommandInset ref
32094 reference "eq:TEOS-reaction-2"
32098 are an example of a multi-stage chemical reaction where every equation
32099 has its own number.
32100 \begin_inset Formula
32102 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32103 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32111 \begin_layout Standard
32122 package provides the command
32129 \begin_inset Index idx
32132 \begin_layout Plain Layout
32140 that has to be used for special cases.
32141 For more information about
32147 and more examples have a look at the documentation of
32152 \begin_inset CommandInset citation
32162 \begin_layout Section
32166 \begin_layout Standard
32168 supports two types of commutative diagrams:
32176 that are explained in the following.
32179 \begin_layout Subsection
32181 \begin_inset Index idx
32184 \begin_layout Plain Layout
32193 \begin_layout Standard
32194 Diagrams of this type visualize relations by vertical and horizontal lines
32196 \begin_inset Formula
32198 \begin{CD}A@>>>B@>>>C\\
32209 \begin_layout Standard
32210 To get them, the command
32215 \begin_inset Index idx
32218 \begin_layout Plain Layout
32228 is inserted to a formula.
32229 A blue box appears with two dashed lines where further commands can be
32234 arg "newline-insert newline"
32237 a new line is created.
32238 Horizontal relations are inserted in odd, vertical in even formula lines.
32241 \begin_layout Standard
32242 To create the relations there are the following commands:
32245 \begin_layout Itemize
32250 creates a left arrow,
32261 \begin_layout Itemize
32266 creates an up arrow,
32274 a vertical equal sign
32277 \begin_layout Itemize
32283 is a placeholder for non-existent relations
32286 \begin_layout Standard
32287 All arrows can be labeled as follows:
32290 \begin_layout Itemize
32291 If text inserted between the first and second < or >, resp., it is placed
32293 When it is inserted between the second and third one, it appears under
32297 \begin_layout Itemize
32298 When text for vertical arrows is inserted between the first and second A
32299 or V, resp., it is placed left beside the arrow.
32300 When it is inserted between the second and third one, it appears right
32302 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32306 \begin_layout Standard
32307 As example a diagram with all possible relations:
32310 \begin_layout Standard
32311 \begin_inset Formula
32313 \begin{CD}A@>j>>B@>>k>C@=F\\
32324 \begin_layout Standard
32325 The command for this is:
32326 \begin_inset Newline newline
32334 \begin_inset space \textvisiblespace{}
32337 A@>j>>B@>>k>C@=F Ctrl+Return
32338 \begin_inset Newline newline
32342 \begin_inset Phantom HPhantom
32345 \begin_layout Plain Layout
32351 \begin_inset space \textvisiblespace{}
32364 \begin_inset Formula $\to$
32370 \begin_inset Newline newline
32374 \begin_inset Phantom HPhantom
32377 \begin_layout Plain Layout
32383 \begin_inset space \textvisiblespace{}
32394 \begin_layout Subsection
32396 \begin_inset Index idx
32399 \begin_layout Plain Layout
32400 Diagrams ! xymatrix
32408 \begin_layout Standard
32409 To be able to use xymatrices, the \SpecialChar LaTeX
32415 A xymatrix is created by inserting the command
32422 Then you are able to add new matrix columns and rows like for normal matrices,
32424 \begin_inset CommandInset ref
32426 reference "sec:Matrices"
32433 \begin_layout Standard
32434 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32436 All possibilities to create commutative diagrams and decorations are explained
32441 that you find in the menu
32443 Help\SpecialChar menuseparator
32445 \begin_inset space ~
32453 \begin_layout Subsection
32459 \begin_inset Index idx
32462 \begin_layout Plain Layout
32471 \begin_layout Standard
32476 -diagrams, the \SpecialChar LaTeX
32486 -diagram is created by inserting the command
32493 Then you are able to add new matrix columns and rows like for normal matrices,
32495 \begin_inset CommandInset ref
32497 reference "sec:Matrices"
32504 \begin_layout Standard
32505 Examples how to create
32509 diagrams in \SpecialChar LyX
32512 Feynman-diagram manual
32514 that you find in the menu
32516 Help\SpecialChar menuseparator
32518 \begin_inset space ~
32526 \begin_layout Section
32527 User-defined Commands
32528 \begin_inset Index idx
32531 \begin_layout Plain Layout
32532 User-defined commands
32540 \begin_layout Standard
32541 \begin_inset Note Greyedout
32544 \begin_layout Plain Layout
32549 The names of user-defined commands and macros may only consist of Latin
32558 \begin_layout Subsection
32562 \begin_inset CommandInset label
32564 name "subsec:The-Command-newcommand"
32569 \begin_inset Index idx
32572 \begin_layout Plain Layout
32573 User-defined commands !
32581 \begin_inset Index idx
32584 \begin_layout Plain Layout
32595 \begin_layout Standard
32596 Many \SpecialChar LaTeX
32597 -commands are too long to be used frequently.
32598 But it is possible to define with the command
32604 new shorter commands.
32607 \begin_layout Standard
32608 The command scheme of
32617 \begin_layout Standard
32622 newcommand{new command name}[number of arguments][optional
32627 \begin_inset Newline newline
32631 \begin_inset Phantom HPhantom
32634 \begin_layout Plain Layout
32644 {command definition}
32647 \begin_layout Standard
32648 \begin_inset Note Greyedout
32651 \begin_layout Plain Layout
32656 Assure that the name of the new command is not already used in your document
32657 or by \SpecialChar LaTeX
32658 -packages that you use.
32659 When you for example define the command
32671 , you get an error message because
32677 is already defined as command for
32678 \begin_inset Quotes eld
32682 \begin_inset Formula $\le$
32686 \begin_inset Quotes erd
32697 \begin_layout Standard
32698 The number of arguments is an integer in the range 0
32699 \begin_inset space \thinspace{}
32703 \begin_inset space \thinspace{}
32706 9 and specifies how many arguments the new command should have.
32707 With the optional value a value for an optional argument can be predefined.
32708 When this is done, the
32716 rgument of the new command is automatically an optional one.
32719 \begin_layout Standard
32720 Here are some examples:
32723 \begin_layout Itemize
32724 To define the command
32736 , the \SpecialChar LaTeX
32738 \begin_inset VSpace medskip
32742 \begin_inset Newline newline
32756 \begin_layout Itemize
32757 To define the command
32769 , the argument (that should be underlined) must be taken into account.
32770 For this the preamble line is:
32771 \begin_inset VSpace medskip
32775 \begin_inset Newline newline
32789 \begin_inset VSpace medskip
32793 \begin_inset Newline newline
32800 acts as argument placeholder, the
32804 behind it denotes that it is the placeholder for the first argument.
32807 \begin_layout Itemize
32815 \begin_inset space \thinspace{}
32819 \begin_inset space \space{}
32829 \begin_inset VSpace medskip
32833 \begin_inset Newline newline
32844 framebox#1#2{$#3$}}
32847 \begin_inset VSpace medskip
32851 \begin_inset Newline newline
32854 The two Dollar signs creates the extra formula needed for
32861 \begin_inset CommandInset ref
32863 reference "subsec:Boxes-with-Frame"
32870 \begin_layout Itemize
32871 To create a new command for
32877 where the color for the box need not be specified, the argument for the
32878 color is defined optional:
32879 \begin_inset VSpace medskip
32883 \begin_inset Newline newline
32894 fcolorbox{#2}{#1}{$#3$}}
32897 \begin_inset VSpace medskip
32901 \begin_inset Newline newline
32904 When the color is not specified when using
32910 , the predefined color
32917 \begin_layout Standard
32918 A test of the new defined commands:
32921 \begin_layout Standard
32923 \begin_inset Tabular
32924 <lyxtabular version="3" rows="6" columns="2">
32925 <features booktabs="true" tabularvalignment="middle">
32926 <column alignment="center" valignment="top" width="0pt">
32927 <column alignment="center" valignment="top">
32929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32932 \begin_layout Plain Layout
32938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32941 \begin_layout Plain Layout
32949 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32952 \begin_layout Plain Layout
32956 \begin_inset space \textvisiblespace{}
32964 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32967 \begin_layout Plain Layout
32968 \begin_inset Formula $A\gr B$
32978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32981 \begin_layout Plain Layout
32989 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32992 \begin_layout Plain Layout
32993 \begin_inset Formula $\us{ABcd}$
33002 <row topspace="1mm">
33003 <cell alignment="center" valignment="top" usebox="none">
33006 \begin_layout Plain Layout
33010 \begin_inset Formula $\to$
33016 \begin_inset Formula $\to$
33024 \begin_inset space \textvisiblespace{}
33032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33035 \begin_layout Plain Layout
33036 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33045 <row topspace="1.5mm">
33046 <cell alignment="center" valignment="top" usebox="none">
33049 \begin_layout Plain Layout
33053 \begin_inset Formula $\to$
33061 \begin_inset space \textvisiblespace{}
33069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33072 \begin_layout Plain Layout
33073 \begin_inset Formula $\cb{red}{\int A=B}$
33082 <row topspace="1.5mm" bottomspace="1mm">
33083 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33086 \begin_layout Plain Layout
33092 \begin_inset Formula $\to$
33100 \begin_inset space \textvisiblespace{}
33108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33111 \begin_layout Plain Layout
33112 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33128 \begin_layout Subsection
33130 \begin_inset Index idx
33133 \begin_layout Plain Layout
33134 User-defined commands! Math macros
33140 \begin_inset Index idx
33143 \begin_layout Plain Layout
33152 \begin_layout Standard
33153 User-defined commands are especially convenient for complex expressions.
33154 When you are for example dealing with a document that has quadratic equations,
33155 the same solution type occurs several times.
33156 The general form of a quadratic equation is
33157 \begin_inset Formula
33159 0=\lambda^{2}+p\lambda+q
33164 The general form of the solution is
33165 \begin_inset Formula
33167 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33175 \begin_layout Standard
33176 To define a command for the solution formula where only the three parameters
33178 \begin_inset Formula $\lambda$
33182 \begin_inset Formula $p$
33186 \begin_inset Formula $q$
33189 need to be specified and the index of
33190 \begin_inset Formula $\lambda$
33193 can be given optionally, the \SpecialChar LaTeX
33195 \begin_inset Newline newline
33211 \begin_inset Newline newline
33215 \begin_inset Phantom HPhantom
33218 \begin_layout Plain Layout
33232 frac{#3^{2}}{4}-#4}}
33235 \begin_layout Standard
33236 To create with this the solution formula, the command
33237 \begin_inset Newline newline
33247 \begin_inset Formula $\to$
33253 \begin_inset Formula $\to$
33260 is inserted to a formula
33265 \begin_layout Standard
33266 The definition of the new command is unintuitive because one has to know
33267 the schemes of all used \SpecialChar LaTeX
33269 \begin_inset space \thinspace{}
33273 \begin_inset space \space{}
33276 that a fraction is inserted in \SpecialChar LaTeX
33281 frac{numerator}{denominator}
33284 Furthermore one can easily forget a brace in the definition and cannot
33285 see in \SpecialChar LyX
33286 what the new command is doing.
33287 To avoid these problems \SpecialChar LyX
33288 offers the possibility to use math macros instead
33298 \begin_layout Standard
33299 A math macro is created by using the menu
33301 Insert\SpecialChar menuseparator
33302 Math\SpecialChar menuseparator
33305 or the toolbar button
33308 arg "math-macro newmacroname_newcommand"
33312 The math macro toolbar appears together with the following box where the
33314 \begin_inset Newline newline
33318 \begin_inset space \hspace*{\fill}
33322 \begin_inset Graphics
33323 filename clipart/macrobox.png
33329 \begin_inset space \hspace*{\fill}
33333 \begin_inset Newline newline
33337 \begin_inset FormulaMacro
33338 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33343 newmacroname is the default name of the macro that should be changed to
33344 something sensible.
33345 The wanted formula is inserted in the first blue box.
33346 An argument placeholder is inserted with the command
33353 \begin_inset space \thinspace{}
33357 \begin_inset space \space{}
33366 or by using the macro toolbar button
33369 arg "math-macro-add-param"
33373 Argument placeholders are displayed red.
33375 \begin_inset space ~
33378 arguments are possible.
33379 Optional arguments are created with the toolbar button
33382 arg "math-macro-add-optional-param"
33386 The first non-optional argument can be transformed to an optional one with
33390 arg "math-macro-make-optional"
33394 In the second blue box the appearance of the macro in \SpecialChar LyX
33396 Normally you want to see it as it is defined, so the box is kept empty.
33397 But when you have created a macro that needs lot of space on the screen,
33398 you can insert in the box for example
33399 \begin_inset Newline newline
33429 \begin_inset Newline newline
33434 For the macro only the arguments with the macro name in front of them will
33435 then be displayed in \SpecialChar LyX
33436 , leading to a better overview.
33437 The formula appears in the output as defined in the first box.
33438 \begin_inset Newline newline
33441 The appearance of macros in formulas can furthermore be changed for single
33442 macros by setting the cursor in the macro and using the menu
33444 View\SpecialChar menuseparator
33446 \begin_inset space ~
33450 \begin_inset space ~
33458 \begin_layout Standard
33459 To use a macro, the macro name is inserted as command to a formula, in our
33467 Our macro looks in \SpecialChar LyX
33469 \begin_inset Newline newline
33473 \begin_inset space \hspace*{\fill}
33477 \begin_inset Graphics
33478 filename clipart/macrouse.png
33484 \begin_inset space \hspace*{\fill}
33488 \begin_inset Newline newline
33491 Here is our macro example with the arguments
33492 \begin_inset Formula $x$
33496 \begin_inset Formula $\ln(x)$
33500 \begin_inset Formula $B$
33506 \begin_layout Standard
33507 \begin_inset Formula
33517 \begin_layout Standard
33521 Tools\SpecialChar menuseparator
33522 Preferences\SpecialChar menuseparator
33523 Editing\SpecialChar menuseparator
33526 different styles to edit macros.
33527 To find the style that suits you the most, choose a style and set the cursor
33528 in a macro formula to see the difference.
33531 \begin_layout Standard
33532 A math macro is transformed internally to a
33538 command when exporting the document.
33545 command is not placed in the \SpecialChar LaTeX
33546 -preamble, therefore macros can only be used
33547 in formulas that are in the document below the macro definition box.
33550 \begin_layout Standard
33551 Math macros can also be directly created from a
33558 When writing for example the command
33561 \begin_inset Newline newline
33570 xleftarrow[#2]{#1}}
33571 \begin_inset Newline newline
33576 in \SpecialChar LyX
33577 as normal text, highlighting it completely and using then the shortcut
33582 , the command will be transformed to a math macro.
33583 Using this method you need to be careful that the
33589 command is typed correctly, otherwise you get a faulty macro leading to
33594 \begin_layout Standard
33595 Math macros currently have the problem that further formulas in macro definition
33596 s are handled wrongly.
33597 Therefore the example
33604 \begin_inset CommandInset ref
33606 reference "subsec:The-Command-newcommand"
33610 cannot be created as macro.
33613 \begin_layout Standard
33614 When the cursor is in a macro definition box, you will see the macro toolbar
33615 in \SpecialChar LyX
33619 \begin_layout Standard
33620 \begin_inset VSpace defskip
33626 \begin_layout Standard
33627 \begin_inset Graphics
33628 filename clipart/MacroToolbar.png
33633 \begin_inset Index idx
33636 \begin_layout Plain Layout
33645 \begin_layout Standard
33646 \begin_inset VSpace defskip
33652 \begin_layout Standard
33653 The macro toolbar contains from left to right the following buttons:
33656 \begin_layout Standard
33657 \begin_inset VSpace defskip
33663 \begin_layout Standard
33664 \begin_inset Tabular
33665 <lyxtabular version="3" rows="9" columns="2">
33666 <features islongtable="true" longtabularalignment="center">
33667 <column alignment="left" valignment="top">
33668 <column alignment="left" valignment="top" width="85col%">
33669 <row interlinespace="2.5mm">
33670 <cell alignment="center" valignment="top" usebox="none">
33673 \begin_layout Plain Layout
33676 arg "math-macro-remove-param"
33684 <cell alignment="center" valignment="top" usebox="none">
33687 \begin_layout Plain Layout
33690 Edit\SpecialChar menuseparator
33691 Math\SpecialChar menuseparator
33693 \begin_inset space ~
33696 Definition\SpecialChar menuseparator
33697 Remove Last Argument
33703 <row interlinespace="2.5mm">
33704 <cell alignment="center" valignment="top" usebox="none">
33707 \begin_layout Plain Layout
33710 arg "math-macro-add-param"
33718 <cell alignment="center" valignment="top" usebox="none">
33721 \begin_layout Plain Layout
33724 Edit\SpecialChar menuseparator
33725 Math\SpecialChar menuseparator
33727 \begin_inset space ~
33730 Definition\SpecialChar menuseparator
33737 <row interlinespace="2.5mm">
33738 <cell alignment="center" valignment="top" usebox="none">
33741 \begin_layout Plain Layout
33744 arg "math-macro-make-optional"
33752 <cell alignment="center" valignment="top" usebox="none">
33755 \begin_layout Plain Layout
33758 Edit\SpecialChar menuseparator
33759 Math\SpecialChar menuseparator
33761 \begin_inset space ~
33764 Definition\SpecialChar menuseparator
33765 Transform First Non-Optional to
33766 \begin_inset Newline newline
33770 \begin_inset Phantom HPhantom
33773 \begin_layout Plain Layout
33776 Edit\SpecialChar menuseparator
33777 Math\SpecialChar menuseparator
33779 \begin_inset space ~
33782 Definition\SpecialChar menuseparator
33794 <row interlinespace="2.5mm">
33795 <cell alignment="center" valignment="top" usebox="none">
33798 \begin_layout Plain Layout
33801 arg "math-macro-make-nonoptional"
33809 <cell alignment="center" valignment="top" usebox="none">
33812 \begin_layout Plain Layout
33815 Edit\SpecialChar menuseparator
33816 Math\SpecialChar menuseparator
33818 \begin_inset space ~
33821 Definition\SpecialChar menuseparator
33822 Transform Last Optional to
33823 \begin_inset Newline newline
33827 \begin_inset Phantom HPhantom
33830 \begin_layout Plain Layout
33833 Edit\SpecialChar menuseparator
33834 Math\SpecialChar menuseparator
33836 \begin_inset space ~
33839 Definition\SpecialChar menuseparator
33845 Non-Optional Argument
33851 <row interlinespace="2.5mm">
33852 <cell alignment="center" valignment="top" usebox="none">
33855 \begin_layout Plain Layout
33858 arg "math-macro-remove-optional-param"
33866 <cell alignment="center" valignment="top" usebox="none">
33869 \begin_layout Plain Layout
33872 Edit\SpecialChar menuseparator
33873 Math\SpecialChar menuseparator
33875 \begin_inset space ~
33878 Definition\SpecialChar menuseparator
33879 Remove Optional Argument
33885 <row interlinespace="2.5mm">
33886 <cell alignment="center" valignment="top" usebox="none">
33889 \begin_layout Plain Layout
33892 arg "math-macro-add-optional-param"
33900 <cell alignment="center" valignment="top" usebox="none">
33903 \begin_layout Plain Layout
33906 Edit\SpecialChar menuseparator
33907 Math\SpecialChar menuseparator
33909 \begin_inset space ~
33912 Definition\SpecialChar menuseparator
33913 Insert Optional Argument
33919 <row interlinespace="2.5mm">
33920 <cell alignment="center" valignment="top" usebox="none">
33923 \begin_layout Plain Layout
33926 arg "math-macro-remove-greedy-param"
33934 <cell alignment="center" valignment="top" usebox="none">
33937 \begin_layout Plain Layout
33940 Edit\SpecialChar menuseparator
33941 Math\SpecialChar menuseparator
33943 \begin_inset space ~
33946 Definition\SpecialChar menuseparator
33947 Remove Last Argument
33948 \begin_inset Newline newline
33952 \begin_inset Phantom HPhantom
33955 \begin_layout Plain Layout
33958 Edit\SpecialChar menuseparator
33959 Math\SpecialChar menuseparator
33961 \begin_inset space ~
33964 Definition\SpecialChar menuseparator
33970 Spitting Out To The Right
33976 <row interlinespace="2.5mm">
33977 <cell alignment="center" valignment="top" usebox="none">
33980 \begin_layout Plain Layout
33983 arg "math-macro-append-greedy-param"
33991 <cell alignment="center" valignment="top" usebox="none">
33994 \begin_layout Plain Layout
33997 Edit\SpecialChar menuseparator
33998 Math\SpecialChar menuseparator
34000 \begin_inset space ~
34003 Definition\SpecialChar menuseparator
34005 \begin_inset Newline newline
34009 \begin_inset Phantom HPhantom
34012 \begin_layout Plain Layout
34015 Edit\SpecialChar menuseparator
34016 Math\SpecialChar menuseparator
34018 \begin_inset space ~
34021 Definition\SpecialChar menuseparator
34027 Eating From The Right
34033 <row interlinespace="2.5mm">
34034 <cell alignment="center" valignment="top" usebox="none">
34037 \begin_layout Plain Layout
34040 arg "math-macro-add-greedy-optional-param"
34048 <cell alignment="center" valignment="top" usebox="none">
34051 \begin_layout Plain Layout
34054 Edit\SpecialChar menuseparator
34055 Math\SpecialChar menuseparator
34057 \begin_inset space ~
34060 Definition\SpecialChar menuseparator
34061 Append Optional Argument
34062 \begin_inset Newline newline
34066 \begin_inset Phantom HPhantom
34069 \begin_layout Plain Layout
34072 Edit\SpecialChar menuseparator
34073 Math\SpecialChar menuseparator
34075 \begin_inset space ~
34078 Definition\SpecialChar menuseparator
34084 Eating From The Right
34097 \begin_layout Section
34098 Computer Algebra Systems
34101 \begin_layout Standard
34103 offers the exchange between mathematical expressions written in \SpecialChar LyX
34105 editor and external applications or user defined scripts.
34106 Currently supported applications are
34123 Note that the set of supported mathematical constructs is limited only
34124 to very simple cases.
34127 \begin_layout Subsection
34131 \begin_layout Standard
34132 Write some expression in a formula, go to the
34134 Edit\SpecialChar menuseparator
34135 Math\SpecialChar menuseparator
34136 Use Computer Algebra System
34138 menu and choose the application you have installed on the computer.
34139 After that the result of computation should show on the right side of the
34140 expression together with the
34141 \begin_inset Quotes eld
34145 \begin_inset Quotes erd
34151 \begin_layout Standard
34152 Here are few simple examples (with results from
34156 ) to show what kind of computations can be performed:
34159 \begin_layout Itemize
34160 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34166 \begin_layout Itemize
34167 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34173 \begin_layout Itemize
34174 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34180 \begin_layout Itemize
34181 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34185 \begin_inset Newline newline
34189 \begin_inset Note Greyedout
34192 \begin_layout Plain Layout
34197 One needs to use proper delimiter insets
34198 \begin_inset Formula $\left(\right)$
34201 instead of simple '(' ')' characters.
34209 \begin_layout Itemize
34210 \begin_inset Formula $\det\left[\begin{array}{ccc}
34214 \end{array}\right]=-56$
34220 \begin_layout Itemize
34221 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34227 \begin_layout Itemize
34228 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34234 \begin_layout Itemize
34235 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34241 \begin_layout Subsection
34245 \begin_layout Standard
34246 Currently there is no keyboard shortcut for calling the algebra applications.
34247 One can easily bind a shortcut to the
34261 \begin_inset space \thinspace{}
34265 \begin_inset space \space{}
34272 key inside the math editor.
34277 one would use this shortcut definition command:
34280 \begin_layout Standard
34283 command-alternatives paragraph-break;math-extern maxima
34286 \begin_layout Section
34288 \begin_inset Index idx
34291 \begin_layout Plain Layout
34300 \begin_layout Subsection
34302 \begin_inset Index idx
34305 \begin_layout Plain Layout
34314 \begin_layout Standard
34315 Negative numbers often look ugly in formulas because the minus sign before
34316 the number is set with the same length as the minus operator sign.
34317 When writing the negative number in normal text, the minus sign appears
34321 \begin_layout Standard
34322 Thus, the problem disappears when converting the minus sign to mathematical
34326 \begin_layout Standard
34327 An example to visualize the problem:
34330 \begin_layout Standard
34332 \begin_inset Tabular
34333 <lyxtabular version="3" rows="3" columns="2">
34334 <features booktabs="true" tabularvalignment="middle">
34335 <column alignment="right" valignment="top" width="0pt">
34336 <column alignment="left" valignment="top">
34338 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34341 \begin_layout Plain Layout
34347 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34350 \begin_layout Plain Layout
34358 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34361 \begin_layout Plain Layout
34367 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34370 \begin_layout Plain Layout
34371 \begin_inset Formula $x=-2$
34381 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34384 \begin_layout Plain Layout
34390 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34393 \begin_layout Plain Layout
34394 \begin_inset Formula $x=\textrm{-}2$
34410 \begin_layout Subsection
34411 Comma as decimal Separator
34412 \begin_inset Index idx
34415 \begin_layout Plain Layout
34424 \begin_layout Standard
34425 In \SpecialChar LaTeX
34426 a comma inside a formula is used, according to the English convention,
34427 as number group separator.
34428 So there will be space added behind all commas in formulas.
34431 \begin_layout Standard
34432 To avoid this, the comma is highlighted and changed to mathematical text
34442 \begin_layout Standard
34443 To use all formula commas in the document as decimal separator, the file
34452 \begin_layout Plain Layout
34457 is part of the \SpecialChar LaTeX
34463 \begin_inset Index idx
34466 \begin_layout Plain Layout
34471 \begin_layout Plain Layout
34491 \begin_inset Index idx
34494 \begin_layout Plain Layout
34500 is loaded with the \SpecialChar LaTeX
34504 \begin_layout Standard
34512 \begin_layout Subsection
34514 \begin_inset CommandInset label
34516 name "subsec:Physical-Vectors"
34521 \begin_inset Index idx
34524 \begin_layout Plain Layout
34533 \begin_layout Standard
34534 Predefined vectors are offered by the \SpecialChar LaTeX
34540 \begin_inset Index idx
34543 \begin_layout Plain Layout
34549 that is loaded with the \SpecialChar LaTeX
34553 \begin_layout Standard
34561 \begin_layout Standard
34565 \begin_layout Plain Layout
34575 \begin_inset Note Note
34578 \begin_layout Plain Layout
34579 The following table will only be displayed when the \SpecialChar LaTeX
34592 \begin_layout Standard
34593 The following commands are defined:
34596 \begin_layout Standard
34598 \begin_inset Tabular
34599 <lyxtabular version="3" rows="4" columns="2">
34600 <features booktabs="true" tabularvalignment="middle">
34601 <column alignment="center" valignment="top" width="0pt">
34602 <column alignment="center" valignment="top">
34604 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34607 \begin_layout Plain Layout
34613 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34616 \begin_layout Plain Layout
34624 <cell alignment="center" valignment="top" usebox="none">
34627 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" usebox="none">
34640 \begin_layout Plain Layout
34641 \begin_inset Formula $\Bra{\psi}$
34651 <cell alignment="center" valignment="top" usebox="none">
34654 \begin_layout Plain Layout
34664 <cell alignment="center" valignment="top" usebox="none">
34667 \begin_layout Plain Layout
34668 \begin_inset Formula $\Ket{\psi}$
34678 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34681 \begin_layout Plain Layout
34693 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34696 \begin_layout Plain Layout
34697 \begin_inset Formula $\Braket{\psi|\phi}$
34713 \begin_layout Standard
34720 assures that all vertical bars are set in the size of the surrounding brackets:
34721 \begin_inset Formula
34723 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34732 \begin_layout Plain Layout
34742 \begin_inset Note Note
34745 \begin_layout Plain Layout
34746 The following will be displayed when the \SpecialChar LaTeX
34759 \begin_layout Standard
34760 You need to install the \SpecialChar LaTeX
34765 to see the rest of this subsection in the output.
34768 \begin_layout Standard
34772 \begin_layout Plain Layout
34784 \begin_layout Standard
34791 can also be achieved using the command
34797 , that is described in
34798 \begin_inset CommandInset ref
34800 reference "subsec:Automatic-Bracket-Size"
34807 \begin_layout Subsection
34808 Self-defined Fractions
34809 \begin_inset CommandInset label
34811 name "subsec:Self-defined-Fractions"
34816 \begin_inset Index idx
34819 \begin_layout Plain Layout
34820 Fractions ! self-defined
34828 \begin_layout Standard
34829 To define custom commands for fractions, the command
34836 \begin_inset Index idx
34839 \begin_layout Plain Layout
34846 \begin_layout Plain Layout
34860 is used in the following scheme:
34863 \begin_layout Standard
34876 bracket}{fraction bar thickness}{style}
34877 \begin_inset Newline newline
34881 \begin_inset Phantom HPhantom
34884 \begin_layout Plain Layout
34894 {numerator}{denominator}
34897 \begin_layout Standard
34898 The style is a number in the range of 0
34899 \begin_inset space \thinspace{}
34903 \begin_inset space \thinspace{}
34909 \begin_layout Standard
34911 \begin_inset Tabular
34912 <lyxtabular version="3" rows="5" columns="2">
34913 <features booktabs="true" tabularvalignment="middle">
34914 <column alignment="center" valignment="top" width="0pt">
34915 <column alignment="center" valignment="top">
34917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34920 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34929 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" usebox="none">
34940 \begin_layout Plain Layout
34946 <cell alignment="center" valignment="top" usebox="none">
34949 \begin_layout Plain Layout
34950 display style formula
34957 <cell alignment="center" valignment="top" usebox="none">
34960 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" usebox="none">
34969 \begin_layout Plain Layout
34977 <cell alignment="center" valignment="top" usebox="none">
34980 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35000 \begin_layout Plain Layout
35006 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35009 \begin_layout Plain Layout
35023 \begin_layout Standard
35024 When no style is given, the size is adjusted to the surrounding environment
35025 like for the command
35034 \begin_layout Standard
35035 When no fraction bar thickness is given, the predefined value of 0.4
35036 \begin_inset space \thinspace{}
35042 \begin_layout Standard
35043 \begin_inset VSpace medskip
35046 For example, the commands
35059 \begin_inset CommandInset ref
35061 reference "subsec:Fractions"
35065 are defined with the commands
35068 \begin_layout Standard
35077 genfrac{}{}{}{0}{#1}{#2}}
35080 \begin_layout Standard
35084 \begin_layout Standard
35093 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35096 \begin_layout Standard
35097 \begin_inset VSpace medskip
35100 To define a fraction where the fraction bar thickness can be given as optional
35101 argument, the following line is inserted to the \SpecialChar LaTeX
35105 \begin_layout Standard
35114 genfrac{}{}{#1}{}{#2}{#3}}
35117 \begin_layout Standard
35119 \begin_inset Formula
35121 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35122 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35127 As one can see, the distance of the numerator and the denominator to the
35128 fraction bar is round about three times the bar thickness.
35131 \begin_layout Subsection
35133 \begin_inset Index idx
35136 \begin_layout Plain Layout
35145 \begin_layout Standard
35146 There are four ways to cancel formulas or parts of formulas:
35149 \begin_layout Standard
35153 \begin_layout Plain Layout
35163 \begin_inset Note Note
35166 \begin_layout Plain Layout
35167 The following table will only be displayed when the \SpecialChar LaTeX
35180 \begin_layout Standard
35182 \begin_inset Tabular
35183 <lyxtabular version="3" rows="5" columns="2">
35184 <features booktabs="true" tabularvalignment="middle">
35185 <column alignment="center" valignment="top" width="0pt">
35186 <column alignment="center" valignment="top">
35188 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35191 \begin_layout Plain Layout
35197 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35200 \begin_layout Plain Layout
35208 <cell alignment="center" valignment="top" usebox="none">
35211 \begin_layout Plain Layout
35215 \begin_inset space \textvisiblespace{}
35221 \begin_inset space \textvisiblespace{}
35229 <cell alignment="center" valignment="top" usebox="none">
35232 \begin_layout Plain Layout
35233 \begin_inset Formula $\cancel{\int A=B}$
35242 <row topspace="1.5mm">
35243 <cell alignment="center" valignment="top" usebox="none">
35246 \begin_layout Plain Layout
35250 \begin_inset space \textvisiblespace{}
35256 \begin_inset space \textvisiblespace{}
35264 <cell alignment="center" valignment="top" usebox="none">
35267 \begin_layout Plain Layout
35268 \begin_inset Formula $\bcancel{\int A=B}$
35277 <row topspace="1.5mm">
35278 <cell alignment="center" valignment="top" usebox="none">
35281 \begin_layout Plain Layout
35285 \begin_inset space \textvisiblespace{}
35291 \begin_inset space \textvisiblespace{}
35299 <cell alignment="center" valignment="top" usebox="none">
35302 \begin_layout Plain Layout
35303 \begin_inset Formula $\xcancel{\int A=B}$
35313 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35316 \begin_layout Plain Layout
35320 \begin_inset space \textvisiblespace{}
35326 \begin_inset space \textvisiblespace{}
35330 \begin_inset Formula $\to$
35338 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35341 \begin_layout Plain Layout
35342 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35358 \begin_layout Standard
35365 is especially suitable to visualize the reduction of fractions within formulas:
35366 \begin_inset Formula
35368 \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}}}
35376 \begin_layout Standard
35377 To change the size of
35384 \begin_inset Quotes eld
35388 \begin_inset Quotes erd
35391 value one can add the \SpecialChar LaTeX
35395 \begin_layout Standard
35400 PassOptionsToPackage{option}{cancel}
35403 \begin_layout Standard
35412 which leads to the same size as for the canceled value, or
35416 which makes is it a bit smaller than normal.
35419 \begin_layout Standard
35420 To color the cancellation bar one adds this command as \SpecialChar TeX
35424 \begin_layout Standard
35436 \begin_layout Standard
35441 can be replaced by a color of your choice.
35444 \begin_layout Standard
35448 \begin_layout Plain Layout
35464 \begin_layout Standard
35465 \begin_inset Formula
35467 \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}}}
35475 \begin_layout Standard
35479 \begin_layout Plain Layout
35493 \begin_inset Note Note
35496 \begin_layout Plain Layout
35505 \begin_layout Standard
35506 For further customizations, see the documentation of the package
35511 \begin_inset CommandInset citation
35519 \begin_inset Index idx
35522 \begin_layout Plain Layout
35531 \begin_layout Standard
35535 \begin_layout Plain Layout
35545 \begin_inset Note Note
35548 \begin_layout Plain Layout
35549 The following will be displayed when the \SpecialChar LaTeX
35562 \begin_layout Standard
35563 You need to install the \SpecialChar LaTeX
35568 to see the rest of this subsection in the output.
35571 \begin_layout Standard
35575 \begin_layout Plain Layout
35587 \begin_layout Subsection
35588 Formulas in Section Headings
35589 \begin_inset CommandInset label
35591 name "subsec:Formulas-in-Section"
35596 \begin_inset Index idx
35599 \begin_layout Plain Layout
35600 Formula ! in section headings
35608 \begin_layout Standard
35609 When formulas are used in section headings, the following has to be taken
35613 \begin_layout Standard
35614 \begin_inset Note Greyedout
35617 \begin_layout Plain Layout
35623 \begin_inset Index idx
35626 \begin_layout Plain Layout
35627 Packages ! hyperref
35632 support is enabled in the document settings dialog under
35635 \begin_inset space ~
35640 , PDF-bookmarks are created for every section heading in the table of contents.
35641 If a section heading contains formulas, they are incorrectly displayed
35642 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35651 \begin_layout Standard
35652 Both problems can be solved by inserting at the end of the section heading
35653 a short title with the menu
35655 Insert\SpecialChar menuseparator
35657 \begin_inset space ~
35663 Short titles are used as alternative for multiline section headings to
35664 keep the table of contents clearly arranged.
35665 Only the short title appears in the table of contents and therefore also
35666 in the PDF-bookmark.
35669 \begin_layout Standard
35670 When formulas should be used in the table of contents but
35674 is used, one can use the following command in \SpecialChar TeX
35678 \begin_layout Standard
35683 texorpdfstring{part}{alternative}
35684 \begin_inset Index idx
35687 \begin_layout Plain Layout
35698 \begin_layout Standard
35699 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35700 This can be characters, formulas, footnotes, but also cross-references.
35701 The alternative is used instead of the part for the bookmark.
35704 \begin_layout Standard
35705 Here are two example headings:
35706 \begin_inset VSpace -3mm
35713 \begin_layout Plain Layout
35725 \begin_layout Subsubsection
35726 Heading without formula in table of contents
35727 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35731 \begin_inset Argument 1
35734 \begin_layout Plain Layout
35735 Heading without formula in table of contents
35743 \begin_layout Subsubsection
35744 Heading with formula in table of contents
35748 \begin_layout Plain Layout
35758 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35765 \begin_layout Plain Layout
35775 \begin_layout Standard
35779 \begin_layout Plain Layout
35788 In the first heading a short title was used, in the second one
35797 \begin_layout Standard
35798 To get the same formatting as for the other headings, the complete heading
35807 \begin_layout Plain Layout
35809 \begin_inset CommandInset ref
35811 reference "subsec:Bold-Formulas"
35823 \begin_layout Subsection
35824 Formulas in multi-column Text
35825 \begin_inset Index idx
35828 \begin_layout Plain Layout
35829 Formula ! in multi-column text
35837 \begin_layout Standard
35838 Formulas in multi-column text are often too wide to fit into a column and
35839 thus need to be set over the whole page width.
35840 This is done by using the \SpecialChar LaTeX
35849 \begin_layout Plain Layout
35854 is part of every \SpecialChar LaTeX
35855 standard installation.
35861 \begin_inset Index idx
35864 \begin_layout Plain Layout
35865 Packages ! multicol
35870 , that is loaded with the \SpecialChar LaTeX
35874 \begin_layout Standard
35879 usepackage{multicol}
35882 \begin_layout Standard
35883 \begin_inset Note Greyedout
35886 \begin_layout Plain Layout
35887 Note that in this case the setting
35890 \begin_inset space ~
35897 Document\SpecialChar menuseparator
35903 \begin_inset space ~
35923 \begin_layout Standard
35924 Before the multi-column text the command
35927 \begin_layout Standard
35932 begin{multicols}{column number}
35935 \begin_layout Standard
35936 is written in \SpecialChar TeX
35938 The column number is a number in the range of 2
35939 \begin_inset space \thinspace{}
35943 \begin_inset space \thinspace{}
35947 Before the formula the multi-column text is ended by inserting the command
35950 \begin_layout Standard
35958 \begin_layout Standard
35959 in \SpecialChar TeX
35963 \begin_layout Standard
35964 Due to the command some space is automatically added before the formula.
35966 \begin_inset space \thinspace{}
35969 mm vertical space is inserted before the formula.
35970 When the formula style
35976 \begin_layout Plain Layout
35978 \begin_inset CommandInset ref
35980 reference "sec:Formula-Styles"
35992 \begin_inset space \thinspace{}
35995 mm space is inserted instead.
35998 \begin_layout Standard
35999 As example a multi-column text with a displayed formula:
36002 \begin_layout Standard
36008 \begin_layout Plain Layout
36012 begin{multicols}{2}
36017 Das Spektrum wird fouriertransformiert.
36018 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36019 , Lösungsmittel) zu trennen.
36020 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36021 nun das Aussehen des Ausgangssignals.
36022 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36023 über alle Phasen integrieren muss.
36025 \begin_inset Formula $S$
36028 unser normiertes Ausgangssignal und
36029 \begin_inset Formula $P$
36032 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36036 \begin_layout Plain Layout
36046 \begin_inset VSpace -6mm
36050 \begin_inset Formula
36052 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36061 \begin_layout Plain Layout
36065 begin{multicols}{2}
36071 \begin_inset Formula $S_{0}$
36074 das Signal ohne Gradient ist und die Normierungsbedingung
36075 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36079 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36081 \begin_inset Formula $\nicefrac{\pi}{2}$
36085 \begin_inset space \thinspace{}
36088 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36089 das Signal zusätzlich abschwächt.
36090 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36092 \begin_inset Formula $T_{2}$
36098 \begin_layout Standard
36104 \begin_layout Plain Layout
36116 \begin_layout Subsection
36117 Formulas with Description of Variables
36118 \begin_inset Index idx
36121 \begin_layout Plain Layout
36122 Formula ! with description of variables
36130 \begin_layout Standard
36131 To describe variables within a formula, like in formula
36132 \begin_inset CommandInset ref
36134 reference "eq:within"
36143 \begin_inset Formula $n$
36147 \begin_inset space ~
36150 matrix is used with left aligned columns for the
36151 \begin_inset Formula $n$
36158 \begin_layout Plain Layout
36160 \begin_inset CommandInset ref
36162 reference "sec:Matrices"
36171 To set the description in a smaller size, before the matrix e.
36172 \begin_inset space \thinspace{}
36176 \begin_inset space \space{}
36189 \begin_layout Plain Layout
36191 \begin_inset CommandInset ref
36193 reference "subsec:Font-Sizes"
36205 \begin_layout Standard
36206 When the formula style
36212 \begin_layout Plain Layout
36214 \begin_inset CommandInset ref
36216 reference "sec:Formula-Styles"
36237 \begin_layout Plain Layout
36244 only works in formulas with the style
36249 \begin_inset CommandInset ref
36251 reference "subsec:Variable-Space"
36260 is inserted before and after the matrix to have the same separation of
36261 the matrix from the equation and the side margin.
36264 \begin_layout Standard
36265 When the formula style
36269 is used, the method described in
36270 \begin_inset CommandInset ref
36272 reference "subsec:Flalign-Environment"
36276 is used to indent formulas.
36278 \begin_inset CommandInset ref
36280 reference "eq:within"
36284 consists of five columns where in the first two columns contain the equation,
36285 the third the matrix and the last one an empty \SpecialChar TeX
36287 \begin_inset Formula
36289 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36290 \rho & \textrm{density}\\
36291 V & \textrm{volume}\\
36292 g & \textrm{gravitational acceleration}
36293 \end{array} & & {}\label{eq:within}
36301 \begin_layout Subsection
36302 Upright small Greek Letters
36303 \begin_inset CommandInset label
36305 name "subsec:Upright-small-Greek"
36310 \begin_inset Index idx
36313 \begin_layout Plain Layout
36314 Greek letters ! upright
36322 \begin_layout Standard
36323 Most of the math fonts only provide italic small Greek letters.
36324 But for symbols of elementary particles like pions and neutrinos, upright
36325 Greek letters are needed.
36334 \begin_layout Plain Layout
36339 is part of the \SpecialChar LaTeX
36345 \begin_inset Index idx
36348 \begin_layout Plain Layout
36353 \begin_layout Plain Layout
36373 \begin_inset Index idx
36376 \begin_layout Plain Layout
36382 that is loaded with the \SpecialChar LaTeX
36386 \begin_layout Standard
36391 usepackage{upgreek}
36394 \begin_layout Standard
36400 \begin_layout Plain Layout
36410 \begin_inset Note Note
36413 \begin_layout Plain Layout
36414 The following table will only be displayed when the \SpecialChar LaTeX
36424 They are created when the command for a small Greek letter is started with
36430 For example the command
36437 \begin_inset Formula $\uptau$
36443 \begin_layout Standard
36444 With these commands reactions of elementary particles can be typeset:
36445 \begin_inset Formula
36447 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36455 \begin_layout Standard
36456 The upright letters are more bold and wider than the italic ones.
36457 They should therefore not be used for units like
36458 \begin_inset Quotes eld
36462 \begin_inset Quotes erd
36468 \begin_layout Standard
36472 \begin_layout Plain Layout
36482 \begin_inset Note Note
36485 \begin_layout Plain Layout
36486 The following will be displayed when the \SpecialChar LaTeX
36499 \begin_layout Standard
36500 You need to install the \SpecialChar LaTeX
36505 to see the rest of this subsection in the output.
36508 \begin_layout Standard
36512 \begin_layout Plain Layout
36524 \begin_layout Subsection
36525 Text Characters in Formulas
36526 \begin_inset Index idx
36529 \begin_layout Plain Layout
36538 \begin_layout Standard
36539 In some cases you might want to insert text characters directly into formulas.
36540 When for example the centered dot · is often used in formulas like
36541 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36544 , one would have to insert the command
36554 \begin_layout Plain Layout
36556 \begin_inset CommandInset ref
36558 reference "subsec:Binary-Operators"
36567 all the time, because this character is defined in all encodings as text
36569 But the encoding can be changed by this \SpecialChar LaTeX
36573 \begin_layout Standard
36578 Declare Inputtext{183}{
36588 f\SpecialChar ligaturebreak
36592 \begin_layout Standard
36593 The character encoding (menu
36595 Document\SpecialChar menuseparator
36596 Settings\SpecialChar menuseparator
36599 ) specifies what character appears when a keyboard key is pressed.
36600 When the key for the character '·' is pressed, internally the command
36607 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36609 With the changed encoding the right command is chosen automatically, depending
36610 on if the character was inserted into a formula or not.
36613 \begin_layout Standard
36614 The encoding of several characters is saved in definition files.
36615 For example the encoding
36619 is defined in the file
36623 which is in the installation folder of \SpecialChar LaTeX
36625 Encodings should only be changed via the \SpecialChar LaTeX
36626 -preamble and not in the definition
36628 Otherwise documents could not be edited by other \SpecialChar LyX
36629 users working on other
36633 \begin_layout Standard
36634 \begin_inset VSpace medskip
36637 Besides the centered dot, in this document the degree sign ° is defined
36638 with the following \SpecialChar LaTeX
36639 -preamble line so that it can be directly inserted into
36643 \begin_layout Standard
36648 DeclareInputtext{176}{
36658 f\SpecialChar ligaturebreak
36662 \begin_layout Subsection
36664 -comments in formulas
36665 \begin_inset Index idx
36668 \begin_layout Plain Layout
36678 \begin_layout Standard
36679 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36681 code of your file with the menu
36683 Insert\SpecialChar menuseparator
36684 Note\SpecialChar menuseparator
36688 This is not possible in a formula but you can insert \SpecialChar LaTeX
36693 \begin_layout Standard
36701 \begin_layout Standard
36702 This creates a box in which you can write your comment.
36703 Due to a bug in \SpecialChar LyX
36708 \begin_layout Plain Layout
36709 \begin_inset CommandInset href
36711 name "LyX-bug #9002"
36712 target "https://www.lyx.org/trac/ticket/9002"
36722 you cannot write normal text inside the comment, even when you use mathematical
36723 text, you will see its \SpecialChar LaTeX
36724 -commands in the \SpecialChar LaTeX
36726 \begin_inset Newline newline
36729 This a formula with a \SpecialChar LaTeX
36731 \begin_inset Formula
36733 A=B%\text{This is the comment}
36741 \begin_layout Standard
36742 \begin_inset Newpage newpage
36748 \begin_layout Section
36751 \begin_inset Index idx
36754 \begin_layout Plain Layout
36763 \begin_layout Standard
36764 This section is a summary of the most important typographic rules, listed
36769 \begin_layout Plain Layout
36770 This collection was partly taken from the German semi-official dictionary
36772 \begin_inset Quotes eld
36776 \begin_inset Quotes erd
36780 \begin_inset CommandInset citation
36787 that lists some of the ISO rules.
36788 More rules are listed in
36789 \begin_inset CommandInset citation
36804 \begin_layout Itemize
36813 \begin_layout Plain Layout
36814 done with font styles, see
36815 \begin_inset CommandInset ref
36817 reference "subsec:Font-Styles"
36826 , no matter if they appear in italic text: 30
36827 \begin_inset space \thinspace{}
36831 \begin_inset Newline newline
36834 Between the value and the unit is the smallest space, see
36835 \begin_inset CommandInset ref
36837 reference "subsec:Predefined-Space"
36842 \begin_inset Newline newline
36845 This convention is automatically fulfilled when the command
36852 When it is entered to a formula, two boxes appear.
36853 In the first one the value is inserted, in the second one the unit, and
36855 \begin_inset Formula $\unit[30]{km/h}$
36859 \begin_inset space \thinspace{}
36869 is not a real \SpecialChar LaTeX
36870 command but the command
36876 , therefore you cannot use it in \SpecialChar TeX
36880 \begin_layout Itemize
36881 Percent and perthousand signs are set like physical units:
36882 \begin_inset Newline newline
36886 \begin_inset space \thinspace{}
36892 \begin_layout Itemize
36893 The degree sign follows directly on the value: 15°, but not when it is used
36895 \begin_inset space \thinspace{}
36901 \begin_layout Itemize
36902 In numbers with more than four digits the smallest space is inserted before
36903 every third digit to group them:
36913 \begin_inset space \thinspace{}
36917 \begin_inset space \thinspace{}
36923 \begin_layout Itemize
36924 For dimensions like 120×90×40
36925 \begin_inset space \thinspace{}
36928 cm the multiplication sign
36929 \begin_inset Quotes eld
36933 \begin_inset Quotes erd
36937 It is available either via the command
36945 Insert\SpecialChar menuseparator
36946 Special Character\SpecialChar menuseparator
36952 \begin_layout Itemize
36953 Functions with names consisting of several letters are set upright to avoid
36955 \begin_inset CommandInset ref
36957 reference "subsec:Predefined-Functions"
36964 \begin_layout Itemize
36965 Indices consisting of several letters, are set upright:
36966 \begin_inset Formula $E_{\mathrm{kin}}$
36970 \begin_inset Newline newline
36973 Components of matrices are set italic:
36974 \begin_inset Formula $\hat{H}_{kl}$
36980 \begin_layout Itemize
36981 The differentiation/integration operator 'd', the Euler's number 'e' and
36982 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36986 \begin_layout Itemize
36987 The character that denotes a
36991 transformation is inserted either by the command
36996 \begin_inset space \textvisiblespace{}
37003 Insert\SpecialChar menuseparator
37004 Special Character\SpecialChar menuseparator
37005 Symbols\SpecialChar menuseparator
37007 \begin_inset space ~
37013 \begin_inset Formula $\mathscr{F}$
37019 \begin_layout Standard
37020 \begin_inset Newpage newpage
37026 \begin_layout Section
37028 \begin_inset Index idx
37031 \begin_layout Plain Layout
37040 \begin_layout Standard
37041 Some characters and symbols can be created with several commands.
37042 Here is a list of the synonym commands:
37045 \begin_layout Standard
37046 \begin_inset VSpace bigskip
37050 \begin_inset space \hfill{}
37054 \begin_inset Tabular
37055 <lyxtabular version="3" rows="12" columns="2">
37056 <features booktabs="true" tabularvalignment="middle">
37057 <column alignment="center" valignment="top" width="0pt">
37058 <column alignment="center" valignment="top" width="0pt">
37060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37063 \begin_layout Plain Layout
37069 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37072 \begin_layout Plain Layout
37080 <cell alignment="center" valignment="top" usebox="none">
37083 \begin_layout Plain Layout
37091 <cell alignment="center" valignment="top" usebox="none">
37094 \begin_layout Plain Layout
37102 <cell alignment="center" valignment="top" usebox="none">
37105 \begin_layout Plain Layout
37113 <cell alignment="center" valignment="top" usebox="none">
37116 \begin_layout Plain Layout
37126 <cell alignment="center" valignment="top" usebox="none">
37129 \begin_layout Plain Layout
37137 <cell alignment="center" valignment="top" usebox="none">
37140 \begin_layout Plain Layout
37150 <cell alignment="center" valignment="top" usebox="none">
37153 \begin_layout Plain Layout
37161 <cell alignment="center" valignment="top" usebox="none">
37164 \begin_layout Plain Layout
37172 <cell alignment="center" valignment="top" usebox="none">
37175 \begin_layout Plain Layout
37183 <cell alignment="center" valignment="top" usebox="none">
37186 \begin_layout Plain Layout
37194 <cell alignment="center" valignment="top" usebox="none">
37197 \begin_layout Plain Layout
37205 <cell alignment="center" valignment="top" usebox="none">
37208 \begin_layout Plain Layout
37218 <cell alignment="center" valignment="top" usebox="none">
37221 \begin_layout Plain Layout
37229 <cell alignment="center" valignment="top" usebox="none">
37232 \begin_layout Plain Layout
37242 <cell alignment="center" valignment="top" usebox="none">
37245 \begin_layout Plain Layout
37253 <cell alignment="center" valignment="top" usebox="none">
37256 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" usebox="none">
37269 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" usebox="none">
37280 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" usebox="none">
37293 \begin_layout Plain Layout
37301 <cell alignment="center" valignment="top" usebox="none">
37304 \begin_layout Plain Layout
37312 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37315 \begin_layout Plain Layout
37323 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37326 \begin_layout Plain Layout
37338 \begin_inset space \hfill{}
37342 \begin_inset Tabular
37343 <lyxtabular version="3" rows="12" columns="2">
37344 <features booktabs="true" tabularvalignment="middle">
37345 <column alignment="center" valignment="top" width="0pt">
37346 <column alignment="center" valignment="top" width="0pt">
37348 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37351 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" usebox="none">
37371 \begin_layout Plain Layout
37379 <cell alignment="center" valignment="top" usebox="none">
37382 \begin_layout Plain Layout
37394 <cell alignment="center" valignment="top" usebox="none">
37397 \begin_layout Plain Layout
37405 <cell alignment="center" valignment="top" usebox="none">
37408 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" usebox="none">
37421 \begin_layout Plain Layout
37429 <cell alignment="center" valignment="top" usebox="none">
37432 \begin_layout Plain Layout
37442 <cell alignment="center" valignment="top" usebox="none">
37445 \begin_layout Plain Layout
37453 <cell alignment="center" valignment="top" usebox="none">
37456 \begin_layout Plain Layout
37464 <cell alignment="center" valignment="top" usebox="none">
37467 \begin_layout Plain Layout
37475 <cell alignment="center" valignment="top" usebox="none">
37478 \begin_layout Plain Layout
37486 <cell alignment="center" valignment="top" usebox="none">
37489 \begin_layout Plain Layout
37497 <cell alignment="center" valignment="top" usebox="none">
37500 \begin_layout Plain Layout
37510 <cell alignment="center" valignment="top" usebox="none">
37513 \begin_layout Plain Layout
37521 <cell alignment="center" valignment="top" usebox="none">
37524 \begin_layout Plain Layout
37534 <cell alignment="center" valignment="top" usebox="none">
37537 \begin_layout Plain Layout
37545 <cell alignment="center" valignment="top" usebox="none">
37548 \begin_layout Plain Layout
37558 <cell alignment="center" valignment="top" usebox="none">
37561 \begin_layout Plain Layout
37569 <cell alignment="center" valignment="top" usebox="none">
37572 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" usebox="none">
37585 \begin_layout Plain Layout
37593 <cell alignment="center" valignment="top" usebox="none">
37596 \begin_layout Plain Layout
37606 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37609 \begin_layout Plain Layout
37617 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37620 \begin_layout Plain Layout
37634 \begin_inset space \hfill{}
37638 \begin_inset CommandInset href
37641 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37649 \begin_layout Standard
37650 \begin_inset Newpage newpage
37656 \begin_layout Bibliography
37657 \begin_inset CommandInset bibitem
37658 LatexCommand bibitem
37672 The \SpecialChar LaTeX
37676 Addison Wesley, 2004
37679 \begin_layout Bibliography
37680 \begin_inset CommandInset bibitem
37681 LatexCommand bibitem
37688 \begin_inset CommandInset href
37691 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37696 of \SpecialChar LaTeX
37700 \begin_layout Bibliography
37701 \begin_inset CommandInset bibitem
37702 LatexCommand bibitem
37709 \begin_inset CommandInset href
37712 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
37721 \begin_layout Plain Layout
37730 -\SpecialChar LaTeX
37734 \begin_layout Bibliography
37735 \begin_inset CommandInset bibitem
37736 LatexCommand bibitem
37743 \begin_inset CommandInset href
37746 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37751 of all symbols available with \SpecialChar LaTeX
37755 \begin_layout Bibliography
37756 \begin_inset CommandInset bibitem
37757 LatexCommand bibitem
37764 \begin_inset CommandInset href
37766 name "Documentation"
37767 target "https://www.ctan.org/tex-archive/macros/latex/contrib/cancel/cancel.pdf"
37772 of the \SpecialChar LaTeX
37778 \begin_inset Index idx
37781 \begin_layout Plain Layout
37790 \begin_layout Bibliography
37791 \begin_inset CommandInset bibitem
37792 LatexCommand bibitem
37799 \begin_inset CommandInset href
37801 name "Documentation"
37802 target "https://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/doc/manual.pdf"
37807 of the \SpecialChar LaTeX
37813 \begin_inset Index idx
37816 \begin_layout Plain Layout
37817 Packages ! hyperref
37825 \begin_layout Bibliography
37826 \begin_inset CommandInset bibitem
37827 LatexCommand bibitem
37834 \begin_inset CommandInset href
37836 name "Documentation"
37837 target "https://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37842 of the \SpecialChar LaTeX
37848 \begin_inset Index idx
37851 \begin_layout Plain Layout
37860 \begin_layout Bibliography
37861 \begin_inset CommandInset bibitem
37862 LatexCommand bibitem
37871 \begin_inset space ~
37878 \begin_inset space ~
37881 Auflage, Dudenverlag, 2000
37884 \begin_layout Bibliography
37885 \begin_inset CommandInset bibitem
37886 LatexCommand bibitem
37893 \begin_inset CommandInset href
37896 target "https://www.nist.gov/physical-measurement-laboratory/special-publication-811"
37901 for reviewing manuscripts
37904 \begin_layout Standard
37905 \begin_inset CommandInset index_print
37906 LatexCommand printindex