1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
95 % ------------------------------------
96 % used to check for needed LaTeX packages
99 % check for package undertilde
100 % used for the command \utilde
101 \newboolean{undertilde}
102 \IfFileExists{undertilde.sty}
103 {\usepackage{undertilde}
104 \setboolean{undertilde}{true}}
105 {\setboolean{undertilde}{false}}
107 % check for package eurosym
108 % used for the Euro symbol
110 \IfFileExists{eurosym.sty}
111 {\usepackage[gennarrow]{eurosym}
112 \setboolean{eurosym}{true}}
113 {\setboolean{eurosym}{false}}
115 % check for package braket
116 % used for physical vectors
118 \IfFileExists{braket.sty}
120 \setboolean{braket}{true}}
121 {\setboolean{braket}{false}}
123 % check for package cancel
125 \IfFileExists{cancel.sty}
127 \setboolean{cancel}{true}}
128 {\setboolean{cancel}{false}}
130 % check for package upgreek
132 \IfFileExists{upgreek.sty}
133 {\usepackage{upgreek}
134 \setboolean{upgreek}{true}}
135 {\setboolean{upgreek}{false}}
137 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
138 \use_default_options false
139 \maintain_unincluded_children false
141 \language_package default
146 \font_typewriter default
148 \font_default_family default
149 \use_non_tex_fonts false
155 \default_output_format default
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 1
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
206 \quotes_language english
209 \paperpagestyle plain
213 \tracking_changes false
214 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
494 \begin_inset Graphics
495 filename ../images/math-mode.png
501 \begin_inset Newline newline
504 To create a display style formula
505 \begin_inset Index idx
508 \begin_layout Plain Layout
509 Formula ! display style
514 which will appear bigger, has a different format, and will be in a separate
515 paragraph, use one of these shortcuts:
524 \begin_layout Standard
525 To change a display style formula to an inline formula, set the cursor into
526 the formula and use one of the shortcuts
534 Edit\SpecialChar \menuseparator
535 Math\SpecialChar \menuseparator
539 The same way is used to change an inline formula to a display style formula.
542 \begin_layout Standard
543 To display parts of an inline formula in the size of a display style formula,
551 \begin_inset Index idx
554 \begin_layout Plain Layout
563 Then a new blue box appears in which the desired formula part is inserted.
566 \begin_layout Standard
567 Only inline formulas are allowed inside tables.
570 \begin_layout Standard
575 can be turned on in the menu
577 View\SpecialChar \menuseparator
581 When you click there on
582 \begin_inset Quotes eld
586 \begin_inset Quotes erd
589 the toolbar will be shown permanently at the bottom; this state is visualized
594 menu with a checkmark.
595 When you click in this state again on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
611 is only shown when the cursor is within a formula; this state is visualized
612 by the renaming of the menu entry from
613 \begin_inset Quotes eld
617 \begin_inset Quotes erd
621 \begin_inset Quotes eld
629 \begin_inset Quotes erd
635 \begin_layout Standard
637 \begin_inset Index idx
640 \begin_layout Plain Layout
646 is invoked by pressing the toolbar button
647 \begin_inset Graphics
648 filename ../images/ert-insert.png
655 Insert\SpecialChar \menuseparator
660 \begin_layout Plain Layout
676 \begin_inset Note Note
679 \begin_layout Plain Layout
680 In LyX there are three
681 \begin_inset Quotes eld
685 \begin_inset Quotes erd
688 that appear in the output with sub- and superscript letters: TeX, LaTeX
692 \begin_layout Plain Layout
693 To avoid that these names are recognized as proper names, a TeX-brace pair
702 \begin_layout Standard
703 To change the LaTeX-preamble
704 \begin_inset Index idx
707 \begin_layout Plain Layout
715 Document\SpecialChar \menuseparator
716 Settings\SpecialChar \menuseparator
721 \begin_layout Plain Layout
737 \begin_layout Standard
738 To edit matrices, case differentiations and multiline formulas subsequently,
741 Edit\SpecialChar \menuseparator
746 Edit\SpecialChar \menuseparator
748 \begin_inset space \thinspace{}
752 \begin_inset space \thinspace{}
762 When lines and columns are swapped via the menu, the column or line where
763 the cursor is in is exchanged with the column to the right or the line
765 Is the cursor in the last column or row, the exchange is done with the
766 column to the left or the line above.
769 \begin_layout Standard
770 To write text in formulas
774 \begin_layout Plain Layout
775 For multiline formulas the command
782 \begin_inset CommandInset ref
784 reference "sub:Text-in-multiline"
798 \begin_inset Index idx
801 \begin_layout Plain Layout
808 \begin_inset Index idx
811 \begin_layout Plain Layout
818 This mode is invoked with the shortcut
824 or by the insertion of the command
831 \begin_inset Index idx
834 \begin_layout Plain Layout
843 The text appears black in LyX and can therefore be distinguished from the
844 other formula parts which appear blue.
845 In the output mathematical text is set upright, in contrary to other formula
849 \begin_layout Subsection*
853 \begin_layout Standard
854 Most of the LaTeX-commands for math constructs have the following scheme:
857 \begin_layout Standard
873 \begin_layout Standard
874 A command always starts with a backslash
875 \begin_inset Quotes gld
885 \begin_inset Quotes grd
889 To omit optional arguments, also omit the associated brackets.
890 The braces around the required arguments are named in this document as
892 \begin_inset Index idx
895 \begin_layout Plain Layout
902 If you add in a formula a left brace to a command name, LyX automatically
904 In all other cases TeX-braces are created in formulas with the command
912 TeX-braces appear red in LyX, in contrary to normal braces which appear
914 In TeX-mode no command is needed to get TeX-braces.
915 TeX-braces don't appear in the output.
918 \begin_layout Standard
919 When commands without arguments, like commands for symbols are entered in
920 TeX-mode, a space character must
924 be behind the command to end it.
925 This space doesn't appear in the output.
926 When the space should appear in the output, the space must be followed
927 by a protected space in normal text.
930 \begin_layout Standard
931 A protected space is inserted with
934 arg "command-alternatives space-insert protected ; math-space"
940 \begin_layout Subsection*
941 \begin_inset Newpage newpage
947 \begin_layout Itemize
949 \begin_inset space \textvisiblespace{}
952 denotes a space character to be input.
955 \begin_layout Itemize
957 \begin_inset Formula $\to$
960 denotes the usage of the corresponding arrow key on the keyboard.
965 key can often be used instead of
966 \begin_inset Formula $\to$
970 \begin_inset Formula $\downarrow$
978 \begin_inset Formula $\leftarrow$
982 \begin_inset Formula $\uparrow$
988 \begin_layout Subsection*
992 \begin_layout Standard
994 \begin_inset Float table
1000 \begin_layout Plain Layout
1002 \begin_inset Caption Standard
1004 \begin_layout Plain Layout
1005 \begin_inset CommandInset label
1007 name "tab:Available-units"
1019 \begin_layout Plain Layout
1021 \begin_inset Tabular
1022 <lyxtabular version="3" rows="13" columns="2">
1023 <features rotate="0" tabularvalignment="middle">
1024 <column alignment="center" valignment="top">
1025 <column alignment="center" valignment="top">
1027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1030 \begin_layout Plain Layout
1036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1039 \begin_layout Plain Layout
1047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1050 \begin_layout Plain Layout
1056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1059 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset space \thinspace{}
1227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1230 \begin_layout Plain Layout
1236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1239 \begin_layout Plain Layout
1241 \begin_inset space \thinspace{}
1245 \begin_inset Formula $\approx$
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1273 \begin_inset space \thinspace{}
1277 \begin_inset space \thinspace{}
1287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1290 \begin_layout Plain Layout
1296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1299 \begin_layout Plain Layout
1303 \begin_inset Quotes eld
1309 \begin_inset Quotes erd
1319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1322 \begin_layout Plain Layout
1328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1331 \begin_layout Plain Layout
1333 \begin_inset Quotes eld
1341 \begin_inset Quotes erd
1351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1354 \begin_layout Plain Layout
1360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1363 \begin_layout Plain Layout
1365 \begin_inset space \thinspace{}
1369 \begin_inset Formula $\nicefrac{1}{18}$
1373 \begin_inset space \thinspace{}
1394 \begin_layout Standard
1395 \begin_inset Newpage newpage
1401 \begin_layout Section
1405 \begin_layout Subsection
1407 \begin_inset Index idx
1410 \begin_layout Plain Layout
1417 \begin_inset Index idx
1420 \begin_layout Plain Layout
1427 \begin_inset Index idx
1430 \begin_layout Plain Layout
1435 \begin_layout Plain Layout
1446 \begin_layout Plain Layout
1459 \begin_inset Index idx
1462 \begin_layout Plain Layout
1467 \begin_layout Plain Layout
1478 \begin_layout Plain Layout
1493 \begin_layout Standard
1494 Indices are created with an underscore
1495 \begin_inset Quotes eld
1499 \begin_inset Quotes erd
1502 or via the math toolbar button
1503 \begin_inset Graphics
1504 filename ../images/math-subscript.png
1509 , exponents with a caret
1510 \begin_inset Quotes eld
1514 \begin_inset Quotes erd
1517 or via the math toolbar button
1518 \begin_inset Graphics
1519 filename ../images/math-superscript.png
1527 \begin_layout Standard
1529 \begin_inset Tabular
1530 <lyxtabular version="3" rows="4" columns="2">
1531 <features rotate="0" tabularvalignment="middle">
1532 <column alignment="center" valignment="top" width="0pt">
1533 <column alignment="center" valignment="top" width="0pt">
1535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1538 \begin_layout Plain Layout
1544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1547 \begin_layout Plain Layout
1549 \begin_inset Note Note
1552 \begin_layout Plain Layout
1559 is only used as spacer.
1571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1574 \begin_layout Plain Layout
1580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1583 \begin_layout Plain Layout
1584 \begin_inset Formula $B_{V}$
1594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1597 \begin_layout Plain Layout
1603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1620 \begin_layout Plain Layout
1622 \begin_inset space \textvisiblespace{}
1630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1633 \begin_layout Plain Layout
1634 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1650 \begin_layout Standard
1651 As the caret is in some languages an accent, vowels will be accentuated
1652 in this case and not set as exponents
1656 \begin_layout Plain Layout
1657 Depending on the used keyboard settings this can also happen for characters
1664 To get exponents in this case, press
1668 after the caret as in the last example.
1671 \begin_layout Subsection
1673 \begin_inset CommandInset label
1675 name "sub:Fractions"
1680 \begin_inset Index idx
1683 \begin_layout Plain Layout
1692 \begin_layout Standard
1693 Fractions are generated with the command
1700 \begin_inset Index idx
1703 \begin_layout Plain Layout
1711 or via the math toolbar button
1712 \begin_inset Graphics
1713 filename ../images/math/frac.png
1719 The font size is adjusted automatically, depending on whether the fraction
1720 is in an inline or display style formula.
1721 With the math toolbar button
1722 \begin_inset Graphics
1723 filename ../images/math/frac-square.png
1728 you can select different fraction types.
1731 \begin_layout Standard
1739 \begin_inset Index idx
1742 \begin_layout Plain Layout
1750 a fraction can be created that always has the size of a display style formula.
1758 \begin_inset Index idx
1761 \begin_layout Plain Layout
1769 the fraction appears always with the size of an inline formula.
1773 \begin_layout Standard
1774 A line with the fraction
1775 \begin_inset Formula $\frac{1}{2}$
1778 that was created with the command
1787 \begin_layout Standard
1788 A line with the fraction
1789 \begin_inset Formula $\dfrac{1}{2}$
1792 that was created with the command
1801 \begin_layout Standard
1803 \begin_inset Tabular
1804 <lyxtabular version="3" rows="4" columns="2">
1805 <features rotate="0" tabularvalignment="middle">
1806 <column alignment="center" valignment="top" width="0pt">
1807 <column alignment="center" valignment="top" width="0pt">
1809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1812 \begin_layout Plain Layout
1818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1821 \begin_layout Plain Layout
1823 \begin_inset Note Note
1826 \begin_layout Plain Layout
1833 is only used as spacer.
1845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1848 \begin_layout Plain Layout
1852 \begin_inset space \textvisiblespace{}
1856 \begin_inset Formula $\downarrow$
1864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1867 \begin_layout Plain Layout
1868 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1881 \begin_layout Plain Layout
1885 \begin_inset space \textvisiblespace{}
1889 \begin_inset Formula $\downarrow$
1897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1900 \begin_layout Plain Layout
1901 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1914 \begin_layout Plain Layout
1918 \begin_inset space \textvisiblespace{}
1924 \begin_inset space \textvisiblespace{}
1928 \begin_inset Formula $\downarrow$
1932 \begin_inset Formula $\downarrow\downarrow$
1940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1943 \begin_layout Plain Layout
1944 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1960 \begin_layout Standard
1961 \begin_inset VSpace bigskip
1965 \begin_inset Newpage newpage
1968 For nested fractions the command
1975 \begin_inset Index idx
1978 \begin_layout Plain Layout
1988 \begin_inset VSpace -3mm
1994 \begin_layout Standard
1995 \begin_inset Formula
1997 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1998 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2006 \begin_layout Standard
2007 The command for the example above is:
2010 \begin_layout Standard
2016 \begin_inset space \textvisiblespace{}
2020 \begin_inset Formula $\downarrow$
2026 \begin_inset space \textvisiblespace{}
2032 \begin_inset space \textvisiblespace{}
2036 \begin_inset Formula $\downarrow$
2040 \begin_inset Formula $\downarrow$
2046 \begin_layout Standard
2047 \begin_inset VSpace medskip
2053 \begin_layout Standard
2060 sets the fraction always in the size of a displayed formula, also when
2061 it is part of another fraction.
2064 \begin_layout Standard
2065 It is possible to specify the alignment of the numerator.
2072 is used to left align it, the command
2085 centers the numerator.
2086 These fractions demonstrate the different alignments:
2089 \begin_layout Standard
2092 \begin_inset Formula
2094 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2102 \begin_layout Standard
2103 \begin_inset Note Greyedout
2106 \begin_layout Plain Layout
2123 are no real LaTeX commands but represent the command
2127 cfrac[alignment]{numerator}{denominator}
2130 Therefore you cannot use them in TeX code.
2138 \begin_layout Standard
2139 \begin_inset VSpace medskip
2142 It is often advantageous to combine
2155 \begin_inset Formula
2157 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2165 \begin_layout Standard
2166 For inline fractions with a sloped fraction stroke you can use the command
2174 \begin_inset Index idx
2177 \begin_layout Plain Layout
2186 \begin_inset Formula $\nicefrac{5}{31}$
2196 \begin_inset Index idx
2199 \begin_layout Plain Layout
2208 \begin_inset Formula $\unitfrac{5}{31}$
2211 There is furthermore the command
2217 that offers to write a fraction in combination with a number:
2218 \begin_inset Formula $\unitfrac[2]{1}{3}$
2224 \begin_layout Standard
2225 \begin_inset Note Greyedout
2228 \begin_layout Plain Layout
2239 is not a real LaTeX command but the command
2240 \begin_inset Newline newline
2247 unitfrac[number]{numerator}{denominator}
2250 Therefore you cannot use it in TeX code.
2258 \begin_layout Standard
2259 How to define own fractions where the fraction stroke can be changed, is
2261 \begin_inset CommandInset ref
2263 reference "sub:Self-defined-Fractions"
2270 \begin_layout Standard
2271 \begin_inset Newpage newpage
2277 \begin_layout Subsection
2279 \begin_inset Index idx
2282 \begin_layout Plain Layout
2291 \begin_layout Standard
2292 Square roots are created with
2299 \begin_inset Index idx
2302 \begin_layout Plain Layout
2310 or the math toolbar button
2311 \begin_inset Graphics
2312 filename ../images/math/sqrt.png
2317 , all other roots with the command
2324 \begin_inset Index idx
2327 \begin_layout Plain Layout
2335 or with the math toolbar button
2336 \begin_inset Graphics
2337 filename ../images/math/root.png
2345 \begin_layout Standard
2347 \begin_inset Tabular
2348 <lyxtabular version="3" rows="3" columns="2">
2349 <features rotate="0" tabularvalignment="middle">
2350 <column alignment="center" valignment="top" width="0pt">
2351 <column alignment="center" valignment="top" width="0pt">
2353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2356 \begin_layout Plain Layout
2362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2365 \begin_layout Plain Layout
2367 \begin_inset Note Note
2370 \begin_layout Plain Layout
2377 is only used as spacer.
2389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2392 \begin_layout Plain Layout
2396 \begin_inset space \textvisiblespace{}
2404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2407 \begin_layout Plain Layout
2408 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2418 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2421 \begin_layout Plain Layout
2425 \begin_inset space \textvisiblespace{}
2429 \begin_inset Formula $\downarrow$
2437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2440 \begin_layout Plain Layout
2441 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2457 \begin_layout Standard
2458 A square root can also be created with
2464 when the root index field is left empty.
2467 \begin_layout Standard
2468 With certain indices the distance to the root is too small, like in this
2470 \begin_inset Formula $\sqrt[\beta]{B}$
2474 \begin_inset Newline newline
2478 \begin_inset Formula $\beta$
2482 To avoid this, the commands
2489 \begin_inset Index idx
2492 \begin_layout Plain Layout
2507 \begin_inset Index idx
2510 \begin_layout Plain Layout
2518 are used with the following scheme:
2521 \begin_layout Standard
2535 \begin_layout Standard
2536 Distance is the number of Big Points (unit bp;
2537 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2540 ), that the index should be moved to the left or top, resp..
2541 The commands are written to the index.
2542 This way the command
2543 \begin_inset Newline newline
2553 \begin_inset Formula $\to$
2559 \begin_inset Formula $\to$
2565 \begin_inset space \textvisiblespace{}
2569 \begin_inset Formula $\to$
2573 \begin_inset Newline newline
2578 produces a correct typeset formula:
2579 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2585 \begin_layout Subsection
2586 Binomial Coefficients
2587 \begin_inset Index idx
2590 \begin_layout Plain Layout
2591 Binomial coefficients
2599 \begin_layout Standard
2600 Binomial coefficients are inserted with the command
2607 \begin_inset Index idx
2610 \begin_layout Plain Layout
2618 or with the submenu of the math toolbar button
2619 \begin_inset Graphics
2620 filename ../images/math/frac-square.png
2638 there are the commands
2645 \begin_inset Index idx
2648 \begin_layout Plain Layout
2663 \begin_inset Index idx
2666 \begin_layout Plain Layout
2675 For other brackets around binomial coeficients there are the commands
2682 \begin_inset Index idx
2685 \begin_layout Plain Layout
2700 \begin_inset Index idx
2703 \begin_layout Plain Layout
2714 \begin_layout Standard
2716 \begin_inset Tabular
2717 <lyxtabular version="3" rows="6" columns="2">
2718 <features rotate="0" tabularvalignment="middle">
2719 <column alignment="center" valignment="top" width="0pt">
2720 <column alignment="center" valignment="top" width="0pt">
2722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2725 \begin_layout Plain Layout
2731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2734 \begin_layout Plain Layout
2736 \begin_inset Note Note
2739 \begin_layout Plain Layout
2746 is only used as spacer.
2758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2761 \begin_layout Plain Layout
2765 \begin_inset space \textvisiblespace{}
2769 \begin_inset Formula $\downarrow$
2777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2780 \begin_layout Plain Layout
2781 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2794 \begin_layout Plain Layout
2798 \begin_inset space \textvisiblespace{}
2802 \begin_inset Formula $\downarrow$
2810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2813 \begin_layout Plain Layout
2814 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2827 \begin_layout Plain Layout
2831 \begin_inset space \textvisiblespace{}
2835 \begin_inset Formula $\downarrow$
2843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2846 \begin_layout Plain Layout
2847 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2860 \begin_layout Plain Layout
2864 \begin_inset space \textvisiblespace{}
2868 \begin_inset Formula $\downarrow$
2876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2879 \begin_layout Plain Layout
2880 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2893 \begin_layout Plain Layout
2897 \begin_inset space \textvisiblespace{}
2901 \begin_inset Formula $\downarrow$
2909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2912 \begin_layout Plain Layout
2913 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2929 \begin_layout Subsection
2930 Case Differentiations
2931 \begin_inset Index idx
2934 \begin_layout Plain Layout
2935 Case differentiations
2943 \begin_layout Standard
2945 \begin_inset Tabular
2946 <lyxtabular version="3" rows="3" columns="2">
2947 <features rotate="0" tabularvalignment="middle">
2948 <column alignment="center" valignment="top" width="0pt">
2949 <column alignment="center" valignment="top" width="0pt">
2951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2954 \begin_layout Plain Layout
2960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2963 \begin_layout Plain Layout
2971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2974 \begin_layout Plain Layout
2978 \begin_inset space \textvisiblespace{}
2982 \begin_inset Formula $\to$
2986 \begin_inset Index idx
2989 \begin_layout Plain Layout
3002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3005 \begin_layout Plain Layout
3006 \begin_inset Formula $\begin{cases}
3017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3020 \begin_layout Plain Layout
3024 \begin_inset space \textvisiblespace{}
3030 arg "newline-insert newline"
3038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\begin{cases}
3043 A & \textrm{for }x>0\\
3044 B & \textrm{for }x=0
3061 \begin_layout Standard
3068 or pressing the math toolbar button
3069 \begin_inset Graphics
3070 filename ../images/math/cases.png
3075 you can create new lines with the shortcut
3078 arg "newline-insert newline"
3081 or the table toolbar button
3082 \begin_inset Graphics
3083 filename ../images/tabular-feature_append-row.png
3091 \begin_layout Standard
3098 is also available via the menu
3100 Insert\SpecialChar \menuseparator
3101 Math\SpecialChar \menuseparator
3107 \begin_layout Subsection
3109 \begin_inset Index idx
3112 \begin_layout Plain Layout
3121 \begin_layout Standard
3129 \begin_inset Index idx
3132 \begin_layout Plain Layout
3140 every character can be displayed canceled.
3141 The characters are quasi accentuated by a slash.
3144 \begin_layout Standard
3146 \begin_inset Tabular
3147 <lyxtabular version="3" rows="4" columns="2">
3148 <features rotate="0" tabularvalignment="middle">
3149 <column alignment="center" valignment="top" width="0pt">
3150 <column alignment="center" valignment="top" width="0pt">
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3155 \begin_layout Plain Layout
3161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3164 \begin_layout Plain Layout
3172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3175 \begin_layout Plain Layout
3183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3186 \begin_layout Plain Layout
3187 \begin_inset Formula $\not=$
3197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3200 \begin_layout Plain Layout
3210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3213 \begin_layout Plain Layout
3214 \begin_inset Formula $\not\le$
3224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3227 \begin_layout Plain Layout
3237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3240 \begin_layout Plain Layout
3241 \begin_inset Formula $\not\parallel$
3257 \begin_layout Standard
3258 The last example shows that not all negations look good.
3259 Therefore there are special commands for some negations (see
3260 \begin_inset CommandInset ref
3262 reference "sub:Mathematical-Symbols"
3267 \begin_inset CommandInset ref
3269 reference "sec:Relations"
3276 \begin_layout Subsection
3278 \begin_inset CommandInset label
3280 name "sub:Placeholders"
3285 \begin_inset Index idx
3288 \begin_layout Plain Layout
3295 \begin_inset Index idx
3298 \begin_layout Plain Layout
3299 Chemical characters ! Isotopes
3305 \begin_inset Index idx
3308 \begin_layout Plain Layout
3313 \begin_layout Plain Layout
3324 \begin_layout Plain Layout
3339 \begin_layout Standard
3341 \begin_inset space \thinspace{}
3345 \begin_inset space \space{}
3352 \begin_layout Plain Layout
3353 Typesetting isotopes and chemical symbols is described in
3354 \begin_inset CommandInset ref
3356 reference "sub:Chemical-Symbols-and"
3365 the following problem occurs:
3368 \begin_layout Standard
3370 \begin_inset Tabular
3371 <lyxtabular version="3" rows="2" columns="2">
3372 <features rotate="0" tabularvalignment="middle">
3373 <column alignment="center" valignment="top" width="0pt">
3374 <column alignment="center" valignment="top" width="0pt">
3376 <cell alignment="center" valignment="top" usebox="none">
3379 \begin_layout Plain Layout
3380 Indices created with sub- and superscripts:
3385 <cell alignment="center" valignment="top" usebox="none">
3388 \begin_layout Plain Layout
3389 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3399 <cell alignment="center" valignment="top" usebox="none">
3402 \begin_layout Plain Layout
3408 <cell alignment="center" valignment="top" usebox="none">
3411 \begin_layout Plain Layout
3412 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3426 \begin_inset Note Note
3429 \begin_layout Plain Layout
3436 is only used as spacer.
3444 \begin_layout Standard
3445 The shorter index is by default placed below or above the first character
3446 of the longer index.
3447 To avoid this there is the command
3454 \begin_inset Index idx
3457 \begin_layout Plain Layout
3465 or the math toolbar button
3466 \begin_inset space \thinspace{}
3473 \begin_layout Plain Layout
3474 can be found in the submenu of the toolbar button
3475 \begin_inset Graphics
3476 filename ../images/math/space.png
3487 \begin_inset Graphics
3488 filename ../images/math/phantom.png
3493 that creates one or more phantom characters.
3500 a small blue box appears that is superposed with two red arrows.
3501 The arrows indicate that the complete width and height of the box content
3502 will be created as placeholder.
3503 Phantom characters are accordingly placeholders with the size of the characters.
3506 \begin_layout Standard
3508 \begin_inset Tabular
3509 <lyxtabular version="3" rows="4" columns="2">
3510 <features rotate="0" tabularvalignment="middle">
3511 <column alignment="center" valignment="top">
3512 <column alignment="center" valignment="top">
3514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3517 \begin_layout Plain Layout
3523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3526 \begin_layout Plain Layout
3528 \begin_inset Note Note
3531 \begin_layout Plain Layout
3538 is only used as spacer.
3550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3553 \begin_layout Plain Layout
3555 \begin_inset space \textvisiblespace{}
3561 \begin_inset space \textvisiblespace{}
3565 \begin_inset Formula $\to$
3569 \begin_inset space \textvisiblespace{}
3577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3580 \begin_layout Plain Layout
3581 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3594 \begin_layout Plain Layout
3596 \begin_inset space \textvisiblespace{}
3602 \begin_inset space \textvisiblespace{}
3606 \begin_inset Formula $\to$
3610 \begin_inset space \textvisiblespace{}
3618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3621 \begin_layout Plain Layout
3622 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3635 \begin_layout Plain Layout
3639 \begin_inset space \textvisiblespace{}
3645 \begin_inset space \textvisiblespace{}
3649 \begin_inset Formula $\to$
3653 \begin_inset space \textvisiblespace{}
3661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3664 \begin_layout Plain Layout
3665 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3681 \begin_layout Standard
3682 Furthermore there are the commands
3689 \begin_inset Index idx
3692 \begin_layout Plain Layout
3701 \begin_inset space ~
3705 \begin_inset Graphics
3706 filename ../images/math/vphantom.png
3718 \begin_inset Index idx
3721 \begin_layout Plain Layout
3730 \begin_inset space ~
3734 \begin_inset Graphics
3735 filename ../images/math/hphantom.png
3747 creates only space for the maximal height of the characters in the box
3748 but not for its width.
3755 creates only space for the width of the box content.
3756 Therefore the boxes of both commands have only one red arrow.
3759 \begin_layout Standard
3760 For example the command
3765 \begin_inset space \textvisiblespace{}
3772 creates space for the height of the integral sign,
3776 \begin_layout Plain Layout
3783 creates an integral sign, see
3784 \begin_inset CommandInset ref
3786 reference "sub:Big-Operators"
3795 because this is the larger character.
3796 An example application is in
3797 \begin_inset CommandInset ref
3799 reference "sub:Multiline-Brackets"
3806 \begin_layout Standard
3807 Placeholders can also be used for text when they are inserted via the menu
3810 Insert\SpecialChar \menuseparator
3811 Formatting\SpecialChar \menuseparator
3817 \begin_layout Standard
3819 \begin_inset Newline newline
3823 \begin_inset Phantom Phantom
3826 \begin_layout Plain Layout
3835 \begin_layout Subsection
3837 \begin_inset Index idx
3840 \begin_layout Plain Layout
3847 \begin_inset Index idx
3850 \begin_layout Plain Layout
3851 Formula ! underlined
3859 \begin_layout Standard
3861 \begin_inset Tabular
3862 <lyxtabular version="3" rows="4" columns="2">
3863 <features rotate="0" tabularvalignment="middle">
3864 <column alignment="center" valignment="top" width="0pt">
3865 <column alignment="center" valignment="top" width="0pt">
3867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3870 \begin_layout Plain Layout
3876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3879 \begin_layout Plain Layout
3881 \begin_inset Note Note
3884 \begin_layout Plain Layout
3891 is only used as spacer.
3903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3906 \begin_layout Plain Layout
3910 \begin_inset space \textvisiblespace{}
3914 \begin_inset Index idx
3917 \begin_layout Plain Layout
3930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3933 \begin_layout Plain Layout
3934 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3947 \begin_layout Plain Layout
3951 \begin_inset space \textvisiblespace{}
3955 \begin_inset Index idx
3958 \begin_layout Plain Layout
3971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3974 \begin_layout Plain Layout
3975 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3988 \begin_layout Plain Layout
3992 \begin_inset space \textvisiblespace{}
3998 \begin_inset space \textvisiblespace{}
4006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4009 \begin_layout Plain Layout
4010 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4026 \begin_layout Standard
4027 In the last example it doesn't matter if first
4042 \begin_layout Standard
4043 To double underline use
4052 \begin_layout Standard
4053 It is possible to place up to 6 lines above or below characters.
4056 \begin_layout Standard
4057 \begin_inset VSpace bigskip
4060 Custom lines can be created using the command
4067 \begin_inset Index idx
4070 \begin_layout Plain Layout
4078 which has the following scheme:
4081 \begin_layout Standard
4086 rule[vertical offset]{length}{thickness}
4089 \begin_layout Standard
4090 The optional vertical offset shifts the line upwards (or downwards, when
4091 the value is negative).
4093 \begin_inset CommandInset ref
4095 reference "tab:Available-units"
4099 can be used for the values.
4100 Here are two example lines created with the commands
4101 \begin_inset Newline newline
4108 rule[-2ex]{3cm}{2pt}
4119 \begin_layout Standard
4121 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4127 \begin_layout Standard
4134 can also be used for text when a line is inserted via the menu
4136 Insert\SpecialChar \menuseparator
4137 Formatting\SpecialChar \menuseparator
4139 \begin_inset space ~
4147 \begin_layout Standard
4149 \begin_inset CommandInset line
4160 \begin_layout Subsection
4162 \begin_inset CommandInset label
4169 \begin_inset Index idx
4172 \begin_layout Plain Layout
4181 \begin_layout Standard
4182 There are different types of ellipses available.
4186 \begin_layout Plain Layout
4187 In the math toolbar in the submenu of the button
4188 \begin_inset Graphics
4189 filename ../images/math/ldots.png
4199 For listings dots at the baseline are used (
4206 \begin_inset Index idx
4209 \begin_layout Plain Layout
4217 ), while for operations dots are needed that are on the same height as the
4225 \begin_inset Index idx
4228 \begin_layout Plain Layout
4237 When using the command
4244 \begin_inset Index idx
4247 \begin_layout Plain Layout
4255 , LaTeX decides on the basis of the next character what type is used.
4258 \begin_layout Standard
4260 \begin_inset Tabular
4261 <lyxtabular version="3" rows="9" columns="2">
4262 <features rotate="0" tabularvalignment="middle">
4263 <column alignment="center" valignment="top" width="0pt">
4264 <column alignment="center" valignment="top" width="0pt">
4266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4269 \begin_layout Plain Layout
4275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4278 \begin_layout Plain Layout
4286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4289 \begin_layout Plain Layout
4291 \begin_inset space \textvisiblespace{}
4297 \begin_inset space \textvisiblespace{}
4305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4308 \begin_layout Plain Layout
4309 \begin_inset Formula $A_{1},\dots,A_{n}$
4319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4322 \begin_layout Plain Layout
4324 \begin_inset space \textvisiblespace{}
4330 \begin_inset space \textvisiblespace{}
4338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4341 \begin_layout Plain Layout
4342 \begin_inset Formula $A_{1}+\dots+A_{n}$
4352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4355 \begin_layout Plain Layout
4357 \begin_inset space \textvisiblespace{}
4363 \begin_inset space \textvisiblespace{}
4371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4374 \begin_layout Plain Layout
4375 \begin_inset Formula $A_{1},\ldots,A_{n}$
4385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4388 \begin_layout Plain Layout
4390 \begin_inset space \textvisiblespace{}
4396 \begin_inset space \textvisiblespace{}
4404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4407 \begin_layout Plain Layout
4408 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4421 \begin_layout Plain Layout
4429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4432 \begin_layout Plain Layout
4433 \begin_inset Formula $\vdots$
4443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4446 \begin_layout Plain Layout
4454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4457 \begin_layout Plain Layout
4458 \begin_inset Formula $\ddots$
4468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4471 \begin_layout Plain Layout
4479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4482 \begin_layout Plain Layout
4483 \begin_inset Formula $\iddots$
4493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4496 \begin_layout Plain Layout
4498 \begin_inset space \thinspace{}
4501 matrix with the different dots
4506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4509 \begin_layout Plain Layout
4510 \begin_inset Formula $\begin{array}{ccc}
4511 A_{11} & \cdots & A_{1m}\\
4512 \vdots & \ddots & \vdots\\
4513 A_{n1} & \cdots & A_{nm}
4530 \begin_layout Standard
4531 The ellipses available in menu
4533 Insert\SpecialChar \menuseparator
4535 \begin_inset space ~
4549 \begin_layout Standard
4550 \begin_inset VSpace medskip
4559 , one of the options
4561 Use mathdots package (automatically)
4563 must be set in the document settings under
4566 \begin_inset space ~
4572 \begin_inset Newline newline
4577 Use mathdots package
4579 will improve the appearance of all dots in the documents if their font
4580 style or size is not the default.
4583 \begin_layout Standard
4584 \begin_inset VSpace medskip
4587 Specially for matrices there are ellipses that span over several columns.
4588 They are created with the command
4595 \begin_inset Index idx
4598 \begin_layout Plain Layout
4606 , that has the following scheme:
4609 \begin_layout Standard
4614 hdotsfor[distance]{number of columns}
4617 \begin_layout Standard
4618 The number of columns specifies how many columns should be spanned.
4619 Distance is a factor for the distance between the dots.
4622 \begin_layout Standard
4623 In the following matrix the command
4629 was inserted in the first box of the second line, to get an ellipsis with
4630 a dot distance twice as long as with the command
4637 \begin_inset Formula
4639 \left(\begin{array}{cccc}
4648 Note that the matrix fields that should be spanned must be empty, otherwise
4649 you get LaTeX-errors.
4652 \begin_layout Standard
4653 \begin_inset VSpace bigskip
4656 Furthermore you can fill with the command
4663 \begin_inset Index idx
4666 \begin_layout Plain Layout
4674 the rest of a line with dots.
4675 The effect of these commands is the same as with
4682 \begin_inset CommandInset ref
4684 reference "sub:Variable-Space"
4691 \begin_layout Standard
4692 For example the command
4697 \begin_inset space \textvisiblespace{}
4705 \begin_layout Standard
4706 \begin_inset Formula $A\dotfill B$
4712 \begin_layout Standard
4719 there is for a line the command
4726 \begin_inset Index idx
4729 \begin_layout Plain Layout
4740 \begin_layout Standard
4741 \begin_inset Formula $A\hrulefill B$
4747 \begin_layout Standard
4748 To use the commands for text, they have to be inserted in TeX-mode.
4751 \begin_layout Section
4753 \begin_inset CommandInset label
4760 \begin_inset Index idx
4763 \begin_layout Plain Layout
4772 \begin_layout Standard
4773 Matrices can be inserted via the math toolbar button
4774 \begin_inset Graphics
4775 filename ../images/dialog-show_mathmatrix.png
4782 Insert\SpecialChar \menuseparator
4783 Math\SpecialChar \menuseparator
4787 In the matrix dialog you can specify the number of columns and rows, the
4788 alignment and the decoration.
4789 The vertical alignment is only of importance for matrices in inline formulas:
4792 \begin_layout Standard
4793 The first matrix is top
4794 \begin_inset Formula $\begin{array}[t]{cccc}
4802 \begin_inset Formula $\begin{array}{cccc}
4809 and the third bottom
4810 \begin_inset Formula $\begin{array}[b]{cccc}
4820 \begin_layout Standard
4821 The horizontal alignment specifies how the column entries should be aligned.
4822 It is set by entering a letter for every column.
4827 denotes left aligned,
4836 To create for example a 4
4841 \begin_inset space ~
4844 matrix where the first column is left aligned, the second and third are
4845 centered and the last one is right aligned, one enters for the horizontal
4851 Normally in a matrix all columns are centered, therefore the default for
4859 \begin_layout Standard
4860 Horizontal alignment:
4863 \begin_layout Standard
4869 \begin_inset Formula $\begin{array}{lll}
4881 \begin_inset Formula $\begin{array}{ccc}
4893 \begin_inset Formula $\begin{array}{rrr}
4903 \begin_layout Standard
4904 To add or delete rows and columns subsequently, the math toolbar buttons
4906 \begin_inset Graphics
4907 filename ../images/tabular-feature_append-row.png
4913 \begin_inset Graphics
4914 filename ../images/tabular-feature_delete-row.png
4920 \begin_inset space \thinspace{}
4925 Edit\SpecialChar \menuseparator
4929 New rows can also be created with
4932 arg "newline-insert newline"
4938 \begin_layout Standard
4939 \begin_inset VSpace bigskip
4946 adds parentheses in the selected style around the matrix.
4947 Alternatively, parentheses can can either be created with the commands
4955 \begin_inset Index idx
4958 \begin_layout Plain Layout
4973 \begin_inset Index idx
4976 \begin_layout Plain Layout
4987 \begin_inset space ~
4993 \begin_inset CommandInset ref
4995 reference "sub:Automatic-Bracket-Size"
4999 , or by using the following commands:
5000 \begin_inset VSpace medskip
5006 \begin_layout Standard
5007 \begin_inset space \hfill{}
5011 \begin_inset Tabular
5012 <lyxtabular version="3" rows="4" columns="2">
5013 <features rotate="0" tabularvalignment="middle">
5014 <column alignment="center" valignment="top">
5015 <column alignment="center" valignment="top">
5017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5020 \begin_layout Plain Layout
5026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5029 \begin_layout Plain Layout
5031 \begin_inset Note Note
5034 \begin_layout Plain Layout
5041 is only used as spacer.
5053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5056 \begin_layout Plain Layout
5060 \begin_inset space \textvisiblespace{}
5068 \begin_inset space \thinspace{}
5076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5079 \begin_layout Plain Layout
5080 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5081 0 & \textrm{-}\mathrm{i}\\
5083 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5096 \begin_layout Plain Layout
5100 \begin_inset space \textvisiblespace{}
5108 \begin_inset space \thinspace{}
5116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5119 \begin_layout Plain Layout
5120 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5121 0 & \textrm{-}\mathrm{i}\\
5123 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5136 \begin_layout Plain Layout
5140 \begin_inset space \textvisiblespace{}
5148 \begin_inset space \thinspace{}
5156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5159 \begin_layout Plain Layout
5160 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5161 0 & \textrm{-}\mathrm{i}\\
5163 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5177 \begin_inset space \hfill{}
5181 \begin_inset Tabular
5182 <lyxtabular version="3" rows="4" columns="2">
5183 <features rotate="0" tabularvalignment="middle">
5184 <column alignment="center" valignment="top">
5185 <column alignment="center" valignment="top">
5187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5190 \begin_layout Plain Layout
5196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5199 \begin_layout Plain Layout
5207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5210 \begin_layout Plain Layout
5214 \begin_inset space \textvisiblespace{}
5222 \begin_inset space \thinspace{}
5230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5233 \begin_layout Plain Layout
5234 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5235 0 & \textrm{-}\mathrm{i}\\
5237 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5250 \begin_layout Plain Layout
5254 \begin_inset space \textvisiblespace{}
5262 \begin_inset space \thinspace{}
5270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5273 \begin_layout Plain Layout
5274 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5275 0 & \textrm{-}\mathrm{i}\\
5277 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5290 \begin_layout Plain Layout
5294 \begin_inset space \textvisiblespace{}
5302 \begin_inset space \thinspace{}
5310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5313 \begin_layout Plain Layout
5314 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5315 0 & \textrm{-}\mathrm{i}\\
5317 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5331 \begin_inset space \hfill{}
5337 \begin_layout Standard
5338 \begin_inset VSpace medskip
5342 \begin_inset space \thinspace{}
5346 \begin_inset space \space{}
5355 is inserted, a blue box appears between two vertical lines where the matrix
5357 \begin_inset Newline newline
5360 Note that decorated matrices ignore the vertical alignment.
5363 \begin_layout Standard
5364 \begin_inset VSpace bigskip
5367 As all multiline formulas are matrices, the length
5374 \begin_inset Index idx
5377 \begin_layout Plain Layout
5385 that is described in
5386 \begin_inset CommandInset ref
5388 reference "sub:Column-Separation"
5392 can also be used to change the column separation of matrices.
5395 \begin_layout Standard
5396 To change the row separation, the command
5403 \begin_inset Index idx
5406 \begin_layout Plain Layout
5415 It is used as follows:
5418 \begin_layout Standard
5425 arraystretch}{stretch factor}
5426 \begin_inset Index idx
5429 \begin_layout Plain Layout
5440 \begin_layout Standard
5447 assigns the stretch factor to the predefined command
5455 \begin_inset space \thinspace{}
5459 \begin_inset space \space{}
5462 the row separation, use the factor 2.
5463 This is then used for all following matrices.
5464 To go back to the original separation, assign the factor 1 to
5473 \begin_layout Standard
5474 To set matrices into a text line, the command
5481 \begin_inset Index idx
5484 \begin_layout Plain Layout
5493 When it is inserted a blue box with two dashed lines appears.
5494 In this box the matrix is inserted.
5497 \begin_layout Standard
5499 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5501 \end{smallmatrix}\right)$
5507 \begin_layout Section
5508 Brackets and Delimiters
5509 \begin_inset Index idx
5512 \begin_layout Plain Layout
5519 \begin_inset Index idx
5522 \begin_layout Plain Layout
5531 \begin_layout Subsection
5532 Vertical Brackets and Delimiters
5533 \begin_inset Index idx
5536 \begin_layout Plain Layout
5545 \begin_layout Standard
5546 \begin_inset space \hfill{}
5550 \begin_inset Tabular
5551 <lyxtabular version="3" rows="9" columns="2">
5552 <features rotate="0" tabularvalignment="middle">
5553 <column alignment="center" valignment="top" width="0pt">
5554 <column alignment="center" valignment="top" width="0pt">
5556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5559 \begin_layout Plain Layout
5565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5568 \begin_layout Plain Layout
5576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5579 \begin_layout Plain Layout
5585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5588 \begin_layout Plain Layout
5589 \begin_inset Formula $($
5599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5602 \begin_layout Plain Layout
5608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5611 \begin_layout Plain Layout
5612 \begin_inset Formula $\{$
5622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5635 \begin_inset Formula $[$
5645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5648 \begin_layout Plain Layout
5656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5659 \begin_layout Plain Layout
5660 \begin_inset Formula $\langle$
5670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5673 \begin_layout Plain Layout
5681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5684 \begin_layout Plain Layout
5685 \begin_inset Formula $\lceil$
5695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5698 \begin_layout Plain Layout
5706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5709 \begin_layout Plain Layout
5710 \begin_inset Formula $\lfloor$
5720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5723 \begin_layout Plain Layout
5729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5732 \begin_layout Plain Layout
5733 \begin_inset Formula $/$
5743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5746 \begin_layout Plain Layout
5752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5755 \begin_layout Plain Layout
5756 \begin_inset Formula $|$
5770 \begin_inset space \hfill{}
5774 \begin_inset Tabular
5775 <lyxtabular version="3" rows="9" columns="2">
5776 <features rotate="0" tabularvalignment="middle">
5777 <column alignment="center" valignment="top" width="0pt">
5778 <column alignment="center" valignment="top" width="0pt">
5780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5783 \begin_layout Plain Layout
5789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5792 \begin_layout Plain Layout
5800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5803 \begin_layout Plain Layout
5809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5812 \begin_layout Plain Layout
5813 \begin_inset Formula $)$
5823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5826 \begin_layout Plain Layout
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5835 \begin_layout Plain Layout
5836 \begin_inset Formula $\}$
5846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5849 \begin_layout Plain Layout
5855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5858 \begin_layout Plain Layout
5859 \begin_inset Formula $]$
5869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5872 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5883 \begin_layout Plain Layout
5884 \begin_inset Formula $\rangle$
5894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5897 \begin_layout Plain Layout
5905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5908 \begin_layout Plain Layout
5909 \begin_inset Formula $\rceil$
5919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5922 \begin_layout Plain Layout
5930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5933 \begin_layout Plain Layout
5934 \begin_inset Formula $\rfloor$
5944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5947 \begin_layout Plain Layout
5957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5960 \begin_layout Plain Layout
5961 \begin_inset Formula $\backslash$
5971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5974 \begin_layout Plain Layout
5982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5985 \begin_layout Plain Layout
5986 \begin_inset Formula $\|$
6000 \begin_inset space \hfill{}
6006 \begin_layout Standard
6009 \begin_inset Note Greyedout
6012 \begin_layout Plain Layout
6017 In TeX-mode the command
6024 \begin_inset Index idx
6027 \begin_layout Plain Layout
6035 must be used for the backslash, because the command
6043 produces a line break there.
6051 \begin_layout Standard
6052 For all characters listed above the size can be adjusted with the commands
6053 described in the following two subsections.
6054 When using these commands, the characters < and > can directly be used
6055 instead of the commands
6070 \begin_layout Subsubsection
6072 \begin_inset CommandInset label
6074 name "sub:Manual-Bracket-Size"
6079 \begin_inset Index idx
6082 \begin_layout Plain Layout
6083 Bracket size ! manual
6091 \begin_layout Standard
6092 The bracket size can be specified manually by the LaTeX-commands
6099 \begin_inset Index idx
6102 \begin_layout Plain Layout
6135 denotes the smallest and
6141 the largest bracket size.
6144 \begin_layout Standard
6145 These commands are used to emphasize levels of brackets:
6148 \begin_layout Standard
6150 \begin_inset Tabular
6151 <lyxtabular version="3" rows="2" columns="2">
6152 <features rotate="0" tabularvalignment="middle">
6153 <column alignment="center" valignment="top" width="0pt">
6154 <column alignment="center" valignment="top" width="0pt">
6156 <cell alignment="center" valignment="top" usebox="none">
6159 \begin_layout Plain Layout
6160 all brackets in the same size:
6165 <cell alignment="center" valignment="top" usebox="none">
6168 \begin_layout Plain Layout
6169 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6179 <cell alignment="center" valignment="top" usebox="none">
6182 \begin_layout Plain Layout
6188 <cell alignment="center" valignment="top" usebox="none">
6191 \begin_layout Plain Layout
6192 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6206 \begin_inset Note Note
6209 \begin_layout Plain Layout
6216 is only used as spacer.
6224 \begin_layout Standard
6225 For the second formula the command
6232 \begin_inset space \textvisiblespace{}
6240 \begin_layout Standard
6241 Here is an overview about all bracket sizes:
6244 \begin_layout Standard
6261 \begin_inset space \textvisiblespace{}
6269 \begin_inset space \textvisiblespace{}
6273 \begin_inset space \textvisiblespace{}
6283 \begin_layout Standard
6285 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6291 \begin_layout Standard
6298 -commands there is the variant
6305 \begin_inset Index idx
6308 \begin_layout Plain Layout
6316 that adds a bit more space between the bracket and its content, and the
6330 \begin_inset Index idx
6333 \begin_layout Plain Layout
6343 , that don't add additional space.
6348 at the end of the command
6354 is for a left bracket; for a right bracket this will be replaced by an
6360 A left or right bracket can each be an opening or closing bracket.
6363 \begin_layout Standard
6364 In the following table is a comparison of the variants:
6367 \begin_layout Standard
6369 \begin_inset Tabular
6370 <lyxtabular version="3" rows="5" columns="2">
6371 <features rotate="0" tabularvalignment="middle">
6372 <column alignment="center" valignment="middle">
6373 <column alignment="center" valignment="middle">
6375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6378 \begin_layout Plain Layout
6384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6387 \begin_layout Plain Layout
6389 \begin_inset Note Note
6392 \begin_layout Plain Layout
6399 is only used as spacer.
6411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6414 \begin_layout Plain Layout
6424 \begin_inset space \textvisiblespace{}
6434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6437 \begin_layout Plain Layout
6438 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6451 \begin_layout Plain Layout
6461 \begin_inset space \textvisiblespace{}
6471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6474 \begin_layout Plain Layout
6475 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6488 \begin_layout Plain Layout
6498 \begin_inset space \textvisiblespace{}
6508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6511 \begin_layout Plain Layout
6512 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6525 \begin_layout Plain Layout
6537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6540 \begin_layout Plain Layout
6541 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6557 \begin_layout Subsubsection
6558 Automatic Bracket Size
6559 \begin_inset CommandInset label
6561 name "sub:Automatic-Bracket-Size"
6566 \begin_inset Index idx
6569 \begin_layout Plain Layout
6570 Bracket size ! automatic
6578 \begin_layout Standard
6579 Brackets with variable size can be inserted with the commands
6586 \begin_inset Index idx
6589 \begin_layout Plain Layout
6604 \begin_inset Index idx
6607 \begin_layout Plain Layout
6615 or via the math toolbar button
6616 \begin_inset Graphics
6617 filename ../images/dialog-show_mathdelimiter.png
6635 the wanted bracket must be inserted.
6636 The bracket size will then automatically be calculated for the output.
6639 \begin_layout Standard
6641 normal bracket: The command
6648 \begin_inset space \textvisiblespace{}
6652 \begin_inset Formula $\downarrow$
6656 \begin_inset space \textvisiblespace{}
6662 \begin_inset Formula
6672 \begin_layout Standard
6674 multiline bracket: The command
6683 \begin_inset space \textvisiblespace{}
6687 \begin_inset Formula $\downarrow$
6691 \begin_inset space \textvisiblespace{}
6699 \begin_inset Formula
6701 \ln\left(\frac{A}{C}\right)
6709 \begin_layout Standard
6725 \begin_inset space ~
6731 This has the advantage that you can see in LyX immediately the real bracket
6732 size and that the matching right bracket will be created too.
6733 \begin_inset Newline newline
6736 The command for the last example would then be:
6747 \begin_inset space \textvisiblespace{}
6751 \begin_inset Formula $\downarrow$
6757 \begin_layout Standard
6758 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6759 For example the command
6766 \begin_inset space \textvisiblespace{}
6770 \begin_inset Formula $\downarrow$
6774 \begin_inset space \textvisiblespace{}
6784 \begin_inset Formula
6786 \left.\frac{A}{B}\right\}
6805 will be converted by LyX to brackets in the right size when the document
6806 is reloaded and an omitted bracket will appear as dashed line.
6809 \begin_layout Standard
6810 \begin_inset VSpace bigskip
6813 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6821 \begin_inset Index idx
6824 \begin_layout Plain Layout
6832 is additionally available for all brackets and limits.
6833 With this command the height of the following character is adapted to the
6834 one of the surrounding brackets, what is e.
6835 \begin_inset space \thinspace{}
6839 \begin_inset space \space{}
6842 needed for physical vectors:
6843 \begin_inset Formula
6845 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6850 For physical vectors there is a special LaTeX-package, described in
6851 \begin_inset CommandInset ref
6853 reference "sub:Physical-Vectors"
6860 \begin_layout Subsection
6862 \begin_inset Index idx
6865 \begin_layout Plain Layout
6866 Brackets ! horizontal
6874 \begin_layout Standard
6876 \begin_inset Tabular
6877 <lyxtabular version="3" rows="4" columns="2">
6878 <features rotate="0" tabularvalignment="middle">
6879 <column alignment="center" valignment="top" width="0pt">
6880 <column alignment="center" valignment="top" width="0pt">
6882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6885 \begin_layout Plain Layout
6887 \begin_inset Note Note
6890 \begin_layout Plain Layout
6897 is only used as spacer.
6907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6910 \begin_layout Plain Layout
6918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6921 \begin_layout Plain Layout
6925 \begin_layout Plain Layout
6937 \begin_inset space \textvisiblespace{}
6941 \begin_inset space \textvisiblespace{}
6948 \begin_layout Plain Layout
6956 \begin_inset Index idx
6959 \begin_layout Plain Layout
6972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6975 \begin_layout Plain Layout
6976 \begin_inset Formula $\overbrace{A+B}^{3}$
6986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6989 \begin_layout Plain Layout
6993 \begin_layout Plain Layout
7005 \begin_inset space \textvisiblespace{}
7009 \begin_inset space \textvisiblespace{}
7016 \begin_layout Plain Layout
7024 \begin_inset Index idx
7027 \begin_layout Plain Layout
7040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7043 \begin_layout Plain Layout
7044 \begin_inset Formula $\underbrace{A+B}_{5}$
7054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7057 \begin_layout Plain Layout
7061 \begin_inset space \textvisiblespace{}
7067 \begin_inset space \textvisiblespace{}
7071 \begin_inset space \textvisiblespace{}
7075 \begin_inset space \textvisiblespace{}
7079 \begin_inset space \textvisiblespace{}
7083 \begin_inset space \textvisiblespace{}
7087 \begin_inset space \textvisiblespace{}
7095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7098 \begin_layout Plain Layout
7099 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7115 \begin_layout Standard
7116 In the last example it doesn't matter if
7128 is inserted at first.
7131 \begin_layout Standard
7132 \begin_inset VSpace bigskip
7135 When brackets are needed that overlap each other, multiline formulas, as
7137 \begin_inset CommandInset ref
7139 reference "sec:Multiline-Formulas"
7144 \begin_inset Formula
7146 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7147 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7152 In the first row the formula is inserted together with the first brace.
7153 It is hereby important that the space command
7157 \begin_layout Plain Layout
7158 Space commands are explained in
7159 \begin_inset CommandInset ref
7161 reference "sub:Predefined-Space"
7176 is inserted before the first
7177 \begin_inset Formula $d$
7180 , because the brace that ends behind the
7181 \begin_inset Formula $q$
7184 prevents that the following
7185 \begin_inset Quotes eld
7189 \begin_inset Quotes erd
7192 is surrounded by space.
7196 \begin_layout Plain Layout
7197 because a bracket is not handled as a character, see
7198 \begin_inset CommandInset ref
7200 reference "sub:Binary-Operators"
7209 In the second row the second brace is inserted.
7210 As it should begin before the
7211 \begin_inset Formula $b$
7226 \begin_layout Plain Layout
7234 \begin_inset CommandInset ref
7236 reference "sub:Placeholders"
7245 This space is needed because the
7246 \begin_inset Quotes eld
7250 \begin_inset Quotes erd
7253 is also surrounded by space in the formula.
7254 The brace is placed under the command
7263 \begin_layout Standard
7264 It gets more complicated when brackets overlap each other, like in the following
7269 \begin_layout Plain Layout
7281 \begin_inset Formula
7283 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7284 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7293 \begin_layout Plain Layout
7304 The first formula row is the same as the second row of the previous example,
7305 with the difference that the brace is above.
7306 The second row contains the formula together with the second brace.
7307 To avoid that there is space between the upper brace in the first row and
7308 the formula, the row spacing needs to be reduced.
7309 This is not easily possible due to a bug in LyX
7313 \begin_layout Plain Layout
7314 \begin_inset CommandInset href
7316 name "LyX-bug #1505"
7317 target "http://www.lyx.org/trac/ticket/1505"
7327 As a solution for the problem, the global formula row separation
7334 \begin_inset Index idx
7337 \begin_layout Plain Layout
7345 must be changed to -6
7346 \begin_inset space \thinspace{}
7349 pt before the formula with the command
7364 is set back after the formula to the standard value of 3
7365 \begin_inset space \thinspace{}
7368 pt using the same command.
7369 More about the row separation in formulas is explained in
7370 \begin_inset CommandInset ref
7372 reference "sub:Line-Separation"
7379 \begin_layout Section
7381 \begin_inset Index idx
7384 \begin_layout Plain Layout
7393 \begin_layout Standard
7394 Arrows can be inserted via the math toolbar button
7395 \begin_inset Graphics
7396 filename ../images/math/leftarrow.png
7401 or the commands listed in the following subsections.
7404 \begin_layout Subsection
7406 \begin_inset Index idx
7409 \begin_layout Plain Layout
7418 \begin_layout Standard
7419 \begin_inset space \hfill{}
7423 \begin_inset Tabular
7424 <lyxtabular version="3" rows="8" columns="2">
7425 <features rotate="0" tabularvalignment="middle">
7426 <column alignment="center" valignment="top" width="0pt">
7427 <column alignment="center" valignment="top" width="0pt">
7429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7432 \begin_layout Plain Layout
7438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7441 \begin_layout Plain Layout
7449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7452 \begin_layout Plain Layout
7460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7463 \begin_layout Plain Layout
7464 \begin_inset Formula $\gets$
7474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7477 \begin_layout Plain Layout
7485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7488 \begin_layout Plain Layout
7489 \begin_inset Formula $\Leftarrow$
7499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7502 \begin_layout Plain Layout
7510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7513 \begin_layout Plain Layout
7514 \begin_inset Formula $\longleftarrow$
7524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7527 \begin_layout Plain Layout
7535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7538 \begin_layout Plain Layout
7539 \begin_inset Formula $\Longleftarrow$
7549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7552 \begin_layout Plain Layout
7560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7563 \begin_layout Plain Layout
7564 \begin_inset Formula $\leftharpoonup$
7574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7577 \begin_layout Plain Layout
7585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7588 \begin_layout Plain Layout
7589 \begin_inset Formula $\leftharpoondown$
7599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7602 \begin_layout Plain Layout
7610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7613 \begin_layout Plain Layout
7614 \begin_inset Formula $\hookleftarrow$
7628 \begin_inset space \hfill{}
7632 \begin_inset Tabular
7633 <lyxtabular version="3" rows="8" columns="2">
7634 <features rotate="0" tabularvalignment="middle">
7635 <column alignment="center" valignment="top" width="0pt">
7636 <column alignment="center" valignment="top" width="0pt">
7638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7641 \begin_layout Plain Layout
7647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7650 \begin_layout Plain Layout
7658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7661 \begin_layout Plain Layout
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7672 \begin_layout Plain Layout
7673 \begin_inset Formula $\to$
7683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7686 \begin_layout Plain Layout
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7697 \begin_layout Plain Layout
7698 \begin_inset Formula $\Rightarrow$
7708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7711 \begin_layout Plain Layout
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7722 \begin_layout Plain Layout
7723 \begin_inset Formula $\longrightarrow$
7733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7736 \begin_layout Plain Layout
7744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7747 \begin_layout Plain Layout
7748 \begin_inset Formula $\Longrightarrow$
7758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7761 \begin_layout Plain Layout
7769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7772 \begin_layout Plain Layout
7773 \begin_inset Formula $\rightharpoonup$
7783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7786 \begin_layout Plain Layout
7794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7797 \begin_layout Plain Layout
7798 \begin_inset Formula $\rightharpoondown$
7808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7811 \begin_layout Plain Layout
7819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7822 \begin_layout Plain Layout
7823 \begin_inset Formula $\hookrightarrow$
7837 \begin_inset space \hfill{}
7843 \begin_layout Standard
7844 \begin_inset space \hfill{}
7848 \begin_inset Tabular
7849 <lyxtabular version="3" rows="6" columns="2">
7850 <features rotate="0" tabularvalignment="middle">
7851 <column alignment="center" valignment="top" width="0pt">
7852 <column alignment="center" valignment="top" width="0pt">
7854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7857 \begin_layout Plain Layout
7863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7866 \begin_layout Plain Layout
7874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7877 \begin_layout Plain Layout
7885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7888 \begin_layout Plain Layout
7889 \begin_inset Formula $\leftrightarrow$
7899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7902 \begin_layout Plain Layout
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7913 \begin_layout Plain Layout
7914 \begin_inset Formula $\Leftrightarrow$
7924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7927 \begin_layout Plain Layout
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7938 \begin_layout Plain Layout
7939 \begin_inset Formula $\longleftrightarrow$
7949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7952 \begin_layout Plain Layout
7960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7963 \begin_layout Plain Layout
7964 \begin_inset Formula $\Longleftrightarrow$
7974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7977 \begin_layout Plain Layout
7985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7988 \begin_layout Plain Layout
7989 \begin_inset Formula $\rightleftharpoons$
8003 \begin_inset space \hspace{}
8008 \begin_inset space \hfill{}
8012 \begin_inset Tabular
8013 <lyxtabular version="3" rows="5" columns="2">
8014 <features rotate="0" tabularvalignment="middle">
8015 <column alignment="center" valignment="top" width="0pt">
8016 <column alignment="center" valignment="top" width="0pt">
8018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8021 \begin_layout Plain Layout
8027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8030 \begin_layout Plain Layout
8038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8041 \begin_layout Plain Layout
8049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8052 \begin_layout Plain Layout
8053 \begin_inset Formula $\mapsto$
8063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8066 \begin_layout Plain Layout
8074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8077 \begin_layout Plain Layout
8078 \begin_inset Formula $\longmapsto$
8088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8091 \begin_layout Plain Layout
8099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8102 \begin_layout Plain Layout
8103 \begin_inset Formula $\leadsto$
8113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8116 \begin_layout Plain Layout
8124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8127 \begin_layout Plain Layout
8128 \begin_inset Formula $\dasharrow$
8142 \begin_inset space \hfill{}
8148 \begin_layout Standard
8149 \begin_inset VSpace medskip
8152 Arrows used as accents like e.
8153 \begin_inset space \thinspace{}
8157 \begin_inset space \space{}
8160 vector arrows are listed in
8161 \begin_inset CommandInset ref
8163 reference "sec:Accents"
8170 \begin_layout Standard
8171 \begin_inset VSpace bigskip
8174 Furthermore there are the labeled arrows
8175 \begin_inset Index idx
8178 \begin_layout Plain Layout
8191 \begin_inset Index idx
8194 \begin_layout Plain Layout
8209 \begin_inset Index idx
8212 \begin_layout Plain Layout
8219 \begin_layout Plain Layout
8234 When inserting one of these commands in a formula, an arrow with two blue
8235 boxes appear where the label can be inserted.
8236 The length of the arrow adapts to the label width.
8239 \begin_layout Standard
8241 \begin_inset Tabular
8242 <lyxtabular version="3" rows="3" columns="2">
8243 <features rotate="0" tabularvalignment="middle">
8244 <column alignment="center" valignment="top" width="0pt">
8245 <column alignment="center" valignment="top" width="0pt">
8247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8250 \begin_layout Plain Layout
8256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8259 \begin_layout Plain Layout
8261 \begin_inset Note Note
8264 \begin_layout Plain Layout
8271 is only used as spacer.
8283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8286 \begin_layout Plain Layout
8290 \begin_inset space \textvisiblespace{}
8294 \begin_inset Formula $\downarrow$
8298 \begin_inset Formula $\to$
8306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8309 \begin_layout Plain Layout
8310 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8323 \begin_layout Plain Layout
8327 \begin_inset space \textvisiblespace{}
8331 \begin_inset Formula $\downarrow$
8335 \begin_inset Formula $\to$
8343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8346 \begin_layout Plain Layout
8347 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8363 \begin_layout Subsection
8364 Vertical and diagonal Arrows
8365 \begin_inset Index idx
8368 \begin_layout Plain Layout
8375 \begin_inset Index idx
8378 \begin_layout Plain Layout
8387 \begin_layout Standard
8388 \begin_inset space \hfill{}
8392 \begin_inset Tabular
8393 <lyxtabular version="3" rows="7" columns="2">
8394 <features rotate="0" tabularvalignment="middle">
8395 <column alignment="center" valignment="top" width="0pt">
8396 <column alignment="center" valignment="top" width="0pt">
8398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8401 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8421 \begin_layout Plain Layout
8429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8432 \begin_layout Plain Layout
8433 \begin_inset Formula $\uparrow$
8443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8446 \begin_layout Plain Layout
8454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8457 \begin_layout Plain Layout
8458 \begin_inset Formula $\Uparrow$
8468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8471 \begin_layout Plain Layout
8479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8482 \begin_layout Plain Layout
8483 \begin_inset Formula $\updownarrow$
8493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8496 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8508 \begin_inset Formula $\Updownarrow$
8518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8521 \begin_layout Plain Layout
8529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8532 \begin_layout Plain Layout
8533 \begin_inset Formula $\Downarrow$
8543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8546 \begin_layout Plain Layout
8554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8557 \begin_layout Plain Layout
8558 \begin_inset Formula $\downarrow$
8572 \begin_inset space \hfill{}
8576 \begin_inset Tabular
8577 <lyxtabular version="3" rows="5" columns="2">
8578 <features rotate="0" tabularvalignment="middle">
8579 <column alignment="center" valignment="top" width="0pt">
8580 <column alignment="center" valignment="top" width="0pt">
8582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8585 \begin_layout Plain Layout
8591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8594 \begin_layout Plain Layout
8602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8605 \begin_layout Plain Layout
8613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8616 \begin_layout Plain Layout
8617 \begin_inset Formula $\nearrow$
8627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8630 \begin_layout Plain Layout
8638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8641 \begin_layout Plain Layout
8642 \begin_inset Formula $\searrow$
8652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8655 \begin_layout Plain Layout
8663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8666 \begin_layout Plain Layout
8667 \begin_inset Formula $\swarrow$
8677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8680 \begin_layout Plain Layout
8688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8691 \begin_layout Plain Layout
8692 \begin_inset Formula $\nwarrow$
8706 \begin_inset space \hfill{}
8712 \begin_layout Standard
8713 \begin_inset VSpace medskip
8716 Vertical arrows can be used also as delimiters together with the commands
8718 \begin_inset CommandInset ref
8720 reference "sub:Manual-Bracket-Size"
8725 \begin_inset CommandInset ref
8727 reference "sub:Automatic-Bracket-Size"
8734 \begin_layout Section
8736 \begin_inset CommandInset label
8743 \begin_inset Index idx
8746 \begin_layout Plain Layout
8755 \begin_layout Standard
8756 Accents can be inserted via the math toolbar button
8757 \begin_inset Graphics
8758 filename ../images/math/hat.png
8763 or the commands listed in the following subsections.
8766 \begin_layout Subsection
8767 Accents for one Character
8771 \begin_layout Plain Layout
8784 \begin_layout Plain Layout
8786 \begin_inset CommandInset ref
8788 reference "sub:Accents-in-Text"
8801 \begin_layout Plain Layout
8809 \begin_inset Note Note
8812 \begin_layout Plain Layout
8819 is used to avoid that the footnote appears in the PDF-bookmark.
8822 \begin_layout Plain Layout
8830 \begin_inset CommandInset ref
8832 reference "sub:Formulas-in-Section"
8842 \begin_inset CommandInset label
8844 name "sub:Accents-for-one"
8849 \begin_inset Index idx
8852 \begin_layout Plain Layout
8853 Accents ! for one character
8861 \begin_layout Standard
8862 \begin_inset space \hfill{}
8866 \begin_inset Tabular
8867 <lyxtabular version="3" rows="8" columns="2">
8868 <features rotate="0" tabularvalignment="middle">
8869 <column alignment="center" valignment="top" width="0pt">
8870 <column alignment="center" valignment="top" width="0pt">
8872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8875 \begin_layout Plain Layout
8881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8884 \begin_layout Plain Layout
8886 \begin_inset Note Note
8889 \begin_layout Plain Layout
8896 is only used as spacer.
8908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8911 \begin_layout Plain Layout
8915 \begin_inset space \textvisiblespace{}
8923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8926 \begin_layout Plain Layout
8927 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8940 \begin_layout Plain Layout
8944 \begin_inset space \textvisiblespace{}
8952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8955 \begin_layout Plain Layout
8956 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8969 \begin_layout Plain Layout
8973 \begin_inset space \textvisiblespace{}
8981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8984 \begin_layout Plain Layout
8985 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8998 \begin_layout Plain Layout
9002 \begin_inset space \textvisiblespace{}
9010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9013 \begin_layout Plain Layout
9014 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9027 \begin_layout Plain Layout
9031 \begin_inset space \textvisiblespace{}
9035 \begin_inset Index idx
9038 \begin_layout Plain Layout
9049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9052 \begin_layout Plain Layout
9053 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9066 \begin_layout Plain Layout
9070 \begin_inset space \textvisiblespace{}
9078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9081 \begin_layout Plain Layout
9082 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9095 \begin_layout Plain Layout
9099 \begin_inset space \textvisiblespace{}
9107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9110 \begin_layout Plain Layout
9111 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9125 \begin_inset space \hfill{}
9129 \begin_inset Tabular
9130 <lyxtabular version="3" rows="7" columns="2">
9131 <features rotate="0" tabularvalignment="middle">
9132 <column alignment="center" valignment="top" width="0pt">
9133 <column alignment="center" valignment="top" width="0pt">
9135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9138 \begin_layout Plain Layout
9144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9147 \begin_layout Plain Layout
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9158 \begin_layout Plain Layout
9162 \begin_inset space \textvisiblespace{}
9170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9173 \begin_layout Plain Layout
9174 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9187 \begin_layout Plain Layout
9191 \begin_inset space \textvisiblespace{}
9199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9202 \begin_layout Plain Layout
9203 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9216 \begin_layout Plain Layout
9220 \begin_inset space \textvisiblespace{}
9228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9231 \begin_layout Plain Layout
9232 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9245 \begin_layout Plain Layout
9249 \begin_inset space \textvisiblespace{}
9257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9260 \begin_layout Plain Layout
9261 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9274 \begin_layout Plain Layout
9278 \begin_inset space \textvisiblespace{}
9286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9289 \begin_layout Plain Layout
9290 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9303 \begin_layout Plain Layout
9307 \begin_inset space \textvisiblespace{}
9315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9318 \begin_layout Plain Layout
9319 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9333 \begin_inset space \hfill{}
9339 \begin_layout Standard
9340 \begin_inset VSpace bigskip
9346 \begin_layout Standard
9347 You can directly insert accents like é to formulas.
9348 LyX will transform them to the corresponding accent command.
9350 \begin_inset Index idx
9353 \begin_layout Plain Layout
9359 it is better to insert a quotation mark before the vowel.
9360 These two characters are then treated by LaTeX as
9364 character when the formula part with the umlaut is marked as German.
9372 \begin_inset Quotes eld
9376 \begin_inset Quotes erd
9379 umlauts are created as demonstrated in the following example:
9382 \begin_layout Standard
9383 \begin_inset VSpace -2mm
9389 \begin_layout Standard
9391 \begin_inset Tabular
9392 <lyxtabular version="3" rows="3" columns="2">
9393 <features rotate="0" tabularvalignment="middle">
9394 <column alignment="center" valignment="top">
9395 <column alignment="center" valignment="top">
9397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9400 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9411 \begin_inset Note Note
9414 \begin_layout Plain Layout
9422 \begin_inset space \thinspace{}
9425 pt space are only used as spacer.
9437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9440 \begin_layout Plain Layout
9443 \begin_inset Quotes grd
9451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9454 \begin_layout Plain Layout
9455 \begin_inset space \hspace{}
9462 \begin_inset Formula $"i$
9472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9475 \begin_layout Plain Layout
9479 \begin_inset space \textvisiblespace{}
9487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9507 \begin_layout Standard
9508 Another advantage to
9514 is that umlauts can directly be converted to mathematical text because
9515 the accent commands above are
9521 in mathematical text
9524 To convert an accented character to mathematical text, only the character
9525 under the accent may be converted.
9526 This applies also for all other conversions, e.
9527 \begin_inset space \thinspace{}
9531 \begin_inset space \space{}
9537 \begin_layout Standard
9538 In mathematical text, umlauts and other accented characters can directly
9542 \begin_layout Standard
9543 \begin_inset VSpace bigskip
9549 \begin_layout Standard
9550 LyX also supports a tilde under the character if the LaTeX-package
9555 \begin_inset Index idx
9558 \begin_layout Plain Layout
9559 Packages ! undertilde
9564 is installed on your system:
9567 \begin_layout Standard
9571 \begin_layout Plain Layout
9581 \begin_inset Note Note
9584 \begin_layout Plain Layout
9585 The following table will only be displayed when the LaTeX-package
9597 \begin_layout Standard
9600 \begin_inset Tabular
9601 <lyxtabular version="3" rows="2" columns="2">
9602 <features rotate="0" tabularvalignment="middle">
9603 <column alignment="center" valignment="top" width="0pt">
9604 <column alignment="center" valignment="top" width="0pt">
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9609 \begin_layout Plain Layout
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9629 \begin_layout Plain Layout
9633 \begin_inset space \textvisiblespace{}
9641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9644 \begin_layout Plain Layout
9645 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9661 \begin_layout Standard
9665 \begin_layout Plain Layout
9675 \begin_inset Note Note
9678 \begin_layout Plain Layout
9679 The following will be displayed when the LaTeX-package
9691 \begin_layout Standard
9692 You need to install the LaTeX-package
9696 to see the rest of this subsection in the output.
9699 \begin_layout Standard
9703 \begin_layout Plain Layout
9715 \begin_layout Subsection
9716 Accents for several Characters
9717 \begin_inset Index idx
9720 \begin_layout Plain Layout
9721 Accents ! for several characters
9729 \begin_layout Standard
9730 \begin_inset space \hfill{}
9734 \begin_inset Tabular
9735 <lyxtabular version="3" rows="5" columns="2">
9736 <features rotate="0" tabularvalignment="middle">
9737 <column alignment="center" valignment="top" width="0pt">
9738 <column alignment="center" valignment="top" width="0pt">
9740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9743 \begin_layout Plain Layout
9749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9752 \begin_layout Plain Layout
9754 \begin_inset Note Note
9757 \begin_layout Plain Layout
9764 is only used as spacer.
9776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9783 \begin_inset space \textvisiblespace{}
9791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9794 \begin_layout Plain Layout
9795 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9808 \begin_layout Plain Layout
9812 \begin_inset space \textvisiblespace{}
9820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9823 \begin_layout Plain Layout
9824 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9837 \begin_layout Plain Layout
9841 \begin_inset space \textvisiblespace{}
9849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9852 \begin_layout Plain Layout
9853 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9866 \begin_layout Plain Layout
9870 \begin_inset space \textvisiblespace{}
9878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9881 \begin_layout Plain Layout
9882 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9896 \begin_inset space \hfill{}
9900 \begin_inset Tabular
9901 <lyxtabular version="3" rows="5" columns="2">
9902 <features rotate="0" tabularvalignment="middle">
9903 <column alignment="center" valignment="top" width="0pt">
9904 <column alignment="center" valignment="top" width="0pt">
9906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9909 \begin_layout Plain Layout
9915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9918 \begin_layout Plain Layout
9926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9929 \begin_layout Plain Layout
9933 \begin_inset space \textvisiblespace{}
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9945 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9958 \begin_layout Plain Layout
9962 \begin_inset space \textvisiblespace{}
9970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9973 \begin_layout Plain Layout
9974 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9987 \begin_layout Plain Layout
9991 \begin_inset space \textvisiblespace{}
9999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10002 \begin_layout Plain Layout
10003 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10016 \begin_layout Plain Layout
10020 \begin_inset space \textvisiblespace{}
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10031 \begin_layout Plain Layout
10032 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10046 \begin_inset space \hfill{}
10052 \begin_layout Standard
10053 \begin_inset VSpace medskip
10056 With these commands as many characters as you like can be accented.
10069 will only be set in the output with a length of three characters, as shown
10070 in the following example:
10071 \begin_inset Formula
10073 \widetilde{A+B=C-D}
10081 \begin_layout Standard
10089 \begin_inset Index idx
10092 \begin_layout Plain Layout
10107 \begin_inset Index idx
10110 \begin_layout Plain Layout
10118 described in the previous subsection it is also possible to accent several
10125 \begin_inset space \textvisiblespace{}
10129 \begin_inset Formula $\downarrow$
10135 \begin_inset Formula
10137 \underset{***}{A=B}
10145 \begin_layout Standard
10146 \begin_inset Newpage newpage
10152 \begin_layout Section
10154 \begin_inset CommandInset label
10161 \begin_inset Index idx
10164 \begin_layout Plain Layout
10173 \begin_layout Subsection
10175 \begin_inset CommandInset label
10177 name "sub:Predefined-Space"
10182 \begin_inset Index idx
10185 \begin_layout Plain Layout
10186 Space ! horizontal ! predefined
10194 \begin_layout Standard
10195 Sometimes it is necessary to insert horizontal space into a formula.
10196 This is done by inserting a protected space (shortcut
10199 arg "command-alternatives space-insert protected ; math-space"
10204 \begin_inset Quotes eld
10210 \begin_inset space \textvisiblespace{}
10216 \begin_inset Quotes erd
10219 appears and by pressing
10223 several times one can select one of eight different space sizes.
10224 The spaces can also be inserted using the math toolbar button
10225 \begin_inset Graphics
10226 filename ../images/math/space.png
10231 or special commands.
10232 Independent from the inserted command, one can select the size again by
10240 \begin_layout Standard
10243 \begin_inset Tabular
10244 <lyxtabular version="3" rows="6" columns="3">
10245 <features rotate="0" tabularvalignment="middle">
10246 <column alignment="center" valignment="top">
10247 <column alignment="center" valignment="top" width="15col%">
10248 <column alignment="center" valignment="top">
10250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10253 \begin_layout Plain Layout
10259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10262 \begin_layout Plain Layout
10272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10275 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10286 \begin_layout Plain Layout
10294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10297 \begin_layout Plain Layout
10303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10306 \begin_layout Plain Layout
10307 \begin_inset Formula $A\, B$
10317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10320 \begin_layout Plain Layout
10328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10331 \begin_layout Plain Layout
10337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10340 \begin_layout Plain Layout
10341 \begin_inset Formula $A\: B$
10351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10354 \begin_layout Plain Layout
10362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10374 \begin_layout Plain Layout
10375 \begin_inset Formula $A\; B$
10385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10388 \begin_layout Plain Layout
10396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10399 \begin_layout Plain Layout
10405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10408 \begin_layout Plain Layout
10409 \begin_inset Formula $A\quad B$
10419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10422 \begin_layout Plain Layout
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10443 \begin_inset Formula $A\qquad B$
10457 \begin_inset space \hfill{}
10461 \begin_inset Tabular
10462 <lyxtabular version="3" rows="6" columns="3">
10463 <features rotate="0" tabularvalignment="middle">
10464 <column alignment="center" valignment="top">
10465 <column alignment="center" valignment="top" width="15col%">
10466 <column alignment="center" valignment="top">
10468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10471 \begin_layout Plain Layout
10477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10480 \begin_layout Plain Layout
10490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10493 \begin_layout Plain Layout
10501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10504 \begin_layout Plain Layout
10512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10515 \begin_layout Plain Layout
10521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10524 \begin_layout Plain Layout
10525 \begin_inset Formula $A\hfill B$
10535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10538 \begin_layout Plain Layout
10546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10549 \begin_layout Plain Layout
10555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10558 \begin_layout Plain Layout
10559 \begin_inset Formula $A\hspace*{1em}B$
10569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10572 \begin_layout Plain Layout
10580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10592 \begin_layout Plain Layout
10593 \begin_inset Formula $A\hspace{1em}B$
10603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10606 \begin_layout Plain Layout
10610 \begin_inset space \textvisiblespace{}
10618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10621 \begin_layout Plain Layout
10627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10630 \begin_layout Plain Layout
10631 \begin_inset Formula $A\ B$
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10644 \begin_layout Plain Layout
10652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10655 \begin_layout Plain Layout
10661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10664 \begin_layout Plain Layout
10665 \begin_inset Formula $A\! B$
10681 \begin_layout Standard
10683 \begin_inset space ~
10687 \begin_inset space \thinspace{}
10691 \begin_inset space \thinspace{}
10694 7 are variable spaces which are explained in
10695 \begin_inset CommandInset ref
10697 reference "sub:Variable-Space"
10703 \begin_inset space ~
10706 9 seems to produce no space.
10707 It is displayed red in LyX contrary to the other sizes, because it is a
10709 There are two more negative spaces:
10712 \begin_layout Standard
10714 \begin_inset Tabular
10715 <lyxtabular version="3" rows="3" columns="3">
10716 <features rotate="0" tabularvalignment="middle">
10717 <column alignment="center" valignment="middle" width="6.8cm">
10718 <column alignment="center" valignment="top" width="0pt">
10719 <column alignment="center" valignment="top" width="0pt">
10721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10724 \begin_layout Plain Layout
10730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10733 \begin_layout Plain Layout
10741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10744 \begin_layout Plain Layout
10754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10757 \begin_layout Plain Layout
10762 keystrokes after inserting the protected space
10767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10779 \begin_layout Plain Layout
10787 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10790 \begin_layout Plain Layout
10796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10799 \begin_layout Plain Layout
10800 \begin_inset Formula $A\negmedspace B$
10808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10811 \begin_layout Plain Layout
10812 \begin_inset Formula $A\negthickspace B$
10828 \begin_layout Standard
10829 Negative spaces can lead to characters overlapping each other.
10830 Thus they can be used to enforce ligatures, which are e.
10831 \begin_inset space \thinspace{}
10835 \begin_inset space \space{}
10838 useful for summation operators:
10841 \begin_layout Standard
10843 \begin_inset Tabular
10844 <lyxtabular version="3" rows="3" columns="2">
10845 <features rotate="0" tabularvalignment="middle">
10846 <column alignment="center" valignment="top">
10847 <column alignment="center" valignment="top">
10849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10852 \begin_layout Plain Layout
10858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10861 \begin_layout Plain Layout
10863 \begin_inset Note Note
10866 \begin_layout Plain Layout
10873 is only used as spacer.
10885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10888 \begin_layout Plain Layout
10894 \begin_inset space \textvisiblespace{}
10902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10905 \begin_layout Plain Layout
10906 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10919 \begin_layout Plain Layout
10927 \begin_inset space \textvisiblespace{}
10935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10938 \begin_layout Plain Layout
10939 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10955 \begin_layout Standard
10957 \begin_inset VSpace medskip
10963 \begin_layout Standard
10965 Relations like for example equal signs, are always surrounded by space.
10966 To suppress this, the equal sign is placed into a TeX-brace.
10967 The following example demonstrates this:
10970 \begin_layout Standard
10972 \begin_inset Tabular
10973 <lyxtabular version="3" rows="2" columns="2">
10974 <features rotate="0" tabularvalignment="middle">
10975 <column alignment="center" valignment="top" width="0pt">
10976 <column alignment="center" valignment="top" width="0pt">
10978 <cell alignment="center" valignment="top" usebox="none">
10981 \begin_layout Plain Layout
10987 <cell alignment="center" valignment="top" usebox="none">
10990 \begin_layout Plain Layout
10991 \begin_inset Formula $A=B$
11001 <cell alignment="center" valignment="top" usebox="none">
11004 \begin_layout Plain Layout
11005 \begin_inset Note Note
11008 \begin_layout Plain Layout
11015 is only used as spacer.
11021 \begin_inset Formula $\raisebox{5mm}{}$
11024 equation without space
11029 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11032 \begin_layout Plain Layout
11033 \begin_inset Formula $A{=}B$
11049 \begin_layout Standard
11051 The command for the last formula is:
11056 \begin_inset Formula $\to$
11062 \begin_layout Standard
11063 \begin_inset VSpace bigskip
11069 \begin_layout Standard
11070 Spaces are needed for physical units, because the space between the value
11071 and the unit is the smallest one and not a normal space.
11072 For units in text, the smallest space is inserted via the menu
11074 Insert\SpecialChar \menuseparator
11075 Formatting\SpecialChar \menuseparator
11077 \begin_inset space ~
11085 arg "space-insert thin"
11091 \begin_layout Standard
11092 An example to visualize the difference:
11095 \begin_layout Standard
11096 \begin_inset Tabular
11097 <lyxtabular version="3" rows="2" columns="2">
11098 <features rotate="0" tabularvalignment="middle">
11099 <column alignment="left" valignment="top">
11100 <column alignment="left" valignment="top">
11102 <cell alignment="center" valignment="top" usebox="none">
11105 \begin_layout Plain Layout
11107 \begin_inset Formula $\cdot$
11115 <cell alignment="center" valignment="top" usebox="none">
11118 \begin_layout Plain Layout
11119 space between value and unit
11126 <cell alignment="center" valignment="top" usebox="none">
11129 \begin_layout Plain Layout
11131 \begin_inset space \thinspace{}
11135 \begin_inset Formula $\cdot$
11143 <cell alignment="center" valignment="top" usebox="none">
11146 \begin_layout Plain Layout
11147 smallest space between value and unit
11160 \begin_layout Subsection
11165 \begin_layout Plain Layout
11178 \begin_layout Plain Layout
11179 for vertical space in formulas see
11180 \begin_inset CommandInset ref
11182 reference "sub:Line-Separation"
11195 \begin_layout Plain Layout
11203 \begin_inset Note Note
11206 \begin_layout Plain Layout
11209 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11212 \begin_layout Plain Layout
11215 texorpdfstring is in section
11216 \begin_inset CommandInset ref
11218 reference "sub:Formulas-in-Section"
11228 \begin_inset CommandInset label
11230 name "sub:Variable-Space"
11235 \begin_inset Index idx
11238 \begin_layout Plain Layout
11239 Space ! horizontal ! variable
11247 \begin_layout Standard
11248 Space with a defined length can be inserted with the command
11255 \begin_inset Index idx
11258 \begin_layout Plain Layout
11268 \begin_inset Quotes eld
11274 \begin_inset space \textvisiblespace{}
11280 \begin_inset Quotes erd
11284 The length can be specified by left-clicking on the
11285 \begin_inset Quotes eld
11291 \begin_inset space \textvisiblespace{}
11297 \begin_inset Quotes erd
11301 The length may also be negative.
11302 When a space would be the first character in a line it would be omitted.
11303 To force its output use the command
11315 or left-click on the
11316 \begin_inset Quotes eld
11322 \begin_inset space \textvisiblespace{}
11328 \begin_inset Quotes erd
11331 and check the option
11336 \begin_inset Newline newline
11339 To insert as much space as is available, the command
11346 \begin_inset Index idx
11349 \begin_layout Plain Layout
11360 \begin_layout Standard
11361 \begin_inset VSpace -1mm
11367 \begin_layout Standard
11369 \begin_inset Tabular
11370 <lyxtabular version="3" rows="4" columns="2">
11371 <features rotate="0" tabularvalignment="middle">
11372 <column alignment="center" valignment="top">
11373 <column alignment="center" valignment="top">
11375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11378 \begin_layout Plain Layout
11386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11389 \begin_layout Plain Layout
11397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11400 \begin_layout Plain Layout
11404 \begin_inset space \textvisiblespace{}
11410 \begin_inset space \thinspace{}
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11421 \begin_layout Plain Layout
11422 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11435 \begin_layout Plain Layout
11439 \begin_inset space \textvisiblespace{}
11445 \begin_inset space \thinspace{}
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11456 \begin_layout Plain Layout
11457 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11474 \begin_inset space \textvisiblespace{}
11482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11485 \begin_layout Plain Layout
11486 \begin_inset Formula $A=A\hfill B=B$
11502 \begin_layout Standard
11503 In the last example the available space is given by the longest column entry
11505 In an inline formula the space depends on the length of the line in which
11513 Thus, when the line uses the full width, no space will be created.
11520 only has an effect on displayed formulas when the formula style
11525 (Formula styles are explained in
11526 \begin_inset CommandInset ref
11528 reference "sec:Formula-Styles"
11535 \begin_layout Standard
11542 , there are the commands
11554 that fill the space with a pattern, see
11555 \begin_inset CommandInset ref
11557 reference "sub:Ellipses"
11564 \begin_layout Standard
11565 For text, variable space can be inserted via the menu
11567 Insert\SpecialChar \menuseparator
11568 Formatting\SpecialChar \menuseparator
11570 \begin_inset space ~
11578 \begin_layout Standard
11579 This is a line with
11580 \begin_inset space \hspace{}
11585 \begin_inset space \thinspace{}
11591 \begin_layout Standard
11592 This is a line with
11593 \begin_inset space \hfill{}
11599 \begin_layout Subsection
11600 Space besides inline Formulas
11601 \begin_inset Index idx
11604 \begin_layout Plain Layout
11605 Space ! besides inline formulas
11613 \begin_layout Standard
11614 The space that surrounds inline formulas can be adjusted with the length
11622 \begin_inset Index idx
11625 \begin_layout Plain Layout
11634 The value of a length is set with the command
11641 \begin_inset Index idx
11644 \begin_layout Plain Layout
11652 which has the following scheme:
11655 \begin_layout Standard
11660 setlength{length name}{value}
11663 \begin_layout Standard
11671 \begin_inset space \thinspace{}
11677 \begin_layout Standard
11687 \begin_layout Standard
11688 is inserted in TeX-mode.
11690 \begin_inset space \thinspace{}
11693 mm space will now be set around all inline formulas:
11697 \begin_layout Plain Layout
11711 \begin_layout Standard
11712 This is a line with an inline formula
11713 \begin_inset Formula $A=B$
11717 \begin_inset space \thinspace{}
11720 mm surrounding space.
11724 \begin_layout Plain Layout
11738 \begin_layout Standard
11739 To return to the predefined value,
11745 is set to the value 0
11746 \begin_inset space \thinspace{}
11752 \begin_layout Section
11754 \begin_inset Index idx
11757 \begin_layout Plain Layout
11764 \begin_inset Index idx
11767 \begin_layout Plain Layout
11772 \begin_layout Plain Layout
11783 \begin_layout Plain Layout
11798 \begin_layout Standard
11799 Boxes for text are described in chapter
11806 \begin_inset space ~
11814 \begin_layout Subsection
11816 \begin_inset CommandInset label
11818 name "sub:Boxes-with-Frame"
11823 \begin_inset Index idx
11826 \begin_layout Plain Layout
11835 \begin_layout Standard
11836 It is possible to frame a formula or part of one with the commands
11843 \begin_inset Index idx
11846 \begin_layout Plain Layout
11861 \begin_inset Index idx
11864 \begin_layout Plain Layout
11875 \begin_layout Standard
11876 When one of these commands is inserted in a formula, a blue box appears
11877 within a frame to enter formula parts.
11884 an additional formula has to be created by
11888 within this box, because the box content will otherwise be treated as mathemati
11896 is used, a new formula is automatically created inside the frame.
11899 \begin_layout Standard
11906 is not suitable to frame displayed formulas because the formula will always
11907 be set in the size of the text.
11914 is in contrary not suitable to frame inline formulas, because the formula
11915 will always be set in the size of a displayed formula.
11918 \begin_layout Standard
11932 \begin_inset Index idx
11935 \begin_layout Plain Layout
11943 where additionally the frame width and the alignment can be specified.
11950 is used in the following scheme:
11953 \begin_layout Standard
11958 framebox[frame width][position]{box content}
11961 \begin_layout Standard
11962 The position can either be
11979 right aligns the formula in the box.
11980 When no position is given, the formula will be centered.
11981 \begin_inset Newline newline
11984 If no width is given, also no position can be given.
11985 In this case the frame width is adjusted to the box content like for
11994 \begin_layout Standard
12001 is inserted, a box appears containing three blue boxes.
12002 The first two boxes are surrounded by brackets and denote the two optional
12004 The third box is for formula parts like for
12013 \begin_layout Standard
12014 \begin_inset Newpage newpage
12020 \begin_layout Standard
12022 \begin_inset Tabular
12023 <lyxtabular version="3" rows="5" columns="2">
12024 <features rotate="0" tabularvalignment="middle">
12025 <column alignment="center" valignment="top">
12026 <column alignment="center" valignment="top">
12028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12031 \begin_layout Plain Layout
12037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12040 \begin_layout Plain Layout
12042 \begin_inset Note Note
12045 \begin_layout Plain Layout
12052 is only used as spacer.
12064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12067 \begin_layout Plain Layout
12071 \begin_inset space \textvisiblespace{}
12081 \begin_inset space \textvisiblespace{}
12089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12092 \begin_layout Plain Layout
12093 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12106 \begin_layout Plain Layout
12110 \begin_inset space \textvisiblespace{}
12116 \begin_inset space \textvisiblespace{}
12124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12127 \begin_layout Plain Layout
12128 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12141 \begin_layout Plain Layout
12145 \begin_inset space \textvisiblespace{}
12153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12156 \begin_layout Plain Layout
12157 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12170 \begin_layout Plain Layout
12174 \begin_inset space \textvisiblespace{}
12178 \begin_inset Formula $\to$
12182 \begin_inset Formula $\to$
12192 \begin_inset space \textvisiblespace{}
12196 \begin_inset Formula $\downarrow$
12204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12207 \begin_layout Plain Layout
12208 \begin_inset Formula $\raisebox{6mm}{}$
12212 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12216 \begin_inset Formula $\raisebox{-4mm}{}$
12232 \begin_layout Standard
12233 The frame thickness can also be adjusted.
12234 To do this the following commands have to be inserted in TeX-mode before
12238 \begin_layout Standard
12248 \begin_inset Quotes eld
12252 \begin_inset Quotes erd
12266 \begin_inset Quotes eld
12270 \begin_inset Quotes erd
12276 \begin_layout Standard
12277 \begin_inset Quotes eld
12281 \begin_inset Quotes erd
12284 specifies the minimal distance between the frame and the first character
12286 An example for this is the following framed formula:
12290 \begin_layout Plain Layout
12302 \begin_inset Formula
12309 Before this formula the commands
12312 \begin_layout Standard
12334 \begin_layout Standard
12335 were inserted in TeX-mode.
12336 The given values are used for all following boxes.
12339 \begin_layout Standard
12340 To return to the standard frame size, the command
12343 \begin_layout Standard
12368 \begin_layout Plain Layout
12382 \begin_layout Standard
12383 is inserted in TeX-mode before the next formula.
12386 \begin_layout Subsection
12387 Boxes without Frame
12388 \begin_inset CommandInset label
12390 name "sub:Boxes-without-Frame"
12395 \begin_inset Index idx
12398 \begin_layout Plain Layout
12399 Boxes ! without frame
12407 \begin_layout Standard
12408 For boxes without a frame there are the following box commands:
12415 \begin_inset Index idx
12418 \begin_layout Plain Layout
12433 \begin_inset Index idx
12436 \begin_layout Plain Layout
12451 \begin_inset Index idx
12454 \begin_layout Plain Layout
12465 \begin_layout Standard
12472 a box can be super- or subscripted.
12473 But in contrary to normal super- and subscripting, the characters in the
12474 box keep their font size.
12481 is used in the following scheme:
12484 \begin_layout Standard
12489 raisebox{height}{box content}
12492 \begin_layout Standard
12493 When the box should contain a formula, an extra formula is needed like for
12504 \begin_inset Note Greyedout
12507 \begin_layout Plain Layout
12518 this extra formula is created by pressing
12522 twice instead of once because LyX doesn't yet support
12536 \begin_layout Standard
12538 \begin_inset Tabular
12539 <lyxtabular version="3" rows="4" columns="2">
12540 <features rotate="0" tabularvalignment="middle">
12541 <column alignment="center" valignment="top">
12542 <column alignment="center" valignment="top">
12544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12547 \begin_layout Plain Layout
12553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12556 \begin_layout Plain Layout
12564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12567 \begin_layout Plain Layout
12571 \begin_inset Formula $\to$
12577 \begin_inset Formula $\to$
12585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12588 \begin_layout Plain Layout
12589 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12602 \begin_layout Plain Layout
12606 \begin_inset Formula $\to$
12612 \begin_inset Formula $\to$
12620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12623 \begin_layout Plain Layout
12624 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12637 \begin_layout Plain Layout
12641 \begin_inset Formula $\to$
12657 \begin_inset space \textvisiblespace{}
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12668 \begin_layout Plain Layout
12669 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12685 \begin_layout Standard
12710 , with the difference that there is no frame.
12713 \begin_layout Subsection
12715 \begin_inset CommandInset label
12717 name "sub:Colored-Boxes"
12722 \begin_inset Index idx
12725 \begin_layout Plain Layout
12734 \begin_layout Standard
12735 To be able to use all commands explained in this section, the LaTeX-package
12744 \begin_layout Plain Layout
12749 is part of every LaTeX standard installation.
12755 \begin_inset Index idx
12758 \begin_layout Plain Layout
12764 has to be loaded in the LaTeX-preamble with the line
12768 \begin_layout Plain Layout
12769 When text is colored somewhere in the document with a predefined color,
12770 LyX loads the LaTeX-package
12775 Thus it is possible that the package is loaded twice, but this does not
12782 \begin_inset Note Note
12785 \begin_layout Plain Layout
12786 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12795 \begin_layout Standard
12803 \begin_layout Standard
12804 \begin_inset VSpace medskip
12807 To color boxes, the command
12814 \begin_inset Index idx
12817 \begin_layout Plain Layout
12825 is used in the following scheme:
12828 \begin_layout Standard
12833 colorbox{color}{box content}
12836 \begin_layout Standard
12837 The box content can also be a box and a
12843 can also be part of another box (see the 2nd and 3rd example).
12844 When the box should contain a formula, an extra formula has to be created,
12845 the same way as for
12855 \begin_layout Plain Layout
12856 This also applies for the command
12870 \begin_layout Standard
12871 One of the following predefined colors can be chosen:
12874 \begin_layout Standard
12908 \begin_layout Standard
12910 \begin_inset Tabular
12911 <lyxtabular version="3" rows="4" columns="2">
12912 <features rotate="0" tabularvalignment="middle">
12913 <column alignment="center" valignment="top">
12914 <column alignment="center" valignment="top">
12916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12919 \begin_layout Plain Layout
12925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12928 \begin_layout Plain Layout
12930 \begin_inset Note Note
12933 \begin_layout Plain Layout
12940 is only used as spacer.
12952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12955 \begin_layout Plain Layout
12959 \begin_inset Formula $\to$
12969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12972 \begin_layout Plain Layout
12973 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12986 \begin_layout Plain Layout
12990 \begin_inset Formula $\to$
12998 \begin_inset space \textvisiblespace{}
13006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13009 \begin_layout Plain Layout
13010 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13023 \begin_layout Plain Layout
13027 \begin_inset space \textvisiblespace{}
13033 \begin_inset Formula $\to$
13049 \begin_inset space \textvisiblespace{}
13057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13060 \begin_layout Plain Layout
13061 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13077 \begin_layout Standard
13084 only colors the box but not the characters in the box.
13085 To color all characters, the whole formula is highlighted and the desired
13086 color is chosen in the
13089 \begin_inset space ~
13095 The dialog can be called with the toolbar button
13096 \begin_inset Graphics
13097 filename ../images/dialog-show_character.png
13104 Edit\SpecialChar \menuseparator
13106 \begin_inset space ~
13109 Style\SpecialChar \menuseparator
13113 The formula number then has the same color as the formula.
13114 When the formula number should get another color than the formula characters,
13115 the color must be changed within the formula.
13118 \begin_layout Standard
13122 \begin_layout Standard
13125 \begin_inset Formula
13127 \int A=B\label{eq:red}
13135 \begin_inset Formula
13137 \textcolor{red}{\int A=B}\label{eq:redgreen}
13145 \begin_layout Standard
13147 \begin_inset CommandInset ref
13153 is completely colored red.
13154 \begin_inset Newline newline
13158 \begin_inset CommandInset ref
13160 reference "eq:redgreen"
13164 was first completely colored green to set the color for the formula number.
13165 Subsequently the formula characters were colored red.
13168 \begin_layout Standard
13169 \begin_inset VSpace bigskip
13172 To color the frame different than the rest of the box, the command
13179 \begin_inset Index idx
13182 \begin_layout Plain Layout
13190 is used in the following scheme:
13193 \begin_layout Standard
13198 fcolorbox{frame color}{color}{box content}
13201 \begin_layout Standard
13208 is an extension of the command
13215 The frame width is set, like for
13238 \begin_layout Plain Layout
13250 \begin_inset Formula
13252 \fcolorbox{cyan}{magenta}{A=B}
13261 \begin_layout Plain Layout
13275 \begin_layout Standard
13276 This formula was created with the command
13277 \begin_inset Newline newline
13285 \begin_inset Formula $\to$
13291 \begin_inset Formula $\to$
13301 \begin_layout Standard
13302 \begin_inset VSpace bigskip
13305 To use other colors than the predefined ones, they have to be defined first.
13308 \begin_layout Standard
13309 One can for example define the color
13310 \begin_inset Quotes eld
13318 \begin_inset Quotes erd
13321 with the LaTeX-preamble line:
13324 \begin_layout Standard
13329 definecolor{darkgreen}{cmyk}{0.5,
13344 \begin_inset Index idx
13347 \begin_layout Plain Layout
13358 \begin_layout Standard
13363 is the color space that denotes the colors
13380 The four comma separated numbers are the portion factor for the corresponding
13381 colors of the color space.
13382 The factors can be in the range of 0
13383 \begin_inset space \thinspace{}
13387 \begin_inset space \thinspace{}
13395 also the color space
13399 can be used for definitions.
13416 , so that there are in this case three portion factors for the corresponding
13418 Furthermore there is the color space
13422 with one portion factor for the gray value.
13425 \begin_layout Standard
13426 As example a framed box with the new defined color
13430 where the characters have been colored
13435 \begin_inset Formula
13437 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13445 \begin_layout Standard
13446 Self-defined colors can also be used for text with the help of the command
13454 \begin_inset Index idx
13457 \begin_layout Plain Layout
13466 \begin_layout Standard
13470 \begin_layout Plain Layout
13474 textcolor{darkgreen}{
13480 \begin_inset Quotes eld
13484 \begin_inset Quotes erd
13491 \begin_layout Plain Layout
13501 \begin_layout Standard
13509 \begin_inset Index idx
13512 \begin_layout Plain Layout
13520 is used in the scheme
13524 textcolor{color}{characters to color}
13529 \begin_layout Subsection
13531 \begin_inset CommandInset label
13533 name "sub:Paragraph-Boxes"
13538 \begin_inset Index idx
13541 \begin_layout Plain Layout
13542 Boxes ! as paragraph
13550 \begin_layout Standard
13551 A box that can contain several lines and paragraphs, a so-called paragraph
13552 box (parbox), can be created with the menu
13554 Insert\SpecialChar \menuseparator
13557 or the toolbar button
13558 \begin_inset Graphics
13559 filename ../images/box-insert.png
13567 \begin_layout Standard
13568 The following example shows a framed parbox in a line:
13571 \begin_layout Standard
13572 \begin_inset VSpace medskip
13576 \begin_inset Box Boxed
13586 height_special "totalheight"
13589 \begin_layout Plain Layout
13590 This is a paragraph box.
13592 \begin_inset space \thinspace{}
13595 cm long and can also contain formulas:
13596 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13607 \begin_layout Standard
13608 \begin_inset VSpace medskip
13614 \begin_layout Standard
13615 Such a box is created by right-clicking on the gray box inset.
13616 A dialog pops up showing the box properties.
13630 \begin_inset space \thinspace{}
13635 Vertical Box Alignment
13640 \begin_layout Standard
13641 \begin_inset VSpace medskip
13644 In LaTeX a parbox is created with the command
13651 \begin_inset Index idx
13654 \begin_layout Plain Layout
13662 which has the following scheme:
13665 \begin_layout Standard
13670 parbox[position]{width}{box content}
13673 \begin_layout Standard
13688 \begin_inset Quotes eld
13692 \begin_inset Quotes erd
13695 means that the box is aligned within the surrounding text with its last
13702 \begin_inset Quotes eld
13706 \begin_inset Quotes erd
13709 this is done with the first line.
13710 When no position is given, the box will be vertically centered, see section
13718 \begin_inset space ~
13723 manual for examples.
13726 \begin_layout Standard
13727 \begin_inset VSpace bigskip
13730 To frame formulas completely, including the formula number, the formula
13731 must be set into a parbox.
13732 To do this, the command
13746 is inserted in TeX-mode before the formula.
13754 \begin_inset Index idx
13757 \begin_layout Plain Layout
13765 is hereby the line width set for the document.
13766 Because the frame is outside the parbox, 2
13767 \begin_inset space \thinspace{}
13770 times the frame separation and the frame thickness must be subtracted from
13772 As this is not automatically done by LyX due to a bug
13776 \begin_layout Plain Layout
13777 \begin_inset CommandInset href
13779 name "LyX-bug #4483"
13780 target "http://www.lyx.org/trac/ticket/4483"
13789 , TeX-mode has to be used.
13790 To be able to multiply and subtract in arguments, the LaTeX-package
13798 \begin_layout Plain Layout
13803 is part of every LaTeX standard installation.
13809 \begin_inset Index idx
13812 \begin_layout Plain Layout
13818 must be loaded in the LaTeX-preamble with the line
13821 \begin_layout Standard
13829 \begin_layout Standard
13830 Behind the formula both boxes are closed by entering
13835 Here is an example:
13839 \begin_layout Plain Layout
13853 \begin_layout Standard
13857 \begin_layout Plain Layout
13875 \begin_inset Formula
13877 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13886 \begin_layout Plain Layout
13897 \begin_layout Plain Layout
13911 \begin_layout Standard
13912 \begin_inset VSpace medskip
13915 As a parbox is used as the argument of
13921 , there is in this case no difference between
13936 \begin_layout Standard
13937 \begin_inset VSpace bigskip
13940 Paragraph boxes are very useful to comment formulas directly.
13947 is used in combination with the command
13961 \begin_inset CommandInset ref
13963 reference "sub:User-defined-Numbering"
13970 \begin_layout Standard
13971 An example of a formula commented with
13980 \begin_layout Standard
13984 \begin_layout Plain Layout
13997 This is a description.
13998 It is distinctly separated from the formula and multiline.
14002 \begin_layout Plain Layout
14014 \begin_layout Standard
14015 Such a formula must be inserted completely in TeX-mode because LyX does
14016 not yet support the command
14023 The formula is created with the following command sequence:
14026 \begin_layout Standard
14039 is inserted in TeX-mode.
14043 \begin_layout Plain Layout
14044 When the formula style
14056 can also be replaced by
14063 (formula styles see
14064 \begin_inset CommandInset ref
14066 reference "sec:Formula-Styles"
14075 Then the description follows as normal text and finally
14081 is inserted in TeX-mode.
14094 hereby create a displayed formula.
14097 \begin_layout Standard
14104 can be seen in this example that was
14105 \begin_inset Quotes eld
14109 \begin_inset Quotes erd
14112 using the mathematical textmode:
14113 \begin_inset Formula
14115 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14123 \begin_layout Section
14125 \begin_inset Index idx
14128 \begin_layout Plain Layout
14137 \begin_layout Subsection
14139 \begin_inset CommandInset label
14141 name "sub:Big-Operators"
14146 \begin_inset Index idx
14149 \begin_layout Plain Layout
14156 \begin_inset Index idx
14159 \begin_layout Plain Layout
14166 \begin_inset Index idx
14169 \begin_layout Plain Layout
14178 \begin_layout Standard
14179 To be able to use all integral operators listed here, the option
14181 Use esint package automatically
14183 must be set in the document settings under
14186 \begin_inset space ~
14194 \begin_layout Standard
14195 \begin_inset space \hfill{}
14199 \begin_inset Tabular
14200 <lyxtabular version="3" rows="11" columns="2">
14201 <features rotate="0" tabularvalignment="middle">
14202 <column alignment="center" valignment="top" width="0pt">
14203 <column alignment="center" valignment="top" width="0pt">
14205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14208 \begin_layout Plain Layout
14214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14217 \begin_layout Plain Layout
14225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14228 \begin_layout Plain Layout
14232 \begin_inset Index idx
14235 \begin_layout Plain Layout
14248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14251 \begin_layout Plain Layout
14252 \begin_inset Formula $\int$
14262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14265 \begin_layout Plain Layout
14273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14276 \begin_layout Plain Layout
14277 \begin_inset Formula $\oint$
14287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14290 \begin_layout Plain Layout
14298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14301 \begin_layout Plain Layout
14302 \begin_inset Formula $\ointctrclockwise$
14312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14315 \begin_layout Plain Layout
14323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14326 \begin_layout Plain Layout
14327 \begin_inset Formula $\ointclockwise$
14337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14340 \begin_layout Plain Layout
14348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14351 \begin_layout Plain Layout
14352 \begin_inset Formula $\sqint$
14362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14365 \begin_layout Plain Layout
14373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14376 \begin_layout Plain Layout
14378 \begin_inset Formula $\fint$
14388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14391 \begin_layout Plain Layout
14399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14402 \begin_layout Plain Layout
14404 \begin_inset Formula $\landupint$
14414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14417 \begin_layout Plain Layout
14425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14428 \begin_layout Plain Layout
14430 \begin_inset Formula $\landdownint$
14440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14443 \begin_layout Plain Layout
14451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14454 \begin_layout Plain Layout
14455 \begin_inset Formula $\bigcap$
14465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14468 \begin_layout Plain Layout
14476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14479 \begin_layout Plain Layout
14480 \begin_inset Formula $\bigcup$
14494 \begin_inset space \hfill{}
14498 \begin_inset Tabular
14499 <lyxtabular version="3" rows="11" columns="2">
14500 <features rotate="0" tabularvalignment="middle">
14501 <column alignment="center" valignment="top" width="0pt">
14502 <column alignment="center" valignment="top" width="0pt">
14504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14507 \begin_layout Plain Layout
14513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14516 \begin_layout Plain Layout
14524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14527 \begin_layout Plain Layout
14531 \begin_inset Index idx
14534 \begin_layout Plain Layout
14547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14550 \begin_layout Plain Layout
14551 \begin_inset Formula $\sum$
14561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14564 \begin_layout Plain Layout
14568 \begin_inset Index idx
14571 \begin_layout Plain Layout
14578 \begin_layout Plain Layout
14597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14600 \begin_layout Plain Layout
14601 \begin_inset Formula $\prod$
14611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14614 \begin_layout Plain Layout
14622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14625 \begin_layout Plain Layout
14626 \begin_inset Formula $\coprod$
14636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14639 \begin_layout Plain Layout
14647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14650 \begin_layout Plain Layout
14651 \begin_inset Formula $\bigodot$
14661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14664 \begin_layout Plain Layout
14672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14675 \begin_layout Plain Layout
14676 \begin_inset Formula $\bigotimes$
14686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14689 \begin_layout Plain Layout
14697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14700 \begin_layout Plain Layout
14701 \begin_inset Formula $\bigoplus$
14711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14714 \begin_layout Plain Layout
14722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14725 \begin_layout Plain Layout
14726 \begin_inset Formula $\bigwedge$
14736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14739 \begin_layout Plain Layout
14747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14750 \begin_layout Plain Layout
14751 \begin_inset Formula $\bigvee$
14761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14764 \begin_layout Plain Layout
14772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14775 \begin_layout Plain Layout
14776 \begin_inset Formula $\bigsqcup$
14786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14789 \begin_layout Plain Layout
14797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14800 \begin_layout Plain Layout
14801 \begin_inset Formula $\biguplus$
14815 \begin_inset space \hfill{}
14821 \begin_layout Standard
14822 All big operators can also be inserted via the math toolbar button
14823 \begin_inset Graphics
14824 filename ../images/math/intop.png
14832 \begin_layout Standard
14833 The operators are called big because they are bigger than the sometimes
14834 equal looking binary operators.
14835 All big operators can have limits as described in the next subsection.
14838 \begin_layout Standard
14839 For all integral operators there is a second version available, ending in
14857 These operators are different from
14864 \begin_inset space \space{}
14867 in the style the operator limits are displayed, see
14868 \begin_inset CommandInset ref
14870 reference "sub:Operator-Limits"
14878 \begin_layout Subsubsection*
14879 Advice for Integrals
14882 \begin_layout Standard
14887 in an integral is an operator, that therefore has to be set upright.
14888 This is done by highlighting the
14892 and using the keyboard shortcut
14902 \begin_layout Plain Layout
14908 \begin_inset CommandInset ref
14910 reference "sub:Font-Styles"
14920 Finally the smallest space is inserted before the
14924 , as this is usual for operators.
14928 \begin_layout Standard
14930 \begin_inset Formula $\int A(x)dx$
14934 \begin_inset Newline newline
14938 \begin_inset Phantom HPhantom
14941 \begin_layout Plain Layout
14948 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14954 \begin_layout Standard
14955 For multiple integrals there are the following commands:
14956 \begin_inset VSpace medskip
14962 \begin_layout Standard
14963 \begin_inset space \hfill{}
14967 \begin_inset Tabular
14968 <lyxtabular version="3" rows="4" columns="2">
14969 <features rotate="0" tabularvalignment="middle">
14970 <column alignment="center" valignment="top">
14971 <column alignment="center" valignment="top">
14973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14985 \begin_layout Plain Layout
14987 \begin_inset Note Note
14990 \begin_layout Plain Layout
14997 is only used as spacer.
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15012 \begin_layout Plain Layout
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15023 \begin_layout Plain Layout
15024 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15037 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15049 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15074 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15088 \begin_inset space \hfill{}
15092 \begin_inset Tabular
15093 <lyxtabular version="3" rows="4" columns="2">
15094 <features rotate="0" tabularvalignment="middle">
15095 <column alignment="center" valignment="top">
15096 <column alignment="center" valignment="top">
15098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15101 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15132 \begin_layout Plain Layout
15133 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15157 \begin_layout Plain Layout
15158 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15171 \begin_layout Plain Layout
15179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15182 \begin_layout Plain Layout
15183 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15197 \begin_inset space \hfill{}
15203 \begin_layout Standard
15204 \begin_inset Newpage newpage
15210 \begin_layout Subsection
15212 \begin_inset CommandInset label
15214 name "sub:Operator-Limits"
15219 \begin_inset Index idx
15222 \begin_layout Plain Layout
15231 \begin_layout Standard
15232 Limits are created by super- and subscripts:
15235 \begin_layout Standard
15237 \begin_inset Tabular
15238 <lyxtabular version="3" rows="2" columns="2">
15239 <features rotate="0" tabularvalignment="middle">
15240 <column alignment="center" valignment="top" width="0pt">
15241 <column alignment="center" valignment="top" width="0pt">
15243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15246 \begin_layout Plain Layout
15252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15255 \begin_layout Plain Layout
15257 \begin_inset Note Note
15260 \begin_layout Plain Layout
15267 is only used as spacer.
15279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15282 \begin_layout Plain Layout
15288 \begin_inset space \textvisiblespace{}
15292 \begin_inset Formula $\to$
15296 \begin_inset Formula $\to$
15304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15307 \begin_layout Plain Layout
15308 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15324 \begin_layout Standard
15325 Limits of inline formulas are set right beside the operator.
15326 Limits in displayed formulas are set above or below the operator, except
15327 for integral limits.
15330 \begin_layout Standard
15331 To force that the limits are set beside the operator, the cursor is set
15332 directly behind the operator and the limits type is changed with the menu
15335 Edit\SpecialChar \menuseparator
15336 Math\SpecialChar \menuseparator
15355 \begin_layout Standard
15356 The default limits type is this:
15357 \begin_inset Formula
15359 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15364 This is how it looks when the limits type was changed to
15371 \begin_inset Formula
15373 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15378 For integrals, except those ending with
15394 etc., the limits are by default set beside the operator.
15395 But for multiple integrals the limits are often set below the operator.
15396 In the following example the limits type was therefore set to
15400 and so set below the integrals:
15401 \begin_inset Formula
15403 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15411 \begin_layout Standard
15412 \begin_inset VSpace medskip
15415 To specify conditions for limits, the commands
15422 \begin_inset Index idx
15425 \begin_layout Plain Layout
15440 \begin_inset Index idx
15443 \begin_layout Plain Layout
15452 To create for example this expression
15453 \begin_inset Formula
15455 \sum_{\begin{subarray}{c}
15459 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15467 \begin_layout Standard
15468 the following has to be done:
15469 \begin_inset Newline newline
15481 \begin_inset space \textvisiblespace{}
15487 One is now in a blue box under the summation operator and insert there
15493 \begin_inset space \textvisiblespace{}
15499 The blue box is now within a purple box and now several lines can be written
15501 A new line is created by inserting a line break (
15504 arg "newline-insert newline"
15509 \begin_inset Newline newline
15514 0<k<1000 Ctrl+Return
15515 \begin_inset Newline newline
15520 is typed in, a new box appears below for the new line.
15523 \begin_layout Standard
15524 The alignment of the lines can be changed to left aligned with the
15534 Edit\SpecialChar \menuseparator
15538 To get right alignment,
15543 \begin_inset space \textvisiblespace{}
15548 is inserted at the beginning of the line.
15551 \begin_layout Standard
15564 with the difference that the lines are always centered.
15567 \begin_layout Standard
15568 \begin_inset VSpace bigskip
15572 \begin_inset CommandInset ref
15574 reference "eq:substack"
15578 there can be too much space beside an operator, because the characters
15579 following the operator are set beside the limits.
15580 To avoid this the command
15587 \begin_inset Index idx
15590 \begin_layout Plain Layout
15599 It sets the width of its content to 0
15600 \begin_inset space \thinspace{}
15604 \begin_inset Newline newline
15608 \begin_inset CommandInset ref
15610 reference "eq:substack"
15614 , one uses the command
15617 \begin_layout Standard
15627 \begin_inset space \textvisiblespace{}
15630 0<k<1000 Ctrl+Return
15633 \begin_layout Standard
15634 to create the lower limit.
15635 The summand is now directly behind the summation operator:
15636 \begin_inset Formula
15638 \sum_{\mathclap{\substack{0<k<1000\\
15650 \begin_layout Standard
15651 \begin_inset VSpace bigskip
15654 How to use one limit for several operators is described in
15655 \begin_inset CommandInset ref
15657 reference "sub:Self-defined-Operators"
15664 \begin_layout Subsection
15665 Decoration for Operators
15666 \begin_inset Index idx
15669 \begin_layout Plain Layout
15670 Operators ! Decoration
15678 \begin_layout Standard
15686 \begin_inset Index idx
15689 \begin_layout Plain Layout
15704 \begin_inset Index idx
15707 \begin_layout Plain Layout
15715 characters can be placed above or below an operator, respectively.
15723 \begin_inset Index idx
15726 \begin_layout Plain Layout
15734 characters can be set before and behind a big operator.
15737 \begin_layout Standard
15739 \begin_inset space ~
15751 \begin_layout Itemize
15758 is used to set characters at the corners of the operator
15761 \begin_layout Itemize
15768 is used to set characters before and/or behind the operator (this variant
15769 represents LaTeX's original
15778 \begin_layout Itemize
15785 is used to set characters at the left corners and/or behind the operator
15788 \begin_layout Itemize
15795 is used to set characters at the right corners and/or before the operator
15798 \begin_layout Standard
15799 For example the command
15804 \begin_inset space \textvisiblespace{}
15810 \begin_inset space \textvisiblespace{}
15814 \begin_inset Formula $\to$
15818 \begin_inset Formula $\to$
15822 \begin_inset space \textvisiblespace{}
15832 \begin_inset Formula
15834 \sideset{}{'}\sum_{k=1}^{n}
15842 \begin_layout Standard
15843 \begin_inset Note Greyedout
15846 \begin_layout Plain Layout
15853 can only be used to decorate big operators, binary operators are not allowed.
15861 \begin_layout Standard
15874 can also be used to decorate symbols and characters.
15875 For example, the command
15880 \begin_inset space \textvisiblespace{}
15886 \begin_inset space \textvisiblespace{}
15892 \begin_inset Formula $\uparrow$
15900 \begin_inset Formula
15902 \overset{a}{\maltese}
15910 \begin_layout Subsection
15912 \begin_inset CommandInset label
15914 name "sub:Binary-Operators"
15919 \begin_inset Index idx
15922 \begin_layout Plain Layout
15931 \begin_layout Standard
15932 Binary operators are surrounded by space when there is a character before
15934 \begin_inset VSpace medskip
15940 \begin_layout Standard
15941 \begin_inset space \hfill{}
15945 \begin_inset Tabular
15946 <lyxtabular version="3" rows="13" columns="2">
15947 <features rotate="0" tabularvalignment="middle">
15948 <column alignment="center" valignment="top" width="0pt">
15949 <column alignment="center" valignment="top" width="0pt">
15951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15954 \begin_layout Plain Layout
15956 \begin_inset Note Note
15959 \begin_layout Plain Layout
15966 is only used as spacer.
15976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15979 \begin_layout Plain Layout
15987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15990 \begin_layout Plain Layout
15996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15999 \begin_layout Plain Layout
16000 \begin_inset Formula $+$
16010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16013 \begin_layout Plain Layout
16019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16022 \begin_layout Plain Layout
16023 \begin_inset Formula $-$
16033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16036 \begin_layout Plain Layout
16044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16047 \begin_layout Plain Layout
16048 \begin_inset Formula $\pm$
16058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16061 \begin_layout Plain Layout
16069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16072 \begin_layout Plain Layout
16073 \begin_inset Formula $\mp$
16083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16086 \begin_layout Plain Layout
16094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16097 \begin_layout Plain Layout
16098 \begin_inset Formula $\cdot$
16108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16111 \begin_layout Plain Layout
16119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16122 \begin_layout Plain Layout
16123 \begin_inset Formula $\times$
16133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16136 \begin_layout Plain Layout
16144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16147 \begin_layout Plain Layout
16148 \begin_inset Formula $\div$
16158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16161 \begin_layout Plain Layout
16165 \begin_layout Plain Layout
16178 \begin_layout Plain Layout
16190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16193 \begin_layout Plain Layout
16194 \begin_inset Formula $*$
16204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16207 \begin_layout Plain Layout
16215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16218 \begin_layout Plain Layout
16219 \begin_inset Formula $\star$
16229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16232 \begin_layout Plain Layout
16240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16243 \begin_layout Plain Layout
16244 \begin_inset Formula $\circ$
16254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16257 \begin_layout Plain Layout
16265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16268 \begin_layout Plain Layout
16269 \begin_inset Formula $\diamond$
16279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16282 \begin_layout Plain Layout
16290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16293 \begin_layout Plain Layout
16294 \begin_inset Formula $\bullet$
16308 \begin_inset space \hfill{}
16312 \begin_inset Tabular
16313 <lyxtabular version="3" rows="13" columns="2">
16314 <features rotate="0" tabularvalignment="middle">
16315 <column alignment="center" valignment="top" width="0pt">
16316 <column alignment="center" valignment="top" width="0pt">
16318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16321 \begin_layout Plain Layout
16327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16330 \begin_layout Plain Layout
16338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16341 \begin_layout Plain Layout
16349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16352 \begin_layout Plain Layout
16353 \begin_inset Formula $\nabla$
16363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16366 \begin_layout Plain Layout
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16377 \begin_layout Plain Layout
16378 \begin_inset Formula $\bigtriangledown$
16388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16391 \begin_layout Plain Layout
16399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16402 \begin_layout Plain Layout
16403 \begin_inset Formula $\bigtriangleup$
16413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16416 \begin_layout Plain Layout
16424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16427 \begin_layout Plain Layout
16428 \begin_inset Formula $\Box$
16438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16441 \begin_layout Plain Layout
16449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16452 \begin_layout Plain Layout
16453 \begin_inset Formula $\cap$
16463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16466 \begin_layout Plain Layout
16474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16477 \begin_layout Plain Layout
16478 \begin_inset Formula $\cup$
16488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16491 \begin_layout Plain Layout
16499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16502 \begin_layout Plain Layout
16503 \begin_inset Formula $\dagger$
16513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16516 \begin_layout Plain Layout
16524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16527 \begin_layout Plain Layout
16528 \begin_inset Formula $\ddagger$
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16541 \begin_layout Plain Layout
16549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16552 \begin_layout Plain Layout
16553 \begin_inset Formula $\wr$
16563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16566 \begin_layout Plain Layout
16574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16577 \begin_layout Plain Layout
16578 \begin_inset Formula $\bigcirc$
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16591 \begin_layout Plain Layout
16599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16602 \begin_layout Plain Layout
16603 \begin_inset Formula $\wedge$
16613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16616 \begin_layout Plain Layout
16624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16627 \begin_layout Plain Layout
16628 \begin_inset Formula $\vee$
16642 \begin_inset space \hfill{}
16646 \begin_inset Tabular
16647 <lyxtabular version="3" rows="13" columns="2">
16648 <features rotate="0" tabularvalignment="middle">
16649 <column alignment="center" valignment="top" width="0pt">
16650 <column alignment="center" valignment="top" width="0pt">
16652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16655 \begin_layout Plain Layout
16661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16664 \begin_layout Plain Layout
16672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16675 \begin_layout Plain Layout
16683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16686 \begin_layout Plain Layout
16687 \begin_inset Formula $\oplus$
16697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16700 \begin_layout Plain Layout
16708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16711 \begin_layout Plain Layout
16712 \begin_inset Formula $\ominus$
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16725 \begin_layout Plain Layout
16733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16736 \begin_layout Plain Layout
16737 \begin_inset Formula $\otimes$
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16750 \begin_layout Plain Layout
16758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16761 \begin_layout Plain Layout
16762 \begin_inset Formula $\oslash$
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16775 \begin_layout Plain Layout
16783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16787 \begin_inset Formula $\odot$
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16800 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $\amalg$
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\uplus$
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\setminus$
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16886 \begin_layout Plain Layout
16887 \begin_inset Formula $\sqcap$
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16900 \begin_layout Plain Layout
16908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16911 \begin_layout Plain Layout
16912 \begin_inset Formula $\sqcup$
16922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16925 \begin_layout Plain Layout
16933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16936 \begin_layout Plain Layout
16937 \begin_inset Formula $\triangleleft$
16947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16950 \begin_layout Plain Layout
16958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16961 \begin_layout Plain Layout
16962 \begin_inset Formula $\triangleright$
16976 \begin_inset space \hfill{}
16982 \begin_layout Standard
16983 All binary operators can also be inserted via the math toolbar button
16984 \begin_inset Graphics
16985 filename ../images/math/pm.png
16993 \begin_layout Standard
16994 To typeset the Laplace operator also
17011 \begin_inset Formula $\nabla^{2}$
17014 ) can be used instead of
17023 \begin_layout Standard
17030 Insert\SpecialChar \menuseparator
17042 \begin_layout Subsection
17043 Self-defined Operators
17044 \begin_inset CommandInset label
17046 name "sub:Self-defined-Operators"
17051 \begin_inset Index idx
17054 \begin_layout Plain Layout
17055 Operators ! self-defined
17063 \begin_layout Standard
17064 With the help of the command
17068 DeclareMathOperator
17071 \begin_inset Index idx
17074 \begin_layout Plain Layout
17079 DeclareMathOperator
17084 custom operators can be defined in the LaTeX-preamble.
17085 Its command scheme is:
17088 \begin_layout Standard
17093 DeclareMathOperator{new command}{display}
17096 \begin_layout Standard
17097 Display can be characters or symbols that define how the operator looks
17099 To define a big operator a * is set behind the command.
17100 All self-defined big operators can have limits as described in
17101 \begin_inset CommandInset ref
17103 reference "sub:Operator-Limits"
17110 \begin_layout Standard
17111 For example the LaTeX-preamble line
17114 \begin_layout Standard
17119 DeclareMathOperator*{
17126 \begin_layout Standard
17127 defines the command
17133 , that inserts a big operator consisting of the lozenge symbol from
17134 \begin_inset CommandInset ref
17136 reference "sub:Miscellaneous-Symbols"
17141 \begin_inset Formula
17143 \Lozenge_{n=1}^{\infty}
17148 The command for this formula is:
17159 \begin_inset Formula $\to$
17165 \begin_layout Standard
17166 \begin_inset VSpace bigskip
17169 When self-defined operators are not used several times in the document,
17170 they can also be defined with the commands
17177 \begin_inset Index idx
17180 \begin_layout Plain Layout
17195 \begin_inset Index idx
17198 \begin_layout Plain Layout
17206 , which have the following scheme:
17209 \begin_layout Standard
17223 \begin_layout Standard
17230 defines big operators,
17239 \begin_layout Standard
17247 \begin_inset space \thinspace{}
17251 \begin_inset space \space{}
17254 be used to use one limit for several operators:
17257 \begin_layout Standard
17258 \begin_inset Formula
17260 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17268 \begin_layout Standard
17269 The command for the formula above is:
17270 \begin_inset Newline newline
17286 \begin_inset space \textvisiblespace{}
17292 \begin_inset Formula $\to$
17298 \begin_inset space \textvisiblespace{}
17306 \begin_layout Section
17308 \begin_inset Index idx
17311 \begin_layout Plain Layout
17320 \begin_layout Subsection
17322 \begin_inset CommandInset label
17324 name "sub:Font-Styles"
17329 \begin_inset Index idx
17332 \begin_layout Plain Layout
17341 \begin_layout Standard
17342 Latin letters in formulas can be set in one of the following font styles:
17343 \begin_inset VSpace -2mm
17349 \begin_layout Standard
17351 \begin_inset Tabular
17352 <lyxtabular version="3" rows="7" columns="3">
17353 <features rotate="0" tabularvalignment="middle">
17354 <column alignment="center" valignment="top">
17355 <column alignment="center" valignment="top">
17356 <column alignment="center" valignment="top">
17358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17361 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17379 \begin_layout Plain Layout
17387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17390 \begin_layout Plain Layout
17396 \begin_inset space \textvisiblespace{}
17406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17410 \begin_inset Formula $\mathbb{ABC}$
17418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17421 \begin_layout Plain Layout
17434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17437 \begin_layout Plain Layout
17443 \begin_inset space \textvisiblespace{}
17453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17457 \begin_inset Formula $\mathbf{AbC}$
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17468 \begin_layout Plain Layout
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17490 \begin_inset space \textvisiblespace{}
17500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17503 \begin_layout Plain Layout
17504 \begin_inset Formula $\boldsymbol{AbC}$
17512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17515 \begin_layout Plain Layout
17518 arg "font-boldsymbol"
17528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17531 \begin_layout Plain Layout
17537 \begin_inset space \textvisiblespace{}
17547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $\mathcal{ABC}$
17559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17562 \begin_layout Plain Layout
17575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17578 \begin_layout Plain Layout
17584 \begin_inset space \textvisiblespace{}
17594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17597 \begin_layout Plain Layout
17598 \begin_inset Formula $\mathfrak{AbC}$
17606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17609 \begin_layout Plain Layout
17617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17626 \begin_inset space \textvisiblespace{}
17636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17640 \begin_inset Formula $\mathscr{AbC}$
17648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17665 \begin_layout Standard
17667 \begin_inset Tabular
17668 <lyxtabular version="3" rows="5" columns="3">
17669 <features rotate="0" tabularvalignment="middle">
17670 <column alignment="center" valignment="top">
17671 <column alignment="center" valignment="top">
17672 <column alignment="center" valignment="top">
17674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17677 \begin_layout Plain Layout
17683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17686 \begin_layout Plain Layout
17692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17695 \begin_layout Plain Layout
17703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17706 \begin_layout Plain Layout
17712 \begin_inset space \textvisiblespace{}
17722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17725 \begin_layout Plain Layout
17726 \begin_inset Formula $\mathit{AbC}$
17734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17737 \begin_layout Plain Layout
17745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17748 \begin_layout Plain Layout
17754 \begin_inset space \textvisiblespace{}
17764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17767 \begin_layout Plain Layout
17768 \begin_inset Formula $\mathrm{AbC}$
17776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17779 \begin_layout Plain Layout
17792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17795 \begin_layout Plain Layout
17801 \begin_inset space \textvisiblespace{}
17811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17814 \begin_layout Plain Layout
17815 \begin_inset Formula $\mathsf{AbC}$
17823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17826 \begin_layout Plain Layout
17839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17842 \begin_layout Plain Layout
17848 \begin_inset space \textvisiblespace{}
17858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17861 \begin_layout Plain Layout
17862 \begin_inset Formula $\mathtt{AbC}$
17870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17873 \begin_layout Plain Layout
17876 arg "font-typewriter"
17892 \begin_layout Standard
17893 \begin_inset Note Greyedout
17896 \begin_layout Plain Layout
17913 can only be used for big letters.
17921 \begin_layout Standard
17922 Predefined is the style
17931 \begin_layout Standard
17932 The style commands work also for letters in mathematical constructs:
17933 \begin_inset Formula
17935 \mathfrak{A=\frac{b}{C}}
17943 \begin_layout Standard
17944 Characters in mathematical text don't appear in a math font style but in
17945 the text font style
17952 That their style can't be set correctly via the text style dialog is a
17957 \begin_layout Plain Layout
17958 \begin_inset CommandInset href
17960 name "LyX-bug #4629"
17961 target "http://www.lyx.org/trac/ticket/4629"
17973 \begin_layout Standard
17974 Instead of the style commands the dialog
17976 Edit\SpecialChar \menuseparator
17977 Math\SpecialChar \menuseparator
17980 or the toolbar button
17981 \begin_inset Graphics
17982 filename ../images/math/font.png
17990 \begin_layout Subsection
17992 \begin_inset CommandInset label
17994 name "sub:Bold-Formulas"
17999 \begin_inset Index idx
18002 \begin_layout Plain Layout
18011 \begin_layout Standard
18012 To make a complete formula bold, the command
18018 from the previous subsection cannot be used, because it doesn't work for
18019 small Greek letters.
18020 Furthermore it prints Latin letters always upright, like in the following
18024 \begin_layout Standard
18025 \begin_inset Formula
18027 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18035 \begin_layout Standard
18036 To display the formula correctly, the command
18043 \begin_inset Formula
18045 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18050 It is also possible to set the formula in a
18052 boldmath environment
18055 This environment is created by inserting the command
18062 \begin_inset Index idx
18065 \begin_layout Plain Layout
18074 To end the environment, the command
18081 \begin_inset Index idx
18084 \begin_layout Plain Layout
18092 is inserted in TeX-mode.
18096 \begin_layout Plain Layout
18106 \begin_inset Formula
18108 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18117 \begin_layout Plain Layout
18129 \begin_layout Subsection
18131 \begin_inset Index idx
18134 \begin_layout Plain Layout
18143 \begin_layout Standard
18144 Formulas can be colored like normal text: Highlight a formula or a formula
18150 Here is a formula in magenta:
18151 \begin_inset Formula
18153 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18161 \begin_layout Standard
18162 You can also define your own colors as described in
18163 \begin_inset CommandInset ref
18165 reference "sub:Colored-Boxes"
18170 They can be used with the TeX code command
18177 \begin_inset Index idx
18180 \begin_layout Plain Layout
18191 \begin_layout Standard
18196 textcolor{color}{characters or formula}
18199 \begin_layout Standard
18200 The following example was colored completely dark green and partly red:
18203 \begin_layout Standard
18207 \begin_layout Plain Layout
18211 textcolor{darkgreen}{
18217 \begin_inset Formula
18219 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18228 \begin_layout Plain Layout
18238 \begin_layout Standard
18239 Due to a bug in LyX only complete formulas can be colored with self-defined
18244 \begin_layout Plain Layout
18245 \begin_inset CommandInset href
18247 name "LyX-bug #5269"
18248 target "http://www.lyx.org/trac/ticket/5269"
18260 \begin_layout Subsection
18262 \begin_inset CommandInset label
18264 name "sub:Font-Sizes"
18269 \begin_inset Index idx
18272 \begin_layout Plain Layout
18281 \begin_layout Standard
18282 For characters in formulas there are, analog to characters in text, the
18283 following size commands:
18286 \begin_layout Standard
18330 \begin_inset Newline newline
18352 \begin_layout Standard
18353 The size produced by the commands depends on the document font size, which
18354 corresponds to the command
18361 The other commands produce smaller or larger sizes than
18368 The font size can however not exceed a certain value.
18369 Is for example the document font size 12
18370 \begin_inset space \thinspace{}
18379 switches to the same size as
18389 \begin_layout Standard
18390 A size command is inserted in TeX-mode before the formula and sets the size
18391 for all following formula and text characters.
18392 To switch back to the initial size, the command
18398 is inserted behind the formula in TeX-mode.
18401 \begin_layout Standard
18402 Within a formula the size can be changed using the following size commands:
18405 \begin_layout Standard
18408 \begin_inset Tabular
18409 <lyxtabular version="3" rows="5" columns="2">
18410 <features rotate="0" tabularvalignment="middle">
18411 <column alignment="center" valignment="top">
18412 <column alignment="center" valignment="top">
18414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18417 \begin_layout Plain Layout
18423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18426 \begin_layout Plain Layout
18428 \begin_inset Note Note
18431 \begin_layout Plain Layout
18438 is only used as spacer.
18450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18453 \begin_layout Plain Layout
18457 \begin_inset Index idx
18460 \begin_layout Plain Layout
18473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18476 \begin_layout Plain Layout
18477 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18490 \begin_layout Plain Layout
18498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18501 \begin_layout Plain Layout
18502 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18515 \begin_layout Plain Layout
18523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18526 \begin_layout Plain Layout
18527 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18540 \begin_layout Plain Layout
18548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18551 \begin_layout Plain Layout
18552 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18568 \begin_layout Standard
18569 After entering these commands, a blue box appears in which the formula parts
18573 \begin_layout Standard
18574 There is a further method to change the font size, that though only works
18575 for symbols or letters in mathematical text.
18576 To use it, one of the above text size commands is inserted in mathematical
18578 All following characters until the end of the mathematical text or until
18579 another size command will have the selected size.
18581 \begin_inset VSpace -2mm
18587 \begin_layout Standard
18591 \begin_layout Plain Layout
18601 \begin_inset Formula
18603 A=\frac{B}{c}\cdot\maltese
18609 \begin_inset Formula
18611 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18620 \begin_layout Plain Layout
18632 \begin_layout Standard
18633 \begin_inset VSpace medskip
18636 Before both formulas the command
18643 The command for the second formula is:
18644 \begin_inset Newline newline
18652 \begin_inset space \textvisiblespace{}
18658 \begin_inset space \textvisiblespace{}
18664 \begin_inset space \textvisiblespace{}
18670 \begin_inset space \textvisiblespace{}
18674 \begin_inset Formula $\to$
18678 \begin_inset Formula $\to$
18682 \begin_inset Newline newline
18686 \begin_inset space \hspace*{}
18697 \begin_inset space \textvisiblespace{}
18703 \begin_inset space \textvisiblespace{}
18709 \begin_inset space \textvisiblespace{}
18715 \begin_layout Standard
18716 If a symbol cannot be displayed in different sizes, it will always be displayed
18717 in the default size.
18720 \begin_layout Section
18722 \begin_inset Index idx
18725 \begin_layout Plain Layout
18734 \begin_layout Standard
18735 Greek letters can also be inserted via the toolbar button
18736 \begin_inset Graphics
18737 filename ../images/math/alpha.png
18743 All international typesetting norms purport that Greek letters in math
18744 have to be typeset italic/slanted.
18745 In some languages, like French or Russian, they are nevertheless sometimes
18749 \begin_layout Subsection
18751 \begin_inset Index idx
18754 \begin_layout Plain Layout
18755 Greek letters ! small
18763 \begin_layout Standard
18764 \begin_inset space \hfill{}
18768 \begin_inset Tabular
18769 <lyxtabular version="3" rows="11" columns="2">
18770 <features rotate="0" tabularvalignment="middle">
18771 <column alignment="center" valignment="top" width="0pt">
18772 <column alignment="center" valignment="top" width="0pt">
18774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18777 \begin_layout Plain Layout
18783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18786 \begin_layout Plain Layout
18794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18797 \begin_layout Plain Layout
18805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18808 \begin_layout Plain Layout
18809 \begin_inset Formula $\alpha$
18819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18822 \begin_layout Plain Layout
18830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18833 \begin_layout Plain Layout
18834 \begin_inset Formula $\beta$
18844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18847 \begin_layout Plain Layout
18855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18858 \begin_layout Plain Layout
18859 \begin_inset Formula $\gamma$
18869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18872 \begin_layout Plain Layout
18880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18883 \begin_layout Plain Layout
18884 \begin_inset Formula $\delta$
18894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18897 \begin_layout Plain Layout
18905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18908 \begin_layout Plain Layout
18909 \begin_inset Formula $\epsilon$
18919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18922 \begin_layout Plain Layout
18930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18933 \begin_layout Plain Layout
18934 \begin_inset Formula $\varepsilon$
18944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18947 \begin_layout Plain Layout
18955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18958 \begin_layout Plain Layout
18959 \begin_inset Formula $\zeta$
18969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18972 \begin_layout Plain Layout
18980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18983 \begin_layout Plain Layout
18984 \begin_inset Formula $\eta$
18994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18997 \begin_layout Plain Layout
19005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19008 \begin_layout Plain Layout
19009 \begin_inset Formula $\theta$
19019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19022 \begin_layout Plain Layout
19030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19033 \begin_layout Plain Layout
19034 \begin_inset Formula $\vartheta$
19048 \begin_inset space \hfill{}
19052 \begin_inset Tabular
19053 <lyxtabular version="3" rows="12" columns="2">
19054 <features rotate="0" tabularvalignment="middle">
19055 <column alignment="center" valignment="top" width="0pt">
19056 <column alignment="center" valignment="top" width="0pt">
19058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19061 \begin_layout Plain Layout
19067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19070 \begin_layout Plain Layout
19078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19081 \begin_layout Plain Layout
19089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19092 \begin_layout Plain Layout
19093 \begin_inset Formula $\iota$
19103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19106 \begin_layout Plain Layout
19114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19117 \begin_layout Plain Layout
19118 \begin_inset Formula $\kappa$
19128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19131 \begin_layout Plain Layout
19139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19142 \begin_layout Plain Layout
19143 \begin_inset Formula $\varkappa$
19153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19156 \begin_layout Plain Layout
19164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19167 \begin_layout Plain Layout
19168 \begin_inset Formula $\lambda$
19178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19181 \begin_layout Plain Layout
19189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19192 \begin_layout Plain Layout
19193 \begin_inset Formula $\mu$
19203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19206 \begin_layout Plain Layout
19214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19217 \begin_layout Plain Layout
19218 \begin_inset Formula $\nu$
19228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19231 \begin_layout Plain Layout
19239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19242 \begin_layout Plain Layout
19243 \begin_inset Formula $\xi$
19253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19256 \begin_layout Plain Layout
19262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19265 \begin_layout Plain Layout
19266 \begin_inset Formula $o$
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19279 \begin_layout Plain Layout
19287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19290 \begin_layout Plain Layout
19291 \begin_inset Formula $\pi$
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19304 \begin_layout Plain Layout
19312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19315 \begin_layout Plain Layout
19316 \begin_inset Formula $\varpi$
19326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19329 \begin_layout Plain Layout
19337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19340 \begin_layout Plain Layout
19341 \begin_inset Formula $\rho$
19355 \begin_inset space \hfill{}
19359 \begin_inset Tabular
19360 <lyxtabular version="3" rows="11" columns="2">
19361 <features rotate="0" tabularvalignment="middle">
19362 <column alignment="center" valignment="top" width="0pt">
19363 <column alignment="center" valignment="top" width="0pt">
19365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19377 \begin_layout Plain Layout
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19399 \begin_layout Plain Layout
19400 \begin_inset Formula $\varrho$
19410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19413 \begin_layout Plain Layout
19421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19424 \begin_layout Plain Layout
19425 \begin_inset Formula $\sigma$
19435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19438 \begin_layout Plain Layout
19446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19449 \begin_layout Plain Layout
19450 \begin_inset Formula $\varsigma$
19460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19463 \begin_layout Plain Layout
19471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19474 \begin_layout Plain Layout
19475 \begin_inset Formula $\tau$
19485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19488 \begin_layout Plain Layout
19496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19499 \begin_layout Plain Layout
19500 \begin_inset Formula $\upsilon$
19510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19513 \begin_layout Plain Layout
19521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19524 \begin_layout Plain Layout
19525 \begin_inset Formula $\phi$
19535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19538 \begin_layout Plain Layout
19546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19549 \begin_layout Plain Layout
19550 \begin_inset Formula $\varphi$
19560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19574 \begin_layout Plain Layout
19575 \begin_inset Formula $\chi$
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\psi$
19610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\omega$
19639 \begin_inset space \hfill{}
19645 \begin_layout Standard
19646 \begin_inset VSpace medskip
19652 \begin_layout Standard
19653 How to create special upright Greek letters is explained in
19654 \begin_inset CommandInset ref
19656 reference "sub:Upright-small-Greek"
19663 \begin_layout Subsection
19665 \begin_inset Index idx
19668 \begin_layout Plain Layout
19669 Greek letters ! big
19677 \begin_layout Standard
19678 \begin_inset space \hfill{}
19682 \begin_inset Tabular
19683 <lyxtabular version="3" rows="7" columns="2">
19684 <features rotate="0" tabularvalignment="middle">
19685 <column alignment="center" valignment="top" width="0pt">
19686 <column alignment="center" valignment="top" width="0pt">
19688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19691 \begin_layout Plain Layout
19697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19700 \begin_layout Plain Layout
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19711 \begin_layout Plain Layout
19719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19722 \begin_layout Plain Layout
19723 \begin_inset Formula $\Gamma$
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19736 \begin_layout Plain Layout
19744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19747 \begin_layout Plain Layout
19748 \begin_inset Formula $\Delta$
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19761 \begin_layout Plain Layout
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Plain Layout
19773 \begin_inset Formula $\Theta$
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19786 \begin_layout Plain Layout
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Plain Layout
19798 \begin_inset Formula $\Lambda$
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Plain Layout
19823 \begin_inset Formula $\Xi$
19833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19848 \begin_inset Formula $\Pi$
19862 \begin_inset space \hfill{}
19866 \begin_inset Tabular
19867 <lyxtabular version="3" rows="6" columns="2">
19868 <features rotate="0" tabularvalignment="middle">
19869 <column alignment="center" valignment="top" width="0pt">
19870 <column alignment="center" valignment="top" width="0pt">
19872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19875 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19895 \begin_layout Plain Layout
19903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19906 \begin_layout Plain Layout
19907 \begin_inset Formula $\Sigma$
19917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19920 \begin_layout Plain Layout
19928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19931 \begin_layout Plain Layout
19932 \begin_inset Formula $\Upsilon$
19942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19945 \begin_layout Plain Layout
19953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19956 \begin_layout Plain Layout
19957 \begin_inset Formula $\Phi$
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19970 \begin_layout Plain Layout
19978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19981 \begin_layout Plain Layout
19982 \begin_inset Formula $\Psi$
19992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19995 \begin_layout Plain Layout
20003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20006 \begin_layout Plain Layout
20007 \begin_inset Formula $\Omega$
20021 \begin_inset space \hfill{}
20027 \begin_layout Standard
20028 \begin_inset VSpace medskip
20031 That the big Greek letters appear upright is caused by a design bug when
20033 To get correct italic big letters, begin every command with
20038 For example the command
20045 \begin_inset Formula $\varGamma$
20049 Another way is to load the package
20057 \begin_layout Plain Layout
20062 is part of the LaTeX-package
20067 \begin_inset Index idx
20070 \begin_layout Plain Layout
20075 \begin_layout Plain Layout
20095 \begin_inset Index idx
20098 \begin_layout Plain Layout
20104 with the LaTeX-preamble line
20107 \begin_layout Standard
20112 usepackage{fixmath}
20115 \begin_layout Standard
20116 Then all big Greek letters in a document will automatically be typeset italic.
20119 \begin_layout Subsection
20121 \begin_inset Index idx
20124 \begin_layout Plain Layout
20125 Greek letters ! bold
20133 \begin_layout Standard
20134 Greek letters cannot be set with different font styles like Latin letters.
20135 They can only be made bold with the command
20142 \begin_inset Index idx
20145 \begin_layout Plain Layout
20156 \begin_layout Standard
20158 \begin_inset Tabular
20159 <lyxtabular version="3" rows="3" columns="2">
20160 <features rotate="0" tabularvalignment="middle">
20161 <column alignment="center" valignment="top">
20162 <column alignment="center" valignment="top">
20164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20167 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20187 \begin_layout Plain Layout
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20202 \begin_layout Plain Layout
20203 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20216 \begin_layout Plain Layout
20228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Plain Layout
20232 \begin_inset Formula $\theta\boldsymbol{\theta}$
20248 \begin_layout Section
20253 \begin_layout Plain Layout
20266 \begin_layout Plain Layout
20267 A list with all symbols of most of the LaTeX-packages can be found in
20268 \begin_inset CommandInset citation
20283 \begin_layout Plain Layout
20291 \begin_inset Note Note
20294 \begin_layout Plain Layout
20297 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20300 \begin_layout Plain Layout
20303 texorpdfstring is in section
20304 \begin_inset CommandInset ref
20306 reference "sub:Formulas-in-Section"
20316 \begin_inset Index idx
20319 \begin_layout Plain Layout
20328 \begin_layout Standard
20329 Many of the symbols listed in this section can also be inserted via the
20331 \begin_inset Graphics
20332 filename ../images/math/nabla.png
20338 \begin_inset Graphics
20339 filename ../images/math/digamma.png
20347 \begin_layout Subsection
20348 Mathematical Symbols
20349 \begin_inset CommandInset label
20351 name "sub:Mathematical-Symbols"
20356 \begin_inset Index idx
20359 \begin_layout Plain Layout
20360 Symbols ! mathematical
20368 \begin_layout Standard
20369 \begin_inset space \hfill{}
20373 \begin_inset Tabular
20374 <lyxtabular version="3" rows="10" columns="2">
20375 <features rotate="0" tabularvalignment="middle">
20376 <column alignment="center" valignment="top" width="0pt">
20377 <column alignment="center" valignment="top" width="0pt">
20379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20382 \begin_layout Plain Layout
20388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20391 \begin_layout Plain Layout
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\neg$
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20439 \begin_inset Formula $\Im$
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20464 \begin_inset Formula $\Re$
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\aleph$
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\partial$
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\infty$
20549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\wp$
20574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\imath$
20599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\jmath$
20628 \begin_inset space \hfill{}
20632 \begin_inset Tabular
20633 <lyxtabular version="3" rows="10" columns="2">
20634 <features rotate="0" tabularvalignment="middle">
20635 <column alignment="center" valignment="top" width="0pt">
20636 <column alignment="center" valignment="top" width="0pt">
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20652 \begin_inset Note Note
20655 \begin_layout Plain Layout
20662 is only used as spacer.
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20677 \begin_layout Plain Layout
20685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Plain Layout
20689 \begin_inset Formula $\forall$
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20713 \begin_layout Plain Layout
20714 \begin_inset Formula $\exists$
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20727 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Plain Layout
20739 \begin_inset Formula $\nexists$
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20752 \begin_layout Plain Layout
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20763 \begin_layout Plain Layout
20764 \begin_inset Formula $\emptyset$
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20777 \begin_layout Plain Layout
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20788 \begin_layout Plain Layout
20789 \begin_inset Formula $\varnothing$
20799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20802 \begin_layout Plain Layout
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20813 \begin_layout Plain Layout
20814 \begin_inset Formula $\dag$
20824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20827 \begin_layout Plain Layout
20835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20838 \begin_layout Plain Layout
20839 \begin_inset Formula $\ddag$
20849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20852 \begin_layout Plain Layout
20860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20863 \begin_layout Plain Layout
20867 \begin_layout Plain Layout
20877 \begin_inset Formula $\complement$
20884 \begin_layout Plain Layout
20898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20901 \begin_layout Plain Layout
20909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20912 \begin_layout Plain Layout
20913 \begin_inset Formula $\Bbbk$
20927 \begin_inset space \hfill{}
20931 \begin_inset Tabular
20932 <lyxtabular version="3" rows="10" columns="2">
20933 <features rotate="0" tabularvalignment="middle">
20934 <column alignment="center" valignment="top" width="0pt">
20935 <column alignment="center" valignment="top" width="0pt">
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20940 \begin_layout Plain Layout
20946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20949 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20960 \begin_layout Plain Layout
20968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20971 \begin_layout Plain Layout
20972 \begin_inset Formula $\prime$
20982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20985 \begin_layout Plain Layout
20993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20996 \begin_layout Plain Layout
20997 \begin_inset Formula $\backprime$
21007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21010 \begin_layout Plain Layout
21018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21021 \begin_layout Plain Layout
21022 \begin_inset Formula $\mho$
21032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21035 \begin_layout Plain Layout
21043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21046 \begin_layout Plain Layout
21047 \begin_inset Formula $\triangle$
21057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21060 \begin_layout Plain Layout
21068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21071 \begin_layout Plain Layout
21072 \begin_inset Formula $\angle$
21082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21085 \begin_layout Plain Layout
21093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21096 \begin_layout Plain Layout
21097 \begin_inset Formula $\measuredangle$
21107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21110 \begin_layout Plain Layout
21118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21121 \begin_layout Plain Layout
21122 \begin_inset Formula $\sphericalangle$
21132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21135 \begin_layout Plain Layout
21143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21146 \begin_layout Plain Layout
21147 \begin_inset Formula $\top$
21157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21160 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21172 \begin_inset Formula $\bot$
21186 \begin_inset space \hfill{}
21192 \begin_layout Subsection
21193 Miscellaneous Symbols
21194 \begin_inset CommandInset label
21196 name "sub:Miscellaneous-Symbols"
21201 \begin_inset Index idx
21204 \begin_layout Plain Layout
21205 Symbols ! miscellaneous
21213 \begin_layout Standard
21216 \begin_inset Tabular
21217 <lyxtabular version="3" rows="10" columns="2">
21218 <features rotate="0" tabularvalignment="middle">
21219 <column alignment="center" valignment="top" width="0pt">
21220 <column alignment="center" valignment="top" width="0pt">
21222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21225 \begin_layout Plain Layout
21231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21234 \begin_layout Plain Layout
21242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21245 \begin_layout Plain Layout
21253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21256 \begin_layout Plain Layout
21257 \begin_inset Formula $\flat$
21267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21270 \begin_layout Plain Layout
21278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21281 \begin_layout Plain Layout
21282 \begin_inset Formula $\natural$
21292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21295 \begin_layout Plain Layout
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21306 \begin_layout Plain Layout
21307 \begin_inset Formula $\sharp$
21317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21320 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21332 \begin_inset Formula $\surd$
21342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\checkmark$
21367 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\yen$
21392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Plain Layout
21407 \begin_inset Formula $\pounds$
21417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21430 \begin_inset Formula $\$$
21440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21443 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $§$
21467 \begin_inset Tabular
21468 <lyxtabular version="3" rows="10" columns="2">
21469 <features rotate="0" tabularvalignment="middle">
21470 <column alignment="center" valignment="top">
21471 <column alignment="center" valignment="top">
21473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21496 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21507 \begin_layout Plain Layout
21508 \begin_inset Formula $\hbar$
21518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21532 \begin_layout Plain Layout
21533 \begin_inset Formula $\hslash$
21543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\clubsuit$
21568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\spadesuit$
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\bigstar$
21618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\blacklozenge$
21643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21658 \begin_inset Formula $\blacktriangle$
21668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21671 \begin_layout Plain Layout
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21682 \begin_layout Plain Layout
21683 \begin_inset Formula $\blacktriangledown$
21693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21707 \begin_layout Plain Layout
21708 \begin_inset Formula $\bullet$
21722 \begin_inset Tabular
21723 <lyxtabular version="3" rows="10" columns="2">
21724 <features rotate="0" tabularvalignment="middle">
21725 <column alignment="center" valignment="top" width="0pt">
21726 <column alignment="center" valignment="top" width="0pt">
21728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21731 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21751 \begin_layout Plain Layout
21759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21762 \begin_layout Plain Layout
21763 \begin_inset Formula $\diamondsuit$
21773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21776 \begin_layout Plain Layout
21784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21787 \begin_layout Plain Layout
21788 \begin_inset Formula $\Diamond$
21798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21801 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21812 \begin_layout Plain Layout
21813 \begin_inset Formula $\heartsuit$
21823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21826 \begin_layout Plain Layout
21834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21837 \begin_layout Plain Layout
21838 \begin_inset Formula $\P$
21848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21851 \begin_layout Plain Layout
21859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21862 \begin_layout Plain Layout
21863 \begin_inset Formula $\copyright$
21873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21876 \begin_layout Plain Layout
21884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21887 \begin_layout Plain Layout
21888 \begin_inset Formula $\circledR$
21898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21901 \begin_layout Plain Layout
21909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21912 \begin_layout Plain Layout
21913 \begin_inset Formula $\maltese$
21923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21926 \begin_layout Plain Layout
21934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21937 \begin_layout Plain Layout
21938 \begin_inset Formula $\diagup$
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21951 \begin_layout Plain Layout
21959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21962 \begin_layout Plain Layout
21963 \begin_inset Formula $\diagdown$
21979 \begin_layout Standard
21980 \begin_inset VSpace medskip
21986 \begin_layout Standard
21987 Some symbols can be displayed in different sizes, see
21988 \begin_inset CommandInset ref
21990 reference "sub:Font-Sizes"
21997 \begin_layout Subsection
21999 \begin_inset Index idx
22002 \begin_layout Plain Layout
22003 Symbols ! Euro-symbol
22009 \begin_inset Index idx
22012 \begin_layout Plain Layout
22019 \begin_layout Plain Layout
22036 \begin_layout Standard
22037 To use the Euro symbol in formulas, the LaTeX-package
22042 \begin_inset Index idx
22045 \begin_layout Plain Layout
22051 must be installed and loaded with the LaTeX-preamble line
22054 \begin_layout Standard
22059 usepackage[gennarrow]{eurosym}
22062 \begin_layout Standard
22063 The Euro symbol can now be inserted with the command
22070 \begin_inset Index idx
22073 \begin_layout Plain Layout
22084 \begin_layout Standard
22085 The Euro symbol can directly be inserted with the € key in mathematical
22086 text, without having
22101 can also be inserted in TeX-mode.
22102 The official currency symbol can then be inserted with the command
22109 \begin_inset Index idx
22112 \begin_layout Plain Layout
22120 , that is only available in TeX-mode.
22123 \begin_layout Standard
22127 \begin_layout Plain Layout
22137 \begin_inset Note Note
22140 \begin_layout Plain Layout
22141 The following table will only be displayed when the LaTeX-package
22153 \begin_layout Standard
22154 An overview about the different Euro symbols:
22157 \begin_layout Standard
22159 \begin_inset Tabular
22160 <lyxtabular version="3" rows="4" columns="3">
22161 <features rotate="0" tabularvalignment="middle">
22162 <column alignment="center" valignment="top" width="0pt">
22163 <column alignment="center" valignment="top" width="0pt">
22164 <column alignment="center" valignment="top" width="0pt">
22166 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22169 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22178 \begin_layout Plain Layout
22184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22187 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22198 \begin_layout Plain Layout
22204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22207 \begin_layout Plain Layout
22215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22218 \begin_layout Plain Layout
22219 \begin_inset Formula $\euro$
22229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22232 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22241 \begin_layout Plain Layout
22247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22250 \begin_layout Plain Layout
22251 \begin_inset Formula $\mbox{€}$
22261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22264 \begin_layout Plain Layout
22270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22273 \begin_layout Plain Layout
22281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22284 \begin_layout Plain Layout
22288 \begin_layout Plain Layout
22310 \begin_layout Standard
22314 \begin_layout Plain Layout
22324 \begin_inset Note Note
22327 \begin_layout Plain Layout
22328 The following will be displayed when the LaTeX-package
22340 \begin_layout Standard
22341 You need to install the LaTeX-package
22345 to see the rest of this subsection in the output.
22348 \begin_layout Standard
22352 \begin_layout Plain Layout
22364 \begin_layout Section
22366 \begin_inset CommandInset label
22368 name "sec:Relations"
22373 \begin_inset Index idx
22376 \begin_layout Plain Layout
22383 \begin_inset Index idx
22386 \begin_layout Plain Layout
22391 \begin_layout Plain Layout
22402 \begin_layout Plain Layout
22417 \begin_layout Standard
22418 All relations can also be inserted via the toolbar button
22419 \begin_inset Graphics
22420 filename ../images/math/leq.png
22428 \begin_layout Standard
22429 \begin_inset space \hfill{}
22433 \begin_inset Tabular
22434 <lyxtabular version="3" rows="17" columns="2">
22435 <features rotate="0" tabularvalignment="middle">
22436 <column alignment="center" valignment="top" width="0pt">
22437 <column alignment="center" valignment="top" width="0pt">
22439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22442 \begin_layout Plain Layout
22448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22451 \begin_layout Plain Layout
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $<$
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\le$
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\ll$
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\prec$
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\preceq$
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Plain Layout
22597 \begin_inset Formula $\subset$
22607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22610 \begin_layout Plain Layout
22618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22621 \begin_layout Plain Layout
22622 \begin_inset Formula $\subseteq$
22632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22635 \begin_layout Plain Layout
22643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22646 \begin_layout Plain Layout
22647 \begin_inset Formula $\sqsubseteq$
22657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22660 \begin_layout Plain Layout
22668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22671 \begin_layout Plain Layout
22672 \begin_inset Formula $\in$
22682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22685 \begin_layout Plain Layout
22693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22696 \begin_layout Plain Layout
22697 \begin_inset Formula $\vdash$
22707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22710 \begin_layout Plain Layout
22718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22721 \begin_layout Plain Layout
22722 \begin_inset Formula $\smile$
22732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22735 \begin_layout Plain Layout
22743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22746 \begin_layout Plain Layout
22747 \begin_inset Formula $\lhd$
22757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22760 \begin_layout Plain Layout
22768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22771 \begin_layout Plain Layout
22772 \begin_inset Formula $\unlhd$
22782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22785 \begin_layout Plain Layout
22793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22796 \begin_layout Plain Layout
22797 \begin_inset Formula $\gtrless$
22807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22810 \begin_layout Plain Layout
22818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22821 \begin_layout Plain Layout
22822 \begin_inset Formula $\mid$
22832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22835 \begin_layout Plain Layout
22843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22846 \begin_layout Plain Layout
22847 \begin_inset Formula $\nmid$
22861 \begin_inset space \hfill{}
22865 \begin_inset Tabular
22866 <lyxtabular version="3" rows="17" columns="2">
22867 <features rotate="0" tabularvalignment="middle">
22868 <column alignment="center" valignment="top" width="0pt">
22869 <column alignment="center" valignment="top" width="0pt">
22871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22874 \begin_layout Plain Layout
22880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22883 \begin_layout Plain Layout
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22894 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $=$
22914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\not=$
22939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22954 \begin_inset Formula $\equiv$
22964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22967 \begin_layout Plain Layout
22975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22978 \begin_layout Plain Layout
22979 \begin_inset Formula $\sim$
22989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23003 \begin_layout Plain Layout
23004 \begin_inset Formula $\simeq$
23014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23017 \begin_layout Plain Layout
23025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23028 \begin_layout Plain Layout
23029 \begin_inset Formula $\approx$
23039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23042 \begin_layout Plain Layout
23050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23053 \begin_layout Plain Layout
23054 \begin_inset Formula $\cong$
23064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23067 \begin_layout Plain Layout
23075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23078 \begin_layout Plain Layout
23079 \begin_inset Formula $\bowtie$
23089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23092 \begin_layout Plain Layout
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23103 \begin_layout Plain Layout
23104 \begin_inset Formula $\notin$
23114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23117 \begin_layout Plain Layout
23125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23128 \begin_layout Plain Layout
23129 \begin_inset Formula $\perp$
23139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23142 \begin_layout Plain Layout
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23153 \begin_layout Plain Layout
23154 \begin_inset Formula $\propto$
23164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23167 \begin_layout Plain Layout
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23178 \begin_layout Plain Layout
23179 \begin_inset Formula $\asymp$
23189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23192 \begin_layout Plain Layout
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23203 \begin_layout Plain Layout
23204 \begin_inset Formula $\doteq$
23214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23217 \begin_layout Plain Layout
23225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23228 \begin_layout Plain Layout
23229 \begin_inset Formula $\circeq$
23239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23242 \begin_layout Plain Layout
23250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23253 \begin_layout Plain Layout
23254 \begin_inset Formula $\models$
23264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23267 \begin_layout Plain Layout
23275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23278 \begin_layout Plain Layout
23279 \begin_inset Formula $\widehat{=}$
23293 \begin_inset space \hfill{}
23297 \begin_inset Tabular
23298 <lyxtabular version="3" rows="17" columns="2">
23299 <features rotate="0" tabularvalignment="middle">
23300 <column alignment="center" valignment="top" width="0pt">
23301 <column alignment="center" valignment="top" width="0pt">
23303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23306 \begin_layout Plain Layout
23312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23315 \begin_layout Plain Layout
23323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23326 \begin_layout Plain Layout
23332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23335 \begin_layout Plain Layout
23336 \begin_inset Formula $>$
23346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23349 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Plain Layout
23361 \begin_inset Formula $\ge$
23371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23374 \begin_layout Plain Layout
23382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23385 \begin_layout Plain Layout
23386 \begin_inset Formula $\gg$
23396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23399 \begin_layout Plain Layout
23407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23410 \begin_layout Plain Layout
23411 \begin_inset Formula $\succ$
23421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23424 \begin_layout Plain Layout
23432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23435 \begin_layout Plain Layout
23436 \begin_inset Formula $\succeq$
23446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23449 \begin_layout Plain Layout
23457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23460 \begin_layout Plain Layout
23461 \begin_inset Formula $\supset$
23471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23474 \begin_layout Plain Layout
23482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23485 \begin_layout Plain Layout
23486 \begin_inset Formula $\supseteq$
23496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23499 \begin_layout Plain Layout
23507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23510 \begin_layout Plain Layout
23511 \begin_inset Formula $\sqsupseteq$
23521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23524 \begin_layout Plain Layout
23532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23535 \begin_layout Plain Layout
23536 \begin_inset Formula $\ni$
23546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23549 \begin_layout Plain Layout
23557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23560 \begin_layout Plain Layout
23561 \begin_inset Formula $\dashv$
23571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23574 \begin_layout Plain Layout
23582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23585 \begin_layout Plain Layout
23586 \begin_inset Formula $\frown$
23596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23599 \begin_layout Plain Layout
23607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23610 \begin_layout Plain Layout
23611 \begin_inset Formula $\rhd$
23621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23624 \begin_layout Plain Layout
23632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23635 \begin_layout Plain Layout
23636 \begin_inset Formula $\unrhd$
23646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23649 \begin_layout Plain Layout
23657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23660 \begin_layout Plain Layout
23661 \begin_inset Formula $\lessgtr$
23671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23674 \begin_layout Plain Layout
23682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23685 \begin_layout Plain Layout
23686 \begin_inset Formula $\parallel$
23696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23699 \begin_layout Plain Layout
23707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23710 \begin_layout Plain Layout
23711 \begin_inset Formula $\nparallel$
23725 \begin_inset space \hfill{}
23731 \begin_layout Standard
23732 \begin_inset VSpace medskip
23747 are bigger than the equal looking operators
23762 \begin_layout Standard
23763 Relations are, in contrary to symbols, always surrounded by space.
23766 \begin_layout Standard
23767 Relations with labels can be created with the command
23774 \begin_inset Index idx
23777 \begin_layout Plain Layout
23788 \begin_layout Standard
23790 \begin_inset Tabular
23791 <lyxtabular version="3" rows="2" columns="2">
23792 <features rotate="0" tabularvalignment="middle">
23793 <column alignment="center" valignment="top">
23794 <column alignment="center" valignment="top">
23796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23799 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23810 \begin_inset Note Note
23813 \begin_layout Plain Layout
23820 is only used as spacer.
23832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23835 \begin_layout Plain Layout
23839 \begin_inset space \textvisiblespace{}
23847 \begin_inset space \textvisiblespace{}
23851 \begin_inset Formula $\downarrow$
23857 \begin_inset space \textvisiblespace{}
23861 \begin_inset space \textvisiblespace{}
23869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23872 \begin_layout Plain Layout
23873 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23889 \begin_layout Section
23893 \begin_layout Subsection
23894 Predefined Functions
23895 \begin_inset CommandInset label
23897 name "sub:Predefined-Functions"
23902 \begin_inset Index idx
23905 \begin_layout Plain Layout
23906 Functions ! predefined
23914 \begin_layout Standard
23915 In general, variables are set
23919 in mathematical expressions, but not function names, because
23920 \begin_inset Formula $sin$
23923 could be misunderstood as
23924 \begin_inset Formula $s\cdot i\cdot n$
23928 Therefore there are predefined functionswhich are additionally a bit separated
23930 They are inserted as commands starting with a backslash before their name.
23933 \begin_layout Standard
23935 \begin_inset Tabular
23936 <lyxtabular version="3" rows="2" columns="4">
23937 <features rotate="0" tabularvalignment="middle">
23938 <column alignment="center" valignment="top" width="0pt">
23939 <column alignment="center" valignment="top" width="0pt">
23940 <column alignment="center" valignment="top" width="0pt">
23941 <column alignment="center" valignment="top" width="0pt">
23943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23946 \begin_layout Plain Layout
23952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23955 \begin_layout Plain Layout
23961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23964 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23993 \begin_layout Plain Layout
23994 \begin_inset Formula $Asin(x)+B$
24002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24005 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24017 \begin_inset Formula $A\sin(x)+B$
24033 \begin_layout Standard
24034 The following functions are predefined:
24037 \begin_layout Standard
24038 \begin_inset VSpace -2mm
24044 \begin_layout Standard
24046 \begin_inset Tabular
24047 <lyxtabular version="3" rows="9" columns="4">
24048 <features rotate="0" tabularvalignment="middle">
24049 <column alignment="center" valignment="top" width="0pt">
24050 <column alignment="center" valignment="top" width="0pt">
24051 <column alignment="center" valignment="top" width="0pt">
24052 <column alignment="center" valignment="top" width="0pt">
24054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24095 \begin_layout Plain Layout
24103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24106 \begin_layout Plain Layout
24114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24141 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24187 \begin_layout Plain Layout
24195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24233 \begin_layout Plain Layout
24241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24255 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24279 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24312 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24371 \begin_layout Plain Layout
24379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24404 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24417 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24450 \begin_layout Plain Layout
24466 \begin_layout Standard
24467 They can also be inserted with the math toolbar button
24468 \begin_inset Graphics
24469 filename ../images/math/functions.png
24477 \begin_layout Subsection
24478 Self-defined Functions
24479 \begin_inset Index idx
24482 \begin_layout Plain Layout
24483 Functions ! self-defined
24491 \begin_layout Standard
24492 To use a function that is not predefined, like for example the sign function
24493 sgn(x), there are two possibilities:
24496 \begin_layout Itemize
24497 Define the function by inserting the following line to the LaTeX-preamble
24501 \begin_layout Plain Layout
24506 DeclareMathOperator
24509 \begin_inset CommandInset ref
24511 reference "sub:Self-defined-Operators"
24521 \begin_inset Newline newline
24525 \begin_inset VSpace -3mm
24529 \begin_inset Newline newline
24536 DeclareMathOperator{
24541 \begin_inset Index idx
24544 \begin_layout Plain Layout
24549 DeclareMathOperator
24555 \begin_inset Newline newline
24559 \begin_inset VSpace -2mm
24563 \begin_inset Newline newline
24566 Now the new defined function can be called with the command
24575 \begin_layout Itemize
24576 Write the formula as usual, mark the formula name, in our example the letters
24581 , and change it to mathematical text.
24582 Finally, a space is inserted between prefactor and function.
24585 \begin_layout Standard
24586 The result is the same with both methods as with a predefined function
24590 \begin_layout Plain Layout
24591 In LyX self-defined functions are displayed red, predefined ones black.
24599 \begin_layout Standard
24601 \begin_inset Tabular
24602 <lyxtabular version="3" rows="3" columns="2">
24603 <features rotate="0" tabularvalignment="middle">
24604 <column alignment="center" valignment="top" width="0pt">
24605 <column alignment="center" valignment="top" width="0pt">
24607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24610 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24619 \begin_layout Plain Layout
24627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24630 \begin_layout Plain Layout
24638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24641 \begin_layout Plain Layout
24642 \begin_inset Formula $A\sgn(x)+B$
24652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24655 \begin_layout Plain Layout
24659 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24670 \begin_layout Plain Layout
24671 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24687 \begin_layout Standard
24688 The first method is more suitable when the self-defined function should
24689 be used several times.
24692 \begin_layout Subsection
24694 \begin_inset Index idx
24697 \begin_layout Plain Layout
24706 \begin_layout Standard
24707 For limits, in addition to the commands
24714 \begin_inset Index idx
24717 \begin_layout Plain Layout
24737 the following functions are defined:
24740 \begin_layout Standard
24742 \begin_inset Tabular
24743 <lyxtabular version="3" rows="5" columns="2">
24744 <features rotate="0" tabularvalignment="middle">
24745 <column alignment="center" valignment="top">
24746 <column alignment="center" valignment="top">
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24751 \begin_layout Plain Layout
24757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24760 \begin_layout Plain Layout
24762 \begin_inset Note Note
24765 \begin_layout Plain Layout
24772 is only used as spacer.
24784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24787 \begin_layout Plain Layout
24795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24798 \begin_layout Plain Layout
24799 \begin_inset Formula $\varliminf$
24809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24812 \begin_layout Plain Layout
24820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24823 \begin_layout Plain Layout
24824 \begin_inset Formula $\varlimsup$
24834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24849 \begin_inset Formula $\varprojlim$
24859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24862 \begin_layout Plain Layout
24870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24873 \begin_layout Plain Layout
24874 \begin_inset Formula $\varinjlim$
24878 \begin_inset Formula $\raisebox{-2.5mm}{}$
24894 \begin_layout Standard
24895 \begin_inset VSpace medskip
24898 The limit is created by inserting a subscript.
24899 It is set right beside the function in an inline formula:
24902 \begin_layout Standard
24904 \begin_inset Tabular
24905 <lyxtabular version="3" rows="2" columns="2">
24906 <features rotate="0" tabularvalignment="middle">
24907 <column alignment="center" valignment="top" width="0pt">
24908 <column alignment="center" valignment="top" width="0pt">
24910 <cell alignment="center" valignment="top" usebox="none">
24913 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" usebox="none">
24922 \begin_layout Plain Layout
24923 \begin_inset space \hspace{}
24928 \begin_inset Note Note
24931 \begin_layout Plain Layout
24938 are used here as spacer.
24950 <cell alignment="center" valignment="top" usebox="none">
24953 \begin_layout Plain Layout
24959 \begin_inset space \textvisiblespace{}
24963 \begin_inset space \textvisiblespace{}
24971 <cell alignment="center" valignment="top" usebox="none">
24974 \begin_layout Plain Layout
24975 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24991 \begin_layout Standard
24992 In a displayed formula the limit is set below the formula, as usual:
24993 \begin_inset Formula
25003 \begin_layout Subsection
25005 \begin_inset Index idx
25008 \begin_layout Plain Layout
25009 Functions ! modulo-
25017 \begin_layout Standard
25018 The modulo-function is special, because it exists in four variants.
25019 The variants in a displayed formula are:
25020 \begin_inset Formula
25022 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25023 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25024 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25025 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25026 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25034 \begin_layout Standard
25035 In an inline formula less space is set before the function names for all
25037 By default the modulo-functions take only the first following character
25039 To use more than one character, one has to put them into TeX-braces:
25040 \begin_inset Formula
25042 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25043 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25044 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25052 \begin_layout Section
25054 \begin_inset Index idx
25057 \begin_layout Plain Layout
25066 \begin_layout Subsection
25067 Special Characters in Mathematical Text
25070 \begin_layout Standard
25071 The following commands can only be used in mathematical text or in TeX-mode:
25074 \begin_layout Standard
25075 \begin_inset space \hfill{}
25079 \begin_inset Tabular
25080 <lyxtabular version="3" rows="8" columns="2">
25081 <features rotate="0" tabularvalignment="middle">
25082 <column alignment="block" valignment="top">
25083 <column alignment="block" valignment="top">
25085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25088 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25119 \begin_layout Plain Layout
25120 \begin_inset Formula $\textrm{œ}$
25130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25133 \begin_layout Plain Layout
25141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25144 \begin_layout Plain Layout
25145 \begin_inset Formula $\textrm{Œ}$
25155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25169 \begin_layout Plain Layout
25170 \begin_inset Formula $\textrm{æ}$
25180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25183 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25194 \begin_layout Plain Layout
25195 \begin_inset Formula $\textrm{Æ}$
25205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25208 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25219 \begin_layout Plain Layout
25220 \begin_inset Formula $\textrm{\aa}$
25230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25233 \begin_layout Plain Layout
25237 \begin_inset Index idx
25240 \begin_layout Plain Layout
25247 \begin_layout Plain Layout
25268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25271 \begin_layout Plain Layout
25272 \begin_inset Formula $\textrm{Å}$
25282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25285 \begin_layout Plain Layout
25293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25296 \begin_layout Plain Layout
25297 \begin_inset Formula $\textrm{ı}$
25311 \begin_inset space \hfill{}
25315 \begin_inset Tabular
25316 <lyxtabular version="3" rows="8" columns="2">
25317 <features rotate="0" tabularvalignment="middle">
25318 <column alignment="block" valignment="top">
25319 <column alignment="center" valignment="top">
25321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25324 \begin_layout Plain Layout
25326 \begin_inset Note Note
25329 \begin_layout Plain Layout
25331 \begin_inset space \thinspace{}
25334 mm is used for separation, because otherwise the output will be ¡ and ¿
25345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25348 \begin_layout Plain Layout
25356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25359 \begin_layout Plain Layout
25367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25370 \begin_layout Plain Layout
25371 \begin_inset Formula $\textrm{ø}$
25381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25396 \begin_inset Formula $\textrm{Ø}$
25406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25409 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25420 \begin_layout Plain Layout
25421 \begin_inset Formula $\textrm{ł}$
25431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25445 \begin_layout Plain Layout
25446 \begin_inset Formula $\textrm{Ł}$
25456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25459 \begin_layout Plain Layout
25461 \begin_inset space \hspace{}
25466 \begin_inset space \textvisiblespace{}
25474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25477 \begin_layout Plain Layout
25478 \begin_inset Formula $\textrm{!`}$
25488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25491 \begin_layout Plain Layout
25493 \begin_inset space \hspace{}
25498 \begin_inset space \textvisiblespace{}
25506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25509 \begin_layout Plain Layout
25510 \begin_inset Formula $\textrm{?`}$
25520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25523 \begin_layout Plain Layout
25531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25534 \begin_layout Plain Layout
25535 \begin_inset Formula $\textrm{ȷ}$
25549 \begin_inset space \hfill{}
25555 \begin_layout Standard
25557 \begin_inset Formula $\textrm{\textrm{Å}}$
25561 \begin_inset Formula $\textrm{\textrm{Ø}}$
25564 can also be inserted via the math toolbar button
25565 \begin_inset Graphics
25566 filename ../images/math/digamma.png
25574 \begin_layout Standard
25575 An exception are the commands
25578 \begin_inset space \hspace{}
25587 \begin_inset space \hspace{}
25593 , because they can be inserted in LyX directly to text.
25596 \begin_layout Subsection
25598 \begin_inset CommandInset label
25600 name "sub:Accents-in-Text"
25605 \begin_inset Index idx
25608 \begin_layout Plain Layout
25617 \begin_layout Standard
25618 With the following commands all letters can be accented.
25619 The commands must be inserted in TeX-mode.
25622 \begin_layout Standard
25623 \begin_inset space \hfill{}
25627 \begin_inset Tabular
25628 <lyxtabular version="3" rows="8" columns="2">
25629 <features rotate="0" tabularvalignment="middle">
25630 <column alignment="block" valignment="top">
25631 <column alignment="block" valignment="top">
25633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25636 \begin_layout Plain Layout
25642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25645 \begin_layout Plain Layout
25653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25656 \begin_layout Plain Layout
25660 \begin_inset Quotes grd
25668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25671 \begin_layout Plain Layout
25675 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25694 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25705 \begin_layout Plain Layout
25709 \begin_layout Plain Layout
25725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25728 \begin_layout Plain Layout
25732 \begin_inset space \textvisiblespace{}
25740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25743 \begin_layout Plain Layout
25747 \begin_layout Plain Layout
25763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25766 \begin_layout Plain Layout
25774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25777 \begin_layout Plain Layout
25781 \begin_layout Plain Layout
25797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25800 \begin_layout Plain Layout
25804 \begin_inset space \textvisiblespace{}
25812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25815 \begin_layout Plain Layout
25819 \begin_layout Plain Layout
25835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25838 \begin_layout Plain Layout
25842 \begin_inset space \textvisiblespace{}
25850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25853 \begin_layout Plain Layout
25857 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25876 \begin_layout Plain Layout
25880 \begin_inset space \textvisiblespace{}
25888 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25891 \begin_layout Plain Layout
25895 \begin_layout Plain Layout
25915 \begin_inset space \hfill{}
25919 \begin_inset Tabular
25920 <lyxtabular version="3" rows="8" columns="2">
25921 <features rotate="0" tabularvalignment="middle">
25922 <column alignment="block" valignment="top">
25923 <column alignment="center" valignment="top">
25925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25928 \begin_layout Plain Layout
25934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25937 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25948 \begin_layout Plain Layout
25952 \begin_inset space \textvisiblespace{}
25960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25963 \begin_layout Plain Layout
25967 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25986 \begin_layout Plain Layout
25994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25997 \begin_layout Plain Layout
26001 \begin_layout Plain Layout
26017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26020 \begin_layout Plain Layout
26024 \begin_inset Index idx
26027 \begin_layout Plain Layout
26038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26041 \begin_layout Plain Layout
26045 \begin_layout Plain Layout
26061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26064 \begin_layout Plain Layout
26072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26075 \begin_layout Plain Layout
26079 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26098 \begin_layout Plain Layout
26102 \begin_inset space \textvisiblespace{}
26110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26117 \begin_layout Plain Layout
26133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26136 \begin_layout Plain Layout
26140 \begin_inset space \textvisiblespace{}
26148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26151 \begin_layout Plain Layout
26155 \begin_layout Plain Layout
26171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26174 \begin_layout Plain Layout
26178 \begin_inset space \textvisiblespace{}
26186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26189 \begin_layout Plain Layout
26193 \begin_layout Plain Layout
26213 \begin_inset space \hfill{}
26219 \begin_layout Standard
26220 \begin_inset VSpace medskip
26229 also two different characters can be accented.
26235 \begin_inset space \textvisiblespace{}
26244 \begin_layout Plain Layout
26256 \begin_layout Standard
26269 can in combination with vowels directly be inserted with the keyboard without
26271 The same applies for the tilde
26275 \begin_layout Plain Layout
26276 This only applies for keyboards where the tilde is defined as accent.
26285 in combination with
26300 \begin_layout Standard
26343 and accents that are inserted directly with the keyboard are also available
26344 in mathematical text.
26345 For the other accents there are special math commands to be used in formulas,
26347 \begin_inset CommandInset ref
26349 reference "sub:Accents-for-one"
26356 \begin_layout Standard
26357 \begin_inset VSpace bigskip
26360 Furthermore, with the command
26367 \begin_inset Index idx
26370 \begin_layout Plain Layout
26378 all numbers and letters can be set into a circle, quasi accented with a
26379 circle, similar to the copyright symbol.
26382 \begin_layout Standard
26384 \begin_inset Tabular
26385 <lyxtabular version="3" rows="3" columns="2">
26386 <features rotate="0" tabularvalignment="middle">
26387 <column alignment="center" valignment="top">
26388 <column alignment="center" valignment="top">
26390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26393 \begin_layout Plain Layout
26399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26402 \begin_layout Plain Layout
26404 \begin_inset Note Note
26407 \begin_layout Plain Layout
26414 is only used as spacer.
26426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26429 \begin_layout Plain Layout
26437 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26440 \begin_layout Plain Layout
26444 \begin_layout Plain Layout
26460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26463 \begin_layout Plain Layout
26474 raisebox{-1.5pt}{W}}
26479 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26482 \begin_layout Plain Layout
26483 \begin_inset Formula $\raisebox{4.5mm}{}$
26490 \begin_layout Plain Layout
26508 \begin_inset Formula $\raisebox{-2mm}{}$
26524 \begin_layout Standard
26525 One has to take care that the character fits in the circle.
26536 \begin_layout Plain Layout
26538 \begin_inset CommandInset ref
26540 reference "sub:Font-Sizes"
26549 specifies thereby the size of the circle.
26560 \begin_layout Plain Layout
26562 \begin_inset CommandInset ref
26564 reference "sub:Boxes-without-Frame"
26573 the character can be centered.
26576 \begin_layout Subsection
26578 \begin_inset Index idx
26581 \begin_layout Plain Layout
26590 \begin_layout Standard
26591 Old-style figures (also known as old-style numerals) are created with the
26599 \begin_inset Index idx
26602 \begin_layout Plain Layout
26611 The command can be used in formulas and in TeX-mode.
26612 The command scheme is:
26615 \begin_layout Standard
26620 oldstylenums{number}
26623 \begin_layout Standard
26628 oldstylenums{0123456789
26631 \begin_inset Formula $\oldstylenums{0123456789}$
26637 \begin_layout Section
26639 \begin_inset CommandInset label
26641 name "sec:Formula-Styles"
26646 \begin_inset Index idx
26649 \begin_layout Plain Layout
26658 \begin_layout Itemize
26659 There are two different alignment styles:
26663 \begin_layout Description
26664 Centered is the predefined standard
26667 \begin_layout Description
26668 Indented for this the option
26672 must be inserted in the menu
26674 Document\SpecialChar \menuseparator
26680 \begin_inset space ~
26686 \begin_layout Standard
26691 is used, the indentation can be adjusted with the length
26698 \begin_inset Index idx
26701 \begin_layout Plain Layout
26710 Should the distance be 15
26711 \begin_inset space \thinspace{}
26714 mm, the following command line is inserted in the LaTeX-preamble
26717 \begin_layout Standard
26727 \begin_layout Standard
26728 When no length is specified, the predefined value of 30
26729 \begin_inset space \thinspace{}
26736 \begin_layout Itemize
26737 And two different numbering styles:
26741 \begin_layout Description
26742 Right is the predefined standard
26745 \begin_layout Description
26746 Left for this the option
26750 must be inserted in the menu
26752 Document\SpecialChar \menuseparator
26758 \begin_inset space ~
26765 \begin_layout Standard
26774 can also be used together.
26775 In this case both options are inserted, separated by a comma.
26778 \begin_layout Standard
26779 The chosen styles are used for all displayed formulas of the document.
26780 When both, centered and indented formulas should be created in a document,
26786 The indented formulas are then set in a flalign environment, see
26787 \begin_inset CommandInset ref
26789 reference "sub:Flalign-Environment"
26796 \begin_layout Section
26798 \begin_inset CommandInset label
26800 name "sec:Multiline-Formulas"
26805 \begin_inset Index idx
26808 \begin_layout Plain Layout
26809 Formula ! multiline
26817 \begin_layout Subsection
26821 \begin_layout Standard
26822 In LyX multiline formulas are created by pressing
26827 arg "newline-insert newline"
26833 This creates either an
26835 eqnarray environment
26837 that is described in
26838 \begin_inset CommandInset ref
26840 reference "sub:Eqnarray-Environment"
26844 or, when the option
26846 Use AMS math package
26848 in the document settings is selected, an
26852 that is described in
26853 \begin_inset CommandInset ref
26855 reference "sub:Standard-align-Environment"
26860 The align environment is recommended because it provides in any case a
26861 typographically correct output.
26864 \begin_layout Standard
26865 There are other multiline formula environments that can be created via the
26868 Insert\SpecialChar \menuseparator
26872 These environments are described in the following sections.
26875 \begin_layout Standard
26876 In all multiline formula environments a new line is created by pressing
26880 arg "newline-insert newline"
26884 To add or delete lines, the math toolbar buttons
26885 \begin_inset Graphics
26886 filename ../images/tabular-feature_append-row.png
26892 \begin_inset Graphics
26893 filename ../images/tabular-feature_delete-row.png
26898 , respectively, or the menu
26900 Edit\SpecialChar \menuseparator
26906 \begin_layout Subsubsection
26908 \begin_inset CommandInset label
26910 name "sub:Line-Separation"
26915 \begin_inset Index idx
26918 \begin_layout Plain Layout
26919 Formula ! multiline ! Line separation
26927 \begin_layout Standard
26928 There is sometimes not enough space in multiline formulas between the lines:
26929 \begin_inset Formula
26931 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}\\
26932 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
26940 \begin_layout Standard
26941 In LaTeX additional line space is specified as optional argument of the
26943 This is not yet possible in LyX
26947 \begin_layout Plain Layout
26949 \begin_inset CommandInset href
26951 name "LyX-bug #1505"
26952 target "http://www.lyx.org/trac/ticket/1505"
26961 , therefore the whole formula must be inserted in TeX-mode.
26962 To add in our example space, the command
26970 is inserted at the end of the first line.
26975 \begin_layout Plain Layout
26982 \begin_layout Plain Layout
26984 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26987 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26994 \begin_layout Plain Layout
26998 left(B^{2}+x_{0}^{2}
27006 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27011 \begin_layout Plain Layout
27023 \begin_layout Standard
27024 \begin_inset VSpace bigskip
27027 To set the line separation for all lines in a formula, the length
27034 \begin_inset Index idx
27037 \begin_layout Plain Layout
27047 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27058 \begin_inset space \thinspace{}
27063 \begin_inset space \thinspace{}
27066 mm additional line separation as in the previous example, the command
27069 \begin_layout Standard
27079 \begin_layout Standard
27080 is inserted in TeX-mode before the formula.
27081 This requires that the LaTeX-package
27089 \begin_layout Plain Layout
27094 is part of every LaTeX standard installation.
27100 \begin_inset Index idx
27103 \begin_layout Plain Layout
27109 was loaded in LaTeX-preamble with the line
27112 \begin_layout Standard
27120 \begin_layout Standard
27125 \begin_layout Plain Layout
27137 \begin_inset Formula
27139 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}\\
27140 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
27148 \begin_layout Standard
27152 \begin_layout Plain Layout
27163 To get back to the predefined distance,
27169 is set to the value 3
27170 \begin_inset space \thinspace{}
27176 \begin_layout Subsubsection
27178 \begin_inset CommandInset label
27180 name "sub:Column-Separation"
27185 \begin_inset Index idx
27188 \begin_layout Plain Layout
27189 Formula ! multiline ! Column separation
27197 \begin_layout Standard
27198 Multiline formulas form a matrix.
27199 A formula in the eqnarray environment is for example a matrix with three
27201 By changing the column separation in this environment, the space beside
27202 the relation sign can be changed.
27205 \begin_layout Standard
27206 The column separation is specified with the length
27213 \begin_inset Index idx
27216 \begin_layout Plain Layout
27225 \begin_inset Newline newline
27228 column separation = 2
27229 \begin_inset space \thinspace{}
27239 \begin_inset Newline newline
27245 \begin_layout Standard
27255 \begin_layout Standard
27256 inserted in TeX-mode, sets for all following formulas a column separation
27258 \begin_inset space \thinspace{}
27262 To get back to the predefined distance,
27269 \begin_inset space \thinspace{}
27275 \begin_layout Standard
27277 \begin_inset space \thinspace{}
27280 cm column separation:
27284 \begin_layout Plain Layout
27296 \begin_inset Formula
27304 A formula with the predefined column separation for matrices of 10
27305 \begin_inset space \thinspace{}
27312 \begin_layout Plain Layout
27324 \begin_inset Formula
27335 \begin_layout Subsubsection
27337 \begin_inset Index idx
27340 \begin_layout Plain Layout
27349 \begin_layout Standard
27350 Long formulas can be typeset using these methods:
27353 \begin_layout Itemize
27354 When one side of the equation is much shorter than the line width, this
27355 one is chosen for the left side and the right side is typeset over two
27357 \begin_inset Formula
27359 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 \\
27360 & & -\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}
27365 The minus sign at the beginning of the second line does normally not appear
27366 as an operator because it is the first character of the line.
27367 Thus it would not be surrounded by space and could not be distinguished
27368 from the fraction bar.
27370 \begin_inset space \thinspace{}
27373 pt space was inserted behind the minus sign with the command
27383 \begin_layout Plain Layout
27391 \begin_inset CommandInset ref
27393 reference "sub:Variable-Space"
27403 \begin_inset Index idx
27406 \begin_layout Plain Layout
27417 \begin_layout Itemize
27418 When both sides of the equation are too long, the command
27425 \begin_inset Index idx
27428 \begin_layout Plain Layout
27437 It is inserted in the first column of the first line and causes all further
27438 insertions to overwrite the following columns:
27439 \begin_inset Formula
27441 \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 \\
27442 & & -\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 \\
27443 & & =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}
27448 After the insertion of
27454 , the cursor is in a purple box that is a bit shifted to the left from the
27456 In this the formula is inserted.
27457 \begin_inset Newline newline
27460 The content of the further lines is inserted to the second or another formula
27462 The greater the column number where it was inserted, the larger the indentation.
27463 \begin_inset VSpace medskip
27467 \begin_inset Newline newline
27471 \begin_inset Note Greyedout
27474 \begin_layout Plain Layout
27475 Note the following when using
27484 \begin_layout Itemize
27485 The formula doesn't use the full page width.
27487 \begin_inset space \thinspace{}
27491 \begin_inset space \space{}
27495 \begin_inset Formula $-B^{2}$
27498 is added to the first line in the above example, it would have been outside
27500 To better use the width, negative space can be inserted at the beginning
27504 \begin_layout Itemize
27505 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27510 \begin_layout Plain Layout
27511 \begin_inset CommandInset href
27513 name "LyX-bug #1429"
27514 target "http://www.lyx.org/trac/ticket/1429"
27523 One can only set the cursor at the beginning of the line and move it with
27532 \begin_layout Itemize
27533 Other methods to set long formulas are offered by the environments described
27535 \begin_inset CommandInset ref
27537 reference "sub:Multline-Environment"
27542 \begin_inset CommandInset ref
27544 reference "sub:Multiline-Formula-Parts"
27551 \begin_layout Subsubsection
27553 \begin_inset CommandInset label
27555 name "sub:Multiline-Brackets"
27560 \begin_inset Index idx
27563 \begin_layout Plain Layout
27564 Brackets ! for multiline expressions
27572 \begin_layout Standard
27573 For brackets spanning multiple lines the following problem occurs:
27574 \begin_inset Formula
27576 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27577 & & \left.\cdots+B-D\right]
27585 \begin_layout Standard
27586 The closing bracket is smaller than the opening bracket because brackets
27587 with variable size may not span multiple lines.
27590 \begin_layout Standard
27591 To set the bracket size for the second line correctly, the first line is
27599 \begin_inset Index idx
27602 \begin_layout Plain Layout
27610 and the second line with
27618 \begin_layout Plain Layout
27632 \begin_inset CommandInset ref
27634 reference "sub:Automatic-Bracket-Size"
27646 \begin_inset Index idx
27649 \begin_layout Plain Layout
27672 \begin_inset space \textvisiblespace{}
27682 \begin_inset space \textvisiblespace{}
27692 \begin_inset space \textvisiblespace{}
27698 \begin_inset Formula $\downarrow$
27704 \begin_inset Index idx
27707 \begin_layout Plain Layout
27715 is inserted, because the multiplication operator with its limits is the
27716 largest symbol in the first line and this should be the size for the bracket
27717 in the second line.
27720 \begin_layout Standard
27721 The result is this:
27722 \begin_inset Formula
27724 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27725 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27733 \begin_layout Subsection
27737 \begin_layout Standard
27738 Align environments can be used for every kind of multiline formulas.
27739 They are especially useful to set several formulas side by side.
27742 \begin_layout Standard
27743 Align environments consist of columns.
27744 The odd columns are right aligned, the even ones left aligned.
27745 Every line in an Align environment can be numbered.
27748 \begin_layout Standard
27749 Align environments are created via the menu
27751 Insert\SpecialChar \menuseparator
27757 Edit\SpecialChar \menuseparator
27758 Math\SpecialChar \menuseparator
27759 Change Formula Type
27761 already existing formulas can be converted to Align environments.
27764 \begin_layout Standard
27765 To add or delete columns, the math toolbar buttons
27766 \begin_inset Graphics
27767 filename ../images/tabular-feature_append-column.png
27773 \begin_inset Graphics
27774 filename ../images/tabular-feature_delete-column.png
27779 , respectively, or the menu
27781 Edit\SpecialChar \menuseparator
27787 \begin_layout Subsubsection
27788 Standard align Environment
27789 \begin_inset CommandInset label
27791 name "sub:Standard-align-Environment"
27796 \begin_inset Index idx
27799 \begin_layout Plain Layout
27800 Formula ! multiline ! align environment
27808 \begin_layout Standard
27809 This Align environment is created by pressing
27812 arg "newline-insert newline"
27815 in a formula or by the menu
27817 Insert\SpecialChar \menuseparator
27818 Math\SpecialChar \menuseparator
27819 AMS align Environment
27824 \begin_layout Standard
27825 An example for two formulas set side by side, that are created with a four
27826 column align environment:
27827 \begin_inset Formula
27829 A & =\sin(B) & C & =D\\
27830 C & \ne A & B & \ne D
27835 As it can be seen, the formulas in this environment are placed so as if
27844 \begin_layout Plain Layout
27852 \begin_inset CommandInset ref
27854 reference "sub:Variable-Space"
27865 before the first and after every even column.
27866 When the formula style
27872 \begin_layout Plain Layout
27874 \begin_inset CommandInset ref
27876 reference "sec:Formula-Styles"
27887 is used, the formula is set without the
27893 before the first column.
27896 \begin_layout Subsubsection
27897 Alignat Environment
27898 \begin_inset Index idx
27901 \begin_layout Plain Layout
27902 Formula ! multiline ! alignat environment
27910 \begin_layout Standard
27911 The alignat environment has no predefined column separation.
27912 It can be inserted manually with the spaces that are described
27913 \begin_inset CommandInset ref
27915 reference "sub:Space"
27922 \begin_layout Standard
27923 The above example in the alignat environment where 1
27924 \begin_inset space \thinspace{}
27927 cm space was inserted at the beginning of the second formula:
27928 \begin_inset Formula
27929 \begin{alignat*}{2}
27930 A & =\sin(B) & \hspace{1cm}C & =D\\
27931 C & \ne A & B & \ne D
27936 Because the column separation can be set separately for every column, this
27937 environment is especially suitable to set three and more formulas side
27941 \begin_layout Subsubsection
27942 Flalign Environment
27943 \begin_inset CommandInset label
27945 name "sub:Flalign-Environment"
27950 \begin_inset Index idx
27953 \begin_layout Plain Layout
27954 Formula ! multiline ! flalign environment
27962 \begin_layout Standard
27963 In this environment the first two columns are always set as much as possible
27964 to the left and the last two ones to the right.
27966 \begin_inset Formula
27968 A & =1 & B & =2 & C & =3\\
27969 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27977 \begin_layout Standard
27978 By creating a flalign environment with an odd number of columns where an
27979 empty TeX-brace is inserted to the last column, several formulas in a document
27980 can be set to the left, although the formula style
27985 As example the indented formula
27986 \begin_inset CommandInset ref
27988 reference "eq:VolInt"
27993 \begin_inset Formula
27995 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28000 The first two columns contain the formula.
28001 To indent it as with the formula style
28006 \begin_inset space \thinspace{}
28009 pt space was inserted at the beginning of the first column.
28012 \begin_layout Subsection
28013 Eqnarray Environment
28014 \begin_inset CommandInset label
28016 name "sub:Eqnarray-Environment"
28021 \begin_inset Index idx
28024 \begin_layout Plain Layout
28025 Formula ! multiline ! eqnarray environment
28033 \begin_layout Standard
28034 When this environment has been created, three blue boxes appear.
28035 The content of the first box is right aligned, the content of the last
28037 The content of the middle box appears centered and a bit smaller, because
28038 it is designed to insert there only relation characters.
28039 \begin_inset Formula
28041 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28051 \begin_layout Subsection
28053 \begin_inset Index idx
28056 \begin_layout Plain Layout
28057 Formula ! multiline ! gather environment
28065 \begin_layout Standard
28066 This environment consists of only one centered column.
28067 Every line can be numbered.
28068 \begin_inset Formula
28079 \begin_layout Subsection
28080 Multline Environment
28081 \begin_inset CommandInset label
28083 name "sub:Multline-Environment"
28088 \begin_inset Index idx
28091 \begin_layout Plain Layout
28092 Formula ! multiline ! multline environment
28100 \begin_layout Standard
28101 The multline environment consists, like the gather environment, of only
28103 But the first line is left aligned, the last one right aligned.
28104 All other lines are centered.
28105 Therefore this environment is suitable for long formulas.
28107 \begin_inset CommandInset ref
28109 reference "eq:lefteqn"
28113 in the multline environment:
28114 \begin_inset Formula
28116 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}\\
28117 -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}\\
28118 =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}}
28126 \begin_layout Standard
28127 In the output only the last (first) line of a multline environment appears
28128 numbered when the document numbering is right (left).
28132 \begin_layout Plain Layout
28133 numbering styles see
28134 \begin_inset CommandInset ref
28136 reference "sec:Formula-Styles"
28148 \begin_layout Standard
28156 \begin_inset Index idx
28159 \begin_layout Plain Layout
28174 \begin_inset Index idx
28177 \begin_layout Plain Layout
28185 a centered line can be right or left aligned, respectively.
28186 The commands are used as follows:
28189 \begin_layout Standard
28194 shoveright{line content}
28200 shoveleft{line content}
28203 \begin_layout Standard
28204 \begin_inset VSpace medskip
28214 \begin_inset Index idx
28217 \begin_layout Plain Layout
28225 specifies the distance of the first line from the left page margin.
28226 Predefined is the length 0
28227 \begin_inset space \thinspace{}
28233 \begin_layout Standard
28234 As example the above formula where the command
28237 \begin_layout Standard
28247 \begin_layout Standard
28248 was inserted in TeX-mode before:
28252 \begin_layout Plain Layout
28264 \begin_inset Formula
28266 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}\\
28267 \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}}\\
28268 =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}}
28277 \begin_layout Plain Layout
28288 The second line was left aligned using
28297 \begin_layout Subsection
28298 Multiline Formula Parts
28299 \begin_inset CommandInset label
28301 name "sub:Multiline-Formula-Parts"
28306 \begin_inset Index idx
28309 \begin_layout Plain Layout
28310 Formula ! multiline ! formula parts
28318 \begin_layout Standard
28319 To display only parts of a formula with multiple lines, one of the following
28320 environments is used:
28337 They can be inserted via the menu
28339 Insert\SpecialChar \menuseparator
28342 or by using the commands described in this section.
28345 \begin_layout Standard
28346 The first three have the same properties as the corresponding multiline
28347 formula environments, but it is possible to set further formula parts beside
28350 \begin_inset Formula
28352 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28353 \Delta E\Delta t & \ge\frac{\hbar}{2}
28355 \right\} \textrm{Uncertainty relations}
28363 \begin_layout Standard
28364 To get this formula, a displayed formula is created where the command
28371 \begin_inset Index idx
28374 \begin_layout Plain Layout
28383 A purple box appears around the blue formula box where now columns and
28384 lines can be added.
28385 Outside the multiline environment other formula parts can be set, like
28389 \begin_layout Standard
28390 The aligned environment is also suitable for long formulas whose lines are
28391 horizontally aligned.
28392 Using aligned in a displayed formula has the advantage that the formula
28393 number is vertically centered behind the lines.
28395 \begin_inset CommandInset ref
28397 reference "eq:shortlong"
28401 in the aligned environment:
28402 \begin_inset Formula
28404 \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}|}\\
28405 & -\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}|}
28414 \begin_layout Standard
28415 To use the environments
28434 \begin_inset Index idx
28437 \begin_layout Plain Layout
28452 \begin_inset Index idx
28455 \begin_layout Plain Layout
28470 \begin_inset Index idx
28473 \begin_layout Plain Layout
28481 are inserted, respectively.
28482 The split environment has the same properties as the aligned environment
28483 but it can only have two columns.
28486 \begin_layout Subsection
28487 Text in multiline Formulas
28488 \begin_inset CommandInset label
28490 name "sub:Text-in-multiline"
28495 \begin_inset Index idx
28498 \begin_layout Plain Layout
28505 \begin_inset Index idx
28508 \begin_layout Plain Layout
28509 Formula ! multiline ! text
28517 \begin_layout Standard
28518 In the Align environments, and the multline and gather environment, text
28519 can be inserted that will appear in a separate line and doesn't affect
28520 the column alignment.
28521 To do this, the command
28528 \begin_inset Index idx
28531 \begin_layout Plain Layout
28539 is used in the following scheme:
28542 \begin_layout Standard
28550 \begin_layout Standard
28551 The text should not be longer than a line because it cannot be hyphenated.
28552 As LyX doesn't yet support
28558 directly, the text is written as mathematical text.
28565 must hereby be at the beginning of a line and appears in the output above
28567 An example where the text was inserted at the beginning of the second line:
28568 \begin_inset Formula
28570 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28571 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28579 \begin_layout Section
28581 \begin_inset Index idx
28584 \begin_layout Plain Layout
28591 \begin_inset Index idx
28594 \begin_layout Plain Layout
28595 Formula ! numbering|see
28599 \begin_layout Plain Layout
28610 \begin_layout Plain Layout
28625 \begin_layout Subsection
28629 \begin_layout Standard
28630 Numbered formulas can be created with the menu
28632 Insert\SpecialChar \menuseparator
28633 Math\SpecialChar \menuseparator
28635 \begin_inset space ~
28643 \begin_inset space ~
28649 Existing formulas can be numbered with the menu
28651 Edit\SpecialChar \menuseparator
28652 Math\SpecialChar \menuseparator
28654 \begin_inset space ~
28662 arg "math-number-toggle"
28666 The formula number is displayed in LyX behind the formula as a number sign
28668 The number sign is replaced in the output by the formula number.
28671 \begin_layout Standard
28672 When numbering is turned on in multiline formulas, all lines will be numbered.
28673 But the numbering can be controlled with the menu
28675 Edit\SpecialChar \menuseparator
28676 Math\SpecialChar \menuseparator
28678 \begin_inset space ~
28682 \begin_inset space ~
28686 \begin_inset space ~
28694 arg "math-number-line-toggle"
28700 \begin_layout Standard
28701 Except for inline formulas, all formulas can be numbered with two different
28703 \begin_inset CommandInset ref
28705 reference "sec:Formula-Styles"
28712 \begin_layout Subsection
28714 \begin_inset Index idx
28717 \begin_layout Plain Layout
28718 Cross-references ! to formulas
28726 \begin_layout Standard
28727 All labeled formulas can be cross-referenced.
28728 A label is added by the menu
28730 Insert\SpecialChar \menuseparator
28733 or the toolbar button
28734 \begin_inset Graphics
28735 filename ../images/label-insert.png
28741 The cursor must hereby be inside a displayed formula.
28742 Alternatively you can right-click on the formula and choose
28747 A dialog pops up displaying the prefix
28752 The label is inserted there behind the prefix.
28753 The predefined prefix means
28754 \begin_inset Quotes eld
28758 \begin_inset Quotes erd
28761 and makes it easier to find labels in large documents because it marks
28762 it as formula label to divide it from e.
28763 \begin_inset space \thinspace{}
28767 \begin_inset space \space{}
28771 To change a label, the menu
28773 Insert\SpecialChar \menuseparator
28776 is used again or you right-click on a formula and then on
28783 \begin_layout Standard
28784 The name of the label is displayed in LyX within two parentheses behind
28786 A formula with a label is always numbered.
28789 \begin_layout Standard
28790 Cross-references are inserted via the menu
28792 Insert\SpecialChar \menuseparator
28795 or with the toolbar button
28796 \begin_inset Graphics
28797 filename ../images/dialog-show-new-inset_ref.png
28803 A formula cross-reference appears in the output as formula number.
28804 When in the cross-reference dialog window the format
28808 is chosen, the cross-reference appears in the output as formula number
28810 \begin_inset Newline newline
28813 By right-clicking on a cross-reference in LyX, one jumps to the formula
28814 that is referenced.
28817 \begin_layout Standard
28818 Here are as examples cross-references to formulas of the following subsections:
28819 \begin_inset Note Note
28822 \begin_layout Plain Layout
28823 Note the different cross-reference types.
28831 \begin_layout Standard
28833 \begin_inset CommandInset ref
28840 \begin_inset CommandInset ref
28848 \begin_inset CommandInset ref
28854 ) big Latin letters are used for the numbering in contrary to (
28855 \begin_inset CommandInset ref
28864 \begin_layout Standard
28865 \begin_inset VSpace medskip
28868 When the argument of
28876 \begin_layout Plain Layout
28884 \begin_inset CommandInset ref
28886 reference "sub:User-defined-Numbering"
28897 contains a box like in
28898 \begin_inset CommandInset ref
28900 reference "sub:Paragraph-Boxes"
28904 , the formula cannot be referenced.
28907 \begin_layout Subsection
28909 \begin_inset Index idx
28912 \begin_layout Plain Layout
28913 Formula numbering ! subnumbering
28921 \begin_layout Standard
28922 With the help of the commands
28926 begin{subequations}
28934 formulas can be subnumbered.
28935 Both commands are inserted in TeX-mode.
28938 \begin_layout Standard
28940 \begin_inset Formula
28951 \begin_layout Plain Layout
28955 addtocounter{equation}{-1}
28964 \begin_layout Plain Layout
28968 begin{subequations}
28974 \begin_inset VSpace -5mm
28978 \begin_inset Formula
28986 \begin_inset Formula
28996 \begin_layout Standard
29000 \begin_layout Plain Layout
29012 \begin_layout Standard
29013 To create the example, the following is done:
29016 \begin_layout Enumerate
29017 first formula is inserted
29020 \begin_layout Enumerate
29025 addtocounter{equation}{-1}
29027 begin{subequations}
29028 \begin_inset Index idx
29031 \begin_layout Plain Layout
29040 \begin_inset Newline newline
29045 is inserted after the first formula
29048 \begin_layout Enumerate
29049 second formula is inserted
29052 \begin_layout Enumerate
29053 third formula is inserted
29056 \begin_layout Enumerate
29063 is inserted after the third formula
29066 \begin_layout Standard
29067 Every formula between the commands
29079 is subnumbered as a, b,
29080 \begin_inset Newline linebreak
29083 c, \SpecialChar \ldots{}
29084 For multiline formulas every line will be subnumbered.
29085 All subnumbered formulas are treated as
29090 But as every numbered formula increases the counter
29094 by one, the command
29100 is needed to decrease it.
29101 Otherwise the formulas
29102 \begin_inset CommandInset ref
29109 \begin_inset CommandInset ref
29116 \begin_inset CommandInset ref
29122 would be numbered as
29123 \begin_inset CommandInset ref
29130 \begin_inset CommandInset ref
29137 \begin_inset CommandInset ref
29146 \begin_layout Standard
29147 By inserting the commands in TeX-mode, a space is created between the first
29150 \begin_inset space \thinspace{}
29153 mm vertical space is inserted after the command
29157 begin{subequations}
29160 When the formula style
29166 \begin_layout Plain Layout
29168 \begin_inset CommandInset ref
29170 reference "sec:Formula-Styles"
29182 \begin_inset space \thinspace{}
29185 mm space is inserted instead.
29188 \begin_layout Standard
29189 Here is an example for a multiline formula where the numbering was turned
29190 off for the second line:
29194 \begin_layout Plain Layout
29198 begin{subequations}
29204 \begin_inset Formula
29206 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29207 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29208 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29217 \begin_layout Plain Layout
29229 \begin_layout Subsection
29230 User-defined Numbering
29231 \begin_inset CommandInset label
29233 name "sub:User-defined-Numbering"
29238 \begin_inset Index idx
29241 \begin_layout Plain Layout
29242 Formula numbering ! user-defined
29250 \begin_layout Standard
29251 \begin_inset Index idx
29254 \begin_layout Plain Layout
29255 Formula numbering ! self-defined delimiters
29260 With the standard numbering parentheses are set around the formula number.
29261 To replace the parentheses for example by vertical bars, the following
29262 line is added to the LaTeX-preamble:
29265 \begin_layout Standard
29277 \begin_inset Note Note
29280 \begin_layout Plain Layout
29281 This macro is already declared in the LaTeX-preamble for testing.
29282 To activate it, remove the percent sign at the beginning.
29290 \begin_layout Standard
29291 To use other characters, the vertical bars besides the
29295 are replaced by one ore more characters.
29296 To get only the formula number the vertical bars are omitted.
29299 \begin_layout Standard
29300 \begin_inset VSpace bigskip
29303 When there should be an expression of your choice instead of the consecutive
29304 formula number in parentheses behind the formula, the command
29311 \begin_inset Index idx
29314 \begin_layout Plain Layout
29323 \begin_inset Formula
29325 A+B=C\tag{something}\label{eq:tag}
29330 In this example the command
29335 \begin_inset space \textvisiblespace{}
29340 was inserted in the formula.
29343 \begin_layout Standard
29349 \begin_inset space \textvisiblespace{}
29354 is inserted instead, the star prevents the parentheses around the expression:
29355 \begin_inset Formula
29357 A+B=C\tag*{something}
29365 \begin_layout Standard
29366 \begin_inset VSpace bigskip
29369 To restart the formula numbering with new document parts or sections, the
29370 following command is used:
29373 \begin_layout Standard
29378 @addtoreset{equation}{part}
29381 \begin_inset Index idx
29384 \begin_layout Plain Layout
29389 \begin_layout Plain Layout
29400 \begin_layout Plain Layout
29413 \begin_layout Plain Layout
29424 \begin_layout Plain Layout
29437 \begin_inset Newline newline
29441 \begin_inset Newline newline
29448 @addtoreset{equation}{section}
29451 \begin_layout Standard
29452 To be able to use these commands in TeX-mode, the
29453 \begin_inset Quotes eld
29457 \begin_inset Quotes erd
29460 character has to be made
29461 \begin_inset Quotes eld
29465 \begin_inset Quotes erd
29468 for LaTeX using the command
29482 So the command sequence in TeX-mode is:
29485 \begin_layout Standard
29491 \begin_inset Newline newline
29496 @addtoreset{equation}{section}
29497 \begin_inset Newline newline
29505 \begin_layout Standard
29506 In the LaTeX-preamble
29518 can be omitted as they are automatically internally inserted by LyX.
29521 \begin_layout Standard
29536 \begin_layout Plain Layout
29541 is part of the LaTeX-package
29546 \begin_inset Index idx
29549 \begin_layout Plain Layout
29550 Packages ! carlisle
29555 that is part of every LaTeX standard installation.
29561 \begin_inset Index idx
29564 \begin_layout Plain Layout
29565 Packages ! remreset
29570 has to be loaded in the LaTeX-preamble with the line
29573 \begin_layout Standard
29578 usepackage{remreset}
29581 \begin_layout Standard
29589 \begin_inset Index idx
29592 \begin_layout Plain Layout
29597 \begin_layout Plain Layout
29608 \begin_layout Plain Layout
29621 \begin_layout Plain Layout
29632 \begin_layout Plain Layout
29644 can be used with the same scheme as
29653 \begin_layout Standard
29654 \begin_inset VSpace bigskip
29657 Sometimes formulas should be numbered in the following form:
29660 \begin_layout Standard
29663 (section number.formula number)
29666 \begin_layout Standard
29667 The formula number should start with every section with
29668 \begin_inset Quotes eld
29672 \begin_inset Quotes erd
29678 \begin_layout Standard
29679 For this case there is the command
29686 \begin_inset Index idx
29689 \begin_layout Plain Layout
29697 , which is used with the following scheme:
29700 \begin_layout Standard
29705 numberwithin{counter}{sectioning}
29708 \begin_layout Standard
29709 Counter denotes what kind of numbering is affected, sectioning denotes what
29710 number is before the dot.
29713 \begin_layout Standard
29714 Thus in our case the following LaTeX-preamble or TeX code line is used:
29717 \begin_layout Standard
29722 numberwithin{equation}{section}
29725 \begin_layout Standard
29726 This is the result:
29730 \begin_layout Plain Layout
29734 numberwithin{equation}{section}
29740 \begin_inset Formula
29750 \begin_layout Standard
29752 \begin_inset space \thinspace{}
29756 \begin_inset space \space{}
29759 tables so that the number of the part is the sectioning,
29760 \begin_inset Newline newline
29767 numberwithin{table}{part}
29772 \begin_layout Standard
29773 To go back to the standard numbering or to prevent this kind of numbering
29774 when it is defined by the document class, the following command is inserted
29775 as TeX code or to the LaTeX-preamble:
29778 \begin_layout Standard
29788 \begin_inset Index idx
29791 \begin_layout Plain Layout
29805 \begin_layout Plain Layout
29821 \begin_inset Newline newline
29829 \begin_inset Newline newline
29841 \begin_layout Standard
29848 uses internally the command
29854 , described above, that also needs to be reverted.
29858 \begin_layout Plain Layout
29865 \begin_layout Plain Layout
29869 @removefromreset{equation}{section}
29872 \begin_layout Plain Layout
29884 \begin_layout Subsection
29885 Numbering with Roman Numbers and Letters
29886 \begin_inset Index idx
29889 \begin_layout Plain Layout
29890 Formula numbering ! with letters
29896 \begin_inset Index idx
29899 \begin_layout Plain Layout
29900 Formula numbering ! with Roman numbers
29908 \begin_layout Standard
29909 Formulas can also be numbered with Roman numbers and Latin letters.
29910 To number for example with small Roman numbers, the command
29913 \begin_layout Standard
29925 \begin_layout Standard
29926 is inserted before the formula in TeX-mode.
29934 \begin_inset Index idx
29937 \begin_layout Plain Layout
29945 redefines the predefined command
29961 \begin_layout Plain Layout
29968 has the same scheme like the command
29974 that is described in
29975 \begin_inset CommandInset ref
29977 reference "sub:The-Command-newcommand"
29990 is the formula counter.
29997 is used as prefix for a counter, the value of the counter is output as
29999 When a formula is numbered, LaTeX sets internally the command
30005 behind the formula.
30011 \begin_inset Index idx
30014 \begin_layout Plain Layout
30024 outputs the counter as small Roman number.
30027 \begin_layout Standard
30028 All formulas behind the command
30038 are now numbered Roman.
30039 To switch to numbering with big Roman numbers, the command is inserted
30053 \begin_inset Index idx
30056 \begin_layout Plain Layout
30068 \begin_inset Quotes eld
30072 \begin_inset Quotes erd
30075 with small Latin letters there is the command
30082 \begin_inset Index idx
30085 \begin_layout Plain Layout
30093 , for big ones there is the command
30100 \begin_inset Index idx
30103 \begin_layout Plain Layout
30116 \begin_layout Standard
30117 \begin_inset Note Greyedout
30120 \begin_layout Plain Layout
30127 \begin_inset space ~
30130 formulas can be numbered with Latin letters in one document.
30138 \begin_layout Standard
30142 \begin_layout Plain Layout
30158 \begin_layout Standard
30159 \begin_inset Formula
30161 A=\textrm{small roman}
30170 \begin_layout Plain Layout
30184 \begin_inset Formula
30186 B=\textrm{big Roman}\label{eq:Rom}
30195 \begin_layout Plain Layout
30209 \begin_inset Formula
30211 C=\textrm{small Latin}
30220 \begin_layout Plain Layout
30234 \begin_inset Formula
30236 D=\textrm{big Latin}\label{eq:Lat}
30244 \begin_layout Standard
30245 To switch back to the default numbering, insert the command:
30248 \begin_layout Standard
30258 \begin_inset Index idx
30261 \begin_layout Plain Layout
30272 \begin_layout Standard
30276 \begin_layout Plain Layout
30290 \begin_inset Formula
30300 \begin_layout Standard
30301 \begin_inset VSpace medskip
30304 As you see, formulas are numbered serially independent from the numbering
30306 When then numbering should start with
30307 \begin_inset Quotes eld
30311 \begin_inset Quotes erd
30314 when the style is changed, new equation counters have to be defined.
30315 A description about this can be found in the file
30316 \begin_inset CommandInset href
30318 name "Formula-numbering.lyx"
30319 target "run:Formula-numbering.lyx"
30326 \begin_layout Standard
30327 \begin_inset Newpage newpage
30333 \begin_layout Section
30334 Chemical Symbols and Equations
30335 \begin_inset CommandInset label
30337 name "sub:Chemical-Symbols-and"
30342 \begin_inset Index idx
30345 \begin_layout Plain Layout
30346 Chemical characters ! Symbols
30352 \begin_inset Index idx
30355 \begin_layout Plain Layout
30362 \begin_inset Index idx
30365 \begin_layout Plain Layout
30374 \begin_layout Standard
30375 An example text from chemistry:
30378 \begin_layout Quote
30380 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30383 -ion reacts with two
30384 \begin_inset Formula $\mathrm{Na^{+}}$
30387 -ions to sodium sulfate
30388 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30392 The chemical equation for this is:
30393 \begin_inset Formula
30395 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30403 \begin_layout Standard
30404 This chemical equation can directly be created as formula.
30405 To avoid that the symbols appear italic, everything is highlighted and
30406 changed by the shortcut
30412 to the upright font style.
30416 \begin_layout Plain Layout
30422 \begin_inset CommandInset ref
30424 reference "sub:Font-Styles"
30436 \begin_layout Standard
30437 A more convenient way to typeset chemical formulas is to use the command
30445 \begin_inset Index idx
30448 \begin_layout Plain Layout
30456 that is available when the LaTeX-package
30461 \begin_inset Index idx
30464 \begin_layout Plain Layout
30477 to a formula a new blue box appears where chemical formulas can be inserted
30478 in an intuitive way.
30481 \begin_layout Standard
30483 \begin_inset Tabular
30484 <lyxtabular version="3" rows="9" columns="2">
30485 <features rotate="0" tabularvalignment="middle">
30486 <column alignment="center" valignment="top">
30487 <column alignment="center" valignment="top">
30489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30492 \begin_layout Plain Layout
30498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30501 \begin_layout Plain Layout
30503 \begin_inset Note Note
30506 \begin_layout Plain Layout
30513 is only used as spacer.
30525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30528 \begin_layout Plain Layout
30532 \begin_inset space \textvisiblespace{}
30540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30543 \begin_layout Plain Layout
30544 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30557 \begin_layout Plain Layout
30561 \begin_inset space \textvisiblespace{}
30569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30572 \begin_layout Plain Layout
30573 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30586 \begin_layout Plain Layout
30590 \begin_inset space \textvisiblespace{}
30598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30601 \begin_layout Plain Layout
30602 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30615 \begin_layout Plain Layout
30619 \begin_inset space \textvisiblespace{}
30627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30630 \begin_layout Plain Layout
30631 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30644 \begin_layout Plain Layout
30648 \begin_inset space \textvisiblespace{}
30654 \begin_inset space \textvisiblespace{}
30660 \begin_inset space \textvisiblespace{}
30668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30671 \begin_layout Plain Layout
30672 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30685 \begin_layout Plain Layout
30689 \begin_inset space \textvisiblespace{}
30693 \begin_inset Formula $\downarrow$
30697 \begin_inset Formula $\to$
30705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30708 \begin_layout Plain Layout
30709 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30722 \begin_layout Plain Layout
30726 \begin_inset space \textvisiblespace{}
30730 \begin_inset space \textvisiblespace{}
30734 \begin_inset space \textvisiblespace{}
30738 \begin_inset space \textvisiblespace{}
30742 \begin_inset space \textvisiblespace{}
30750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30753 \begin_layout Plain Layout
30754 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30767 \begin_layout Plain Layout
30771 \begin_inset space \textvisiblespace{}
30775 \begin_inset space \textvisiblespace{}
30779 \begin_inset space \textvisiblespace{}
30783 \begin_inset space \textvisiblespace{}
30791 \begin_inset space \textvisiblespace{}
30799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30802 \begin_layout Plain Layout
30803 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30819 \begin_layout Standard
30820 \begin_inset Note Greyedout
30823 \begin_layout Plain Layout
30829 Inserting a formula to a
30835 box will lead to LaTeX errors due to a LyX bug.
30841 \begin_layout Plain Layout
30842 \begin_inset CommandInset href
30844 name "LyX-bug #8566"
30845 target "http://www.lyx.org/trac/ticket/8566"
30856 In this case TeX code has to be used like for
30870 \begin_layout Plain Layout
30891 \begin_layout Standard
30892 \begin_inset Note Greyedout
30895 \begin_layout Plain Layout
30901 It is not possible in LyX to use the character ^ to get an up-arrow as
30907 One instead uses a negative thin space followed by the command
30914 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30925 \begin_layout Standard
30932 the command for equation
30933 \begin_inset space ~
30937 \begin_inset CommandInset ref
30939 reference "eq:chem-reaction"
30944 \begin_inset Newline newline
30952 \begin_inset space \textvisiblespace{}
30956 \begin_inset space \textvisiblespace{}
30960 \begin_inset space \textvisiblespace{}
30964 \begin_inset space \textvisiblespace{}
30968 \begin_inset space \textvisiblespace{}
30972 \begin_inset space \textvisiblespace{}
30978 \begin_layout Standard
30979 To create multiline chemical equations first a multiline formula is created
30981 \begin_inset CommandInset ref
30983 reference "sec:Multiline-Formulas"
30988 Afterwards the command
30994 is used in every small blue box of the formula.
30996 \begin_inset CommandInset ref
30998 reference "eq:TEOS-reaction-1"
31003 \begin_inset CommandInset ref
31005 reference "eq:TEOS-reaction-2"
31009 are an example of a multi-stage chemical reaction where every equation
31010 has its own number.
31011 \begin_inset Formula
31013 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31014 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31022 \begin_layout Standard
31033 package provides the command
31040 \begin_inset Index idx
31043 \begin_layout Plain Layout
31051 that has to be used for special cases.
31052 For more information about
31058 and more examples have a look at the documentation of
31063 \begin_inset CommandInset citation
31072 \begin_layout Section
31076 \begin_layout Standard
31077 LyX supports two types of commutative diagrams:
31085 that are explained in the following.
31088 \begin_layout Subsection
31090 \begin_inset Index idx
31093 \begin_layout Plain Layout
31102 \begin_layout Standard
31103 Diagrams of this type visualize relations by vertical and horizontal lines
31105 \begin_inset Formula
31107 \begin{CD}A@>>>B@>>>C\\
31118 \begin_layout Standard
31119 To get them, the command
31124 \begin_inset Index idx
31127 \begin_layout Plain Layout
31137 is inserted to a formula.
31138 A blue box appears with two dashed lines where further commands can be
31143 arg "newline-insert newline"
31146 a new line is created.
31147 Horizontal relations are inserted in odd, vertical in even formula lines.
31150 \begin_layout Standard
31151 To create the relations there are the following commands:
31154 \begin_layout Itemize
31159 creates a left arrow,
31170 \begin_layout Itemize
31175 creates an up arrow,
31183 a vertical equal sign
31186 \begin_layout Itemize
31192 is a placeholder for non-existent relations
31195 \begin_layout Standard
31196 All arrows can be labeled as follows:
31199 \begin_layout Itemize
31200 If text inserted between the first and second < or >, resp., it is placed
31202 When it is inserted between the second and third one, it appears under
31206 \begin_layout Itemize
31207 When text for vertical arrows is inserted between the first and second A
31208 or V, resp., it is placed left beside the arrow.
31209 When it is inserted between the second and third one, it appears right
31211 If the text contains an A or V, these letters must be set into a TeX-brace.
31214 \begin_layout Standard
31215 As example a diagram with all possible relations:
31218 \begin_layout Standard
31219 \begin_inset Formula
31221 \begin{CD}A@>j>>B@>>k>C@=F\\
31232 \begin_layout Standard
31233 The command for this is:
31234 \begin_inset Newline newline
31242 \begin_inset space \textvisiblespace{}
31245 A@>j>>B@>>k>C@=F Ctrl+Return
31246 \begin_inset Newline newline
31250 \begin_inset Phantom HPhantom
31253 \begin_layout Plain Layout
31259 \begin_inset space \textvisiblespace{}
31272 \begin_inset Formula $\to$
31278 \begin_inset Newline newline
31282 \begin_inset Phantom HPhantom
31285 \begin_layout Plain Layout
31291 \begin_inset space \textvisiblespace{}
31302 \begin_layout Subsection
31304 \begin_inset Index idx
31307 \begin_layout Plain Layout
31308 Diagrams ! xymatrix
31316 \begin_layout Standard
31317 To be able to use xymatrices, the LaTeX-package
31322 A xymatrix is created by inserting the command
31329 Then you are able to add new matrix columns and rows like for normal matrices,
31331 \begin_inset CommandInset ref
31333 reference "sec:Matrices"
31340 \begin_layout Standard
31341 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31343 All possibilities to create commutative diagrams and decorations are explained
31348 that you find in the menu
31350 Help\SpecialChar \menuseparator
31352 \begin_inset space ~
31360 \begin_layout Subsection
31366 \begin_inset Index idx
31369 \begin_layout Plain Layout
31378 \begin_layout Standard
31383 -diagrams, the LaTeX-package
31392 -diagram is created by inserting the command
31399 Then you are able to add new matrix columns and rows like for normal matrices,
31401 \begin_inset CommandInset ref
31403 reference "sec:Matrices"
31410 \begin_layout Standard
31411 Examples how to create
31415 diagrams in LyX is given in the
31417 Feynman-diagram manual
31419 that you find in the menu
31421 Help\SpecialChar \menuseparator
31423 \begin_inset space ~
31431 \begin_layout Standard
31432 \begin_inset Newpage newpage
31438 \begin_layout Section
31439 User-defined Commands
31440 \begin_inset Index idx
31443 \begin_layout Plain Layout
31444 User-defined commands
31452 \begin_layout Standard
31453 \begin_inset Note Greyedout
31456 \begin_layout Plain Layout
31461 The names of user-defined commands and macros may only consist of Latin
31470 \begin_layout Subsection
31474 \begin_inset CommandInset label
31476 name "sub:The-Command-newcommand"
31481 \begin_inset Index idx
31484 \begin_layout Plain Layout
31485 User-defined commands !
31493 \begin_inset Index idx
31496 \begin_layout Plain Layout
31507 \begin_layout Standard
31508 Many LaTeX-commands are too long to be used frequently.
31509 But it is possible to define with the command
31515 new shorter commands.
31518 \begin_layout Standard
31519 The command scheme of
31528 \begin_layout Standard
31533 newcommand{new command name}[number of arguments][optional
31538 \begin_inset Newline newline
31542 \begin_inset Phantom HPhantom
31545 \begin_layout Plain Layout
31555 {command definition}
31558 \begin_layout Standard
31559 \begin_inset Note Greyedout
31562 \begin_layout Plain Layout
31567 Assure that the name of the new command is not already used in your document
31568 or by LaTeX-packages that you use.
31569 When you for example define the command
31581 , you get an error message because
31587 is already defined as command for
31588 \begin_inset Quotes eld
31592 \begin_inset Formula $\le$
31596 \begin_inset Quotes erd
31607 \begin_layout Standard
31608 The number of arguments is an integer in the range 0
31609 \begin_inset space \thinspace{}
31613 \begin_inset space \thinspace{}
31616 9 and specifies how many arguments the new command should have.
31617 With the optional value a value for an optional argument can be predefined.
31618 When this is done, the
31626 rgument of the new command is automatically an optional one.
31629 \begin_layout Standard
31630 Here are some examples:
31633 \begin_layout Itemize
31634 To define the command
31646 , the LaTeX-preamble line is:
31647 \begin_inset VSpace medskip
31651 \begin_inset Newline newline
31665 \begin_layout Itemize
31666 To define the command
31678 , the argument (that should be underlined) must be taken into account.
31679 For this the preamble line is:
31680 \begin_inset VSpace medskip
31684 \begin_inset Newline newline
31698 \begin_inset VSpace medskip
31702 \begin_inset Newline newline
31709 acts as argument placeholder, the
31713 behind it denotes that it is the placeholder for the first argument.
31716 \begin_layout Itemize
31724 \begin_inset space \thinspace{}
31728 \begin_inset space \space{}
31738 \begin_inset VSpace medskip
31742 \begin_inset Newline newline
31753 framebox#1#2{$#3$}}
31756 \begin_inset VSpace medskip
31760 \begin_inset Newline newline
31763 The two Dollar signs creates the extra formula needed for
31770 \begin_inset CommandInset ref
31772 reference "sub:Boxes-with-Frame"
31779 \begin_layout Itemize
31780 To create a new command for
31786 where the color for the box need not be specified, the argument for the
31787 color is defined optional:
31788 \begin_inset VSpace medskip
31792 \begin_inset Newline newline
31803 fcolorbox{#2}{#1}{$#3$}}
31806 \begin_inset VSpace medskip
31810 \begin_inset Newline newline
31813 When the color is not specified when using
31819 , the predefined color
31826 \begin_layout Standard
31827 A test of the new defined commands:
31830 \begin_layout Standard
31832 \begin_inset Tabular
31833 <lyxtabular version="3" rows="6" columns="2">
31834 <features rotate="0" tabularvalignment="middle">
31835 <column alignment="center" valignment="top">
31836 <column alignment="center" valignment="top">
31838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31841 \begin_layout Plain Layout
31847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31850 \begin_layout Plain Layout
31852 \begin_inset Note Note
31855 \begin_layout Plain Layout
31862 is only used as spacer.
31874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31877 \begin_layout Plain Layout
31881 \begin_inset space \textvisiblespace{}
31889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31892 \begin_layout Plain Layout
31893 \begin_inset Formula $A\gr B$
31903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31906 \begin_layout Plain Layout
31914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31917 \begin_layout Plain Layout
31918 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31931 \begin_layout Plain Layout
31935 \begin_inset Formula $\to$
31941 \begin_inset Formula $\to$
31949 \begin_inset space \textvisiblespace{}
31957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31960 \begin_layout Plain Layout
31961 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31974 \begin_layout Plain Layout
31978 \begin_inset Formula $\to$
31986 \begin_inset space \textvisiblespace{}
31994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31997 \begin_layout Plain Layout
31998 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32011 \begin_layout Plain Layout
32017 \begin_inset Formula $\to$
32025 \begin_inset space \textvisiblespace{}
32033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32036 \begin_layout Plain Layout
32037 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32053 \begin_layout Subsection
32055 \begin_inset Index idx
32058 \begin_layout Plain Layout
32059 User-defined commands! Math macros
32065 \begin_inset Index idx
32068 \begin_layout Plain Layout
32077 \begin_layout Standard
32078 User-defined commands are especially convenient for complex expressions.
32079 When you are for example dealing with a document that has quadratic equations,
32080 the same solution type occurs several times.
32081 The general form of a quadratic equation is
32082 \begin_inset Formula
32084 0=\lambda^{2}+p\lambda+q
32089 The general form of the solution is
32090 \begin_inset Formula
32092 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32100 \begin_layout Standard
32101 To define a command for the solution formula where only the three parameters
32103 \begin_inset Formula $\lambda$
32107 \begin_inset Formula $p$
32111 \begin_inset Formula $q$
32114 need to be specified and the index of
32115 \begin_inset Formula $\lambda$
32118 can be given optionally, the LaTeX-preamble line is
32119 \begin_inset Newline newline
32135 \begin_inset Newline newline
32139 \begin_inset Phantom HPhantom
32142 \begin_layout Plain Layout
32156 frac{#3^{2}}{4}-#4}}
32159 \begin_layout Standard
32160 To create with this the solution formula, the command
32161 \begin_inset Newline newline
32171 \begin_inset Formula $\to$
32177 \begin_inset Formula $\to$
32184 is inserted to a formula
32189 \begin_layout Standard
32190 The definition of the new command is unintuitive because one has to know
32191 the schemes of all used LaTeX commands, e.
32192 \begin_inset space \thinspace{}
32196 \begin_inset space \space{}
32199 that a fraction is inserted in LaTeX as
32203 frac{numerator}{denominator}
32206 Furthermore one can easily forget a brace in the definition and cannot
32207 see in LyX what the new command is doing.
32208 To avoid these problems LyX offers the possibility to use math macros instead
32218 \begin_layout Standard
32219 A math macro is created by using the menu
32221 Insert\SpecialChar \menuseparator
32222 Math\SpecialChar \menuseparator
32225 or the toolbar button
32226 \begin_inset Graphics
32227 filename ../images/math-macro_newmacroname_newcommand.png
32233 The math macro toolbar appears together with the following box where the
32235 \begin_inset Newline newline
32239 \begin_inset space \hspace*{\fill}
32243 \begin_inset Graphics
32244 filename clipart/macrobox.png
32249 \begin_inset space \hspace*{\fill}
32253 \begin_inset Newline newline
32257 \begin_inset FormulaMacro
32258 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32263 newmacroname is the default name of the macro that should be changed to
32264 something sensible.
32265 The wanted formula is inserted in the first blue box.
32266 An argument placeholder is inserted with the command
32273 \begin_inset space \thinspace{}
32277 \begin_inset space \space{}
32286 or by using the macro toolbar button
32287 \begin_inset Graphics
32288 filename ../images/math-macro-add-param.png
32294 Argument placeholders are displayed red.
32296 \begin_inset space ~
32299 arguments are possible.
32300 Optional arguments are created with the toolbar button
32301 \begin_inset Graphics
32302 filename ../images/math-macro-add-optional-param.png
32308 The first non-optional argument can be transformed to an optional one with
32310 \begin_inset Graphics
32311 filename ../images/math-macro-make-optional.png
32317 In the second blue box the appearance of the macro in LyX can be defined.
32318 Normally you want to see it as it is defined, so the box is kept empty.
32319 But when you have created a macro that needs lot of space on the screen,
32320 you can insert in the box for example
32321 \begin_inset Newline newline
32351 \begin_inset Newline newline
32356 For the macro only the arguments with the macro name in front of them will
32357 then be displayed in LyX, leading to a better overview.
32358 The formula appears in the output as defined in the first box.
32359 \begin_inset Newline newline
32362 The appearance of macros in formulas can furthermore be changed for single
32363 macros by setting the cursor in the macro and using the menu
32365 View\SpecialChar \menuseparator
32367 \begin_inset space ~
32371 \begin_inset space ~
32379 \begin_layout Standard
32380 To use a macro, the macro name is inserted as command to a formula, in our
32388 Our macro looks in LyX like this:
32389 \begin_inset Newline newline
32393 \begin_inset space \hspace*{\fill}
32397 \begin_inset Graphics
32398 filename clipart/macrouse.png
32403 \begin_inset space \hspace*{\fill}
32407 \begin_inset Newline newline
32410 Here is our macro example with the arguments
32411 \begin_inset Formula $x$
32415 \begin_inset Formula $\ln(x)$
32419 \begin_inset Formula $B$
32425 \begin_layout Standard
32426 \begin_inset Formula
32436 \begin_layout Standard
32437 LyX offers in the menu
32439 Tools\SpecialChar \menuseparator
32440 Preferences\SpecialChar \menuseparator
32441 Editing\SpecialChar \menuseparator
32444 different styles to edit macros.
32445 To find the style that suits you the most, choose a style and set the cursor
32446 in a macro formula to see the difference.
32449 \begin_layout Standard
32450 A math macro is transformed internally to a
32456 command when exporting the document.
32463 command is not placed in the LaTeX-preamble, therefore macros can only
32464 be used in formulas that are in the document below the macro definition
32468 \begin_layout Standard
32469 Math macros can also be directly created from a
32476 When writing for example the command
32479 \begin_inset Newline newline
32488 xleftarrow[#2]{#1}}
32489 \begin_inset Newline newline
32494 in LyX as normal text, highlighting it completely and using then the shortcut
32499 , the command will be transformed to a math macro.
32500 Using this method you need to be careful that the
32506 command is typed correctly, otherwise you get a faulty macro leading to
32510 \begin_layout Standard
32511 Math macros currently have the problem that further formulas in macro definition
32512 s are handled wrongly.
32513 Therefore the example
32520 \begin_inset CommandInset ref
32522 reference "sub:The-Command-newcommand"
32526 cannot be created as macro.
32529 \begin_layout Standard
32530 When the cursor is in a macro definition box, you will see the macro toolbar
32534 \begin_layout Standard
32535 \begin_inset VSpace defskip
32541 \begin_layout Standard
32542 \begin_inset Graphics
32543 filename clipart/MacroToolbar.png
32548 \begin_inset Index idx
32551 \begin_layout Plain Layout
32560 \begin_layout Standard
32561 \begin_inset VSpace defskip
32567 \begin_layout Standard
32568 The macro toolbar contains from left to right the following buttons:
32571 \begin_layout Standard
32572 \begin_inset VSpace defskip
32578 \begin_layout Standard
32579 \begin_inset Tabular
32580 <lyxtabular version="3" rows="9" columns="2">
32581 <features rotate="0" islongtable="true" longtabularalignment="center">
32582 <column alignment="left" valignment="top">
32583 <column alignment="left" valignment="top" width="85col%">
32584 <row interlinespace="2.5mm">
32585 <cell alignment="center" valignment="top" usebox="none">
32588 \begin_layout Plain Layout
32589 \begin_inset Graphics
32590 filename ../images/math-macro-remove-param.png
32591 rotateOrigin center
32600 <cell alignment="center" valignment="top" usebox="none">
32603 \begin_layout Plain Layout
32606 Edit\SpecialChar \menuseparator
32607 Math\SpecialChar \menuseparator
32609 \begin_inset space ~
32612 Definition\SpecialChar \menuseparator
32613 Remove Last Argument
32619 <row interlinespace="2.5mm">
32620 <cell alignment="center" valignment="top" usebox="none">
32623 \begin_layout Plain Layout
32624 \begin_inset Graphics
32625 filename ../images/math-macro-add-param.png
32626 rotateOrigin center
32635 <cell alignment="center" valignment="top" usebox="none">
32638 \begin_layout Plain Layout
32641 Edit\SpecialChar \menuseparator
32642 Math\SpecialChar \menuseparator
32644 \begin_inset space ~
32647 Definition\SpecialChar \menuseparator
32654 <row interlinespace="2.5mm">
32655 <cell alignment="center" valignment="top" usebox="none">
32658 \begin_layout Plain Layout
32659 \begin_inset Graphics
32660 filename ../images/math-macro-make-optional.png
32661 rotateOrigin center
32670 <cell alignment="center" valignment="top" usebox="none">
32673 \begin_layout Plain Layout
32676 Edit\SpecialChar \menuseparator
32677 Math\SpecialChar \menuseparator
32679 \begin_inset space ~
32682 Definition\SpecialChar \menuseparator
32683 Make First Non-Optional into
32684 \begin_inset Newline newline
32688 \begin_inset Phantom HPhantom
32691 \begin_layout Plain Layout
32694 Edit\SpecialChar \menuseparator
32695 Math\SpecialChar \menuseparator
32697 \begin_inset space ~
32700 Definition\SpecialChar \menuseparator
32712 <row interlinespace="2.5mm">
32713 <cell alignment="center" valignment="top" usebox="none">
32716 \begin_layout Plain Layout
32717 \begin_inset Graphics
32718 filename ../images/math-macro-make-nonoptional.png
32719 rotateOrigin center
32728 <cell alignment="center" valignment="top" usebox="none">
32731 \begin_layout Plain Layout
32734 Edit\SpecialChar \menuseparator
32735 Math\SpecialChar \menuseparator
32737 \begin_inset space ~
32740 Definition\SpecialChar \menuseparator
32741 Make Last Optional into
32742 \begin_inset Newline newline
32746 \begin_inset Phantom HPhantom
32749 \begin_layout Plain Layout
32752 Edit\SpecialChar \menuseparator
32753 Math\SpecialChar \menuseparator
32755 \begin_inset space ~
32758 Definition\SpecialChar \menuseparator
32764 Non-Optional Argument
32770 <row interlinespace="2.5mm">
32771 <cell alignment="center" valignment="top" usebox="none">
32774 \begin_layout Plain Layout
32775 \begin_inset Graphics
32776 filename ../images/math-macro-remove-optional-param.png
32777 rotateOrigin center
32786 <cell alignment="center" valignment="top" usebox="none">
32789 \begin_layout Plain Layout
32792 Edit\SpecialChar \menuseparator
32793 Math\SpecialChar \menuseparator
32795 \begin_inset space ~
32798 Definition\SpecialChar \menuseparator
32799 Remove Optional Argument
32805 <row interlinespace="2.5mm">
32806 <cell alignment="center" valignment="top" usebox="none">
32809 \begin_layout Plain Layout
32810 \begin_inset Graphics
32811 filename ../images/math-macro-add-optional-param.png
32812 rotateOrigin center
32821 <cell alignment="center" valignment="top" usebox="none">
32824 \begin_layout Plain Layout
32827 Edit\SpecialChar \menuseparator
32828 Math\SpecialChar \menuseparator
32830 \begin_inset space ~
32833 Definition\SpecialChar \menuseparator
32834 Insert Optional Argument
32840 <row interlinespace="2.5mm">
32841 <cell alignment="center" valignment="top" usebox="none">
32844 \begin_layout Plain Layout
32845 \begin_inset Graphics
32846 filename ../images/math-macro-remove-greedy-param.png
32847 rotateOrigin center
32856 <cell alignment="center" valignment="top" usebox="none">
32859 \begin_layout Plain Layout
32862 Edit\SpecialChar \menuseparator
32863 Math\SpecialChar \menuseparator
32865 \begin_inset space ~
32868 Definition\SpecialChar \menuseparator
32869 Remove Last Argument
32870 \begin_inset Newline newline
32874 \begin_inset Phantom HPhantom
32877 \begin_layout Plain Layout
32880 Edit\SpecialChar \menuseparator
32881 Math\SpecialChar \menuseparator
32883 \begin_inset space ~
32886 Definition\SpecialChar \menuseparator
32892 Spitting Out To The Right
32898 <row interlinespace="2.5mm">
32899 <cell alignment="center" valignment="top" usebox="none">
32902 \begin_layout Plain Layout
32903 \begin_inset Graphics
32904 filename ../images/math-macro-append-greedy-param.png
32905 rotateOrigin center
32914 <cell alignment="center" valignment="top" usebox="none">
32917 \begin_layout Plain Layout
32920 Edit\SpecialChar \menuseparator
32921 Math\SpecialChar \menuseparator
32923 \begin_inset space ~
32926 Definition\SpecialChar \menuseparator
32928 \begin_inset Newline newline
32932 \begin_inset Phantom HPhantom
32935 \begin_layout Plain Layout
32938 Edit\SpecialChar \menuseparator
32939 Math\SpecialChar \menuseparator
32941 \begin_inset space ~
32944 Definition\SpecialChar \menuseparator
32950 Eating From The Right
32956 <row interlinespace="2.5mm">
32957 <cell alignment="center" valignment="top" usebox="none">
32960 \begin_layout Plain Layout
32961 \begin_inset Graphics
32962 filename ../images/math-macro-add-greedy-optional-param.png
32963 rotateOrigin center
32972 <cell alignment="center" valignment="top" usebox="none">
32975 \begin_layout Plain Layout
32978 Edit\SpecialChar \menuseparator
32979 Math\SpecialChar \menuseparator
32981 \begin_inset space ~
32984 Definition\SpecialChar \menuseparator
32985 Append Optional Argument
32986 \begin_inset Newline newline
32990 \begin_inset Phantom HPhantom
32993 \begin_layout Plain Layout
32996 Edit\SpecialChar \menuseparator
32997 Math\SpecialChar \menuseparator
32999 \begin_inset space ~
33002 Definition\SpecialChar \menuseparator
33008 Eating From The Right
33021 \begin_layout Section
33022 Computer Algebra Systems
33025 \begin_layout Standard
33026 LyX offers the exchange between mathematical expressions written in LyX's
33027 math editor and external applications or user defined scripts.
33028 Currently supported applications are
33045 Note that the set of supported mathematical constructs is limited only
33046 to very simple cases.
33049 \begin_layout Subsection
33053 \begin_layout Standard
33054 Write some expression in a formula, go to the
33056 Edit\SpecialChar \menuseparator
33057 Math\SpecialChar \menuseparator
33058 Use Computer Algebra System
33060 menu and choose the application you have installed on the computer.
33061 After that the result of computation should show on the right side of the
33062 expression together with the
33063 \begin_inset Quotes eld
33067 \begin_inset Quotes erd
33073 \begin_layout Standard
33074 Here are few simple examples (with results from
33078 ) to show what kind of computations can be performed:
33081 \begin_layout Itemize
33082 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33088 \begin_layout Itemize
33089 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33095 \begin_layout Itemize
33096 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33102 \begin_layout Itemize
33103 \begin_inset Formula $\det\left[\begin{array}{ccc}
33107 \end{array}\right]=-56$
33113 \begin_layout Itemize
33114 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33120 \begin_layout Subsection
33124 \begin_layout Standard
33125 Currently there is no keyboard shortcut for calling the algebra applications.
33126 One can easily bind a shortcut to the
33130 LyX function (see the
33138 \begin_inset space \thinspace{}
33142 \begin_inset space \space{}
33149 key inside the math editor.
33154 one would use this shortcut definition command:
33157 \begin_layout Standard
33160 command-alternatives break-paragraph;math-extern maxima
33163 \begin_layout Section
33165 \begin_inset Index idx
33168 \begin_layout Plain Layout
33177 \begin_layout Subsection
33179 \begin_inset Index idx
33182 \begin_layout Plain Layout
33191 \begin_layout Standard
33192 Negative numbers often look ugly in formulas because the minus sign before
33193 the number is set with the same length as the minus operator sign.
33194 When writing the negative number in normal text, the minus sign appears
33198 \begin_layout Standard
33199 Thus, the problem disappears when converting the minus sign to mathematical
33203 \begin_layout Standard
33204 An example to visualize the problem:
33207 \begin_layout Standard
33209 \begin_inset Tabular
33210 <lyxtabular version="3" rows="3" columns="2">
33211 <features rotate="0" tabularvalignment="middle">
33212 <column alignment="right" valignment="top">
33213 <column alignment="left" valignment="top">
33215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33218 \begin_layout Plain Layout
33224 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33227 \begin_layout Plain Layout
33235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33238 \begin_layout Plain Layout
33244 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33247 \begin_layout Plain Layout
33248 \begin_inset Formula $x=-2$
33258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33261 \begin_layout Plain Layout
33267 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33270 \begin_layout Plain Layout
33271 \begin_inset Formula $x=\textrm{-}2$
33287 \begin_layout Subsection
33288 Comma as decimal Separator
33289 \begin_inset Index idx
33292 \begin_layout Plain Layout
33301 \begin_layout Standard
33302 In LaTeX a comma inside a formula is used, according to the English convention,
33303 as number group separator.
33304 So there will be space added behind all commas in formulas.
33307 \begin_layout Standard
33308 To avoid this, the comma is highlighted and changed to mathematical text
33318 \begin_layout Standard
33319 To use all formula commas in the document as decimal separator, the file
33328 \begin_layout Plain Layout
33333 is part of the LaTeX-package
33338 \begin_inset Index idx
33341 \begin_layout Plain Layout
33346 \begin_layout Plain Layout
33366 \begin_inset Index idx
33369 \begin_layout Plain Layout
33375 is loaded with the LaTeX-preamble line
33378 \begin_layout Standard
33386 \begin_layout Subsection
33388 \begin_inset CommandInset label
33390 name "sub:Physical-Vectors"
33395 \begin_inset Index idx
33398 \begin_layout Plain Layout
33407 \begin_layout Standard
33408 Predefined vectors are offered by the LaTeX-package
33413 \begin_inset Index idx
33416 \begin_layout Plain Layout
33422 that is loaded with the LaTeX-preamble line
33425 \begin_layout Standard
33433 \begin_layout Standard
33437 \begin_layout Plain Layout
33447 \begin_inset Note Note
33450 \begin_layout Plain Layout
33451 The following table will only be displayed when the LaTeX-package
33463 \begin_layout Standard
33464 The following commands are defined:
33467 \begin_layout Standard
33469 \begin_inset Tabular
33470 <lyxtabular version="3" rows="4" columns="2">
33471 <features rotate="0" tabularvalignment="middle">
33472 <column alignment="center" valignment="top">
33473 <column alignment="center" valignment="top">
33475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33478 \begin_layout Plain Layout
33484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33487 \begin_layout Plain Layout
33495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33498 \begin_layout Plain Layout
33508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33511 \begin_layout Plain Layout
33512 \begin_inset Formula $\Bra{\psi}$
33522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33525 \begin_layout Plain Layout
33535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33538 \begin_layout Plain Layout
33539 \begin_inset Formula $\Ket{\psi}$
33549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33552 \begin_layout Plain Layout
33564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33567 \begin_layout Plain Layout
33568 \begin_inset Formula $\Braket{\psi|\phi}$
33584 \begin_layout Standard
33591 assures that all vertical bars are set in the size of the surrounding brackets:
33592 \begin_inset Formula
33594 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33603 \begin_layout Plain Layout
33613 \begin_inset Note Note
33616 \begin_layout Plain Layout
33617 The following will be displayed when the LaTeX-package
33629 \begin_layout Standard
33630 You need to install the LaTeX-package
33634 to see the rest of this subsection in the output.
33637 \begin_layout Standard
33641 \begin_layout Plain Layout
33653 \begin_layout Standard
33660 can also be achieved using the command
33666 , that is described in
33667 \begin_inset CommandInset ref
33669 reference "sub:Automatic-Bracket-Size"
33676 \begin_layout Subsection
33677 Self-defined Fractions
33678 \begin_inset CommandInset label
33680 name "sub:Self-defined-Fractions"
33685 \begin_inset Index idx
33688 \begin_layout Plain Layout
33689 Fractions ! self-defined
33697 \begin_layout Standard
33698 To define custom commands for fractions, the command
33705 \begin_inset Index idx
33708 \begin_layout Plain Layout
33715 \begin_layout Plain Layout
33729 is used in the following scheme:
33732 \begin_layout Standard
33745 bracket}{fraction bar thickness}{style}
33746 \begin_inset Newline newline
33750 \begin_inset Phantom HPhantom
33753 \begin_layout Plain Layout
33763 {numerator}{denominator}
33766 \begin_layout Standard
33767 The style is a number in the range of 0
33768 \begin_inset space \thinspace{}
33772 \begin_inset space \thinspace{}
33778 \begin_layout Standard
33780 \begin_inset Tabular
33781 <lyxtabular version="3" rows="5" columns="2">
33782 <features rotate="0" tabularvalignment="middle">
33783 <column alignment="center" valignment="top">
33784 <column alignment="center" valignment="top">
33786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33789 \begin_layout Plain Layout
33795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33798 \begin_layout Plain Layout
33806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33809 \begin_layout Plain Layout
33815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33818 \begin_layout Plain Layout
33819 display style formula
33826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33829 \begin_layout Plain Layout
33835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33838 \begin_layout Plain Layout
33846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33849 \begin_layout Plain Layout
33855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33858 \begin_layout Plain Layout
33866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33869 \begin_layout Plain Layout
33875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33878 \begin_layout Plain Layout
33892 \begin_layout Standard
33893 When no style is given, the size is adjusted to the surrounding environment
33894 like for the command
33903 \begin_layout Standard
33904 When no fraction bar thickness is given, the predefined value of 0.4
33905 \begin_inset space \thinspace{}
33911 \begin_layout Standard
33912 \begin_inset VSpace medskip
33915 For example, the commands
33928 \begin_inset CommandInset ref
33930 reference "sub:Fractions"
33934 are defined with the commands
33937 \begin_layout Standard
33946 genfrac{}{}{}{0}{#1}{#2}}
33949 \begin_layout Standard
33953 \begin_layout Standard
33962 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33965 \begin_layout Standard
33966 \begin_inset VSpace medskip
33969 To define a fraction where the fraction bar thickness can be given as optional
33970 argument, the following line is inserted to the LaTeX-preamble:
33973 \begin_layout Standard
33982 genfrac{}{}{#1}{}{#2}{#3}}
33985 \begin_layout Standard
33987 \begin_inset Formula
33989 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33990 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33995 As one can see, the distance of the numerator and the denominator to the
33996 fraction bar is round about three times the bar thickness.
33999 \begin_layout Subsection
34001 \begin_inset Index idx
34004 \begin_layout Plain Layout
34013 \begin_layout Standard
34014 There are four ways to cancel formulas or parts of formulas:
34017 \begin_layout Standard
34021 \begin_layout Plain Layout
34031 \begin_inset Note Note
34034 \begin_layout Plain Layout
34035 The following table will only be displayed when the LaTeX-package
34047 \begin_layout Standard
34049 \begin_inset Tabular
34050 <lyxtabular version="3" rows="5" columns="2">
34051 <features rotate="0" tabularvalignment="middle">
34052 <column alignment="center" valignment="top">
34053 <column alignment="center" valignment="top">
34055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34058 \begin_layout Plain Layout
34064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34067 \begin_layout Plain Layout
34069 \begin_inset Note Note
34072 \begin_layout Plain Layout
34079 are used here as spacer.
34091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34094 \begin_layout Plain Layout
34098 \begin_inset space \textvisiblespace{}
34104 \begin_inset space \textvisiblespace{}
34112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34115 \begin_layout Plain Layout
34116 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34129 \begin_layout Plain Layout
34133 \begin_inset space \textvisiblespace{}
34139 \begin_inset space \textvisiblespace{}
34147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34150 \begin_layout Plain Layout
34151 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34164 \begin_layout Plain Layout
34168 \begin_inset space \textvisiblespace{}
34174 \begin_inset space \textvisiblespace{}
34182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34185 \begin_layout Plain Layout
34186 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34199 \begin_layout Plain Layout
34203 \begin_inset space \textvisiblespace{}
34209 \begin_inset space \textvisiblespace{}
34213 \begin_inset Formula $\to$
34221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34224 \begin_layout Plain Layout
34225 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34241 \begin_layout Standard
34248 is especially suitable to visualize the reduction of fractions within formulas:
34249 \begin_inset Formula
34251 \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}}}
34259 \begin_layout Standard
34260 To change the size of
34267 \begin_inset Quotes eld
34271 \begin_inset Quotes erd
34274 value one can add the LaTeX-preamble line
34277 \begin_layout Standard
34282 PassOptionsToPackage{option}{cancel}
34285 \begin_layout Standard
34294 which leads to the same size as for the canceled value, or
34298 which makes is it a bit smaller than normal.
34301 \begin_layout Standard
34302 To color the cancellation bar one adds this command as TeX code:
34305 \begin_layout Standard
34317 \begin_layout Standard
34322 can be replaced by a color of your choice.
34325 \begin_layout Standard
34329 \begin_layout Plain Layout
34345 \begin_layout Standard
34346 \begin_inset Formula
34348 \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}}}
34356 \begin_layout Standard
34360 \begin_layout Plain Layout
34374 \begin_inset Note Note
34377 \begin_layout Plain Layout
34386 \begin_layout Standard
34387 For further customizations, see the documentation of the package
34392 \begin_inset CommandInset citation
34399 \begin_inset Index idx
34402 \begin_layout Plain Layout
34411 \begin_layout Standard
34415 \begin_layout Plain Layout
34425 \begin_inset Note Note
34428 \begin_layout Plain Layout
34429 The following will be displayed when the LaTeX-package
34441 \begin_layout Standard
34442 You need to install the LaTeX-package
34446 to see the rest of this subsection in the output.
34449 \begin_layout Standard
34453 \begin_layout Plain Layout
34465 \begin_layout Standard
34466 \begin_inset Newpage newpage
34472 \begin_layout Subsection
34473 Formulas in Section Headings
34474 \begin_inset CommandInset label
34476 name "sub:Formulas-in-Section"
34481 \begin_inset Index idx
34484 \begin_layout Plain Layout
34485 Formula ! in section headings
34493 \begin_layout Standard
34494 When formulas are used in section headings, the following has to be taken
34498 \begin_layout Standard
34499 \begin_inset Note Greyedout
34502 \begin_layout Plain Layout
34508 \begin_inset Index idx
34511 \begin_layout Plain Layout
34512 Packages ! hyperref
34517 support is enabled in the document settings dialog under
34520 \begin_inset space ~
34525 , PDF-bookmarks are created for every section heading in the table of contents.
34526 If a section heading contains formulas, they are incorrectly displayed
34527 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34536 \begin_layout Standard
34537 Both problems can be solved by inserting at the end of the section heading
34538 a short title with the menu
34540 Insert\SpecialChar \menuseparator
34542 \begin_inset space ~
34548 Short titles are used as alternative for multiline section headings to
34549 keep the table of contents clearly arranged.
34550 Only the short title appears in the table of contents and therefore also
34551 in the PDF-bookmark.
34554 \begin_layout Standard
34555 When formulas should be used in the table of contents but
34559 is used, one can use the following command in TeX-mode:
34562 \begin_layout Standard
34567 texorpdfstring{part}{alternative}
34568 \begin_inset Index idx
34571 \begin_layout Plain Layout
34582 \begin_layout Standard
34583 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34584 This can be characters, formulas, footnotes, but also cross-references.
34585 The alternative is used instead of the part for the bookmark.
34588 \begin_layout Standard
34589 Here are two example headings:
34590 \begin_inset VSpace -3mm
34597 \begin_layout Plain Layout
34609 \begin_layout Subsubsection
34610 Heading without formula in table of contents
34611 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34615 \begin_inset Argument 1
34618 \begin_layout Plain Layout
34619 Heading without formula in table of contents
34627 \begin_layout Subsubsection
34628 Heading with formula in table of contents
34632 \begin_layout Plain Layout
34642 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34649 \begin_layout Plain Layout
34659 \begin_layout Standard
34663 \begin_layout Plain Layout
34672 In the first heading a short title was used, in the second one
34681 \begin_layout Standard
34682 To get the same formatting as for the other headings, the complete heading
34691 \begin_layout Plain Layout
34693 \begin_inset CommandInset ref
34695 reference "sub:Bold-Formulas"
34707 \begin_layout Subsection
34708 Formulas in multi-column Text
34709 \begin_inset Index idx
34712 \begin_layout Plain Layout
34713 Formula ! in multi-column text
34721 \begin_layout Standard
34722 Formulas in multi-column text are often too wide to fit into a column and
34723 thus need to be set over the whole page width.
34724 This is done by using the LaTeX-package
34732 \begin_layout Plain Layout
34737 is part of every LaTeX standard installation.
34743 \begin_inset Index idx
34746 \begin_layout Plain Layout
34747 Packages ! multicol
34752 , that is loaded with the LaTeX-preamble line
34755 \begin_layout Standard
34760 usepackage{multicol}
34763 \begin_layout Standard
34764 \begin_inset Note Greyedout
34767 \begin_layout Plain Layout
34768 Note that in this case the setting
34771 \begin_inset space ~
34778 Document\SpecialChar \menuseparator
34784 \begin_inset space ~
34804 \begin_layout Standard
34805 Before the multi-column text the command
34808 \begin_layout Standard
34813 begin{multicols}{column number}
34816 \begin_layout Standard
34817 is written in TeX-mode.
34818 The column number is a number in the range of 2
34819 \begin_inset space \thinspace{}
34823 \begin_inset space \thinspace{}
34827 Before the formula the multi-column text is ended by inserting the command
34830 \begin_layout Standard
34838 \begin_layout Standard
34842 \begin_layout Standard
34843 Due to the command some space is automatically added before the formula.
34845 \begin_inset space \thinspace{}
34848 mm vertical space is inserted before the formula.
34849 When the formula style
34855 \begin_layout Plain Layout
34857 \begin_inset CommandInset ref
34859 reference "sec:Formula-Styles"
34871 \begin_inset space \thinspace{}
34874 mm space is inserted instead.
34877 \begin_layout Standard
34878 As example a multi-column text with a displayed formula:
34881 \begin_layout Standard
34887 \begin_layout Plain Layout
34891 begin{multicols}{2}
34896 Das Spektrum wird fouriertransformiert.
34897 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34898 , Lösungsmittel) zu trennen.
34899 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34900 nun das Aussehen des Ausgangssignals.
34901 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34902 über alle Phasen integrieren muss.
34904 \begin_inset Formula $S$
34907 unser normiertes Ausgangssignal und
34908 \begin_inset Formula $P$
34911 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34915 \begin_layout Plain Layout
34925 \begin_inset VSpace -6mm
34929 \begin_inset Formula
34931 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34940 \begin_layout Plain Layout
34944 begin{multicols}{2}
34950 \begin_inset Formula $S_{0}$
34953 das Signal ohne Gradient ist und die Normierungsbedingung
34954 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34958 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34960 \begin_inset Formula $\nicefrac{\pi}{2}$
34964 \begin_inset space \thinspace{}
34967 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34968 das Signal zusätzlich abschwächt.
34969 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34971 \begin_inset Formula $T_{2}$
34977 \begin_layout Standard
34983 \begin_layout Plain Layout
34995 \begin_layout Subsection
34996 Formulas with Description of Variables
34997 \begin_inset Index idx
35000 \begin_layout Plain Layout
35001 Formula ! with description of variables
35009 \begin_layout Standard
35010 To describe variables within a formula, like in formula
35011 \begin_inset CommandInset ref
35013 reference "eq:within"
35022 \begin_inset Formula $n$
35026 \begin_inset space ~
35029 matrix is used with left aligned columns for the
35030 \begin_inset Formula $n$
35037 \begin_layout Plain Layout
35039 \begin_inset CommandInset ref
35041 reference "sec:Matrices"
35050 To set the description in a smaller size, before the matrix e.
35051 \begin_inset space \thinspace{}
35055 \begin_inset space \space{}
35068 \begin_layout Plain Layout
35070 \begin_inset CommandInset ref
35072 reference "sub:Font-Sizes"
35084 \begin_layout Standard
35085 When the formula style
35091 \begin_layout Plain Layout
35093 \begin_inset CommandInset ref
35095 reference "sec:Formula-Styles"
35116 \begin_layout Plain Layout
35123 only works in formulas with the style
35128 \begin_inset CommandInset ref
35130 reference "sub:Variable-Space"
35139 is inserted before and after the matrix to have the same separation of
35140 the matrix from the equation and the side margin.
35143 \begin_layout Standard
35144 When the formula style
35148 is used, the method described in
35149 \begin_inset CommandInset ref
35151 reference "sub:Flalign-Environment"
35155 is used to indent formulas.
35157 \begin_inset CommandInset ref
35159 reference "eq:within"
35163 consists of five columns where in the first two columns contain the equation,
35164 the third the matrix and the last one an empty TeX-brace.
35165 \begin_inset Formula
35167 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35168 \rho & \textrm{density}\\
35169 V & \textrm{volume}\\
35170 g & \textrm{gravitational acceleration}
35171 \end{array} & & {}\label{eq:within}
35179 \begin_layout Subsection
35180 Upright small Greek Letters
35181 \begin_inset CommandInset label
35183 name "sub:Upright-small-Greek"
35188 \begin_inset Index idx
35191 \begin_layout Plain Layout
35192 Greek letters ! upright
35200 \begin_layout Standard
35201 Most of the math fonts only provide italic small Greek letters.
35202 But for symbols of elementary particles like pions and neutrinos, upright
35203 Greek letters are needed.
35212 \begin_layout Plain Layout
35217 is part of the LaTeX-package
35222 \begin_inset Index idx
35225 \begin_layout Plain Layout
35230 \begin_layout Plain Layout
35250 \begin_inset Index idx
35253 \begin_layout Plain Layout
35259 that is loaded with the LaTeX-preamble line
35262 \begin_layout Standard
35267 usepackage{upgreek}
35270 \begin_layout Standard
35276 \begin_layout Plain Layout
35286 \begin_inset Note Note
35289 \begin_layout Plain Layout
35290 The following table will only be displayed when the LaTeX-package
35299 They are created when the command for a small Greek letter is started with
35305 For example the command
35312 \begin_inset Formula $\uptau$
35318 \begin_layout Standard
35319 With these commands reactions of elementary particles can be typeset:
35320 \begin_inset Formula
35322 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35330 \begin_layout Standard
35331 The upright letters are more bold and wider than the italic ones.
35332 They should therefore not be used for units like
35333 \begin_inset Quotes eld
35337 \begin_inset Quotes erd
35343 \begin_layout Standard
35347 \begin_layout Plain Layout
35357 \begin_inset Note Note
35360 \begin_layout Plain Layout
35361 The following will be displayed when the LaTeX-package
35373 \begin_layout Standard
35374 You need to install the LaTeX-package
35378 to see the rest of this subsection in the output.
35381 \begin_layout Standard
35385 \begin_layout Plain Layout
35397 \begin_layout Subsection
35398 Text Characters in Formulas
35399 \begin_inset CommandInset label
35401 name "sub:Text-Characters-in"
35406 \begin_inset Index idx
35409 \begin_layout Plain Layout
35418 \begin_layout Standard
35419 In some cases you might want to insert text characters directly into formulas.
35420 When for example the centered dot · is often used in formulas like
35421 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35424 , one would have to insert the command
35434 \begin_layout Plain Layout
35436 \begin_inset CommandInset ref
35438 reference "sub:Binary-Operators"
35447 all the time, because this character is defined in all encodings as text
35449 But the encoding can be changed by this LaTeX-preamble line:
35452 \begin_layout Standard
35457 Declare Inputtext{183}{
35467 f\SpecialChar \textcompwordmark{}
35471 \begin_layout Standard
35472 The character encoding (menu
35474 Document\SpecialChar \menuseparator
35475 Settings\SpecialChar \menuseparator
35478 ) specifies what character appears when a keyboard key is pressed.
35479 When the key for the character '·' is pressed, internally the command
35486 But this command is not available in a formula so that you would get LaTeX-erro
35488 With the changed encoding the right command is chosen automatically, depending
35489 on if the character was inserted into a formula or not.
35492 \begin_layout Standard
35493 The encoding of several characters is saved in definition files.
35494 For example the encoding
35498 is defined in the file
35502 which is in the installation folder of LaTeX.
35503 Encodings should only be changed via the LaTeX-preamble and not in the
35505 Otherwise documents could not be edited by other LyX users working on other
35509 \begin_layout Standard
35510 \begin_inset VSpace medskip
35513 Besides the centered dot, in this document the degree sign ° is defined
35514 with the following LaTeX-preamble line so that it can be directly inserted
35518 \begin_layout Standard
35523 DeclareInputtext{176}{
35533 f\SpecialChar \textcompwordmark{}
35537 \begin_layout Standard
35538 \begin_inset Newpage newpage
35544 \begin_layout Section
35547 \begin_inset Index idx
35550 \begin_layout Plain Layout
35559 \begin_layout Standard
35560 This section is a summary of the most important typographic rules, listed
35565 \begin_layout Plain Layout
35566 This collection was partly taken from the German semi-official dictionary
35568 \begin_inset Quotes eld
35572 \begin_inset Quotes erd
35576 \begin_inset CommandInset citation
35582 that lists some of the ISO rules.
35583 More rules are listed in
35584 \begin_inset CommandInset citation
35598 \begin_layout Itemize
35607 \begin_layout Plain Layout
35608 done with font styles, see
35609 \begin_inset CommandInset ref
35611 reference "sub:Font-Styles"
35620 , no matter if they appear in italic text: 30
35621 \begin_inset space \thinspace{}
35625 \begin_inset Newline newline
35628 Between the value and the unit is the smallest space, see
35629 \begin_inset CommandInset ref
35631 reference "sub:Predefined-Space"
35636 \begin_inset Newline newline
35639 This convention is automatically fulfilled when the command
35646 When it is entered to a formula, two boxes appear.
35647 In the first one the value is inserted, in the second one the unit, and
35649 \begin_inset Formula $\unit[30]{km/h}$
35653 \begin_inset space \thinspace{}
35663 is not a real LaTeX command but the command
35669 , therefore you cannot use it in TeX code.
35672 \begin_layout Itemize
35673 Percent and perthousand signs are set like physical units:
35674 \begin_inset Newline newline
35678 \begin_inset space \thinspace{}
35684 \begin_layout Itemize
35685 The degree sign follows directly on the value: 15°, but not when it is used
35687 \begin_inset space \thinspace{}
35693 \begin_layout Itemize
35694 In numbers with more than four digits the smallest space is inserted before
35695 every third digit to group them:
35705 \begin_inset space \thinspace{}
35709 \begin_inset space \thinspace{}
35715 \begin_layout Itemize
35716 For dimensions like 120×90×40
35717 \begin_inset space \thinspace{}
35720 cm the multiplication sign
35721 \begin_inset Quotes eld
35725 \begin_inset Quotes erd
35729 It is available either via the command
35737 Insert\SpecialChar \menuseparator
35738 Special Character\SpecialChar \menuseparator
35744 \begin_layout Itemize
35745 Functions with names consisting of several letters are set upright to avoid
35747 \begin_inset CommandInset ref
35749 reference "sub:Predefined-Functions"
35756 \begin_layout Itemize
35757 Indices consisting of several letters, are set upright:
35758 \begin_inset Formula $E_{\mathrm{kin}}$
35762 \begin_inset Newline newline
35765 Components of matrices are set italic:
35766 \begin_inset Formula $\hat{H}_{kl}$
35772 \begin_layout Itemize
35773 The differentiation/integration operator 'd', the Euler's number 'e' and
35774 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35778 \begin_layout Itemize
35779 The character that denotes a
35783 transformation is inserted either by the command
35788 \begin_inset space \textvisiblespace{}
35795 Insert\SpecialChar \menuseparator
35796 Special Character\SpecialChar \menuseparator
35797 Symbols\SpecialChar \menuseparator
35799 \begin_inset space ~
35805 \begin_inset Formula $\mathscr{F}$
35811 \begin_layout Standard
35812 \begin_inset Newpage newpage
35818 \begin_layout Section
35820 \begin_inset Index idx
35823 \begin_layout Plain Layout
35832 \begin_layout Standard
35833 Some characters and symbols can be created with several commands.
35834 Here is a list of the synonym commands:
35837 \begin_layout Standard
35838 \begin_inset VSpace bigskip
35842 \begin_inset space \hfill{}
35846 \begin_inset Tabular
35847 <lyxtabular version="3" rows="12" columns="2">
35848 <features rotate="0" tabularvalignment="middle">
35849 <column alignment="center" valignment="top" width="0pt">
35850 <column alignment="center" valignment="top" width="0pt">
35852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35855 \begin_layout Plain Layout
35861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35864 \begin_layout Plain Layout
35866 \begin_inset Note Note
35869 \begin_layout Plain Layout
35876 is only used as spacer.
35888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35891 \begin_layout Plain Layout
35899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35902 \begin_layout Plain Layout
35906 \begin_layout Plain Layout
35919 \begin_layout Plain Layout
35933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35936 \begin_layout Plain Layout
35944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35947 \begin_layout Plain Layout
35957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35960 \begin_layout Plain Layout
35968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35971 \begin_layout Plain Layout
35981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35984 \begin_layout Plain Layout
35992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35995 \begin_layout Plain Layout
36003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36006 \begin_layout Plain Layout
36014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36017 \begin_layout Plain Layout
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