1 #LyX 1.6.0rc1 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
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
77 \usepackage[samesize]{cancel}
79 % enables calculation of values,
82 % for multiple table row and column cells
89 % center multirows (e.g. in sec. 13.3)
90 \renewcommand{\multirowsetup}{\centering}
92 % define a color, used in sec.9.3
93 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
95 % declare operators (see sec. 10.4 and sec. 15.2)
96 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
97 \DeclareMathOperator{\sgn}{sgn}
99 \newcommand{\spce}{\textvisiblespace}
101 % example definitions for sec. 20.1
102 \newcommand{\gr}{\Longrightarrow}
103 \newcommand{\us}[1]{\underline{#1}}
104 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
105 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
106 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
108 % example macro from sec. 19.4
109 %\def\tagform@#1{\maketag@@@{|#1|}}
111 % macro from sec. 10.2
112 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
113 \def\mathclap {\mathpalette \mathclapinternal}
114 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
116 % redefine the greyed out note
117 \renewenvironment{lyxgreyedout}
118 {\textcolor{blue}\bgroup}{\egroup}
120 % ------------------------------------
121 % used to check for needed LaTeX packages
124 % check for package eurosym
125 % used for the Euro symbol
127 \IfFileExists{eurosym.sty}
128 {\usepackage[gennarrow]{eurosym}
129 \setboolean{eurosym}{true}}
130 {\setboolean{eurosym}{false}}
132 % needed in sec. 22.4
133 % check for package braket
135 \IfFileExists{braket.sty}
137 \setboolean{braket}{true}}
138 {\setboolean{braket}{false}}
140 % needed in sec. 22.10
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
153 \font_typewriter default
154 \font_default_family default
164 \pdf_title "LyX's Math Manual"
165 \pdf_author "LyX Team, Uwe Stöhr"
166 \pdf_subject "LyX-documentation about math"
167 \pdf_keywords "LyX, Mathed"
169 \pdf_bookmarksnumbered true
170 \pdf_bookmarksopen true
171 \pdf_bookmarksopenlevel 1
172 \pdf_breaklinks false
176 \pdf_pagebackref false
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178 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
185 \paperorientation portrait
188 \paragraph_separation skip
190 \quotes_language english
193 \paperpagestyle plain
197 \tracking_changes false
198 \output_changes false
206 LyX's detailed Math manual
214 \begin_layout Plain Layout
216 If you have comments or error corrections, please send them to the LyX Documenta
220 \begin_inset CommandInset href
222 name "lyx-docs@lists.lyx.org"
223 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
234 \begin_inset Note Note
237 \begin_layout Plain Layout
244 \begin_inset Newline newline
248 \begin_inset Newline newline
256 \begin_layout Standard
257 \begin_inset CommandInset toc
258 LatexCommand tableofcontents
265 \begin_layout Standard
266 \begin_inset Note Note
269 \begin_layout Plain Layout
270 To export this document to PDF, PS, or DVI the LaTeX-packages
283 If they are not installed you can export the document anyway but the sections
284 where the packages are required won't appear in the output.
287 \begin_layout Plain Layout
288 The latest PDF-version of this document can be found here:
289 \begin_inset Newline newline
294 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
302 \begin_layout Standard
303 \begin_inset Newpage newpage
309 \begin_layout Section
311 \begin_inset CommandInset label
313 name "sec:Introduction"
320 \begin_layout Standard
321 This document explains LyX's math features and is furthermore a collection
322 of LaTeX-commands used for mathematical characters and constructs.
323 The explanations are designed for the usage of commands.
324 It is therefore required that you have read the section
335 \begin_layout Standard
336 Most of the characters and many constructs explained in this manual are
337 also accessible via the menu
341 \SpecialChar \menuseparator
357 But everybody who has to write lots of formulas will notice that it is
358 much faster to use commands instead of the math toolbar.
359 Therefore this manual is focused on commands but also mentions the correspondin
360 g toolbar buttons when available.
363 \begin_layout Standard
364 If not specially mentioned the commands are only available within formulas.
365 To be able to use all commands explained in this document, the option
369 must be used in the document settings (menu
371 Document\SpecialChar \menuseparator
372 Settings\SpecialChar \menuseparator
383 \begin_layout Plain Layout
386 Use AMS math package automatically
392 \begin_layout Plain Layout
401 -math when math constructs are found that are supported by LyX.
409 \begin_layout Standard
410 This document doesn't list all
414 \begin_layout Plain Layout
427 \begin_layout Plain Layout
432 \begin_layout Plain Layout
441 -math commands is in the file
444 \begin_inset CommandInset href
447 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
453 , which is part of every LaTeX standard installation.
458 for lucidity reasons.
461 \begin_layout Section
463 \begin_inset CommandInset label
465 name "sec:General-Instructions"
472 \begin_layout Standard
473 To create an inline formula
477 \begin_layout Plain Layout
483 that is embedded into a text line, press
487 or the toolbar button
488 \begin_inset Graphics
489 filename ../images/math-mode.png
495 \begin_inset Newline newline
498 To create a display style formula
502 \begin_layout Plain Layout
503 Formula ! display style
508 that will appear bigger and in an own paragraph, press
515 \begin_layout Standard
516 To change a display style formula to an inline formula, set the cursor into
517 the formula and press
523 Edit\SpecialChar \menuseparator
524 Math\SpecialChar \menuseparator
528 The same way is used to change an inline formula to a display style formula.
531 \begin_layout Standard
532 To display parts of an inline formula in the size of a display style formula,
541 \begin_layout Plain Layout
552 Then a new blue box appears in which the desired formula part is inserted.
555 \begin_layout Standard
556 Only inline formulas are allowed inside tables.
559 \begin_layout Standard
564 can be turned on in the menu
566 View\SpecialChar \menuseparator
570 When you click there on
571 \begin_inset Quotes eld
575 \begin_inset Quotes erd
578 the toolbar will be shown permanently at the bottom; this state is visualized
583 menu with a checkmark.
584 When you click in this state again on
585 \begin_inset Quotes eld
589 \begin_inset Quotes erd
600 is only shown when the cursor is within a formula; this state is visualized
601 by the renaming of the menu entry from
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
610 \begin_inset Quotes eld
618 \begin_inset Quotes erd
624 \begin_layout Standard
629 \begin_layout Plain Layout
635 is invoked by pressing the toolbar button
636 \begin_inset Graphics
637 filename ../images/ert-insert.png
644 Insert\SpecialChar \menuseparator
649 \begin_layout Plain Layout
663 \begin_inset Note Note
666 \begin_layout Plain Layout
667 In LyX there are three
668 \begin_inset Quotes eld
672 \begin_inset Quotes erd
675 that appear in the output with sub- and superscript letters: TeX, LaTeX,
679 \begin_layout Plain Layout
680 To avoid that these names are recognized as proper names, a TeX-brace pair
689 \begin_layout Standard
690 To change the LaTeX-preamble
694 \begin_layout Plain Layout
702 Document\SpecialChar \menuseparator
703 Settings\SpecialChar \menuseparator
708 \begin_layout Plain Layout
724 \begin_layout Standard
725 To edit matrices, case differentiations, and multiline formulas subsequently,
728 Edit\SpecialChar \menuseparator
733 Edit\SpecialChar \menuseparator
735 \begin_inset space \thinspace{}
739 \begin_inset space \thinspace{}
749 When lines and columns are swapped via the menu, the column or line where
750 the cursor is in is exchanged with the column to the right or the line
752 Is the cursor in the last column or row, the exchange is done with the
753 column to the left or the line above.
756 \begin_layout Standard
757 To write text in formulas
761 \begin_layout Plain Layout
762 For multiline formulas the command
769 \begin_inset CommandInset ref
771 reference "sub:Text-in-multiline"
788 \begin_layout Plain Layout
798 \begin_layout Plain Layout
805 This mode is invoked with the the shortcut
813 or by the insertion of the command
821 \begin_layout Plain Layout
832 The text appears black in LyX and can therefore be distinguished from the
833 other formula parts that appear blue.
834 In the output mathematical text is set upright, in contrary to other formula
838 \begin_layout Subsection*
842 \begin_layout Standard
843 Most of the LaTeX-commands for math constructs have the following scheme:
846 \begin_layout Standard
862 \begin_layout Standard
863 A command starts always with a backslash
864 \begin_inset Quotes gld
874 \begin_inset Quotes grd
878 To omit optional arguments, also omit the associated brackets.
879 The braces around the required arguments are named in this document as
884 \begin_layout Plain Layout
891 If you add in a formula a left brace to a command name, LyX creates automatical
893 In all other cases TeX-braces are created in formulas with the command
901 TeX-braces appear red in LyX, in contrary to normal braces that appear
903 In TeX-mode no command is needed to get TeX-braces.
904 TeX-braces don't appear in the output.
907 \begin_layout Standard
908 When commands without arguments, like commands for symbols are entered in
909 TeX-mode, a space character must
913 be behind the command to end it.
914 This space doesn't appear in the output.
915 When the space should appear in the output, the space must be followed
916 by a protected space in normal text.
919 \begin_layout Standard
920 A protected space is inserted with
927 \begin_layout Subsection*
928 \begin_inset Newpage newpage
934 \begin_layout Itemize
939 \begin_layout Plain Layout
940 This visible space character can be created with the command
950 \begin_layout Plain Layout
958 , inserted in TeX-mode.
967 \begin_layout Plain Layout
980 denotes a space character to be input.
983 \begin_layout Itemize
985 \begin_inset Formula $\to$
988 denotes the usage of the corresponding arrow key on the keyboard.
991 \begin_layout Subsection*
995 \begin_layout Standard
997 \begin_inset Float table
1003 \begin_layout Plain Layout
1005 \begin_inset Caption
1007 \begin_layout Plain Layout
1008 \begin_inset CommandInset label
1010 name "tab:Available-units"
1022 \begin_layout Plain Layout
1024 \begin_inset Tabular
1025 <lyxtabular version="3" rows="13" columns="2">
1027 <column alignment="center" valignment="top" width="0">
1028 <column alignment="center" valignment="top" width="0">
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1033 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1042 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1053 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1062 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1104 \begin_inset space \thinspace{}
1108 \begin_inset space \thinspace{}
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1121 \begin_layout Plain Layout
1127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1130 \begin_layout Plain Layout
1132 \begin_inset space \thinspace{}
1136 \begin_inset space \thinspace{}
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1149 \begin_layout Plain Layout
1155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1158 \begin_layout Plain Layout
1160 \begin_inset space \thinspace{}
1164 \begin_inset space \thinspace{}
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1177 \begin_layout Plain Layout
1183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1186 \begin_layout Plain Layout
1188 \begin_inset space \thinspace{}
1192 \begin_inset space \thinspace{}
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1205 \begin_layout Plain Layout
1211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1214 \begin_layout Plain Layout
1216 \begin_inset space \thinspace{}
1220 \begin_inset space \thinspace{}
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1233 \begin_layout Plain Layout
1239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1242 \begin_layout Plain Layout
1244 \begin_inset space \thinspace{}
1248 \begin_inset Formula $\approx$
1252 \begin_inset space \thinspace{}
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1265 \begin_layout Plain Layout
1271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1274 \begin_layout Plain Layout
1276 \begin_inset space \thinspace{}
1280 \begin_inset space \thinspace{}
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1293 \begin_layout Plain Layout
1299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1302 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1312 \begin_inset Quotes erd
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1325 \begin_layout Plain Layout
1331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1334 \begin_layout Plain Layout
1336 \begin_inset Quotes eld
1344 \begin_inset Quotes erd
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1357 \begin_layout Plain Layout
1363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1366 \begin_layout Plain Layout
1368 \begin_inset space \thinspace{}
1372 \begin_inset Formula $\nicefrac{1}{18}$
1376 \begin_inset space \thinspace{}
1397 \begin_layout Standard
1398 \begin_inset Newpage newpage
1404 \begin_layout Section
1408 \begin_layout Subsection
1413 \begin_layout Plain Layout
1423 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1470 \begin_layout Plain Layout
1481 \begin_layout Plain Layout
1496 \begin_layout Standard
1497 Indices are created with an underscore
1498 \begin_inset Quotes eld
1502 \begin_inset Quotes erd
1505 or via the math toolbar button
1506 \begin_inset Graphics
1507 filename ../images/math-subscript.png
1512 , exponents with a caret
1513 \begin_inset Quotes eld
1517 \begin_inset Quotes erd
1520 or via the math toolbar button
1521 \begin_inset Graphics
1522 filename ../images/math-superscript.png
1530 \begin_layout Standard
1532 \begin_inset Tabular
1533 <lyxtabular version="3" rows="4" columns="2">
1535 <column alignment="center" valignment="top" width="0pt">
1536 <column alignment="center" valignment="top" width="0pt">
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1541 \begin_layout Plain Layout
1547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1550 \begin_layout Plain Layout
1552 \begin_inset Note Note
1555 \begin_layout Plain Layout
1562 is only used as spacer.
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1577 \begin_layout Plain Layout
1583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1586 \begin_layout Plain Layout
1587 \begin_inset Formula $B_{V}$
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1600 \begin_layout Plain Layout
1606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1609 \begin_layout Plain Layout
1610 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1623 \begin_layout Plain Layout
1628 \begin_layout Plain Layout
1642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1645 \begin_layout Plain Layout
1646 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1662 \begin_layout Standard
1663 As the caret is in some languages an accent, vowels will be accentuated
1664 in this case and not set as exponents
1668 \begin_layout Plain Layout
1669 Depending on the used keyboard settings this can also happen for other character
1676 To get in this case exponents, press
1680 after the caret as in the last example.
1683 \begin_layout Subsection
1685 \begin_inset CommandInset label
1687 name "sub:Fractions"
1695 \begin_layout Plain Layout
1704 \begin_layout Standard
1705 Fractions are generated with the command
1715 \begin_layout Plain Layout
1723 or via the math toolbar button
1724 \begin_inset Graphics
1725 filename ../images/math/frac.png
1731 The font size is adjusted automatically, depending on whether the fraction
1732 is in an inline or display style formula.
1733 With the math toolbar button
1734 \begin_inset Graphics
1735 filename ../images/math/frac-square.png
1740 you can select different fraction types.
1743 \begin_layout Standard
1752 \begin_layout Plain Layout
1762 a fraction can be created that has in any case the size of a display style
1772 \begin_layout Plain Layout
1782 the fraction appears always with the size of an inline formula.
1786 \begin_layout Standard
1787 A line with the fraction
1788 \begin_inset Formula $\frac{1}{2}$
1791 that was created with the command
1800 \begin_layout Standard
1801 A line with the fraction
1802 \begin_inset Formula $\dfrac{1}{2}$
1805 that was created with the command
1814 \begin_layout Standard
1816 \begin_inset Tabular
1817 <lyxtabular version="3" rows="4" columns="2">
1819 <column alignment="center" valignment="top" width="0pt">
1820 <column alignment="center" valignment="top" width="0pt">
1822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1825 \begin_layout Plain Layout
1831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1834 \begin_layout Plain Layout
1836 \begin_inset Note Note
1839 \begin_layout Plain Layout
1846 is only used as spacer.
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1861 \begin_layout Plain Layout
1868 \begin_layout Plain Layout
1878 \begin_inset Formula $\downarrow$
1886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1889 \begin_layout Plain Layout
1890 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1903 \begin_layout Plain Layout
1910 \begin_layout Plain Layout
1920 \begin_inset Formula $\downarrow$
1928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1931 \begin_layout Plain Layout
1932 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1945 \begin_layout Plain Layout
1952 \begin_layout Plain Layout
1965 \begin_layout Plain Layout
1980 \begin_layout Plain Layout
1990 \begin_inset Formula $\downarrow$
1994 \begin_inset Formula $\downarrow\downarrow$
2002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2005 \begin_layout Plain Layout
2006 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2022 \begin_layout Standard
2023 \begin_inset VSpace bigskip
2027 \begin_inset Newpage newpage
2030 For nested fractions the command
2040 \begin_layout Plain Layout
2050 \begin_inset VSpace -3mm
2056 \begin_layout Standard
2057 \begin_inset Formula \begin{align*}
2058 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2059 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2066 \begin_layout Standard
2067 The command for the example above is:
2070 \begin_layout Standard
2076 \begin_inset Formula $\to$
2086 \begin_inset Formula $\to$
2092 \begin_inset Formula $\to\to$
2100 \begin_layout Standard
2101 \begin_inset VSpace medskip
2107 \begin_layout Standard
2114 sets the fraction always in the size of a displayed formula, also when
2115 it is part of another fraction.
2122 has the following command scheme:
2125 \begin_layout Standard
2130 cfrac[numerator position]{numerator}{denominator}
2133 \begin_layout Standard
2134 The numerator position can be
2147 l or r aligns the numerator to the left or right, resp.
2148 \begin_inset space ~
2151 with the fraction stroke.
2156 or no position is given, the numerator appears centered.
2157 These fractions demonstrate the different alignments:
2158 \begin_inset Newline newline
2164 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2168 \begin_inset Formula $\cfrac{A}{B+C}$
2172 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2178 \begin_layout Standard
2179 \begin_inset VSpace medskip
2182 It is often advantageous to combine
2195 \begin_inset Formula \[
2196 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2203 \begin_layout Standard
2204 For inline fractions with a sloped fraction stroke you can use the command
2215 \begin_layout Plain Layout
2224 \begin_inset Formula $\nicefrac{5}{31}$
2237 \begin_layout Plain Layout
2246 \begin_inset Formula $\unitfrac{5}{31}$
2249 There is furthermore the command
2255 that offers to write a fraction in combination with a number:
2256 \begin_inset Formula $\unitfrac[2]{1}{3}$
2260 \begin_inset Newline newline
2269 is not a real LaTeX command but the command
2270 \begin_inset Newline newline
2277 unitfrac[number]{numerator}{denominator}
2279 , therefore you cannot use it in TeX code.
2282 \begin_layout Standard
2283 How to define own fractions where the fraction stroke can be changed, is
2285 \begin_inset CommandInset ref
2287 reference "sub:Self-defined-Fractions"
2294 \begin_layout Subsection
2299 \begin_layout Plain Layout
2308 \begin_layout Standard
2309 Square roots are created with
2319 \begin_layout Plain Layout
2327 or the math toolbar button
2328 \begin_inset Graphics
2329 filename ../images/math/sqrt.png
2334 , all other roots with the command
2344 \begin_layout Plain Layout
2352 or with the math toolbar button
2353 \begin_inset Graphics
2354 filename ../images/math/root.png
2362 \begin_layout Standard
2364 \begin_inset Tabular
2365 <lyxtabular version="3" rows="3" columns="2">
2367 <column alignment="center" valignment="top" width="0pt">
2368 <column alignment="center" valignment="top" width="0pt">
2370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2373 \begin_layout Plain Layout
2379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2382 \begin_layout Plain Layout
2384 \begin_inset Note Note
2387 \begin_layout Plain Layout
2394 is only used as spacer.
2406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2409 \begin_layout Plain Layout
2416 \begin_layout Plain Layout
2430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2433 \begin_layout Plain Layout
2434 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2447 \begin_layout Plain Layout
2454 \begin_layout Plain Layout
2464 \begin_inset Formula $\downarrow$
2472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2475 \begin_layout Plain Layout
2476 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2492 \begin_layout Standard
2493 A square root can also be created with
2499 when the root index field is left empty.
2502 \begin_layout Standard
2503 With certain indices the distance to the root is too small, like in this
2505 \begin_inset Formula $\sqrt[\beta]{B}$
2509 \begin_inset Newline newline
2513 \begin_inset Formula $\beta$
2517 To avoid this, the commands
2527 \begin_layout Plain Layout
2545 \begin_layout Plain Layout
2553 are used with the following scheme:
2556 \begin_layout Standard
2570 \begin_layout Standard
2571 Distance is the number of Big Points (unit bp;
2572 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2575 ), that the index should be moved to the left or top, resp..
2576 The commands are written to the index.
2577 This way the command
2578 \begin_inset Newline newline
2588 \begin_inset Formula $\to$
2594 \begin_inset Formula $\to$
2603 \begin_layout Plain Layout
2613 \begin_inset Formula $\to$
2617 \begin_inset Newline newline
2622 produces a correct typeset formula:
2623 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2629 \begin_layout Subsection
2630 Binomial Coefficients
2634 \begin_layout Plain Layout
2635 Binomial coefficients
2643 \begin_layout Standard
2644 Binomial coefficients are inserted with the command
2654 \begin_layout Plain Layout
2662 or with the submenu of the math toolbar button
2663 \begin_inset Graphics
2664 filename ../images/math/frac-square.png
2670 Analog to fractions (
2690 \begin_layout Plain Layout
2710 \begin_layout Plain Layout
2719 For other brackets around binomial coeficients there are the commands
2729 \begin_layout Plain Layout
2747 \begin_layout Plain Layout
2758 \begin_layout Standard
2760 \begin_inset Tabular
2761 <lyxtabular version="3" rows="6" columns="2">
2763 <column alignment="center" valignment="top" width="0pt">
2764 <column alignment="center" valignment="top" width="0pt">
2766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2769 \begin_layout Plain Layout
2775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2778 \begin_layout Plain Layout
2780 \begin_inset Note Note
2783 \begin_layout Plain Layout
2790 is only used as spacer.
2802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2805 \begin_layout Plain Layout
2812 \begin_layout Plain Layout
2822 \begin_inset Formula $\downarrow$
2830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2833 \begin_layout Plain Layout
2834 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2847 \begin_layout Plain Layout
2854 \begin_layout Plain Layout
2864 \begin_inset Formula $\downarrow$
2872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2875 \begin_layout Plain Layout
2876 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2889 \begin_layout Plain Layout
2896 \begin_layout Plain Layout
2906 \begin_inset Formula $\downarrow$
2914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2917 \begin_layout Plain Layout
2918 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2931 \begin_layout Plain Layout
2938 \begin_layout Plain Layout
2948 \begin_inset Formula $\downarrow$
2956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2959 \begin_layout Plain Layout
2960 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2973 \begin_layout Plain Layout
2980 \begin_layout Plain Layout
2990 \begin_inset Formula $\downarrow$
2998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3001 \begin_layout Plain Layout
3002 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3018 \begin_layout Subsection
3019 Case Differentiations
3023 \begin_layout Plain Layout
3024 Case differentiations
3032 \begin_layout Standard
3034 \begin_inset Tabular
3035 <lyxtabular version="3" rows="3" columns="2">
3037 <column alignment="center" valignment="top" width="0pt">
3038 <column alignment="center" valignment="top" width="0pt">
3040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3043 \begin_layout Plain Layout
3049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3052 \begin_layout Plain Layout
3060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3063 \begin_layout Plain Layout
3070 \begin_layout Plain Layout
3080 \begin_inset Formula $\to$
3087 \begin_layout Plain Layout
3100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3103 \begin_layout Plain Layout
3104 \begin_inset Formula $\begin{cases}
3115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3118 \begin_layout Plain Layout
3125 \begin_layout Plain Layout
3139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3142 \begin_layout Plain Layout
3143 \begin_inset Formula $\begin{cases}
3144 A & \textrm{for }x>0\\
3145 B & \textrm{for }x=0\end{cases}$
3161 \begin_layout Standard
3168 or the usage of the math toolbar button
3169 \begin_inset Graphics
3170 filename ../images/math/cases.png
3175 you can create new lines with the shortcut
3179 or the table toolbar button
3180 \begin_inset Graphics
3181 filename ../images/tabular-feature_append-row.png
3189 \begin_layout Standard
3196 is also available via the menu
3198 Insert\SpecialChar \menuseparator
3199 Math\SpecialChar \menuseparator
3205 \begin_layout Subsection
3210 \begin_layout Plain Layout
3219 \begin_layout Standard
3230 \begin_layout Plain Layout
3238 every character can be displayed canceled.
3239 The characters are quasi accentuated by a slash.
3242 \begin_layout Standard
3244 \begin_inset Tabular
3245 <lyxtabular version="3" rows="4" columns="2">
3247 <column alignment="center" valignment="top" width="0pt">
3248 <column alignment="center" valignment="top" width="0pt">
3250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3253 \begin_layout Plain Layout
3259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3262 \begin_layout Plain Layout
3270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3273 \begin_layout Plain Layout
3281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3284 \begin_layout Plain Layout
3285 \begin_inset Formula $\not=$
3295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3298 \begin_layout Plain Layout
3308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3311 \begin_layout Plain Layout
3312 \begin_inset Formula $\not\le$
3322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3325 \begin_layout Plain Layout
3335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3338 \begin_layout Plain Layout
3339 \begin_inset Formula $\not\parallel$
3355 \begin_layout Standard
3356 The last example shows, that not all negations look good.
3357 Therefore there are for some negations special commands (see
3358 \begin_inset CommandInset ref
3360 reference "sub:Mathematical-Symbols"
3365 \begin_inset CommandInset ref
3367 reference "sec:Relations"
3374 \begin_layout Subsection
3376 \begin_inset CommandInset label
3378 name "sub:Placeholders"
3386 \begin_layout Plain Layout
3396 \begin_layout Plain Layout
3397 Chemical characters ! Isotopes
3406 \begin_layout Plain Layout
3411 \begin_layout Plain Layout
3422 \begin_layout Plain Layout
3437 \begin_layout Standard
3439 \begin_inset space \thinspace{}
3443 \begin_inset space ~
3450 \begin_layout Plain Layout
3451 More about chemical symbols is written in
3452 \begin_inset CommandInset ref
3454 reference "sub:Chemical-Symbols-and"
3463 the following problem occurs:
3466 \begin_layout Standard
3468 \begin_inset Tabular
3469 <lyxtabular version="3" rows="2" columns="2">
3471 <column alignment="center" valignment="top" width="0pt">
3472 <column alignment="center" valignment="top" width="0pt">
3474 <cell alignment="center" valignment="top" usebox="none">
3477 \begin_layout Plain Layout
3478 Indices created with sub- and superscripts:
3483 <cell alignment="center" valignment="top" usebox="none">
3486 \begin_layout Plain Layout
3487 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3497 <cell alignment="center" valignment="top" usebox="none">
3500 \begin_layout Plain Layout
3506 <cell alignment="center" valignment="top" usebox="none">
3509 \begin_layout Plain Layout
3510 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3524 \begin_inset Note Note
3527 \begin_layout Plain Layout
3534 is only used as spacer.
3542 \begin_layout Standard
3543 The shorter index is by default placed below or above the first character
3544 of the longer index.
3545 To avoid this there is the command
3555 \begin_layout Plain Layout
3563 or the math toolbar button
3564 \begin_inset space \thinspace{}
3571 \begin_layout Plain Layout
3572 can be found in the submenu of the toolbar button
3573 \begin_inset Graphics
3574 filename ../images/math/space.png
3585 \begin_inset Graphics
3586 filename ../images/math/phantom.png
3591 that creates one or more phantom characters.
3598 a small blue box appears that is superposed with two red arrows.
3599 The arrows indicate that the complete width and height of the box content
3600 will be created as placeholder.
3601 Phantom characters are accordingly placeholders with the size of the characters.
3604 \begin_layout Standard
3606 \begin_inset Tabular
3607 <lyxtabular version="3" rows="4" columns="2">
3609 <column alignment="center" valignment="top" width="0">
3610 <column alignment="center" valignment="top" width="0">
3612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3615 \begin_layout Plain Layout
3621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3624 \begin_layout Plain Layout
3626 \begin_inset Note Note
3629 \begin_layout Plain Layout
3636 is only used as spacer.
3648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3651 \begin_layout Plain Layout
3656 \begin_layout Plain Layout
3671 \begin_layout Plain Layout
3681 \begin_inset Formula $\to$
3688 \begin_layout Plain Layout
3702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3705 \begin_layout Plain Layout
3706 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3719 \begin_layout Plain Layout
3724 \begin_layout Plain Layout
3739 \begin_layout Plain Layout
3749 \begin_inset Formula $\to$
3756 \begin_layout Plain Layout
3770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3773 \begin_layout Plain Layout
3774 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3787 \begin_layout Plain Layout
3794 \begin_layout Plain Layout
3809 \begin_layout Plain Layout
3819 \begin_inset Formula $\to$
3826 \begin_layout Plain Layout
3840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3843 \begin_layout Plain Layout
3844 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3860 \begin_layout Standard
3861 Furthermore there are the commands
3871 \begin_layout Plain Layout
3880 \begin_inset space ~
3884 \begin_inset Graphics
3885 filename ../images/math/vphantom.png
3900 \begin_layout Plain Layout
3909 \begin_inset space ~
3913 \begin_inset Graphics
3914 filename ../images/math/hphantom.png
3926 creates only space for the maximal height of the characters in the box
3927 but not for its width.
3934 creates only space for the width of the box content.
3935 Therefore the boxes of both commands have only one red arrow.
3938 \begin_layout Standard
3949 \begin_layout Plain Layout
3964 space for the height of the integral sign,
3968 \begin_layout Plain Layout
3975 creates an integral sign, see
3976 \begin_inset CommandInset ref
3978 reference "sub:Big-Operators"
3987 because this is the larger character.
3988 An example application is in
3989 \begin_inset CommandInset ref
3991 reference "sub:Multiline-Brackets"
3998 \begin_layout Subsection
4003 \begin_layout Plain Layout
4013 \begin_layout Plain Layout
4014 Formula ! underlined
4022 \begin_layout Standard
4024 \begin_inset Tabular
4025 <lyxtabular version="3" rows="4" columns="2">
4027 <column alignment="center" valignment="top" width="0pt">
4028 <column alignment="center" valignment="top" width="0pt">
4030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4033 \begin_layout Plain Layout
4039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4042 \begin_layout Plain Layout
4044 \begin_inset Note Note
4047 \begin_layout Plain Layout
4054 is only used as spacer.
4066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4069 \begin_layout Plain Layout
4076 \begin_layout Plain Layout
4089 \begin_layout Plain Layout
4102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4105 \begin_layout Plain Layout
4106 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4119 \begin_layout Plain Layout
4126 \begin_layout Plain Layout
4139 \begin_layout Plain Layout
4152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4155 \begin_layout Plain Layout
4156 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4169 \begin_layout Plain Layout
4176 \begin_layout Plain Layout
4191 \begin_layout Plain Layout
4205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4208 \begin_layout Plain Layout
4209 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4225 \begin_layout Standard
4226 In the last example it doesn't matter if first
4241 \begin_layout Standard
4242 To double underline e.
4243 \begin_inset space \thinspace{}
4256 \begin_layout Standard
4257 It is possible to place up to 6 lines above or below characters.
4260 \begin_layout Standard
4261 \begin_inset VSpace bigskip
4264 Custom lines can be created using the command
4274 \begin_layout Plain Layout
4282 which has the following scheme:
4285 \begin_layout Standard
4290 rule[vertical offset]{length}{thickness}
4293 \begin_layout Standard
4294 The optional vertical offset shifts the line upwards (or downwards, when
4295 the value is negative).
4297 \begin_inset CommandInset ref
4299 reference "tab:Available-units"
4303 can be used for the values.
4304 Here are two example lines created with the commands
4305 \begin_inset Newline newline
4312 rule[-2ex]{3cm}{2pt}
4323 \begin_layout Standard
4325 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4331 \begin_layout Standard
4338 can also be used for text when it is inserted in TeX-mode.
4341 \begin_layout Subsection
4343 \begin_inset CommandInset label
4353 \begin_layout Plain Layout
4362 \begin_layout Standard
4363 There are different types of ellipses available.
4367 \begin_layout Plain Layout
4368 In the math toolbar in the submenu of the button
4369 \begin_inset Graphics
4370 filename ../images/math/ldots.png
4380 For listings dots at the baseline are used (
4390 \begin_layout Plain Layout
4398 ), while for operations dots are needed that are on the same height as the
4409 \begin_layout Plain Layout
4418 When using the command
4428 \begin_layout Plain Layout
4436 , LaTeX decides on the basis of the next character what type is used.
4439 \begin_layout Standard
4441 \begin_inset Tabular
4442 <lyxtabular version="3" rows="8" columns="2">
4444 <column alignment="center" valignment="top" width="0pt">
4445 <column alignment="center" valignment="top" width="0pt">
4447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4450 \begin_layout Plain Layout
4456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4459 \begin_layout Plain Layout
4467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4470 \begin_layout Plain Layout
4475 \begin_layout Plain Layout
4490 \begin_layout Plain Layout
4504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4507 \begin_layout Plain Layout
4508 \begin_inset Formula $A_{1},\dots,A_{n}$
4518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4521 \begin_layout Plain Layout
4526 \begin_layout Plain Layout
4541 \begin_layout Plain Layout
4555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4558 \begin_layout Plain Layout
4559 \begin_inset Formula $A_{1}+\dots+A_{n}$
4569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4572 \begin_layout Plain Layout
4577 \begin_layout Plain Layout
4592 \begin_layout Plain Layout
4606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4609 \begin_layout Plain Layout
4610 \begin_inset Formula $A_{1},\ldots,A_{n}$
4620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4623 \begin_layout Plain Layout
4628 \begin_layout Plain Layout
4643 \begin_layout Plain Layout
4657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4660 \begin_layout Plain Layout
4661 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4674 \begin_layout Plain Layout
4682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4685 \begin_layout Plain Layout
4686 \begin_inset Formula $\vdots$
4696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4699 \begin_layout Plain Layout
4707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4710 \begin_layout Plain Layout
4711 \begin_inset Formula $\ddots$
4721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4724 \begin_layout Plain Layout
4726 \begin_inset space \thinspace{}
4729 matrix with the different dots
4734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4737 \begin_layout Plain Layout
4738 \begin_inset Formula $\begin{array}{ccc}
4739 A_{11} & \cdots & A_{1m}\\
4740 \vdots & \ddots & \vdots\\
4741 A_{n1} & \cdots & A_{nm}\end{array}$
4757 \begin_layout Standard
4758 The ellipses available in menu
4760 Insert\SpecialChar \menuseparator
4762 \begin_inset space ~
4776 \begin_layout Standard
4777 \begin_inset VSpace medskip
4780 Specially for matrices there are ellipses that span over several columns.
4781 They are created with the command
4791 \begin_layout Plain Layout
4799 , that has the following scheme:
4802 \begin_layout Standard
4807 hdotsfor[distance]{number of columns}
4810 \begin_layout Standard
4811 The number of columns specifies how many columns should be spanned.
4812 Distance is a factor for the distance between the dots.
4815 \begin_layout Standard
4816 In the following matrix the command
4822 was inserted in the first box of the second line, to get an ellipsis with
4823 a dot distance twice as long as with the command
4830 \begin_inset Formula \[
4831 \left(\begin{array}{cccc}
4834 q & w & e & r\end{array}\right)\]
4838 Note that the matrix fields that should be spanned must be empty, otherwise
4839 you get LaTeX-errors.
4842 \begin_layout Standard
4843 \begin_inset VSpace bigskip
4846 Furthermore you can fill with the command
4856 \begin_layout Plain Layout
4864 the rest of a line with dots.
4865 The effect of these commands is the same like with
4872 \begin_inset CommandInset ref
4874 reference "sub:Variable-Space"
4881 \begin_layout Standard
4882 For example the command
4890 \begin_layout Plain Layout
4904 \begin_layout Standard
4905 \begin_inset Formula $A\dotfill B$
4911 \begin_layout Standard
4918 there is for a line the command
4928 \begin_layout Plain Layout
4939 \begin_layout Standard
4940 \begin_inset Formula $A\hrulefill B$
4946 \begin_layout Standard
4947 To use the commands for text, they have to be inserted in TeX-mode.
4950 \begin_layout Section
4952 \begin_inset CommandInset label
4962 \begin_layout Plain Layout
4971 \begin_layout Standard
4972 Matrices can be inserted via the math toolbar button
4973 \begin_inset Graphics
4974 filename ../images/dialog-show_mathmatrix.png
4981 Insert\SpecialChar \menuseparator
4982 Math\SpecialChar \menuseparator
4986 You will be asked for the number of matrix columns and rows, and the alignment.
4987 The vertical alignment is hereby only of importance for matrices in inline
4991 \begin_layout Standard
4992 The first matrix is top
4993 \begin_inset Formula $\begin{array}[t]{cccc}
4996 C & F & I & L\end{array}$
5000 \begin_inset Formula $\begin{array}{cccc}
5003 C & F & I & L\end{array}$
5006 , and the third bottom
5007 \begin_inset Formula $\begin{array}[b]{cccc}
5010 C & F & I & L\end{array}$
5016 \begin_layout Standard
5017 The horizontal alignment specifies how the column entries should be aligned.
5018 It is set by entering a letter for every column.
5023 denotes left aligned,
5032 To create for example a 4
5037 \begin_inset space ~
5040 matrix where the first column is left aligned, the second and third are
5041 centered, and the last one is right aligned, one enters for the horizontal
5047 Normally are in a matrix all columns centered, therefore the default is
5048 for every column is a
5055 \begin_layout Standard
5056 Horizontal alignment:
5059 \begin_layout Standard
5065 \begin_inset Formula $\begin{array}{lll}
5068 C & F & 10000\end{array}$
5076 \begin_inset Formula $\begin{array}{ccc}
5079 C & F & 10000\end{array}$
5087 \begin_inset Formula $\begin{array}{rrr}
5090 C & F & 10000\end{array}$
5096 \begin_layout Standard
5097 To add or delete rows and columns subsequently, the math toolbar buttons
5099 \begin_inset Graphics
5100 filename ../images/tabular-feature_append-row.png
5106 \begin_inset Graphics
5107 filename ../images/tabular-feature_delete-row.png
5113 \begin_inset space \thinspace{}
5118 Edit\SpecialChar \menuseparator
5122 New rows can also be created with
5129 \begin_layout Standard
5130 \begin_inset VSpace bigskip
5133 Parentheses around a matrix can can either be created with the commands
5144 \begin_layout Plain Layout
5162 \begin_layout Plain Layout
5173 \begin_inset space ~
5179 \begin_inset CommandInset ref
5181 reference "sub:Automatic-Bracket-Size"
5185 , or by using the following commands:
5186 \begin_inset VSpace medskip
5192 \begin_layout Standard
5193 \begin_inset space \hfill{}
5197 \begin_inset Tabular
5198 <lyxtabular version="3" rows="4" columns="2">
5200 <column alignment="center" valignment="top" width="0">
5201 <column alignment="center" valignment="top" width="0">
5203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5206 \begin_layout Plain Layout
5212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5215 \begin_layout Plain Layout
5217 \begin_inset Note Note
5220 \begin_layout Plain Layout
5227 is only used as spacer.
5239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5242 \begin_layout Plain Layout
5249 \begin_layout Plain Layout
5263 \begin_inset space \thinspace{}
5271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5274 \begin_layout Plain Layout
5275 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5276 0 & \textrm{-}\mathrm{i}\\
5277 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5290 \begin_layout Plain Layout
5297 \begin_layout Plain Layout
5311 \begin_inset space \thinspace{}
5319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5322 \begin_layout Plain Layout
5323 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5324 0 & \textrm{-}\mathrm{i}\\
5325 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5338 \begin_layout Plain Layout
5345 \begin_layout Plain Layout
5359 \begin_inset space \thinspace{}
5367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5370 \begin_layout Plain Layout
5371 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5372 0 & \textrm{-}\mathrm{i}\\
5373 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5387 \begin_inset space \hfill{}
5391 \begin_inset Tabular
5392 <lyxtabular version="3" rows="4" columns="2">
5394 <column alignment="center" valignment="top" width="0">
5395 <column alignment="center" valignment="top" width="0">
5397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5400 \begin_layout Plain Layout
5406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5409 \begin_layout Plain Layout
5417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5420 \begin_layout Plain Layout
5427 \begin_layout Plain Layout
5441 \begin_inset space \thinspace{}
5449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5452 \begin_layout Plain Layout
5453 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5454 0 & \textrm{-}\mathrm{i}\\
5455 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5468 \begin_layout Plain Layout
5475 \begin_layout Plain Layout
5489 \begin_inset space \thinspace{}
5497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5500 \begin_layout Plain Layout
5501 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5502 0 & \textrm{-}\mathrm{i}\\
5503 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5516 \begin_layout Plain Layout
5523 \begin_layout Plain Layout
5537 \begin_inset space \thinspace{}
5545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5548 \begin_layout Plain Layout
5549 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5550 0 & \textrm{-}\mathrm{i}\\
5551 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5565 \begin_inset space \hfill{}
5571 \begin_layout Standard
5572 \begin_inset VSpace medskip
5576 \begin_inset space \thinspace{}
5580 \begin_inset space ~
5589 is inserted, a blue box appears between two vertical lines where the matrix
5593 \begin_layout Standard
5594 \begin_inset VSpace bigskip
5597 As all multiline formulas are matrices, the length
5607 \begin_layout Plain Layout
5615 that is described in
5616 \begin_inset CommandInset ref
5618 reference "sub:Column-Separation"
5622 can also be used to change the column separation of matrices.
5625 \begin_layout Standard
5626 To change the row separation, the command
5636 \begin_layout Plain Layout
5645 It is used as follows:
5648 \begin_layout Standard
5655 arraystretch}{stretch factor}
5659 \begin_layout Plain Layout
5670 \begin_layout Standard
5677 assigns the stretch factor to the predefined command
5685 \begin_inset space \thinspace{}
5689 \begin_inset space ~
5692 the row separation, use the factor 2.
5693 This is then used for all following matrices.
5694 To go back to the original separation, assign the factor 1 to
5703 \begin_layout Standard
5704 To set matrices into a text line, the command
5714 \begin_layout Plain Layout
5723 When it is inserted a blue box with two dashed lines appears.
5724 In this box the matrix is inserted.
5727 \begin_layout Standard
5729 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5730 C & D\end{smallmatrix}\right)$
5736 \begin_layout Section
5737 Brackets and Delimiters
5741 \begin_layout Plain Layout
5751 \begin_layout Plain Layout
5760 \begin_layout Subsection
5761 Vertical Brackets and Delimiters
5765 \begin_layout Plain Layout
5774 \begin_layout Standard
5775 \begin_inset space \hfill{}
5779 \begin_inset Tabular
5780 <lyxtabular version="3" rows="9" columns="2">
5782 <column alignment="center" valignment="top" width="0pt">
5783 <column alignment="center" valignment="top" width="0pt">
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5788 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5797 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5808 \begin_layout Plain Layout
5814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5817 \begin_layout Plain Layout
5818 \begin_inset Formula $($
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5831 \begin_layout Plain Layout
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5840 \begin_layout Plain Layout
5841 \begin_inset Formula $\{$
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5854 \begin_layout Plain Layout
5860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5863 \begin_layout Plain Layout
5864 \begin_inset Formula $[$
5874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5877 \begin_layout Plain Layout
5885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5888 \begin_layout Plain Layout
5889 \begin_inset Formula $\langle$
5899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5902 \begin_layout Plain Layout
5910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5913 \begin_layout Plain Layout
5914 \begin_inset Formula $\lceil$
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5938 \begin_layout Plain Layout
5939 \begin_inset Formula $\lfloor$
5949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5952 \begin_layout Plain Layout
5958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5961 \begin_layout Plain Layout
5962 \begin_inset Formula $/$
5972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5975 \begin_layout Plain Layout
5981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5984 \begin_layout Plain Layout
5985 \begin_inset Formula $|$
5999 \begin_inset space \hfill{}
6003 \begin_inset Tabular
6004 <lyxtabular version="3" rows="9" columns="2">
6006 <column alignment="center" valignment="top" width="0pt">
6007 <column alignment="center" valignment="top" width="0pt">
6009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6012 \begin_layout Plain Layout
6018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6021 \begin_layout Plain Layout
6029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6032 \begin_layout Plain Layout
6038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6041 \begin_layout Plain Layout
6042 \begin_inset Formula $)$
6052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6055 \begin_layout Plain Layout
6061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6064 \begin_layout Plain Layout
6065 \begin_inset Formula $\}$
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6078 \begin_layout Plain Layout
6084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6087 \begin_layout Plain Layout
6088 \begin_inset Formula $]$
6098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6101 \begin_layout Plain Layout
6109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6112 \begin_layout Plain Layout
6113 \begin_inset Formula $\rangle$
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6126 \begin_layout Plain Layout
6134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6137 \begin_layout Plain Layout
6138 \begin_inset Formula $\rceil$
6148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6151 \begin_layout Plain Layout
6159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6162 \begin_layout Plain Layout
6163 \begin_inset Formula $\rfloor$
6173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6176 \begin_layout Plain Layout
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6189 \begin_layout Plain Layout
6190 \begin_inset Formula $\backslash$
6200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6203 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $\|$
6229 \begin_inset space \hfill{}
6235 \begin_layout Standard
6238 \begin_inset Note Greyedout
6241 \begin_layout Plain Layout
6246 In TeX-mode the command
6256 \begin_layout Plain Layout
6264 must be used for the backslash, because the command
6272 produces there a line break.
6280 \begin_layout Standard
6281 For all characters listed above the size can be adjusted with the commands
6282 described in the following two subsections.
6283 When using these commands, the characters < and > can directly be used
6284 instead of the commands
6299 \begin_layout Subsubsection
6301 \begin_inset CommandInset label
6303 name "sub:Manual-Bracket-Size"
6311 \begin_layout Plain Layout
6312 Bracket size ! manual
6320 \begin_layout Standard
6321 The bracket size can be specified manually by the LaTeX-commands
6331 \begin_layout Plain Layout
6364 denotes the smallest and
6370 the largest bracket size.
6373 \begin_layout Standard
6374 These commands are used to emphasize levels of brackets:
6377 \begin_layout Standard
6379 \begin_inset Tabular
6380 <lyxtabular version="3" rows="2" columns="2">
6382 <column alignment="center" valignment="top" width="0pt">
6383 <column alignment="center" valignment="top" width="0pt">
6385 <cell alignment="center" valignment="top" usebox="none">
6388 \begin_layout Plain Layout
6389 all brackets in the same size:
6394 <cell alignment="center" valignment="top" usebox="none">
6397 \begin_layout Plain Layout
6398 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6408 <cell alignment="center" valignment="top" usebox="none">
6411 \begin_layout Plain Layout
6417 <cell alignment="center" valignment="top" usebox="none">
6420 \begin_layout Plain Layout
6421 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6435 \begin_inset Note Note
6438 \begin_layout Plain Layout
6445 is only used as spacer.
6453 \begin_layout Standard
6454 For the second formula the command
6464 \begin_layout Plain Layout
6478 \begin_layout Standard
6479 Here is an overview about all bracket sizes:
6482 \begin_layout Standard
6502 \begin_layout Plain Layout
6519 \begin_layout Plain Layout
6532 \begin_layout Plain Layout
6548 \begin_layout Standard
6550 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6556 \begin_layout Standard
6563 -commands there is the variant
6573 \begin_layout Plain Layout
6581 that adds a bit more space between the bracket and its content, and the
6598 \begin_layout Plain Layout
6608 , that don't add additional space.
6613 at the end of the command
6619 is for a left bracket; for a right bracket this will be replaced by an
6625 A left or right bracket can each be an opening or closing bracket.
6628 \begin_layout Standard
6629 In the following table is a comparison of the variants:
6632 \begin_layout Standard
6634 \begin_inset Tabular
6635 <lyxtabular version="3" rows="5" columns="2">
6637 <column alignment="center" valignment="middle" width="0">
6638 <column alignment="center" valignment="middle" width="0">
6640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6643 \begin_layout Plain Layout
6649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6652 \begin_layout Plain Layout
6654 \begin_inset Note Note
6657 \begin_layout Plain Layout
6664 is only used as spacer.
6676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6679 \begin_layout Plain Layout
6694 \begin_layout Plain Layout
6712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6715 \begin_layout Plain Layout
6716 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6729 \begin_layout Plain Layout
6744 \begin_layout Plain Layout
6762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6765 \begin_layout Plain Layout
6766 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6779 \begin_layout Plain Layout
6794 \begin_layout Plain Layout
6812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6815 \begin_layout Plain Layout
6816 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6829 \begin_layout Plain Layout
6841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6844 \begin_layout Plain Layout
6845 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6861 \begin_layout Subsubsection
6862 Automatic Bracket Size
6863 \begin_inset CommandInset label
6865 name "sub:Automatic-Bracket-Size"
6873 \begin_layout Plain Layout
6874 Bracket size ! automatic
6882 \begin_layout Standard
6883 Brackets with variable size can be inserted with the commands
6893 \begin_layout Plain Layout
6911 \begin_layout Plain Layout
6919 or via the math toolbar button
6920 \begin_inset Graphics
6921 filename ../images/dialog-show_mathdelimiter.png
6939 the wanted bracket must be inserted.
6940 The bracket size will then automatically be calculated for the output.
6943 \begin_layout Standard
6945 normal bracket: The command
6955 \begin_layout Plain Layout
6965 \begin_inset Formula $\downarrow$
6972 \begin_layout Plain Layout
6984 \begin_inset Formula \[
6992 \begin_layout Standard
6994 multiline bracket: The command
7006 \begin_layout Plain Layout
7016 \begin_inset Formula $\downarrow$
7023 \begin_layout Plain Layout
7037 \begin_inset Formula \[
7038 \ln\left(\frac{A}{C}\right)\]
7045 \begin_layout Standard
7061 \begin_inset space ~
7067 This has the advantage that you can see in LyX immediately the real bracket
7068 size and that the matching right bracket will be created too.
7069 \begin_inset Newline newline
7072 The command for the last example would then be:
7086 \begin_layout Plain Layout
7096 \begin_inset Formula $\downarrow$
7102 \begin_layout Standard
7103 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7104 For example the command
7114 \begin_layout Plain Layout
7124 \begin_inset Formula $\downarrow$
7131 \begin_layout Plain Layout
7147 \begin_inset Formula \[
7148 \left.\frac{A}{B}\right\} \]
7166 will be converted by LyX to brackets in the right size when the document
7167 is reloaded and an omitted bracket will appear as dashed line.
7170 \begin_layout Standard
7171 \begin_inset VSpace bigskip
7174 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7185 \begin_layout Plain Layout
7193 is additionally available for all brackets and limits.
7194 With this command the height of the following character is adapted to the
7195 one of the surrounding brackets, what is e.
7196 \begin_inset space \thinspace{}
7200 \begin_inset space ~
7203 needed for physical vectors:
7204 \begin_inset Formula \[
7205 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7209 For physical vectors there is a special LaTeX-package, described in
7210 \begin_inset CommandInset ref
7212 reference "sub:Physical-Vectors"
7219 \begin_layout Subsection
7224 \begin_layout Plain Layout
7225 Brackets ! horizontal
7233 \begin_layout Standard
7235 \begin_inset Tabular
7236 <lyxtabular version="3" rows="4" columns="2">
7238 <column alignment="center" valignment="top" width="0pt">
7239 <column alignment="center" valignment="top" width="0pt">
7241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7244 \begin_layout Plain Layout
7246 \begin_inset Note Note
7249 \begin_layout Plain Layout
7256 is only used as spacer.
7266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7269 \begin_layout Plain Layout
7277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7280 \begin_layout Plain Layout
7284 \begin_layout Plain Layout
7299 \begin_layout Plain Layout
7312 \begin_layout Plain Layout
7325 \begin_layout Plain Layout
7338 \begin_layout Plain Layout
7349 \begin_layout Plain Layout
7362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7365 \begin_layout Plain Layout
7366 \begin_inset Formula $\overbrace{A+B}^{3}$
7376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7379 \begin_layout Plain Layout
7383 \begin_layout Plain Layout
7398 \begin_layout Plain Layout
7411 \begin_layout Plain Layout
7424 \begin_layout Plain Layout
7435 \begin_layout Plain Layout
7448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7451 \begin_layout Plain Layout
7452 \begin_inset Formula $\underbrace{A+B}_{5}$
7462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7465 \begin_layout Plain Layout
7472 \begin_layout Plain Layout
7487 \begin_layout Plain Layout
7500 \begin_layout Plain Layout
7513 \begin_layout Plain Layout
7526 \begin_layout Plain Layout
7539 \begin_layout Plain Layout
7552 \begin_layout Plain Layout
7566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7569 \begin_layout Plain Layout
7570 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7586 \begin_layout Standard
7587 In the last example it doesn't matter if
7599 is inserted at first.
7602 \begin_layout Standard
7603 \begin_inset VSpace bigskip
7606 When brackets are needed that overlap each other, multiline formulas, as
7608 \begin_inset CommandInset ref
7610 reference "sec:Multiline-Formulas"
7615 \begin_inset Formula \begin{eqnarray*}
7616 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7617 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7621 In the first row the formula is inserted together with the first brace.
7622 It is hereby important that the space command
7626 \begin_layout Plain Layout
7627 Space commands are explained in
7628 \begin_inset CommandInset ref
7630 reference "sub:Predefined-Space"
7645 is inserted before the first
7646 \begin_inset Formula $d$
7649 , because the brace that ends behind the
7650 \begin_inset Formula $q$
7653 prevents that the following
7654 \begin_inset Quotes eld
7658 \begin_inset Quotes erd
7661 is surrounded by space.
7665 \begin_layout Plain Layout
7666 because a bracket is not handled as character, see
7667 \begin_inset CommandInset ref
7669 reference "sub:Binary-Operators"
7678 In the second row the second brace is inserted.
7679 As it should begin before the
7680 \begin_inset Formula $b$
7695 \begin_layout Plain Layout
7703 \begin_inset CommandInset ref
7705 reference "sub:Placeholders"
7714 This space is needed because the
7715 \begin_inset Quotes eld
7719 \begin_inset Quotes erd
7722 is also surrounded by space in the formula.
7723 The brace is placed under the command
7732 \begin_layout Standard
7733 It gets more complicated when brackets overlap each other, like in the following
7738 \begin_layout Plain Layout
7750 \begin_inset Formula \begin{eqnarray*}
7751 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7752 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7760 \begin_layout Plain Layout
7771 The first formula row is the same as the second row of the previous example,
7772 with the difference that the brace is above.
7773 The second row contains the formula together with the second brace.
7774 To avoid that there is space between the upper brace in the first row and
7775 the formula, the row spacing need to be reduced.
7776 This is not easily possible due to a bug in LyX
7780 \begin_layout Plain Layout
7781 \begin_inset CommandInset href
7783 name "LyX-bug #1505"
7784 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7794 As solution for the problem, the global formula row separation
7804 \begin_layout Plain Layout
7812 must be changed to -6
7813 \begin_inset space \thinspace{}
7816 pt before the formula with the command
7831 is set back after the formula to the standard value of 3
7832 \begin_inset space \thinspace{}
7835 pt using the same command.
7836 More about the row separation in formulas is explained in
7837 \begin_inset CommandInset ref
7839 reference "sub:Line-Separation"
7846 \begin_layout Section
7851 \begin_layout Plain Layout
7860 \begin_layout Standard
7861 Arrows can be inserted via the math toolbar button
7862 \begin_inset Graphics
7863 filename ../images/math/leftarrow.png
7868 or the commands listed in the following subsections.
7871 \begin_layout Standard
7872 \begin_inset Newpage newpage
7878 \begin_layout Subsection
7883 \begin_layout Plain Layout
7892 \begin_layout Standard
7893 \begin_inset space \hfill{}
7897 \begin_inset Tabular
7898 <lyxtabular version="3" rows="8" columns="2">
7900 <column alignment="center" valignment="top" width="0pt">
7901 <column alignment="center" valignment="top" width="0pt">
7903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7906 \begin_layout Plain Layout
7912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7915 \begin_layout Plain Layout
7923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7926 \begin_layout Plain Layout
7934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7937 \begin_layout Plain Layout
7938 \begin_inset Formula $\gets$
7948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7951 \begin_layout Plain Layout
7959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7962 \begin_layout Plain Layout
7963 \begin_inset Formula $\Leftarrow$
7973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7976 \begin_layout Plain Layout
7984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7987 \begin_layout Plain Layout
7988 \begin_inset Formula $\longleftarrow$
7998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8001 \begin_layout Plain Layout
8009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8012 \begin_layout Plain Layout
8013 \begin_inset Formula $\Longleftarrow$
8023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8026 \begin_layout Plain Layout
8034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8037 \begin_layout Plain Layout
8038 \begin_inset Formula $\leftharpoonup$
8048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8051 \begin_layout Plain Layout
8059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8062 \begin_layout Plain Layout
8063 \begin_inset Formula $\leftharpoondown$
8073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8076 \begin_layout Plain Layout
8084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8087 \begin_layout Plain Layout
8088 \begin_inset Formula $\hookleftarrow$
8102 \begin_inset space \hfill{}
8106 \begin_inset Tabular
8107 <lyxtabular version="3" rows="8" columns="2">
8109 <column alignment="center" valignment="top" width="0pt">
8110 <column alignment="center" valignment="top" width="0pt">
8112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8115 \begin_layout Plain Layout
8121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8124 \begin_layout Plain Layout
8132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8135 \begin_layout Plain Layout
8143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8146 \begin_layout Plain Layout
8147 \begin_inset Formula $\to$
8157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8160 \begin_layout Plain Layout
8168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8171 \begin_layout Plain Layout
8172 \begin_inset Formula $\Rightarrow$
8182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8185 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8196 \begin_layout Plain Layout
8197 \begin_inset Formula $\longrightarrow$
8207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\Longrightarrow$
8232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\rightharpoonup$
8257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\rightharpoondown$
8282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\hookrightarrow$
8311 \begin_inset space \hfill{}
8317 \begin_layout Standard
8318 \begin_inset space \hfill{}
8322 \begin_inset Tabular
8323 <lyxtabular version="3" rows="6" columns="2">
8325 <column alignment="center" valignment="top" width="0pt">
8326 <column alignment="center" valignment="top" width="0pt">
8328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8331 \begin_layout Plain Layout
8337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8340 \begin_layout Plain Layout
8348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8351 \begin_layout Plain Layout
8359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8362 \begin_layout Plain Layout
8363 \begin_inset Formula $\leftrightarrow$
8373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8376 \begin_layout Plain Layout
8384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8387 \begin_layout Plain Layout
8388 \begin_inset Formula $\Leftrightarrow$
8398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8401 \begin_layout Plain Layout
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8412 \begin_layout Plain Layout
8413 \begin_inset Formula $\longleftrightarrow$
8423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8426 \begin_layout Plain Layout
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8437 \begin_layout Plain Layout
8438 \begin_inset Formula $\Longleftrightarrow$
8448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8451 \begin_layout Plain Layout
8459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8462 \begin_layout Plain Layout
8463 \begin_inset Formula $\rightleftharpoons$
8477 \begin_inset space \hspace{}
8482 \begin_inset space \hfill{}
8486 \begin_inset Tabular
8487 <lyxtabular version="3" rows="5" columns="2">
8489 <column alignment="center" valignment="top" width="0pt">
8490 <column alignment="center" valignment="top" width="0pt">
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8495 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8504 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8515 \begin_layout Plain Layout
8523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8526 \begin_layout Plain Layout
8527 \begin_inset Formula $\mapsto$
8537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8540 \begin_layout Plain Layout
8548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8551 \begin_layout Plain Layout
8552 \begin_inset Formula $\longmapsto$
8562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8565 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8576 \begin_layout Plain Layout
8577 \begin_inset Formula $\leadsto$
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8601 \begin_layout Plain Layout
8602 \begin_inset Formula $\dasharrow$
8616 \begin_inset space \hfill{}
8622 \begin_layout Standard
8623 \begin_inset VSpace medskip
8626 Arrows used as accent like e.
8627 \begin_inset space \thinspace{}
8631 \begin_inset space ~
8634 vector arrows are listed in
8635 \begin_inset CommandInset ref
8637 reference "sec:Accents"
8644 \begin_layout Standard
8645 \begin_inset VSpace bigskip
8648 Furthermore there are the labeled arrows
8652 \begin_layout Plain Layout
8668 \begin_layout Plain Layout
8686 \begin_layout Plain Layout
8693 \begin_layout Plain Layout
8708 When inserting one of these commands in a formula, an arrow with two blue
8709 boxes appear where the label can be inserted.
8710 The length of the arrow adapts to the label width.
8713 \begin_layout Standard
8715 \begin_inset Tabular
8716 <lyxtabular version="3" rows="3" columns="2">
8718 <column alignment="center" valignment="top" width="0pt">
8719 <column alignment="center" valignment="top" width="0pt">
8721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8724 \begin_layout Plain Layout
8730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8733 \begin_layout Plain Layout
8735 \begin_inset Note Note
8738 \begin_layout Plain Layout
8745 is only used as spacer.
8757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8760 \begin_layout Plain Layout
8767 \begin_layout Plain Layout
8777 \begin_inset Formula $\downarrow$
8781 \begin_inset Formula $\to$
8789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8792 \begin_layout Plain Layout
8793 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8806 \begin_layout Plain Layout
8813 \begin_layout Plain Layout
8823 \begin_inset Formula $\downarrow$
8827 \begin_inset Formula $\to$
8835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8855 \begin_layout Subsection
8856 Vertical and diagonal Arrows
8860 \begin_layout Plain Layout
8870 \begin_layout Plain Layout
8879 \begin_layout Standard
8880 \begin_inset space \hfill{}
8884 \begin_inset Tabular
8885 <lyxtabular version="3" rows="7" columns="2">
8887 <column alignment="center" valignment="top" width="0pt">
8888 <column alignment="center" valignment="top" width="0pt">
8890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8893 \begin_layout Plain Layout
8899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8902 \begin_layout Plain Layout
8910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8913 \begin_layout Plain Layout
8921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8924 \begin_layout Plain Layout
8925 \begin_inset Formula $\uparrow$
8935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8938 \begin_layout Plain Layout
8946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8949 \begin_layout Plain Layout
8950 \begin_inset Formula $\Uparrow$
8960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8963 \begin_layout Plain Layout
8971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8974 \begin_layout Plain Layout
8975 \begin_inset Formula $\updownarrow$
8985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8988 \begin_layout Plain Layout
8996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8999 \begin_layout Plain Layout
9000 \begin_inset Formula $\Updownarrow$
9010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9013 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9025 \begin_inset Formula $\Downarrow$
9035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9038 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\downarrow$
9064 \begin_inset space \hfill{}
9068 \begin_inset Tabular
9069 <lyxtabular version="3" rows="5" columns="2">
9071 <column alignment="center" valignment="top" width="0pt">
9072 <column alignment="center" valignment="top" width="0pt">
9074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9077 \begin_layout Plain Layout
9083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9086 \begin_layout Plain Layout
9094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9097 \begin_layout Plain Layout
9105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9108 \begin_layout Plain Layout
9109 \begin_inset Formula $\nearrow$
9119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9122 \begin_layout Plain Layout
9130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9133 \begin_layout Plain Layout
9134 \begin_inset Formula $\searrow$
9144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9147 \begin_layout Plain Layout
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9158 \begin_layout Plain Layout
9159 \begin_inset Formula $\swarrow$
9169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9172 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9184 \begin_inset Formula $\nwarrow$
9198 \begin_inset space \hfill{}
9204 \begin_layout Standard
9205 \begin_inset VSpace medskip
9208 Vertical arrows can be used also as delimiter together with the commands
9210 \begin_inset CommandInset ref
9212 reference "sub:Manual-Bracket-Size"
9217 \begin_inset CommandInset ref
9219 reference "sub:Automatic-Bracket-Size"
9226 \begin_layout Standard
9227 \begin_inset Newpage newpage
9233 \begin_layout Section
9235 \begin_inset CommandInset label
9245 \begin_layout Plain Layout
9254 \begin_layout Standard
9255 Accents can be inserted via the math toolbar button
9256 \begin_inset Graphics
9257 filename ../images/math/hat.png
9262 or the commands listed in the following subsections.
9265 \begin_layout Subsection
9266 Accents for one Character
9270 \begin_layout Plain Layout
9283 \begin_layout Plain Layout
9285 \begin_inset CommandInset ref
9287 reference "sub:Accents-in-Text"
9300 \begin_layout Plain Layout
9308 \begin_inset Note Note
9311 \begin_layout Plain Layout
9314 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9317 \begin_layout Plain Layout
9320 texorpdfstring is in section
9321 \begin_inset CommandInset ref
9323 reference "sub:Formulas-in-Section"
9333 \begin_inset CommandInset label
9335 name "sub:Accents-for-one"
9343 \begin_layout Plain Layout
9344 Accents ! for one character
9352 \begin_layout Standard
9353 \begin_inset space \hfill{}
9357 \begin_inset Tabular
9358 <lyxtabular version="3" rows="8" columns="2">
9360 <column alignment="center" valignment="top" width="0pt">
9361 <column alignment="center" valignment="top" width="0pt">
9363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9366 \begin_layout Plain Layout
9372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9375 \begin_layout Plain Layout
9377 \begin_inset Note Note
9380 \begin_layout Plain Layout
9387 is only used as spacer.
9399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9402 \begin_layout Plain Layout
9409 \begin_layout Plain Layout
9423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9426 \begin_layout Plain Layout
9427 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9440 \begin_layout Plain Layout
9447 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9464 \begin_layout Plain Layout
9465 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9478 \begin_layout Plain Layout
9485 \begin_layout Plain Layout
9499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9502 \begin_layout Plain Layout
9503 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9516 \begin_layout Plain Layout
9524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9527 \begin_layout Plain Layout
9528 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9541 \begin_layout Plain Layout
9548 \begin_layout Plain Layout
9561 \begin_layout Plain Layout
9572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9575 \begin_layout Plain Layout
9576 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9589 \begin_layout Plain Layout
9596 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Plain Layout
9614 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9634 \begin_layout Plain Layout
9648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9651 \begin_layout Plain Layout
9652 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9666 \begin_inset space \hfill{}
9670 \begin_inset Tabular
9671 <lyxtabular version="3" rows="7" columns="2">
9673 <column alignment="center" valignment="top" width="0pt">
9674 <column alignment="center" valignment="top" width="0pt">
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9679 \begin_layout Plain Layout
9685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9688 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9699 \begin_layout Plain Layout
9706 \begin_layout Plain Layout
9720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9723 \begin_layout Plain Layout
9724 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9737 \begin_layout Plain Layout
9744 \begin_layout Plain Layout
9758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9761 \begin_layout Plain Layout
9762 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9775 \begin_layout Plain Layout
9782 \begin_layout Plain Layout
9796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9799 \begin_layout Plain Layout
9800 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9813 \begin_layout Plain Layout
9820 \begin_layout Plain Layout
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9837 \begin_layout Plain Layout
9838 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9851 \begin_layout Plain Layout
9858 \begin_layout Plain Layout
9872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9875 \begin_layout Plain Layout
9876 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9886 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9889 \begin_layout Plain Layout
9896 \begin_layout Plain Layout
9910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9913 \begin_layout Plain Layout
9914 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9928 \begin_inset space \hfill{}
9934 \begin_layout Standard
9935 \begin_inset VSpace bigskip
9942 \begin_layout Plain Layout
9948 in formulas, a quotation mark is inserted before the vowel.
9949 These two characters are then treated by LaTeX as
9953 character when the formula part with the umlaut is marked as German.
9961 \begin_inset Quotes eld
9965 \begin_inset Quotes erd
9968 umlauts are created as demonstrated in the following example:
9971 \begin_layout Standard
9972 \begin_inset VSpace -2mm
9978 \begin_layout Standard
9980 \begin_inset Tabular
9981 <lyxtabular version="3" rows="3" columns="2">
9983 <column alignment="center" valignment="top" width="0">
9984 <column alignment="center" valignment="top" width="0">
9986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9989 \begin_layout Plain Layout
9995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9998 \begin_layout Plain Layout
10000 \begin_inset Note Note
10003 \begin_layout Plain Layout
10010 is only used as spacer.
10022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10025 \begin_layout Plain Layout
10028 \begin_inset Quotes grd
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10039 \begin_layout Plain Layout
10042 \begin_inset Formula $"i$
10052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10055 \begin_layout Plain Layout
10062 \begin_layout Plain Layout
10076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10079 \begin_layout Plain Layout
10080 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10096 \begin_layout Standard
10097 Another advantage to
10103 is that umlauts can directly be converted to mathematical text because
10104 the accent commands above are
10110 in mathematical text
10113 To convert an accented character to mathematical text, only the character
10114 under the accent may be converted.
10115 This applies also for all other conversions, e.
10116 \begin_inset space \thinspace{}
10120 \begin_inset space ~
10126 \begin_layout Standard
10127 In mathematical text, umlauts and other accented characters can directly
10131 \begin_layout Subsection
10132 Accents for Operators
10136 \begin_layout Plain Layout
10137 Accents ! for operators
10145 \begin_layout Standard
10156 \begin_layout Plain Layout
10174 \begin_layout Plain Layout
10182 characters can be placed above or below an operator, respectively, to accent
10194 \begin_layout Plain Layout
10202 characters can be set before and behind an operator.
10203 The command scheme is:
10206 \begin_layout Standard
10222 \begin_layout Standard
10229 must always be before the operator that should be accented.
10230 You can accent with several characters and even with other operators and
10238 for example only characters behind an operator, write nothing between the
10239 first braces but don't omit the braces.
10242 \begin_layout Standard
10243 For example the command
10248 \begin_inset Formula $\to$
10258 \begin_inset Formula $\to$
10267 \begin_layout Plain Layout
10283 \begin_inset Formula \[
10284 \sideset{}{'}\sum_{k=1}^{n}\]
10291 \begin_layout Standard
10300 \begin_layout Plain Layout
10315 \begin_layout Plain Layout
10327 \begin_inset Formula $\uparrow$
10335 \begin_inset Formula \[
10336 \overset{a}{\maltese}\]
10340 As seen in the last example, with
10352 also symbols and characters can be accented; with
10358 this is not possible.
10361 \begin_layout Subsection
10362 Accents for several Characters
10363 \begin_inset CommandInset label
10365 name "sub:Accents-for-several"
10373 \begin_layout Plain Layout
10374 Accents ! for several characters
10382 \begin_layout Standard
10383 \begin_inset space \hfill{}
10387 \begin_inset Tabular
10388 <lyxtabular version="3" rows="5" columns="2">
10390 <column alignment="center" valignment="top" width="0pt">
10391 <column alignment="center" valignment="top" width="0pt">
10393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10396 \begin_layout Plain Layout
10402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10405 \begin_layout Plain Layout
10407 \begin_inset Note Note
10410 \begin_layout Plain Layout
10417 is only used as spacer.
10429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10432 \begin_layout Plain Layout
10439 \begin_layout Plain Layout
10453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10456 \begin_layout Plain Layout
10457 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10470 \begin_layout Plain Layout
10477 \begin_layout Plain Layout
10491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10494 \begin_layout Plain Layout
10495 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10508 \begin_layout Plain Layout
10515 \begin_layout Plain Layout
10529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10532 \begin_layout Plain Layout
10533 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10546 \begin_layout Plain Layout
10549 underleftrightarrow
10553 \begin_layout Plain Layout
10567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10570 \begin_layout Plain Layout
10571 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10585 \begin_inset space \hfill{}
10589 \begin_inset Tabular
10590 <lyxtabular version="3" rows="5" columns="2">
10592 <column alignment="center" valignment="top" width="0pt">
10593 <column alignment="center" valignment="top" width="0pt">
10595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10598 \begin_layout Plain Layout
10604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Plain Layout
10615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10618 \begin_layout Plain Layout
10625 \begin_layout Plain Layout
10639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10642 \begin_layout Plain Layout
10643 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10656 \begin_layout Plain Layout
10663 \begin_layout Plain Layout
10677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10680 \begin_layout Plain Layout
10681 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10694 \begin_layout Plain Layout
10701 \begin_layout Plain Layout
10715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10718 \begin_layout Plain Layout
10719 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10732 \begin_layout Plain Layout
10739 \begin_layout Plain Layout
10753 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10756 \begin_layout Plain Layout
10757 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10771 \begin_inset space \hfill{}
10777 \begin_layout Standard
10778 \begin_inset VSpace medskip
10781 With these commands as many characters as you like can be accented.
10794 will only be set in the output with a length of three characters, as shown
10795 in the following example:
10796 \begin_inset Formula \[
10797 \widetilde{A+B=C-D}\]
10804 \begin_layout Standard
10815 \begin_layout Plain Layout
10833 \begin_layout Plain Layout
10841 described in the previous subsection it is also possible to accent several
10851 \begin_layout Plain Layout
10861 \begin_inset Formula $\downarrow$
10867 \begin_inset Formula \[
10868 \underset{***}{A=B}\]
10875 \begin_layout Section
10877 \begin_inset CommandInset label
10887 \begin_layout Plain Layout
10896 \begin_layout Subsection
10898 \begin_inset CommandInset label
10900 name "sub:Predefined-Space"
10908 \begin_layout Plain Layout
10909 Space ! horizontal ! predefined
10917 \begin_layout Standard
10918 Sometimes it is necessary to insert horizontal space to a formula.
10919 This is done by inserting a protected space (shortcut
10925 \begin_inset Quotes eld
10935 \begin_layout Plain Layout
10948 \begin_inset Quotes erd
10951 appears and by pressing
10955 several times one can select one of eight different space sizes.
10956 The spaces can also be inserted using the math toolbar button
10957 \begin_inset Graphics
10958 filename ../images/math/space.png
10963 or special commands.
10964 Independent from the inserted command, one can select the size again by
10972 \begin_layout Standard
10975 \begin_inset VSpace -5mm
10979 \begin_inset Tabular
10980 <lyxtabular version="3" rows="3" columns="7">
10982 <column alignment="center" valignment="middle" width="6.8cm">
10983 <column alignment="center" valignment="top" width="0">
10984 <column alignment="center" valignment="top" width="0">
10985 <column alignment="center" valignment="top" width="0">
10986 <column alignment="center" valignment="top" width="0">
10987 <column alignment="center" valignment="top" width="0">
10988 <column alignment="center" valignment="top" width="0">
10990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10993 \begin_layout Plain Layout
10999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11002 \begin_layout Plain Layout
11010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11013 \begin_layout Plain Layout
11021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11024 \begin_layout Plain Layout
11032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11035 \begin_layout Plain Layout
11043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11046 \begin_layout Plain Layout
11054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11057 \begin_layout Plain Layout
11067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11070 \begin_layout Plain Layout
11075 keystrokes after inserting the protected space
11080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11083 \begin_layout Plain Layout
11089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11092 \begin_layout Plain Layout
11098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11101 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11128 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11139 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11148 \begin_layout Plain Layout
11149 \begin_inset Formula $A\, B$
11157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11161 \begin_inset Formula $A\: B$
11169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11173 \begin_inset Formula $A\; B$
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11185 \begin_inset Formula $A\quad B$
11193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11196 \begin_layout Plain Layout
11197 \begin_inset Formula $A\qquad B$
11205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11208 \begin_layout Plain Layout
11209 \begin_inset Formula $A\! B$
11225 \begin_layout Standard
11226 The last size seem to produce no space.
11227 It is displayed red in LyX contrary to the other sizes, because it is a
11229 There are two more negative spaces:
11232 \begin_layout Standard
11234 \begin_inset Tabular
11235 <lyxtabular version="3" rows="3" columns="3">
11237 <column alignment="center" valignment="middle" width="6.8cm">
11238 <column alignment="center" valignment="top" width="0pt">
11239 <column alignment="center" valignment="top" width="0pt">
11241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11244 \begin_layout Plain Layout
11250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11253 \begin_layout Plain Layout
11261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11264 \begin_layout Plain Layout
11274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11277 \begin_layout Plain Layout
11282 keystrokes after inserting the protected space
11287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11299 \begin_layout Plain Layout
11307 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11320 \begin_inset Formula $A\negmedspace B$
11328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11331 \begin_layout Plain Layout
11332 \begin_inset Formula $A\negthickspace B$
11348 \begin_layout Standard
11349 Negative spaces can lead to characters overlapping each other.
11350 Thus they can be used to enforce ligatures, what is e.
11351 \begin_inset space \thinspace{}
11355 \begin_inset space ~
11358 useful for summation operators:
11361 \begin_layout Standard
11363 \begin_inset Tabular
11364 <lyxtabular version="3" rows="3" columns="2">
11366 <column alignment="center" valignment="top" width="0">
11367 <column alignment="center" valignment="top" width="0">
11369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11372 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11381 \begin_layout Plain Layout
11383 \begin_inset Note Note
11386 \begin_layout Plain Layout
11393 is only used as spacer.
11405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11408 \begin_layout Plain Layout
11417 \begin_layout Plain Layout
11431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11434 \begin_layout Plain Layout
11435 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11448 \begin_layout Plain Layout
11459 \begin_layout Plain Layout
11473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11476 \begin_layout Plain Layout
11477 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11493 \begin_layout Standard
11494 Relations like for example equal signs, are always surrounded by space.
11495 To suppress this, the equal sign is placed into a TeX-brace.
11496 The following example demonstrates this:
11499 \begin_layout Standard
11501 \begin_inset Tabular
11502 <lyxtabular version="3" rows="2" columns="2">
11504 <column alignment="center" valignment="top" width="0pt">
11505 <column alignment="center" valignment="top" width="0pt">
11507 <cell alignment="center" valignment="top" usebox="none">
11510 \begin_layout Plain Layout
11516 <cell alignment="center" valignment="top" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $A=B$
11530 <cell alignment="center" valignment="top" usebox="none">
11533 \begin_layout Plain Layout
11534 \begin_inset Note Note
11537 \begin_layout Plain Layout
11544 is only used as spacer.
11550 \begin_inset Formula $\raisebox{5mm}{}$
11553 equation without space
11558 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11561 \begin_layout Plain Layout
11562 \begin_inset Formula $A{=}B$
11578 \begin_layout Standard
11580 The command for the last formula is:
11585 \begin_inset Formula $\to$
11591 \begin_layout Standard
11592 \begin_inset VSpace bigskip
11595 Spaces are needed for physical units, because the space between the value
11596 and the unit is the smallest one and not a normal space.
11597 For units in text, the smallest space is inserted via the menu
11599 Insert\SpecialChar \menuseparator
11600 Formatting\SpecialChar \menuseparator
11602 \begin_inset space ~
11614 \begin_layout Standard
11615 An example to visualize the difference:
11618 \begin_layout Standard
11619 \begin_inset Tabular
11620 <lyxtabular version="3" rows="2" columns="2">
11622 <column alignment="left" valignment="top" width="0">
11623 <column alignment="left" valignment="top" width="0">
11625 <cell alignment="center" valignment="top" usebox="none">
11628 \begin_layout Plain Layout
11630 \begin_inset Formula $\cdot$
11638 <cell alignment="center" valignment="top" usebox="none">
11641 \begin_layout Plain Layout
11642 space between value and unit
11649 <cell alignment="center" valignment="top" usebox="none">
11652 \begin_layout Plain Layout
11654 \begin_inset space \thinspace{}
11658 \begin_inset Formula $\cdot$
11666 <cell alignment="center" valignment="top" usebox="none">
11669 \begin_layout Plain Layout
11670 smallest space between value and unit
11683 \begin_layout Subsection
11688 \begin_layout Plain Layout
11701 \begin_layout Plain Layout
11702 for vertical space in formulas see
11703 \begin_inset CommandInset ref
11705 reference "sub:Line-Separation"
11718 \begin_layout Plain Layout
11726 \begin_inset Note Note
11729 \begin_layout Plain Layout
11732 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11735 \begin_layout Plain Layout
11738 texorpdfstring is in section
11739 \begin_inset CommandInset ref
11741 reference "sub:Formulas-in-Section"
11751 \begin_inset CommandInset label
11753 name "sub:Variable-Space"
11761 \begin_layout Plain Layout
11762 Space ! horizontal ! variable
11770 \begin_layout Standard
11771 Space with a defined length can be inserted in LyX with the command
11772 \begin_inset Newline newline
11785 \begin_layout Plain Layout
11794 For the length all units listed in
11795 \begin_inset CommandInset ref
11797 reference "tab:Available-units"
11801 are allowed, except of the unit
11802 \begin_inset Quotes eld
11806 \begin_inset Quotes erd
11810 The length may also be negative.
11811 To insert so many space that the formula uses all available space, the
11822 \begin_layout Plain Layout
11833 \begin_layout Standard
11834 \begin_inset VSpace -1mm
11840 \begin_layout Standard
11842 \begin_inset Tabular
11843 <lyxtabular version="3" rows="4" columns="2">
11845 <column alignment="center" valignment="top" width="0">
11846 <column alignment="center" valignment="top" width="0">
11848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11851 \begin_layout Plain Layout
11857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11860 \begin_layout Plain Layout
11868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11871 \begin_layout Plain Layout
11875 \begin_inset Formula $\to$
11885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11888 \begin_layout Plain Layout
11889 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11902 \begin_layout Plain Layout
11906 \begin_inset Formula $\to$
11916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11919 \begin_layout Plain Layout
11920 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11933 \begin_layout Plain Layout
11940 \begin_layout Plain Layout
11954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11957 \begin_layout Plain Layout
11958 \begin_inset Formula $A=A\hfill B=B$
11974 \begin_layout Standard
11975 In the last example the available space is given by the longest column entry
11977 In an inline formula the space depends on the length of the line in which
11985 Thus, when the line uses the full width, no space will be created.
11992 only has an effect on displayed formulas when the formula style
11997 (Formula styles are explained in
11998 \begin_inset CommandInset ref
12000 reference "sec:Formula-Styles"
12007 \begin_layout Standard
12014 , there are the commands
12026 that fill the space with a pattern, see
12027 \begin_inset CommandInset ref
12029 reference "sub:Ellipses"
12036 \begin_layout Standard
12037 For text, variable space can be inserted via the menu
12039 Insert\SpecialChar \menuseparator
12040 Formatting\SpecialChar \menuseparator
12042 \begin_inset space ~
12047 , what is not possible in formulas:
12050 \begin_layout Standard
12051 This is a line with
12052 \begin_inset space \hspace{}
12057 \begin_inset space \thinspace{}
12063 \begin_layout Standard
12064 This is a line with
12065 \begin_inset space \hfill{}
12071 \begin_layout Subsection
12072 Space besides inline Formulas
12076 \begin_layout Plain Layout
12077 Space ! besides inline formulas
12085 \begin_layout Standard
12086 The space that surrounds inline formulas can be adjusted with the length
12095 \begin_layout Plain Layout
12106 The value of a length is set with the command
12114 \begin_layout Plain Layout
12124 that has the following scheme:
12127 \begin_layout Standard
12132 setlength{length name}{value}
12135 \begin_layout Standard
12143 \begin_inset space \thinspace{}
12149 \begin_layout Standard
12159 \begin_layout Standard
12160 is inserted in TeX-mode.
12162 \begin_inset space \thinspace{}
12165 mm space will now be set around all inline formulas:
12169 \begin_layout Plain Layout
12183 \begin_layout Standard
12184 This is a line with an inline formula
12185 \begin_inset Formula $A=B$
12189 \begin_inset space \thinspace{}
12192 mm surrounding space.
12196 \begin_layout Plain Layout
12210 \begin_layout Standard
12211 To return to the predefined value,
12217 is set to the value 0
12218 \begin_inset space \thinspace{}
12224 \begin_layout Section
12229 \begin_layout Plain Layout
12239 \begin_layout Plain Layout
12244 \begin_layout Plain Layout
12255 \begin_layout Plain Layout
12270 \begin_layout Standard
12271 Boxes for text are described in chapter
12278 \begin_inset space ~
12286 \begin_layout Subsection
12288 \begin_inset CommandInset label
12290 name "sub:Boxes-with-Frame"
12298 \begin_layout Plain Layout
12307 \begin_layout Standard
12308 It is possible to frame formulas or parts of it with the commands
12318 \begin_layout Plain Layout
12336 \begin_layout Plain Layout
12347 \begin_layout Standard
12348 When one of these commands is inserted to a formula, a blue box appears
12349 within a frame to enter formula parts.
12356 an additional formula has to be created by
12364 \begin_layout Plain Layout
12365 Due to a bug in LyX it is not possible to create a new formula with
12370 \begin_inset CommandInset href
12372 name "LyX-bug #1435"
12373 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12382 , because the box content will otherwise be treated as mathematical text.
12389 is used, a new formula is automatically created inside the frame.
12392 \begin_layout Standard
12399 is not suitable to frame displayed formulas, because the formula will always
12400 be set in the size of the text.
12407 is in contrary not suitable to frame inline formulas, because the formula
12408 will always be set in the size of a displayed formula.
12411 \begin_layout Standard
12418 there is the command
12428 \begin_layout Plain Layout
12436 where additionally the frame width and the alignment can be specified.
12443 is used in the following scheme:
12446 \begin_layout Standard
12451 framebox[frame width][position]{box content}
12454 \begin_layout Standard
12455 The position can either be
12472 right aligns the formula in the box.
12473 When no position is given, the formula will be centered.
12474 \begin_inset Newline newline
12477 Is no width given, also no position can be given.
12478 In this case the frame width is adjusted to the box content like for
12487 \begin_layout Standard
12494 is inserted, a box appears containing three blue boxes.
12495 The first two boxes are surrounded by brackets and denote the two optional
12497 The third box is for formula parts like for
12506 \begin_layout Standard
12508 \begin_inset Note Note
12511 \begin_layout Plain Layout
12512 The table has been set into a minipage to make the footnote appearing.
12513 Otherwise the footnote text would not be displayed.
12519 \begin_inset Box Frameless
12528 height_special "totalheight"
12531 \begin_layout Plain Layout
12533 \begin_inset Tabular
12534 <lyxtabular version="3" rows="5" columns="2">
12536 <column alignment="center" valignment="top" width="0">
12537 <column alignment="center" valignment="top" width="0">
12539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12542 \begin_layout Plain Layout
12547 \begin_layout Plain Layout
12548 Due to a bug in LyX it is not possible to create a new formula with
12553 \begin_inset CommandInset href
12555 name "LyX-bug #1435"
12556 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12573 \begin_layout Plain Layout
12575 \begin_inset Note Note
12578 \begin_layout Plain Layout
12585 is only used as spacer.
12597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12600 \begin_layout Plain Layout
12607 \begin_layout Plain Layout
12626 \begin_layout Plain Layout
12640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12643 \begin_layout Plain Layout
12644 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12658 \begin_layout Plain Layout
12665 \begin_layout Plain Layout
12680 \begin_layout Plain Layout
12694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12697 \begin_layout Plain Layout
12698 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12711 \begin_layout Plain Layout
12718 \begin_layout Plain Layout
12732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12735 \begin_layout Plain Layout
12736 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12749 \begin_layout Plain Layout
12756 \begin_layout Plain Layout
12766 \begin_inset Formula $\to$
12770 \begin_inset Formula $\to$
12783 \begin_layout Plain Layout
12793 \begin_inset Formula $\downarrow$
12801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12804 \begin_layout Plain Layout
12805 \begin_inset Formula $\raisebox{6mm}{}$
12809 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12813 \begin_inset Formula $\raisebox{-4mm}{}$
12834 \begin_layout Standard
12835 The frame thickness can also be adjusted.
12836 To do this the following commands have to be inserted in TeX-mode before
12840 \begin_layout Standard
12850 \begin_inset Quotes eld
12854 \begin_inset Quotes erd
12868 \begin_inset Quotes eld
12872 \begin_inset Quotes erd
12878 \begin_layout Standard
12879 \begin_inset Quotes eld
12883 \begin_inset Quotes erd
12886 specifies the minimal distance between the frame and the first character
12888 An example for this is the following framed formula:
12892 \begin_layout Plain Layout
12904 \begin_inset Formula \[
12909 Before this formula the commands
12912 \begin_layout Standard
12934 \begin_layout Standard
12935 were inserted in TeX-mode.
12936 The given values are used for all following boxes.
12939 \begin_layout Standard
12940 To return to the standard frame size, the command
12943 \begin_layout Standard
12968 \begin_layout Plain Layout
12982 \begin_layout Standard
12983 is inserted in TeX-mode before the next formula.
12986 \begin_layout Subsection
12987 Boxes without Frame
12988 \begin_inset CommandInset label
12990 name "sub:Boxes-without-Frame"
12998 \begin_layout Plain Layout
12999 Boxes ! without frame
13007 \begin_layout Standard
13008 For boxes without a frame there are the following box commands:
13018 \begin_layout Plain Layout
13036 \begin_layout Plain Layout
13054 \begin_layout Plain Layout
13065 \begin_layout Standard
13072 a box can be super- or subscripted.
13073 But in contrary to normal super- and subscripting, the characters in the
13074 box keep their font size.
13081 is used in the following scheme:
13084 \begin_layout Standard
13089 raisebox{height}{box content}
13092 \begin_layout Standard
13093 When the box should contain a formula, an extra formula is needed like for
13103 \begin_layout Standard
13105 \begin_inset Tabular
13106 <lyxtabular version="3" rows="4" columns="2">
13108 <column alignment="center" valignment="top" width="0">
13109 <column alignment="center" valignment="top" width="0">
13111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13114 \begin_layout Plain Layout
13120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13123 \begin_layout Plain Layout
13131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13134 \begin_layout Plain Layout
13138 \begin_inset Formula $\to$
13144 \begin_inset Formula $\to$
13152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13155 \begin_layout Plain Layout
13156 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13169 \begin_layout Plain Layout
13173 \begin_inset Formula $\to$
13179 \begin_inset Formula $\to$
13187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13190 \begin_layout Plain Layout
13191 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13204 \begin_layout Plain Layout
13208 \begin_inset Formula $\to$
13223 \begin_layout Plain Layout
13237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13240 \begin_layout Plain Layout
13244 \begin_layout Plain Layout
13268 \begin_layout Standard
13269 The last formula can currently only be created using TeX-mode because LyX
13270 inserts a box instead of the needed extra formula.
13274 \begin_layout Plain Layout
13276 \begin_inset CommandInset href
13278 name "LyX-bug #1435"
13279 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13291 \begin_layout Standard
13316 , with the difference that there is no frame.
13319 \begin_layout Subsection
13321 \begin_inset CommandInset label
13323 name "sub:Colored-Boxes"
13331 \begin_layout Plain Layout
13340 \begin_layout Standard
13341 To be able to use all commands explained in this section, the LaTeX-package
13350 \begin_layout Plain Layout
13355 is part of every LaTeX standard installation.
13364 \begin_layout Plain Layout
13370 has to be loaded in the LaTeX-preamble with the line
13374 \begin_layout Plain Layout
13375 When text is colored somewhere in the document with a predefined color,
13376 LyX loads the LaTeX-package
13381 Thus it is possible that the package is loaded twice, but this doesn't
13388 \begin_inset Note Note
13391 \begin_layout Plain Layout
13392 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13401 \begin_layout Standard
13409 \begin_layout Standard
13410 \begin_inset VSpace medskip
13413 To color boxes, the command
13423 \begin_layout Plain Layout
13431 is used in the following scheme:
13434 \begin_layout Standard
13439 colorbox{color}{box content}
13442 \begin_layout Standard
13443 The box content can also be a box and a
13449 can also be part of another box (see the 2nd and 3rd example).
13450 When the box should contain a formula, an extra formula has to be created,
13461 \begin_layout Plain Layout
13462 This also applies for the command
13470 \begin_inset CommandInset href
13472 name "LyX-bug #1435"
13473 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13485 \begin_layout Standard
13486 One of the following predefined colors can be chosen:
13489 \begin_layout Standard
13523 \begin_layout Standard
13525 \begin_inset Tabular
13526 <lyxtabular version="3" rows="4" columns="2">
13528 <column alignment="center" valignment="top" width="0">
13529 <column alignment="center" valignment="top" width="0">
13531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13534 \begin_layout Plain Layout
13540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13543 \begin_layout Plain Layout
13545 \begin_inset Note Note
13548 \begin_layout Plain Layout
13555 is only used as spacer.
13567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13570 \begin_layout Plain Layout
13574 \begin_inset Formula $\to$
13584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13587 \begin_layout Plain Layout
13588 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13601 \begin_layout Plain Layout
13605 \begin_inset Formula $\to$
13616 \begin_layout Plain Layout
13630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13633 \begin_layout Plain Layout
13634 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13647 \begin_layout Plain Layout
13654 \begin_layout Plain Layout
13666 \begin_inset Formula $\to$
13676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13679 \begin_layout Plain Layout
13680 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13696 \begin_layout Standard
13703 only colors the box but not the characters in the box.
13704 To color all characters, the whole formula is highlighted and the wanted
13705 color is chosen in the
13708 \begin_inset space ~
13714 The dialog can be called with the toolbar button
13715 \begin_inset Graphics
13716 filename ../images/dialog-show_character.png
13723 Edit\SpecialChar \menuseparator
13725 \begin_inset space ~
13728 Style\SpecialChar \menuseparator
13732 The formula number has then the same color as the formula.
13733 When the formula number should get another color than the formula characters,
13734 the color must be changed within the formula.
13737 \begin_layout Standard
13741 \begin_layout Standard
13744 \begin_inset Formula \begin{equation}
13745 \int A=B\label{eq:red}\end{equation}
13752 \begin_inset Formula \begin{equation}
13753 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13760 \begin_layout Standard
13762 \begin_inset CommandInset ref
13768 is completely colored red.
13769 \begin_inset Newline newline
13773 \begin_inset CommandInset ref
13775 reference "eq:redgreen"
13779 was first completely colored green to set the color for the formula number.
13780 Subsequently the formula characters were colored red.
13783 \begin_layout Standard
13784 \begin_inset VSpace bigskip
13787 To color the frame different than the rest of the box, the command
13797 \begin_layout Plain Layout
13805 is used in the following scheme:
13808 \begin_layout Standard
13813 fcolorbox{frame color}{color}{box content}
13816 \begin_layout Standard
13823 is an extension of the command
13830 The frame width is set, like for
13853 \begin_layout Plain Layout
13865 \begin_inset Formula \[
13866 \fcolorbox{cyan}{magenta}{A=B}\]
13874 \begin_layout Plain Layout
13888 \begin_layout Standard
13889 This formula was created with the command
13890 \begin_inset Newline newline
13898 \begin_inset Formula $\to$
13904 \begin_inset Formula $\to$
13914 \begin_layout Standard
13915 \begin_inset VSpace bigskip
13918 To use other colors than the predefined ones, they have to be defined first.
13921 \begin_layout Standard
13922 One can for example define the color
13923 \begin_inset Quotes eld
13931 \begin_inset Quotes erd
13934 with the LaTeX-preamble line:
13937 \begin_layout Standard
13942 definecolor{darkgreen}{cmyk}{0.5,
13960 \begin_layout Plain Layout
13971 \begin_layout Standard
13976 is the color space that denotes the colors
13993 The four comma separated numbers are the portion factor for the corresponding
13994 colors of the color space.
13995 The factors can be in the range of 0
13996 \begin_inset space \thinspace{}
14000 \begin_inset space \thinspace{}
14008 also the color space
14012 can be used for definitions.
14029 , so that there are in this case three portion factors for the corresponding
14031 Furthermore there is the color space
14035 with one portion factor for the gray value.
14038 \begin_layout Standard
14039 As example a framed box with the new defined color
14043 where the characters have been colored
14048 \begin_inset Formula \begin{equation}
14049 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14056 \begin_layout Standard
14057 Self-defined colors can also be used for text with the help of the command
14068 \begin_layout Plain Layout
14077 \begin_layout Standard
14081 \begin_layout Plain Layout
14085 textcolor{darkgreen}{
14091 \begin_inset Quotes eld
14095 \begin_inset Quotes erd
14102 \begin_layout Plain Layout
14112 \begin_layout Standard
14123 \begin_layout Plain Layout
14131 is used in the scheme
14135 textcolor{color}{characters to color}
14140 \begin_layout Subsection
14142 \begin_inset CommandInset label
14144 name "sub:Paragraph-Boxes"
14152 \begin_layout Plain Layout
14153 Boxes ! as paragraph
14161 \begin_layout Standard
14162 A box that can contain several lines and paragraphs, a so called paragraph
14163 box (parbox), can be created with the menu
14165 Insert\SpecialChar \menuseparator
14168 or the toolbar button
14169 \begin_inset Graphics
14170 filename ../images/box-insert.png
14178 \begin_layout Standard
14179 The following example shows a framed parbox in a line:
14182 \begin_layout Standard
14183 \begin_inset VSpace medskip
14187 \begin_inset Box Boxed
14196 height_special "totalheight"
14199 \begin_layout Plain Layout
14200 This is a paragraph box.
14202 \begin_inset space \thinspace{}
14205 cm long and can also contain formulas:
14206 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14217 \begin_layout Standard
14218 \begin_inset VSpace medskip
14224 \begin_layout Standard
14225 Such a box is created by right-clicking on the gray box inset.
14226 A dialog pops up showing the box properties.
14240 \begin_inset space \thinspace{}
14245 Vertical Box Alignment
14250 \begin_layout Standard
14251 \begin_inset VSpace medskip
14254 In LaTeX a parbox is created with the command
14264 \begin_layout Plain Layout
14272 that has the following scheme:
14275 \begin_layout Standard
14280 parbox[position]{width}{box content}
14283 \begin_layout Standard
14297 for bottom means that the box is aligned within the surrounding text with
14303 for top this is done with the first line.
14304 When no position is given, the box will be vertically centered, see section
14312 \begin_inset space ~
14317 manual for examples.
14320 \begin_layout Standard
14321 \begin_inset VSpace bigskip
14324 To frame formulas completely, including the formula number, the formula
14325 must be set into a parbox.
14326 To do this, the command
14340 is inserted in TeX-mode before the formula.
14349 \begin_layout Plain Layout
14359 is hereby the line width set for the document.
14360 Because the frame is outside the parbox, 2
14361 \begin_inset space \thinspace{}
14364 times the frame separation and the frame thickness must be subtracted from
14366 As this is not automatically done by LyX due to a bug
14370 \begin_layout Plain Layout
14371 \begin_inset CommandInset href
14373 name "LyX-bug #4483"
14374 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14383 , TeX-mode has to be used.
14384 To be able to multiply and subtract in arguments, the LaTeX-package
14392 \begin_layout Plain Layout
14397 is part of every LaTeX standard installation.
14406 \begin_layout Plain Layout
14412 must be loaded in the LaTeX-preamble with the line
14415 \begin_layout Standard
14423 \begin_layout Standard
14424 Behind the formula both boxes are closed by entering
14429 Here is an example:
14433 \begin_layout Plain Layout
14447 \begin_layout Standard
14451 \begin_layout Plain Layout
14469 \begin_inset Formula \begin{equation}
14470 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14478 \begin_layout Plain Layout
14489 \begin_layout Plain Layout
14503 \begin_layout Standard
14504 \begin_inset VSpace medskip
14507 As a parbox is used as argument of
14513 , there is in this case no difference between
14528 \begin_layout Standard
14529 \begin_inset VSpace bigskip
14532 Paragraph boxes are very useful to comment formulas directly.
14539 is used in combination with the command
14553 \begin_inset CommandInset ref
14555 reference "sub:User-defined-Numbering"
14562 \begin_layout Standard
14563 An example of a formula commented with
14572 \begin_layout Standard
14576 \begin_layout Plain Layout
14589 This is a description.
14590 It is distinctly separated from the formula and multiline.
14594 \begin_layout Plain Layout
14606 \begin_layout Standard
14607 Such a formula must be inserted completely in TeX-mode because LyX does
14608 not yet support the command
14615 The formula is created with the following command sequence:
14618 \begin_layout Standard
14631 is inserted in TeX-mode.
14635 \begin_layout Plain Layout
14636 When the formula style
14648 can also be replaced by
14655 (formula styles see
14656 \begin_inset CommandInset ref
14658 reference "sec:Formula-Styles"
14667 Then the description follows as normal text, and finally
14673 is inserted in TeX-mode.
14686 hereby create a displayed formula.
14689 \begin_layout Standard
14696 can be seen in this example that was
14697 \begin_inset Quotes eld
14701 \begin_inset Quotes erd
14704 using the mathematical textmode:
14705 \begin_inset Formula \[
14706 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14713 \begin_layout Section
14718 \begin_layout Plain Layout
14727 \begin_layout Subsection
14729 \begin_inset CommandInset label
14731 name "sub:Big-Operators"
14739 \begin_layout Plain Layout
14749 \begin_layout Plain Layout
14759 \begin_layout Plain Layout
14768 \begin_layout Standard
14769 To be able to use all integral operators listed here, the option
14771 Use esint package automatically
14773 must be set in the document settings under
14776 \begin_inset space ~
14784 \begin_layout Standard
14785 \begin_inset space \hfill{}
14789 \begin_inset Tabular
14790 <lyxtabular version="3" rows="11" columns="2">
14792 <column alignment="center" valignment="top" width="0pt">
14793 <column alignment="center" valignment="top" width="0pt">
14795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14798 \begin_layout Plain Layout
14804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14807 \begin_layout Plain Layout
14815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14818 \begin_layout Plain Layout
14825 \begin_layout Plain Layout
14838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14841 \begin_layout Plain Layout
14842 \begin_inset Formula $\sum$
14852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14855 \begin_layout Plain Layout
14862 \begin_layout Plain Layout
14875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14878 \begin_layout Plain Layout
14879 \begin_inset Formula $\int$
14889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14892 \begin_layout Plain Layout
14900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14903 \begin_layout Plain Layout
14904 \begin_inset Formula $\intop$
14914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14917 \begin_layout Plain Layout
14925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14928 \begin_layout Plain Layout
14929 \begin_inset Formula $\oint$
14939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14942 \begin_layout Plain Layout
14950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14953 \begin_layout Plain Layout
14954 \begin_inset Formula $\ointop$
14964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14967 \begin_layout Plain Layout
14975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14978 \begin_layout Plain Layout
14979 \begin_inset Formula $\ointctrclockwise$
14989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14992 \begin_layout Plain Layout
15000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15003 \begin_layout Plain Layout
15004 \begin_inset Formula $\ointclockwise$
15014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15017 \begin_layout Plain Layout
15025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15028 \begin_layout Plain Layout
15029 \begin_inset Formula $\sqint$
15039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15042 \begin_layout Plain Layout
15050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15053 \begin_layout Plain Layout
15054 \begin_inset Formula $\bigcap$
15064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15067 \begin_layout Plain Layout
15075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15078 \begin_layout Plain Layout
15079 \begin_inset Formula $\bigcup$
15093 \begin_inset space \hfill{}
15097 \begin_inset Tabular
15098 <lyxtabular version="3" rows="10" columns="2">
15100 <column alignment="center" valignment="top" width="0pt">
15101 <column alignment="center" valignment="top" width="0pt">
15103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15115 \begin_layout Plain Layout
15123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15126 \begin_layout Plain Layout
15133 \begin_layout Plain Layout
15146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15149 \begin_layout Plain Layout
15150 \begin_inset Formula $\prod$
15160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15163 \begin_layout Plain Layout
15171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15174 \begin_layout Plain Layout
15175 \begin_inset Formula $\coprod$
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15188 \begin_layout Plain Layout
15196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15199 \begin_layout Plain Layout
15200 \begin_inset Formula $\bigodot$
15210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15213 \begin_layout Plain Layout
15221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15224 \begin_layout Plain Layout
15225 \begin_inset Formula $\bigotimes$
15235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15238 \begin_layout Plain Layout
15246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15249 \begin_layout Plain Layout
15250 \begin_inset Formula $\bigoplus$
15260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15263 \begin_layout Plain Layout
15271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15274 \begin_layout Plain Layout
15275 \begin_inset Formula $\bigwedge$
15285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15288 \begin_layout Plain Layout
15296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15299 \begin_layout Plain Layout
15300 \begin_inset Formula $\bigvee$
15310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15313 \begin_layout Plain Layout
15321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15324 \begin_layout Plain Layout
15325 \begin_inset Formula $\bigsqcup$
15335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15338 \begin_layout Plain Layout
15346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15349 \begin_layout Plain Layout
15350 \begin_inset Formula $\biguplus$
15364 \begin_inset space \hfill{}
15370 \begin_layout Standard
15371 All big operators can also be inserted via the math toolbar button
15372 \begin_inset Graphics
15373 filename ../images/math/intop.png
15381 \begin_layout Standard
15382 The operators are called big because they are bigger than the sometimes
15383 equal looking binary operators.
15384 All big operators can have limits as described in the next subsection.
15387 \begin_layout Standard
15413 \begin_inset space ~
15416 in the style the operator limits are displayed, see
15417 \begin_inset CommandInset ref
15419 reference "sub:Operator-Limits"
15427 \begin_layout Subsubsection*
15428 Advices for Integrals
15431 \begin_layout Standard
15436 in an integral is an operator, that therefore has to be set upright.
15437 This is done by highlighting the
15441 and using the keyboard shortcut
15444 \begin_inset space ~
15453 \begin_layout Plain Layout
15459 \begin_inset CommandInset ref
15461 reference "sub:Font-Styles"
15471 Finally the smallest space is inserted before the
15475 , as this is usual for operators.
15479 \begin_layout Standard
15481 \begin_inset Formula $\int A(x)dx$
15485 \begin_inset Newline newline
15492 \begin_layout Plain Layout
15502 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15508 \begin_layout Standard
15509 For multiple integrals there are the following commands:
15510 \begin_inset VSpace medskip
15516 \begin_layout Standard
15517 \begin_inset space \hfill{}
15521 \begin_inset Tabular
15522 <lyxtabular version="3" rows="4" columns="2">
15524 <column alignment="center" valignment="top" width="0">
15525 <column alignment="center" valignment="top" width="0">
15527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15530 \begin_layout Plain Layout
15536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15539 \begin_layout Plain Layout
15541 \begin_inset Note Note
15544 \begin_layout Plain Layout
15551 is only used as spacer.
15563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15566 \begin_layout Plain Layout
15574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15577 \begin_layout Plain Layout
15578 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15591 \begin_layout Plain Layout
15599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15602 \begin_layout Plain Layout
15603 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15616 \begin_layout Plain Layout
15624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15627 \begin_layout Plain Layout
15628 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15642 \begin_inset space \hfill{}
15646 \begin_inset Tabular
15647 <lyxtabular version="3" rows="4" columns="2">
15649 <column alignment="center" valignment="top" width="0">
15650 <column alignment="center" valignment="top" width="0">
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15655 \begin_layout Plain Layout
15661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15664 \begin_layout Plain Layout
15672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15675 \begin_layout Plain Layout
15683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15686 \begin_layout Plain Layout
15687 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15700 \begin_layout Plain Layout
15708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15711 \begin_layout Plain Layout
15712 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15725 \begin_layout Plain Layout
15733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15736 \begin_layout Plain Layout
15737 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15751 \begin_inset space \hfill{}
15757 \begin_layout Subsection
15759 \begin_inset CommandInset label
15761 name "sub:Operator-Limits"
15769 \begin_layout Plain Layout
15778 \begin_layout Standard
15779 Limits are created by super- and subscripts:
15782 \begin_layout Standard
15784 \begin_inset Tabular
15785 <lyxtabular version="3" rows="2" columns="2">
15787 <column alignment="center" valignment="top" width="0pt">
15788 <column alignment="center" valignment="top" width="0pt">
15790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15793 \begin_layout Plain Layout
15799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15802 \begin_layout Plain Layout
15804 \begin_inset Note Note
15807 \begin_layout Plain Layout
15814 is only used as spacer.
15826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15829 \begin_layout Plain Layout
15838 \begin_layout Plain Layout
15848 \begin_inset Formula $\to$
15852 \begin_inset Formula $\to$
15860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15863 \begin_layout Plain Layout
15864 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15880 \begin_layout Standard
15881 Limits of inline formulas are set right beside the operator.
15882 Limits in displayed formulas are set above or below the operator, except
15883 of integral limits.
15886 \begin_layout Standard
15887 To force that the limits are set beside the operator, the cursor is set
15888 directly behind the operator and the limits type is changed with the menu
15891 Edit\SpecialChar \menuseparator
15892 Math\SpecialChar \menuseparator
15904 \begin_inset space ~
15913 \begin_layout Standard
15914 The default limits type is this:
15915 \begin_inset Formula \[
15916 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15920 This is how it looks when the limits type was changed to
15927 \begin_inset Formula \[
15928 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15932 For integrals, except of
15944 , the limits are by default set beside the operator.
15945 But for multiple integrals the limits are often set below the operator.
15946 In the following example the limits type was therefore set to
15950 and so set below the integrals:
15951 \begin_inset Formula \begin{equation}
15952 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15959 \begin_layout Standard
15960 \begin_inset VSpace medskip
15963 To specify conditions for limits, the commands
15973 \begin_layout Plain Layout
15991 \begin_layout Plain Layout
16000 To create for example this expression
16001 \begin_inset Formula \begin{equation}
16002 \sum_{\begin{subarray}{c}
16004 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16011 \begin_layout Standard
16012 the following has to be done:
16013 \begin_inset Newline newline
16028 \begin_layout Plain Layout
16040 One is now in a blue box under the summation operator and insert there
16049 \begin_layout Plain Layout
16061 The blue box is now within a purple box and now several lines can be written
16063 A new line is created by inserting a line break (
16069 \begin_inset Newline newline
16074 0<k<1000 Ctrl-Return
16075 \begin_inset Newline newline
16080 is typed in, a new box appears below for the new line.
16083 \begin_layout Standard
16084 The alignment of the lines can be changed to left aligned with the
16094 Edit\SpecialChar \menuseparator
16098 To get right alignment,
16106 \begin_layout Plain Layout
16117 is inserted at the beginning of the line.
16120 \begin_layout Standard
16133 with the difference that the lines are always centered.
16136 \begin_layout Standard
16137 \begin_inset VSpace bigskip
16141 \begin_inset CommandInset ref
16143 reference "eq:substack"
16147 there can be too much space beside an operator, because the characters
16148 following the operator are set beside the limits.
16151 \begin_layout Standard
16152 To avoid this, the following macro can be used in the LaTeX-preamble:
16155 \begin_layout Standard
16169 \begin_inset Newline newline
16181 \begin_inset Newline newline
16188 mathclapinternal #1#2{
16192 mathsurround =0pt #1{#2}$}}
16195 \begin_layout Standard
16196 This defines the command
16206 \begin_layout Plain Layout
16214 that sets the width of the limit to 0
16215 \begin_inset space \thinspace{}
16219 The command scheme is
16222 \begin_layout Standard
16230 \begin_layout Standard
16231 where the limit can consist of several conditions.
16234 \begin_layout Standard
16236 \begin_inset CommandInset ref
16238 reference "eq:substack"
16242 , one uses the command
16245 \begin_layout Standard
16258 \begin_layout Plain Layout
16267 0<k<1000 Ctrl-Enter
16270 \begin_layout Standard
16271 to create the lower limit.
16272 The summand is now directly behind the summation operator:
16273 \begin_inset Formula \[
16274 \sum_{\mathclap{\substack{0<k<1000\\
16275 \\k\,\in\,\mathbb{N}}
16283 \begin_layout Standard
16284 \begin_inset VSpace bigskip
16287 How to use one limit for several operators is described in
16288 \begin_inset CommandInset ref
16290 reference "sub:Self-defined-Operators"
16297 \begin_layout Standard
16298 \begin_inset Newpage newpage
16304 \begin_layout Subsection
16306 \begin_inset CommandInset label
16308 name "sub:Binary-Operators"
16316 \begin_layout Plain Layout
16325 \begin_layout Standard
16326 Binary operators are surrounded by space when there is a character before
16328 \begin_inset VSpace medskip
16334 \begin_layout Standard
16335 \begin_inset space \hfill{}
16339 \begin_inset Tabular
16340 <lyxtabular version="3" rows="13" columns="2">
16342 <column alignment="center" valignment="top" width="0pt">
16343 <column alignment="center" valignment="top" width="0pt">
16345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16348 \begin_layout Plain Layout
16350 \begin_inset Note Note
16353 \begin_layout Plain Layout
16360 is only used as spacer.
16370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16373 \begin_layout Plain Layout
16381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16384 \begin_layout Plain Layout
16390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16393 \begin_layout Plain Layout
16394 \begin_inset Formula $+$
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16407 \begin_layout Plain Layout
16413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16416 \begin_layout Plain Layout
16417 \begin_inset Formula $-$
16427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16430 \begin_layout Plain Layout
16438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16441 \begin_layout Plain Layout
16442 \begin_inset Formula $\pm$
16452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16455 \begin_layout Plain Layout
16463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16466 \begin_layout Plain Layout
16467 \begin_inset Formula $\mp$
16477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16480 \begin_layout Plain Layout
16488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16491 \begin_layout Plain Layout
16492 \begin_inset Formula $\cdot$
16502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16505 \begin_layout Plain Layout
16513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16516 \begin_layout Plain Layout
16517 \begin_inset Formula $\times$
16527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16530 \begin_layout Plain Layout
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16541 \begin_layout Plain Layout
16542 \begin_inset Formula $\div$
16552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16555 \begin_layout Plain Layout
16559 \begin_layout Plain Layout
16572 \begin_layout Plain Layout
16584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16587 \begin_layout Plain Layout
16588 \begin_inset Formula $*$
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16601 \begin_layout Plain Layout
16609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16612 \begin_layout Plain Layout
16613 \begin_inset Formula $\star$
16623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16626 \begin_layout Plain Layout
16634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16637 \begin_layout Plain Layout
16638 \begin_inset Formula $\circ$
16648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16651 \begin_layout Plain Layout
16659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16662 \begin_layout Plain Layout
16663 \begin_inset Formula $\diamond$
16673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16676 \begin_layout Plain Layout
16684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16687 \begin_layout Plain Layout
16688 \begin_inset Formula $\bullet$
16702 \begin_inset space \hfill{}
16706 \begin_inset Tabular
16707 <lyxtabular version="3" rows="13" columns="2">
16709 <column alignment="center" valignment="top" width="0pt">
16710 <column alignment="center" valignment="top" width="0pt">
16712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16715 \begin_layout Plain Layout
16721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16724 \begin_layout Plain Layout
16732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16735 \begin_layout Plain Layout
16743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16746 \begin_layout Plain Layout
16747 \begin_inset Formula $\nabla$
16757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16760 \begin_layout Plain Layout
16768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16771 \begin_layout Plain Layout
16772 \begin_inset Formula $\bigtriangledown$
16782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16785 \begin_layout Plain Layout
16793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16796 \begin_layout Plain Layout
16797 \begin_inset Formula $\bigtriangleup$
16807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16810 \begin_layout Plain Layout
16818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16821 \begin_layout Plain Layout
16822 \begin_inset Formula $\Box$
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16835 \begin_layout Plain Layout
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16846 \begin_layout Plain Layout
16847 \begin_inset Formula $\cap$
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16860 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $\cup$
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16896 \begin_layout Plain Layout
16897 \begin_inset Formula $\dagger$
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16910 \begin_layout Plain Layout
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16921 \begin_layout Plain Layout
16922 \begin_inset Formula $\ddagger$
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16935 \begin_layout Plain Layout
16943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16946 \begin_layout Plain Layout
16947 \begin_inset Formula $\wr$
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16960 \begin_layout Plain Layout
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16971 \begin_layout Plain Layout
16972 \begin_inset Formula $\bigcirc$
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16985 \begin_layout Plain Layout
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16996 \begin_layout Plain Layout
16997 \begin_inset Formula $\wedge$
17007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17010 \begin_layout Plain Layout
17018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17021 \begin_layout Plain Layout
17022 \begin_inset Formula $\vee$
17036 \begin_inset space \hfill{}
17040 \begin_inset Tabular
17041 <lyxtabular version="3" rows="13" columns="2">
17043 <column alignment="center" valignment="top" width="0pt">
17044 <column alignment="center" valignment="top" width="0pt">
17046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17049 \begin_layout Plain Layout
17055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17058 \begin_layout Plain Layout
17066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17069 \begin_layout Plain Layout
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17080 \begin_layout Plain Layout
17081 \begin_inset Formula $\oplus$
17091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17094 \begin_layout Plain Layout
17102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17105 \begin_layout Plain Layout
17106 \begin_inset Formula $\ominus$
17116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17119 \begin_layout Plain Layout
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17130 \begin_layout Plain Layout
17131 \begin_inset Formula $\otimes$
17141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17144 \begin_layout Plain Layout
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17155 \begin_layout Plain Layout
17156 \begin_inset Formula $\oslash$
17166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17169 \begin_layout Plain Layout
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17180 \begin_layout Plain Layout
17181 \begin_inset Formula $\odot$
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17194 \begin_layout Plain Layout
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17205 \begin_layout Plain Layout
17206 \begin_inset Formula $\amalg$
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17219 \begin_layout Plain Layout
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17230 \begin_layout Plain Layout
17231 \begin_inset Formula $\uplus$
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17244 \begin_layout Plain Layout
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17255 \begin_layout Plain Layout
17256 \begin_inset Formula $\setminus$
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17269 \begin_layout Plain Layout
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17280 \begin_layout Plain Layout
17281 \begin_inset Formula $\sqcap$
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17294 \begin_layout Plain Layout
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17305 \begin_layout Plain Layout
17306 \begin_inset Formula $\sqcup$
17316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17319 \begin_layout Plain Layout
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17330 \begin_layout Plain Layout
17331 \begin_inset Formula $\triangleleft$
17341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17344 \begin_layout Plain Layout
17352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17355 \begin_layout Plain Layout
17356 \begin_inset Formula $\triangleright$
17370 \begin_inset space \hfill{}
17376 \begin_layout Standard
17377 All binary operators can also be inserted via the math toolbar button
17378 \begin_inset Graphics
17379 filename ../images/math/pm.png
17387 \begin_layout Standard
17388 To typeset the Laplace operator also
17405 \begin_inset Formula $\nabla^{2}$
17408 ) can be used instead of
17417 \begin_layout Standard
17424 Insert\SpecialChar \menuseparator
17436 \begin_layout Subsection
17437 Self-defined Operators
17438 \begin_inset CommandInset label
17440 name "sub:Self-defined-Operators"
17448 \begin_layout Plain Layout
17449 Operators ! self-defined
17457 \begin_layout Standard
17458 With the help of the command
17462 DeclareMathOperator
17468 \begin_layout Plain Layout
17473 DeclareMathOperator
17478 custom operators can be defined in the LaTeX-preamble.
17479 Its command scheme is:
17482 \begin_layout Standard
17487 DeclareMathOperator{new command}{display}
17490 \begin_layout Standard
17491 Display can be characters or symbols that define how the operator looks
17493 To define a big operator a * is set behind the command.
17494 All self-defined big operators can have limits as described in
17495 \begin_inset CommandInset ref
17497 reference "sub:Operator-Limits"
17504 \begin_layout Standard
17505 For example the LaTeX-preamble line
17508 \begin_layout Standard
17513 DeclareMathOperator*{
17520 \begin_layout Standard
17521 defines the command
17527 , that inserts a big operator consisting of the lozenge symbol from
17528 \begin_inset CommandInset ref
17530 reference "sub:Miscellaneous-Symbols"
17535 \begin_inset Formula \[
17536 \Lozenge_{n=1}^{\infty}\]
17540 The command for this formula is:
17551 \begin_inset Formula $\to$
17557 \begin_layout Standard
17558 \begin_inset VSpace bigskip
17561 When self-defined operators are not used several times in the document,
17562 they can also be defined with the commands
17572 \begin_layout Plain Layout
17590 \begin_layout Plain Layout
17598 , which have the following scheme:
17601 \begin_layout Standard
17615 \begin_layout Standard
17622 defines big operators,
17631 \begin_layout Standard
17639 \begin_inset space \thinspace{}
17643 \begin_inset space ~
17646 be used to use one limit for several operators:
17649 \begin_layout Standard
17650 \begin_inset Formula \[
17651 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17658 \begin_layout Standard
17659 The command for the formula above is:
17660 \begin_inset Newline newline
17679 \begin_layout Plain Layout
17691 \begin_inset Formula $\to$
17700 \begin_layout Plain Layout
17714 \begin_layout Section
17719 \begin_layout Plain Layout
17728 \begin_layout Subsection
17730 \begin_inset CommandInset label
17732 name "sub:Font-Styles"
17740 \begin_layout Plain Layout
17749 \begin_layout Standard
17750 Latin letters in formulas can be set in one of the following font styles:
17751 \begin_inset VSpace -2mm
17757 \begin_layout Standard
17759 \begin_inset Tabular
17760 <lyxtabular version="3" rows="6" columns="3">
17762 <column alignment="center" valignment="top" width="0">
17763 <column alignment="center" valignment="top" width="0">
17764 <column alignment="center" valignment="top" width="0">
17766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17769 \begin_layout Plain Layout
17775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17778 \begin_layout Plain Layout
17784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17787 \begin_layout Plain Layout
17795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17798 \begin_layout Plain Layout
17807 \begin_layout Plain Layout
17823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17826 \begin_layout Plain Layout
17827 \begin_inset Formula $\mathbb{ABC}$
17835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17838 \begin_layout Plain Layout
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17849 \begin_layout Plain Layout
17858 \begin_layout Plain Layout
17874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17877 \begin_layout Plain Layout
17878 \begin_inset Formula $\mathbf{AbC}$
17886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17889 \begin_layout Plain Layout
17897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17900 \begin_layout Plain Layout
17909 \begin_layout Plain Layout
17925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17928 \begin_layout Plain Layout
17929 \begin_inset Formula $\boldsymbol{AbC}$
17937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17940 \begin_layout Plain Layout
17948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17951 \begin_layout Plain Layout
17960 \begin_layout Plain Layout
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17980 \begin_inset Formula $\mathcal{ABC}$
17988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17991 \begin_layout Plain Layout
17999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18002 \begin_layout Plain Layout
18011 \begin_layout Plain Layout
18027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18030 \begin_layout Plain Layout
18031 \begin_inset Formula $\mathfrak{AbC}$
18039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18042 \begin_layout Plain Layout
18056 \begin_layout Standard
18058 \begin_inset Tabular
18059 <lyxtabular version="3" rows="5" columns="3">
18061 <column alignment="center" valignment="top" width="0">
18062 <column alignment="center" valignment="top" width="0">
18063 <column alignment="center" valignment="top" width="0">
18065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18068 \begin_layout Plain Layout
18074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18077 \begin_layout Plain Layout
18083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18086 \begin_layout Plain Layout
18094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18097 \begin_layout Plain Layout
18106 \begin_layout Plain Layout
18122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18125 \begin_layout Plain Layout
18126 \begin_inset Formula $\mathit{AbC}$
18134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18137 \begin_layout Plain Layout
18145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18148 \begin_layout Plain Layout
18157 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18177 \begin_inset Formula $\mathrm{AbC}$
18185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18188 \begin_layout Plain Layout
18196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18199 \begin_layout Plain Layout
18208 \begin_layout Plain Layout
18224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18227 \begin_layout Plain Layout
18228 \begin_inset Formula $\mathsf{AbC}$
18236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18239 \begin_layout Plain Layout
18247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18250 \begin_layout Plain Layout
18259 \begin_layout Plain Layout
18275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18278 \begin_layout Plain Layout
18279 \begin_inset Formula $\mathtt{AbC}$
18287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18290 \begin_layout Plain Layout
18304 \begin_layout Standard
18305 \begin_inset Note Greyedout
18308 \begin_layout Plain Layout
18325 can only be used for big letters.
18333 \begin_layout Standard
18334 Predefined is the style
18343 \begin_layout Standard
18344 The style commands work also for letters in mathematical constructs:
18345 \begin_inset Formula \[
18346 \mathfrak{A=\frac{b}{C}}\]
18353 \begin_layout Standard
18354 Characters in mathematical text don't appear in a math font style but in
18355 the text font style
18362 That their style can't be set correctly via the text style dialog is a
18367 \begin_layout Plain Layout
18368 \begin_inset CommandInset href
18370 name "LyX-bug #4091"
18371 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18383 \begin_layout Standard
18384 Instead of the style commands the dialog
18386 Edit\SpecialChar \menuseparator
18387 Math\SpecialChar \menuseparator
18390 or the toolbar button
18391 \begin_inset Graphics
18392 filename ../images/math/font.png
18400 \begin_layout Subsection
18402 \begin_inset CommandInset label
18404 name "sub:Bold-Formulas"
18412 \begin_layout Plain Layout
18421 \begin_layout Standard
18422 To make a complete formula bold, the command
18428 from the previous subsection cannot be used, because it doesn't work for
18429 small Greek letters.
18430 Furthermore it prints Latin letters always upright, like in the following
18434 \begin_layout Standard
18435 \begin_inset Formula \[
18436 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18443 \begin_layout Standard
18444 To display the formula correctly, the command
18451 \begin_inset Formula \[
18452 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18456 It is also possible to set the formula in a
18458 boldmath environment
18461 This environment is created by inserting the command
18469 \begin_layout Plain Layout
18480 To end the environment, the command
18488 \begin_layout Plain Layout
18498 is inserted in TeX-mode.
18502 \begin_layout Plain Layout
18512 \begin_inset Formula \[
18513 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18521 \begin_layout Plain Layout
18533 \begin_layout Subsection
18535 \begin_inset CommandInset label
18537 name "sub:Font-Sizes"
18545 \begin_layout Plain Layout
18554 \begin_layout Standard
18555 For characters in formulas there are, analog to characters in text, the
18556 following size commands:
18559 \begin_layout Standard
18603 \begin_inset Newline newline
18625 \begin_layout Standard
18626 The size produced by the commands depends on the document font size, that
18627 corresponds with the command
18634 The other commands produce smaller or larger sizes than
18641 The font size can however not exceed a certain value.
18642 Is for example the document font size 12
18643 \begin_inset space \thinspace{}
18652 switches to the same size as
18662 \begin_layout Standard
18663 A size command is inserted in TeX-mode before the formula and sets the size
18664 for all following formula and text characters.
18665 To switch back to the initial size, the command
18671 is inserted behind the formula in TeX-mode.
18674 \begin_layout Standard
18675 Within a formula the size can only be changed for symbols or letters in
18677 To do this, the size command is inserted in mathematical text.
18678 All following characters until the end of the mathematical text or until
18679 another size command will have the selected size.
18681 \begin_inset VSpace -2mm
18687 \begin_layout Standard
18691 \begin_layout Plain Layout
18701 \begin_inset Formula \[
18702 A=\frac{B}{c}\cdot\maltese\]
18707 \begin_inset Formula \[
18708 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18716 \begin_layout Plain Layout
18728 \begin_layout Standard
18729 \begin_inset VSpace medskip
18732 Before both formulas the command
18739 The command for the second formula is:
18740 \begin_inset Newline newline
18751 \begin_layout Plain Layout
18766 \begin_layout Plain Layout
18781 \begin_layout Plain Layout
18796 \begin_layout Plain Layout
18806 \begin_inset Formula $\to$
18810 \begin_inset Formula $\to$
18814 \begin_inset Newline newline
18818 \begin_inset space \hspace*{}
18832 \begin_layout Plain Layout
18847 \begin_layout Plain Layout
18862 \begin_layout Plain Layout
18874 \begin_layout Standard
18875 If a symbol cannot be displayed in different sizes, it will always be displayed
18876 in the default size.
18879 \begin_layout Section
18884 \begin_layout Plain Layout
18893 \begin_layout Standard
18894 All Greek letters can also be inserted via the toolbar button
18895 \begin_inset Graphics
18896 filename ../images/math/alpha.png
18904 \begin_layout Subsection
18906 \begin_inset CommandInset label
18908 name "sub:Small-Letters"
18916 \begin_layout Plain Layout
18917 Greek letters ! small
18925 \begin_layout Standard
18926 \begin_inset space \hfill{}
18930 \begin_inset Tabular
18931 <lyxtabular version="3" rows="11" columns="2">
18933 <column alignment="center" valignment="top" width="0pt">
18934 <column alignment="center" valignment="top" width="0pt">
18936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18939 \begin_layout Plain Layout
18945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18948 \begin_layout Plain Layout
18956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18959 \begin_layout Plain Layout
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18970 \begin_layout Plain Layout
18971 \begin_inset Formula $\alpha$
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18995 \begin_layout Plain Layout
18996 \begin_inset Formula $\beta$
19006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19009 \begin_layout Plain Layout
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19020 \begin_layout Plain Layout
19021 \begin_inset Formula $\gamma$
19031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19045 \begin_layout Plain Layout
19046 \begin_inset Formula $\delta$
19056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19059 \begin_layout Plain Layout
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19070 \begin_layout Plain Layout
19071 \begin_inset Formula $\epsilon$
19081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19084 \begin_layout Plain Layout
19092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19095 \begin_layout Plain Layout
19096 \begin_inset Formula $\varepsilon$
19106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19109 \begin_layout Plain Layout
19117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19120 \begin_layout Plain Layout
19121 \begin_inset Formula $\zeta$
19131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19134 \begin_layout Plain Layout
19142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19145 \begin_layout Plain Layout
19146 \begin_inset Formula $\eta$
19156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19159 \begin_layout Plain Layout
19167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19170 \begin_layout Plain Layout
19171 \begin_inset Formula $\theta$
19181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19184 \begin_layout Plain Layout
19192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19195 \begin_layout Plain Layout
19196 \begin_inset Formula $\vartheta$
19210 \begin_inset space \hfill{}
19214 \begin_inset Tabular
19215 <lyxtabular version="3" rows="12" columns="2">
19217 <column alignment="center" valignment="top" width="0pt">
19218 <column alignment="center" valignment="top" width="0pt">
19220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19223 \begin_layout Plain Layout
19229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19232 \begin_layout Plain Layout
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19243 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula $\iota$
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula $\kappa$
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula $\varkappa$
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula $\lambda$
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19343 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula $\mu$
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula $\nu$
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19393 \begin_layout Plain Layout
19401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Plain Layout
19405 \begin_inset Formula $\xi$
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19418 \begin_layout Plain Layout
19424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19427 \begin_layout Plain Layout
19428 \begin_inset Formula $o$
19438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19441 \begin_layout Plain Layout
19449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19452 \begin_layout Plain Layout
19453 \begin_inset Formula $\pi$
19463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19466 \begin_layout Plain Layout
19474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19477 \begin_layout Plain Layout
19478 \begin_inset Formula $\varpi$
19488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19491 \begin_layout Plain Layout
19499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19502 \begin_layout Plain Layout
19503 \begin_inset Formula $\rho$
19517 \begin_inset space \hfill{}
19521 \begin_inset Tabular
19522 <lyxtabular version="3" rows="11" columns="2">
19524 <column alignment="center" valignment="top" width="0pt">
19525 <column alignment="center" valignment="top" width="0pt">
19527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19530 \begin_layout Plain Layout
19536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19539 \begin_layout Plain Layout
19547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19550 \begin_layout Plain Layout
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19561 \begin_layout Plain Layout
19562 \begin_inset Formula $\varrho$
19572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19575 \begin_layout Plain Layout
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19586 \begin_layout Plain Layout
19587 \begin_inset Formula $\sigma$
19597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19600 \begin_layout Plain Layout
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19611 \begin_layout Plain Layout
19612 \begin_inset Formula $\varsigma$
19622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19625 \begin_layout Plain Layout
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19636 \begin_layout Plain Layout
19637 \begin_inset Formula $\tau$
19647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19650 \begin_layout Plain Layout
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19661 \begin_layout Plain Layout
19662 \begin_inset Formula $\upsilon$
19672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19675 \begin_layout Plain Layout
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19686 \begin_layout Plain Layout
19687 \begin_inset Formula $\phi$
19697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19700 \begin_layout Plain Layout
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19711 \begin_layout Plain Layout
19712 \begin_inset Formula $\varphi$
19722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19725 \begin_layout Plain Layout
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19736 \begin_layout Plain Layout
19737 \begin_inset Formula $\chi$
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19750 \begin_layout Plain Layout
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19761 \begin_layout Plain Layout
19762 \begin_inset Formula $\psi$
19772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19775 \begin_layout Plain Layout
19783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19786 \begin_layout Plain Layout
19787 \begin_inset Formula $\omega$
19801 \begin_inset space \hfill{}
19807 \begin_layout Standard
19808 \begin_inset VSpace medskip
19814 \begin_layout Standard
19815 How to create upright Greek letters is explained in
19816 \begin_inset CommandInset ref
19818 reference "sub:Upright-small-Greek"
19825 \begin_layout Subsection
19830 \begin_layout Plain Layout
19831 Greek letters ! big
19839 \begin_layout Standard
19840 \begin_inset space \hfill{}
19844 \begin_inset Tabular
19845 <lyxtabular version="3" rows="7" columns="2">
19847 <column alignment="center" valignment="top" width="0pt">
19848 <column alignment="center" valignment="top" width="0pt">
19850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19862 \begin_layout Plain Layout
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\Gamma$
19895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19909 \begin_layout Plain Layout
19910 \begin_inset Formula $\Delta$
19920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19923 \begin_layout Plain Layout
19931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19934 \begin_layout Plain Layout
19935 \begin_inset Formula $\Theta$
19945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19959 \begin_layout Plain Layout
19960 \begin_inset Formula $\Lambda$
19970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19973 \begin_layout Plain Layout
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19984 \begin_layout Plain Layout
19985 \begin_inset Formula $\Xi$
19995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\Pi$
20024 \begin_inset space \hfill{}
20028 \begin_inset Tabular
20029 <lyxtabular version="3" rows="6" columns="2">
20031 <column alignment="center" valignment="top" width="0pt">
20032 <column alignment="center" valignment="top" width="0pt">
20034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20037 \begin_layout Plain Layout
20043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20046 \begin_layout Plain Layout
20054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20057 \begin_layout Plain Layout
20065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20068 \begin_layout Plain Layout
20069 \begin_inset Formula $\Sigma$
20079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20082 \begin_layout Plain Layout
20090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20093 \begin_layout Plain Layout
20094 \begin_inset Formula $\Upsilon$
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20107 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Plain Layout
20119 \begin_inset Formula $\Phi$
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20132 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20144 \begin_inset Formula $\Psi$
20154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Plain Layout
20169 \begin_inset Formula $\Omega$
20183 \begin_inset space \hfill{}
20189 \begin_layout Standard
20190 \begin_inset VSpace medskip
20193 That the big Greek letters appear upright is caused by a design bug when
20195 To get correct italic big letters, begin every command with
20200 For example the command
20207 \begin_inset Formula $\varGamma$
20213 \begin_layout Subsection
20218 \begin_layout Plain Layout
20219 Greek letters ! bold
20227 \begin_layout Standard
20228 Greek letters cannot be set with different font styles like Latin letters.
20229 They can only be made bold with the command
20239 \begin_layout Plain Layout
20250 \begin_layout Standard
20252 \begin_inset Tabular
20253 <lyxtabular version="3" rows="3" columns="2">
20255 <column alignment="center" valignment="top" width="0">
20256 <column alignment="center" valignment="top" width="0">
20258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20261 \begin_layout Plain Layout
20267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20270 \begin_layout Plain Layout
20278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20281 \begin_layout Plain Layout
20293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20296 \begin_layout Plain Layout
20297 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20310 \begin_layout Plain Layout
20322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20325 \begin_layout Plain Layout
20326 \begin_inset Formula $\theta\boldsymbol{\theta}$
20342 \begin_layout Section
20347 \begin_layout Plain Layout
20360 \begin_layout Plain Layout
20361 A list with all symbols of most of the LaTeX-packages can be found in
20362 \begin_inset CommandInset citation
20377 \begin_layout Plain Layout
20385 \begin_inset Note Note
20388 \begin_layout Plain Layout
20391 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20394 \begin_layout Plain Layout
20397 texorpdfstring is in section
20398 \begin_inset CommandInset ref
20400 reference "sub:Formulas-in-Section"
20413 \begin_layout Plain Layout
20422 \begin_layout Standard
20423 Many of the symbols listed in this section can also be inserted via the
20425 \begin_inset Graphics
20426 filename ../images/math/nabla.png
20432 \begin_inset Graphics
20433 filename ../images/math/digamma.png
20441 \begin_layout Subsection
20442 Mathematical Symbols
20443 \begin_inset CommandInset label
20445 name "sub:Mathematical-Symbols"
20453 \begin_layout Plain Layout
20454 Symbols ! mathematical
20462 \begin_layout Standard
20463 \begin_inset space \hfill{}
20467 \begin_inset Tabular
20468 <lyxtabular version="3" rows="10" columns="2">
20470 <column alignment="center" valignment="top" width="0pt">
20471 <column alignment="center" valignment="top" width="0pt">
20473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20476 \begin_layout Plain Layout
20482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20485 \begin_layout Plain Layout
20493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20496 \begin_layout Plain Layout
20504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20507 \begin_layout Plain Layout
20508 \begin_inset Formula $\neg$
20518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20521 \begin_layout Plain Layout
20529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20532 \begin_layout Plain Layout
20533 \begin_inset Formula $\Im$
20543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20546 \begin_layout Plain Layout
20554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20557 \begin_layout Plain Layout
20558 \begin_inset Formula $\Re$
20568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20571 \begin_layout Plain Layout
20579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20582 \begin_layout Plain Layout
20583 \begin_inset Formula $\aleph$
20593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20596 \begin_layout Plain Layout
20604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20607 \begin_layout Plain Layout
20608 \begin_inset Formula $\partial$
20618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20621 \begin_layout Plain Layout
20629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20632 \begin_layout Plain Layout
20633 \begin_inset Formula $\infty$
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20646 \begin_layout Plain Layout
20654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20657 \begin_layout Plain Layout
20658 \begin_inset Formula $\wp$
20668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20682 \begin_layout Plain Layout
20683 \begin_inset Formula $\imath$
20693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20696 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20708 \begin_inset Formula $\jmath$
20722 \begin_inset space \hfill{}
20726 \begin_inset Tabular
20727 <lyxtabular version="3" rows="10" columns="2">
20729 <column alignment="center" valignment="top" width="0pt">
20730 <column alignment="center" valignment="top" width="0pt">
20732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20735 \begin_layout Plain Layout
20741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20744 \begin_layout Plain Layout
20746 \begin_inset Note Note
20749 \begin_layout Plain Layout
20756 is only used as spacer.
20768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20771 \begin_layout Plain Layout
20779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20782 \begin_layout Plain Layout
20783 \begin_inset Formula $\forall$
20793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20796 \begin_layout Plain Layout
20804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20807 \begin_layout Plain Layout
20808 \begin_inset Formula $\exists$
20818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20821 \begin_layout Plain Layout
20829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20832 \begin_layout Plain Layout
20833 \begin_inset Formula $\nexists$
20843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20846 \begin_layout Plain Layout
20854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20857 \begin_layout Plain Layout
20858 \begin_inset Formula $\emptyset$
20868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20871 \begin_layout Plain Layout
20879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20882 \begin_layout Plain Layout
20883 \begin_inset Formula $\varnothing$
20893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20896 \begin_layout Plain Layout
20904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20907 \begin_layout Plain Layout
20908 \begin_inset Formula $\dag$
20918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20921 \begin_layout Plain Layout
20929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20932 \begin_layout Plain Layout
20933 \begin_inset Formula $\ddag$
20943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20946 \begin_layout Plain Layout
20954 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20957 \begin_layout Plain Layout
20961 \begin_layout Plain Layout
20971 \begin_inset Formula $\complement$
20978 \begin_layout Plain Layout
20992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Plain Layout
21003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21006 \begin_layout Plain Layout
21007 \begin_inset Formula $\Bbbk$
21021 \begin_inset space \hfill{}
21025 \begin_inset Tabular
21026 <lyxtabular version="3" rows="10" columns="2">
21028 <column alignment="center" valignment="top" width="0pt">
21029 <column alignment="center" valignment="top" width="0pt">
21031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21034 \begin_layout Plain Layout
21040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21043 \begin_layout Plain Layout
21051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21054 \begin_layout Plain Layout
21062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21065 \begin_layout Plain Layout
21066 \begin_inset Formula $\prime$
21076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21079 \begin_layout Plain Layout
21087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21090 \begin_layout Plain Layout
21091 \begin_inset Formula $\backprime$
21101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21104 \begin_layout Plain Layout
21112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21115 \begin_layout Plain Layout
21116 \begin_inset Formula $\mho$
21126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21129 \begin_layout Plain Layout
21137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21140 \begin_layout Plain Layout
21141 \begin_inset Formula $\triangle$
21151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21154 \begin_layout Plain Layout
21162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21165 \begin_layout Plain Layout
21166 \begin_inset Formula $\angle$
21176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21179 \begin_layout Plain Layout
21187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21190 \begin_layout Plain Layout
21191 \begin_inset Formula $\measuredangle$
21201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21204 \begin_layout Plain Layout
21212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21215 \begin_layout Plain Layout
21216 \begin_inset Formula $\sphericalangle$
21226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21229 \begin_layout Plain Layout
21237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21240 \begin_layout Plain Layout
21241 \begin_inset Formula $\top$
21251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21254 \begin_layout Plain Layout
21262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21265 \begin_layout Plain Layout
21266 \begin_inset Formula $\bot$
21280 \begin_inset space \hfill{}
21286 \begin_layout Standard
21287 \begin_inset Newpage newpage
21293 \begin_layout Subsection
21294 Miscellaneous Symbols
21295 \begin_inset CommandInset label
21297 name "sub:Miscellaneous-Symbols"
21305 \begin_layout Plain Layout
21306 Symbols ! miscellaneous
21314 \begin_layout Standard
21317 \begin_inset Tabular
21318 <lyxtabular version="3" rows="10" columns="2">
21320 <column alignment="center" valignment="top" width="0pt">
21321 <column alignment="center" valignment="top" width="0pt">
21323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21335 \begin_layout Plain Layout
21343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21346 \begin_layout Plain Layout
21354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21357 \begin_layout Plain Layout
21358 \begin_inset Formula $\flat$
21368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21371 \begin_layout Plain Layout
21379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21382 \begin_layout Plain Layout
21383 \begin_inset Formula $\natural$
21393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21396 \begin_layout Plain Layout
21404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21407 \begin_layout Plain Layout
21408 \begin_inset Formula $\sharp$
21418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21421 \begin_layout Plain Layout
21429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21432 \begin_layout Plain Layout
21433 \begin_inset Formula $\surd$
21443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21446 \begin_layout Plain Layout
21454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21457 \begin_layout Plain Layout
21458 \begin_inset Formula $\checkmark$
21468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21471 \begin_layout Plain Layout
21479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21482 \begin_layout Plain Layout
21483 \begin_inset Formula $\yen$
21493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21496 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21507 \begin_layout Plain Layout
21508 \begin_inset Formula $\pounds$
21518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21530 \begin_layout Plain Layout
21531 \begin_inset Formula $\$$
21541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21544 \begin_layout Plain Layout
21550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21553 \begin_layout Plain Layout
21554 \begin_inset Formula $§$
21568 \begin_inset Tabular
21569 <lyxtabular version="3" rows="10" columns="2">
21571 <column alignment="center" valignment="top" width="0">
21572 <column alignment="center" valignment="top" width="0">
21574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21586 \begin_layout Plain Layout
21594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21597 \begin_layout Plain Layout
21605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21608 \begin_layout Plain Layout
21609 \begin_inset Formula $\hbar$
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21622 \begin_layout Plain Layout
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21633 \begin_layout Plain Layout
21634 \begin_inset Formula $\hslash$
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21647 \begin_layout Plain Layout
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21658 \begin_layout Plain Layout
21659 \begin_inset Formula $\clubsuit$
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21672 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21683 \begin_layout Plain Layout
21684 \begin_inset Formula $\spadesuit$
21694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21697 \begin_layout Plain Layout
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21708 \begin_layout Plain Layout
21709 \begin_inset Formula $\bigstar$
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21722 \begin_layout Plain Layout
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21733 \begin_layout Plain Layout
21734 \begin_inset Formula $\blacklozenge$
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21747 \begin_layout Plain Layout
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21758 \begin_layout Plain Layout
21759 \begin_inset Formula $\blacktriangle$
21769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21772 \begin_layout Plain Layout
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21783 \begin_layout Plain Layout
21784 \begin_inset Formula $\blacktriangledown$
21794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21797 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21809 \begin_inset Formula $\bullet$
21823 \begin_inset Tabular
21824 <lyxtabular version="3" rows="10" columns="2">
21826 <column alignment="center" valignment="top" width="0pt">
21827 <column alignment="center" valignment="top" width="0pt">
21829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21832 \begin_layout Plain Layout
21838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21841 \begin_layout Plain Layout
21849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21852 \begin_layout Plain Layout
21860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21863 \begin_layout Plain Layout
21864 \begin_inset Formula $\diamondsuit$
21874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21877 \begin_layout Plain Layout
21885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21888 \begin_layout Plain Layout
21889 \begin_inset Formula $\Diamond$
21899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21902 \begin_layout Plain Layout
21910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21913 \begin_layout Plain Layout
21914 \begin_inset Formula $\heartsuit$
21924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21927 \begin_layout Plain Layout
21935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21938 \begin_layout Plain Layout
21939 \begin_inset Formula $\P$
21949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21952 \begin_layout Plain Layout
21960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21963 \begin_layout Plain Layout
21964 \begin_inset Formula $\copyright$
21974 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21977 \begin_layout Plain Layout
21985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21988 \begin_layout Plain Layout
21989 \begin_inset Formula $\circledR$
21999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22002 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22013 \begin_layout Plain Layout
22014 \begin_inset Formula $\maltese$
22024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22027 \begin_layout Plain Layout
22035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22038 \begin_layout Plain Layout
22039 \begin_inset Formula $\diagup$
22049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22052 \begin_layout Plain Layout
22060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22063 \begin_layout Plain Layout
22064 \begin_inset Formula $\diagdown$
22080 \begin_layout Standard
22081 \begin_inset VSpace medskip
22084 More symbols are listed in
22085 \begin_inset CommandInset ref
22087 reference "sub:Miscellaneous-special-Characters"
22094 \begin_layout Standard
22095 Some symbols can be displayed in different sizes, see
22096 \begin_inset CommandInset ref
22098 reference "sub:Font-Sizes"
22105 \begin_layout Subsection
22110 \begin_layout Plain Layout
22111 Symbols ! Euro-symbol
22120 \begin_layout Plain Layout
22124 \begin_layout Plain Layout
22141 \begin_layout Standard
22142 To use the Euro symbol in formulas, the LaTeX-package
22150 \begin_layout Plain Layout
22156 must be installed and loaded with the LaTeX-preamble line
22159 \begin_layout Standard
22164 usepackage[gennarrow]{eurosym}
22167 \begin_layout Standard
22168 The Euro symbol can now be inserted with the command
22178 \begin_layout Plain Layout
22189 \begin_layout Standard
22190 The Euro symbol can directly be inserted with the € key in mathematical
22191 text, without having
22206 can also be inserted in TeX-mode.
22207 The official currency symbol can then be inserted with the command
22217 \begin_layout Plain Layout
22225 , that is only available in TeX-mode.
22228 \begin_layout Standard
22232 \begin_layout Plain Layout
22242 \begin_inset Note Note
22245 \begin_layout Plain Layout
22246 The following table will only be displayed when the LaTeX-package
22258 \begin_layout Standard
22259 An overview about the different Euro symbols:
22262 \begin_layout Standard
22264 \begin_inset Tabular
22265 <lyxtabular version="3" rows="4" columns="3">
22267 <column alignment="center" valignment="top" width="0pt">
22268 <column alignment="center" valignment="top" width="0pt">
22269 <column alignment="center" valignment="top" width="0pt">
22271 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22274 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22283 \begin_layout Plain Layout
22289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22303 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22312 \begin_layout Plain Layout
22320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22323 \begin_layout Plain Layout
22324 \begin_inset Formula $\euro$
22334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22337 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22346 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\mbox{€}$
22366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22378 \begin_layout Plain Layout
22386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22389 \begin_layout Plain Layout
22393 \begin_layout Plain Layout
22415 \begin_layout Standard
22419 \begin_layout Plain Layout
22429 \begin_inset Note Note
22432 \begin_layout Plain Layout
22433 The following will be displayed when the LaTeX-package
22445 \begin_layout Standard
22446 You need to install the LaTeX-package
22450 to see the rest of this subsection in the output.
22453 \begin_layout Standard
22457 \begin_layout Plain Layout
22469 \begin_layout Section
22471 \begin_inset CommandInset label
22473 name "sec:Relations"
22481 \begin_layout Plain Layout
22491 \begin_layout Plain Layout
22496 \begin_layout Plain Layout
22507 \begin_layout Plain Layout
22522 \begin_layout Standard
22523 All relations can also be inserted via the toolbar button
22524 \begin_inset Graphics
22525 filename ../images/math/leq.png
22533 \begin_layout Standard
22534 \begin_inset space \hfill{}
22538 \begin_inset Tabular
22539 <lyxtabular version="3" rows="17" columns="2">
22541 <column alignment="center" valignment="top" width="0pt">
22542 <column alignment="center" valignment="top" width="0pt">
22544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22547 \begin_layout Plain Layout
22553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22567 \begin_layout Plain Layout
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22576 \begin_layout Plain Layout
22577 \begin_inset Formula $<$
22587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22590 \begin_layout Plain Layout
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22601 \begin_layout Plain Layout
22602 \begin_inset Formula $\le$
22612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22615 \begin_layout Plain Layout
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Plain Layout
22627 \begin_inset Formula $\ll$
22637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22652 \begin_inset Formula $\prec$
22662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22665 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $\preceq$
22687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\subset$
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\subseteq$
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\sqsubseteq$
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\in$
22787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\vdash$
22812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\smile$
22837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22840 \begin_layout Plain Layout
22848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22851 \begin_layout Plain Layout
22852 \begin_inset Formula $\lhd$
22862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22865 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22876 \begin_layout Plain Layout
22877 \begin_inset Formula $\unlhd$
22887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22901 \begin_layout Plain Layout
22902 \begin_inset Formula $\gtrless$
22912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22926 \begin_layout Plain Layout
22927 \begin_inset Formula $\mid$
22937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22940 \begin_layout Plain Layout
22948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22951 \begin_layout Plain Layout
22952 \begin_inset Formula $\nmid$
22966 \begin_inset space \hfill{}
22970 \begin_inset Tabular
22971 <lyxtabular version="3" rows="17" columns="2">
22973 <column alignment="center" valignment="top" width="0pt">
22974 <column alignment="center" valignment="top" width="0pt">
22976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23008 \begin_layout Plain Layout
23009 \begin_inset Formula $=$
23019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23022 \begin_layout Plain Layout
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23033 \begin_layout Plain Layout
23034 \begin_inset Formula $\not=$
23044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23047 \begin_layout Plain Layout
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23058 \begin_layout Plain Layout
23059 \begin_inset Formula $\equiv$
23069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23072 \begin_layout Plain Layout
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23083 \begin_layout Plain Layout
23084 \begin_inset Formula $\sim$
23094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23097 \begin_layout Plain Layout
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23108 \begin_layout Plain Layout
23109 \begin_inset Formula $\simeq$
23119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23122 \begin_layout Plain Layout
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23133 \begin_layout Plain Layout
23134 \begin_inset Formula $\approx$
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23147 \begin_layout Plain Layout
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23158 \begin_layout Plain Layout
23159 \begin_inset Formula $\cong$
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23172 \begin_layout Plain Layout
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23183 \begin_layout Plain Layout
23184 \begin_inset Formula $\bowtie$
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23197 \begin_layout Plain Layout
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23208 \begin_layout Plain Layout
23209 \begin_inset Formula $\notin$
23219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23222 \begin_layout Plain Layout
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23233 \begin_layout Plain Layout
23234 \begin_inset Formula $\perp$
23244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23247 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23259 \begin_inset Formula $\propto$
23269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23272 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23284 \begin_inset Formula $\asymp$
23294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23297 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $\doteq$
23319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\circeq$
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\models$
23369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\widehat{=}$
23398 \begin_inset space \hfill{}
23402 \begin_inset Tabular
23403 <lyxtabular version="3" rows="17" columns="2">
23405 <column alignment="center" valignment="top" width="0pt">
23406 <column alignment="center" valignment="top" width="0pt">
23408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23411 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23440 \begin_layout Plain Layout
23441 \begin_inset Formula $>$
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23454 \begin_layout Plain Layout
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23465 \begin_layout Plain Layout
23466 \begin_inset Formula $\ge$
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23479 \begin_layout Plain Layout
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23490 \begin_layout Plain Layout
23491 \begin_inset Formula $\gg$
23501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23504 \begin_layout Plain Layout
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23515 \begin_layout Plain Layout
23516 \begin_inset Formula $\succ$
23526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23529 \begin_layout Plain Layout
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23540 \begin_layout Plain Layout
23541 \begin_inset Formula $\succeq$
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23554 \begin_layout Plain Layout
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23565 \begin_layout Plain Layout
23566 \begin_inset Formula $\supset$
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23579 \begin_layout Plain Layout
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23590 \begin_layout Plain Layout
23591 \begin_inset Formula $\supseteq$
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23604 \begin_layout Plain Layout
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23615 \begin_layout Plain Layout
23616 \begin_inset Formula $\sqsupseteq$
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23629 \begin_layout Plain Layout
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23640 \begin_layout Plain Layout
23641 \begin_inset Formula $\ni$
23651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23654 \begin_layout Plain Layout
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23665 \begin_layout Plain Layout
23666 \begin_inset Formula $\dashv$
23676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23679 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23690 \begin_layout Plain Layout
23691 \begin_inset Formula $\frown$
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23704 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23716 \begin_inset Formula $\rhd$
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23729 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $\unrhd$
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\lessgtr$
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\parallel$
23801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\nparallel$
23830 \begin_inset space \hfill{}
23836 \begin_layout Standard
23837 \begin_inset VSpace medskip
23852 are bigger than the equal looking operators
23867 \begin_layout Standard
23868 Relations are, in contrary to symbols, always surrounded by space.
23871 \begin_layout Standard
23872 Relations with labels can be created with the command
23882 \begin_layout Plain Layout
23893 \begin_layout Standard
23895 \begin_inset Tabular
23896 <lyxtabular version="3" rows="2" columns="2">
23898 <column alignment="center" valignment="top" width="0">
23899 <column alignment="center" valignment="top" width="0">
23901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23913 \begin_layout Plain Layout
23915 \begin_inset Note Note
23918 \begin_layout Plain Layout
23925 is only used as spacer.
23937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23940 \begin_layout Plain Layout
23947 \begin_layout Plain Layout
23964 \begin_layout Plain Layout
23974 \begin_inset Formula $\downarrow$
23983 \begin_layout Plain Layout
23996 \begin_layout Plain Layout
24010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24013 \begin_layout Plain Layout
24014 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24030 \begin_layout Section
24034 \begin_layout Subsection
24035 Predefined Functions
24036 \begin_inset CommandInset label
24038 name "sub:Predefined-Functions"
24046 \begin_layout Plain Layout
24047 Functions ! predefined
24055 \begin_layout Standard
24056 In general, variables are set
24060 in mathematical expressions, but not function names, because
24061 \begin_inset Formula $sin$
24064 could be misunderstood as
24065 \begin_inset Formula $s\cdot i\cdot n$
24069 Therefore there are predefined functions, that are additionally a bit separated
24071 They are inserted as commands starting with a backslash before their name.
24074 \begin_layout Standard
24076 \begin_inset Tabular
24077 <lyxtabular version="3" rows="2" columns="4">
24079 <column alignment="center" valignment="top" width="0pt">
24080 <column alignment="center" valignment="top" width="0pt">
24081 <column alignment="center" valignment="top" width="0pt">
24082 <column alignment="center" valignment="top" width="0pt">
24084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24087 \begin_layout Plain Layout
24093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24096 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24105 \begin_layout Plain Layout
24111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24114 \begin_layout Plain Layout
24122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24125 \begin_layout Plain Layout
24131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24134 \begin_layout Plain Layout
24135 \begin_inset Formula $Asin(x)+B$
24143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24157 \begin_layout Plain Layout
24158 \begin_inset Formula $A\sin(x)+B$
24172 \begin_inset Newpage pagebreak
24178 \begin_layout Standard
24179 The following functions are predefined:
24182 \begin_layout Standard
24183 \begin_inset VSpace -2mm
24189 \begin_layout Standard
24191 \begin_inset Tabular
24192 <lyxtabular version="3" rows="9" columns="4">
24194 <column alignment="center" valignment="top" width="0pt">
24195 <column alignment="center" valignment="top" width="0pt">
24196 <column alignment="center" valignment="top" width="0pt">
24197 <column alignment="center" valignment="top" width="0pt">
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24220 \begin_layout Plain Layout
24226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24229 \begin_layout Plain Layout
24237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24240 \begin_layout Plain Layout
24248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24251 \begin_layout Plain Layout
24259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24262 \begin_layout Plain Layout
24270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24273 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24297 \begin_layout Plain Layout
24305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24308 \begin_layout Plain Layout
24316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24319 \begin_layout Plain Layout
24329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24332 \begin_layout Plain Layout
24340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24343 \begin_layout Plain Layout
24351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24354 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24378 \begin_layout Plain Layout
24386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24389 \begin_layout Plain Layout
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24400 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24411 \begin_layout Plain Layout
24421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24424 \begin_layout Plain Layout
24432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24435 \begin_layout Plain Layout
24443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24446 \begin_layout Plain Layout
24454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24457 \begin_layout Plain Layout
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24481 \begin_layout Plain Layout
24489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24492 \begin_layout Plain Layout
24500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24503 \begin_layout Plain Layout
24513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24538 \begin_layout Plain Layout
24546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24549 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24562 \begin_layout Plain Layout
24570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24573 \begin_layout Plain Layout
24581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24584 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24595 \begin_layout Plain Layout
24611 \begin_layout Standard
24612 They can also be inserted with the math toolbar button
24613 \begin_inset Graphics
24614 filename ../images/math/functions.png
24622 \begin_layout Subsection
24623 Self-defined Functions
24627 \begin_layout Plain Layout
24628 Functions ! self-defined
24636 \begin_layout Standard
24637 To use a function that is not predefined, like for example the sign function
24638 sgn(x), there are two possibilities:
24641 \begin_layout Itemize
24642 Define the function by inserting the following line to the LaTeX-preamble
24646 \begin_layout Plain Layout
24651 DeclareMathOperator
24654 \begin_inset CommandInset ref
24656 reference "sub:Self-defined-Operators"
24666 \begin_inset Newline newline
24670 \begin_inset VSpace -3mm
24674 \begin_inset Newline newline
24681 DeclareMathOperator{
24689 \begin_layout Plain Layout
24694 DeclareMathOperator
24700 \begin_inset Newline newline
24704 \begin_inset VSpace -2mm
24708 \begin_inset Newline newline
24711 Now the new defined function can be called with the command
24720 \begin_layout Itemize
24721 Write the the formula as usual, mark the formula name, in our example the
24726 , and change it to mathematical text.
24727 At last a space is inserted between prefactor and function.
24730 \begin_layout Standard
24731 The result is the same with both methods as with a predefined function
24735 \begin_layout Plain Layout
24736 In LyX self-defined functions are displayed red, predefined ones black.
24744 \begin_layout Standard
24746 \begin_inset Tabular
24747 <lyxtabular version="3" rows="3" columns="2">
24749 <column alignment="center" valignment="top" width="0pt">
24750 <column alignment="center" valignment="top" width="0pt">
24752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24755 \begin_layout Plain Layout
24761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24764 \begin_layout Plain Layout
24772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24775 \begin_layout Plain Layout
24783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24786 \begin_layout Plain Layout
24787 \begin_inset Formula $A\sgn(x)+B$
24797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24800 \begin_layout Plain Layout
24804 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24816 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24832 \begin_layout Standard
24833 The first method is more suitable when the self-defined function should
24834 be used several times.
24837 \begin_layout Subsection
24842 \begin_layout Plain Layout
24851 \begin_layout Standard
24852 For limits there are defined besides
24862 \begin_layout Plain Layout
24882 furthermore the following functions:
24885 \begin_layout Standard
24887 \begin_inset Tabular
24888 <lyxtabular version="3" rows="5" columns="2">
24890 <column alignment="center" valignment="top" width="0">
24891 <column alignment="center" valignment="top" width="0">
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24896 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24905 \begin_layout Plain Layout
24907 \begin_inset Note Note
24910 \begin_layout Plain Layout
24917 is only used as spacer.
24929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24944 \begin_inset Formula $\varliminf$
24954 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24957 \begin_layout Plain Layout
24965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24968 \begin_layout Plain Layout
24969 \begin_inset Formula $\varlimsup$
24979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24982 \begin_layout Plain Layout
24990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24993 \begin_layout Plain Layout
24994 \begin_inset Formula $\varprojlim$
25004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25007 \begin_layout Plain Layout
25015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25018 \begin_layout Plain Layout
25019 \begin_inset Formula $\varinjlim$
25023 \begin_inset Formula $\raisebox{-2.5mm}{}$
25039 \begin_layout Standard
25040 \begin_inset VSpace medskip
25043 The limit is created by inserting a subscript.
25044 It is set right beside the function in an inline formula:
25047 \begin_layout Standard
25049 \begin_inset Tabular
25050 <lyxtabular version="3" rows="2" columns="2">
25052 <column alignment="center" valignment="top" width="0pt">
25053 <column alignment="center" valignment="top" width="0pt">
25055 <cell alignment="center" valignment="top" usebox="none">
25058 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" usebox="none">
25067 \begin_layout Plain Layout
25068 \begin_inset space \hspace{}
25073 \begin_inset Note Note
25076 \begin_layout Plain Layout
25089 are used here as spacer.
25101 <cell alignment="center" valignment="top" usebox="none">
25104 \begin_layout Plain Layout
25113 \begin_layout Plain Layout
25126 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" usebox="none">
25143 \begin_layout Plain Layout
25144 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25160 \begin_layout Standard
25161 In a displayed formula the limit is set below the formula, as usual:
25162 \begin_inset Formula \[
25170 \begin_layout Subsection
25175 \begin_layout Plain Layout
25176 Functions ! modulo-
25184 \begin_layout Standard
25185 The modulo-function is special, because it exists in four variants.
25188 \begin_layout Standard
25189 The variants in a displayed formula:
25190 \begin_inset Formula \begin{align*}
25191 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25192 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25193 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25194 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25195 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25202 \begin_layout Standard
25203 In an inline formula less space is set before the function names for all
25207 \begin_layout Section
25212 \begin_layout Plain Layout
25221 \begin_layout Subsection
25222 Special Characters in Mathematical Text
25225 \begin_layout Standard
25226 The following commands can only be used in mathematical text or in TeX-mode:
25229 \begin_layout Standard
25230 \begin_inset space \hfill{}
25234 \begin_inset Tabular
25235 <lyxtabular version="3" rows="8" columns="2">
25237 <column alignment="block" valignment="top" width="0">
25238 <column alignment="block" valignment="top" width="0">
25240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25243 \begin_layout Plain Layout
25249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25252 \begin_layout Plain Layout
25260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25263 \begin_layout Plain Layout
25271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25274 \begin_layout Plain Layout
25275 \begin_inset Formula $\textrm{œ}$
25285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25288 \begin_layout Plain Layout
25296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25299 \begin_layout Plain Layout
25300 \begin_inset Formula $\textrm{Œ}$
25310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25313 \begin_layout Plain Layout
25321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25324 \begin_layout Plain Layout
25325 \begin_inset Formula $\textrm{æ}$
25335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25338 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25349 \begin_layout Plain Layout
25350 \begin_inset Formula $\textrm{Æ}$
25360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25363 \begin_layout Plain Layout
25371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25374 \begin_layout Plain Layout
25375 \begin_inset Formula $\textrm{\aa}$
25385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25388 \begin_layout Plain Layout
25395 \begin_layout Plain Layout
25399 \begin_layout Plain Layout
25422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25425 \begin_layout Plain Layout
25426 \begin_inset Formula $\textrm{Å}$
25436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25439 \begin_layout Plain Layout
25447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25450 \begin_layout Plain Layout
25451 \begin_inset Formula $\textrm{ı}$
25465 \begin_inset space \hfill{}
25469 \begin_inset Tabular
25470 <lyxtabular version="3" rows="8" columns="2">
25472 <column alignment="block" valignment="top" width="0">
25473 <column alignment="center" valignment="top" width="0">
25475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25478 \begin_layout Plain Layout
25480 \begin_inset Note Note
25483 \begin_layout Plain Layout
25490 is used for separation, because otherwise the output will be ¡ and ¿ respective
25501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25515 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25527 \begin_inset Formula $\textrm{ø}$
25537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25540 \begin_layout Plain Layout
25548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25551 \begin_layout Plain Layout
25552 \begin_inset Formula $\textrm{Ø}$
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25565 \begin_layout Plain Layout
25573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25576 \begin_layout Plain Layout
25577 \begin_inset Formula $\textrm{ł}$
25587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25601 \begin_layout Plain Layout
25602 \begin_inset Formula $\textrm{Ł}$
25612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25615 \begin_layout Plain Layout
25617 \begin_inset space \hspace{}
25625 \begin_layout Plain Layout
25639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25642 \begin_layout Plain Layout
25643 \begin_inset Formula $\textrm{!`}$
25653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25656 \begin_layout Plain Layout
25658 \begin_inset space \hspace{}
25666 \begin_layout Plain Layout
25680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25683 \begin_layout Plain Layout
25684 \begin_inset Formula $\textrm{?`}$
25694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25697 \begin_layout Plain Layout
25705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25708 \begin_layout Plain Layout
25709 \begin_inset Formula $\textrm{ȷ}$
25723 \begin_inset space \hfill{}
25729 \begin_layout Standard
25731 \begin_inset Formula $\textrm{\textrm{Å}}$
25735 \begin_inset Formula $\textrm{\textrm{Ø}}$
25738 can also be inserted via the math toolbar button
25739 \begin_inset Graphics
25740 filename ../images/math/digamma.png
25748 \begin_layout Standard
25749 An exception are the commands
25752 \begin_inset space \hspace{}
25761 \begin_inset space \hspace{}
25767 , because they can be inserted in LyX directly to text.
25770 \begin_layout Subsection
25772 \begin_inset CommandInset label
25774 name "sub:Accents-in-Text"
25782 \begin_layout Plain Layout
25791 \begin_layout Standard
25792 With the following commands all letters can be accented.
25793 The commands must be inserted in TeX-mode.
25796 \begin_layout Standard
25797 \begin_inset space \hfill{}
25801 \begin_inset Tabular
25802 <lyxtabular version="3" rows="8" columns="2">
25804 <column alignment="block" valignment="top" width="0">
25805 <column alignment="block" valignment="top" width="0">
25807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25810 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25830 \begin_layout Plain Layout
25834 \begin_inset Quotes grd
25842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25845 \begin_layout Plain Layout
25849 \begin_layout Plain Layout
25865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25868 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25879 \begin_layout Plain Layout
25883 \begin_layout Plain Layout
25899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25902 \begin_layout Plain Layout
25909 \begin_layout Plain Layout
25923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25926 \begin_layout Plain Layout
25930 \begin_layout Plain Layout
25946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25949 \begin_layout Plain Layout
25957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25960 \begin_layout Plain Layout
25964 \begin_layout Plain Layout
25980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25983 \begin_layout Plain Layout
25990 \begin_layout Plain Layout
26004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26007 \begin_layout Plain Layout
26011 \begin_layout Plain Layout
26027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26030 \begin_layout Plain Layout
26037 \begin_layout Plain Layout
26051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26054 \begin_layout Plain Layout
26058 \begin_layout Plain Layout
26074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26084 \begin_layout Plain Layout
26098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26101 \begin_layout Plain Layout
26105 \begin_layout Plain Layout
26125 \begin_inset space \hfill{}
26129 \begin_inset Tabular
26130 <lyxtabular version="3" rows="8" columns="2">
26132 <column alignment="block" valignment="top" width="0">
26133 <column alignment="center" valignment="top" width="0">
26135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26138 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26158 \begin_layout Plain Layout
26165 \begin_layout Plain Layout
26179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26182 \begin_layout Plain Layout
26186 \begin_layout Plain Layout
26202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26205 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26220 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26246 \begin_layout Plain Layout
26257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26260 \begin_layout Plain Layout
26264 \begin_layout Plain Layout
26280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26283 \begin_layout Plain Layout
26291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26294 \begin_layout Plain Layout
26298 \begin_layout Plain Layout
26314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26317 \begin_layout Plain Layout
26324 \begin_layout Plain Layout
26338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26341 \begin_layout Plain Layout
26345 \begin_layout Plain Layout
26361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26364 \begin_layout Plain Layout
26371 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26392 \begin_layout Plain Layout
26408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26411 \begin_layout Plain Layout
26418 \begin_layout Plain Layout
26432 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26435 \begin_layout Plain Layout
26439 \begin_layout Plain Layout
26459 \begin_inset space \hfill{}
26465 \begin_layout Standard
26466 \begin_inset VSpace medskip
26475 also two different characters can be accented.
26484 \begin_layout Plain Layout
26499 \begin_layout Plain Layout
26511 \begin_layout Standard
26524 can in combination with vowels directly be inserted with the keyboard without
26526 The same applies for the tilde
26530 \begin_layout Plain Layout
26531 This only applies for keyboards where the tilde is defined as accent.
26540 in combination with
26555 \begin_layout Standard
26598 , and accents inserted directly with the keyboard are also available in
26600 For the other accents there are special math commands to be used in formulas,
26602 \begin_inset CommandInset ref
26604 reference "sub:Accents-for-one"
26611 \begin_layout Standard
26612 \begin_inset VSpace bigskip
26615 Furthermore, with the command
26625 \begin_layout Plain Layout
26633 all numbers and letters can be set into a circle, quasi accented with a
26634 circle, similar to the the copyright symbol.
26637 \begin_layout Standard
26639 \begin_inset Tabular
26640 <lyxtabular version="3" rows="3" columns="2">
26642 <column alignment="center" valignment="top" width="0">
26643 <column alignment="center" valignment="top" width="0">
26645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26648 \begin_layout Plain Layout
26654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26657 \begin_layout Plain Layout
26659 \begin_inset Note Note
26662 \begin_layout Plain Layout
26669 is only used as spacer.
26681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26684 \begin_layout Plain Layout
26692 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26695 \begin_layout Plain Layout
26699 \begin_layout Plain Layout
26715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26729 raisebox{-1.5pt}{W}}
26734 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26737 \begin_layout Plain Layout
26738 \begin_inset Formula $\raisebox{4.5mm}{}$
26745 \begin_layout Plain Layout
26763 \begin_inset Formula $\raisebox{-2mm}{}$
26779 \begin_layout Standard
26780 One has to take care that the character fits in the circle.
26791 \begin_layout Plain Layout
26793 \begin_inset CommandInset ref
26795 reference "sub:Font-Sizes"
26804 specifies thereby the size of the circle.
26815 \begin_layout Plain Layout
26817 \begin_inset CommandInset ref
26819 reference "sub:Boxes-without-Frame"
26828 the character can be centered.
26831 \begin_layout Subsection
26836 \begin_layout Plain Layout
26845 \begin_layout Standard
26846 Minuscule numbers are created with the command
26856 \begin_layout Plain Layout
26865 The command can be used in formulas and in TeX-mode.
26866 The command scheme is:
26869 \begin_layout Standard
26874 oldstylenums{number}
26877 \begin_layout Standard
26882 oldstylenums{0123456789
26885 \begin_inset Formula $\oldstylenums{0123456789}$
26891 \begin_layout Subsection
26892 Miscellaneous special Characters
26893 \begin_inset CommandInset label
26895 name "sub:Miscellaneous-special-Characters"
26903 \begin_layout Plain Layout
26904 Special characters ! miscellaneous
26912 \begin_layout Standard
26913 The following characters can only be inserted to formulas by using commands:
26916 \begin_layout Standard
26918 \begin_inset Tabular
26919 <lyxtabular version="3" rows="4" columns="2">
26921 <column alignment="center" valignment="top" width="0">
26922 <column alignment="center" valignment="top" width="0">
26924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26927 \begin_layout Plain Layout
26933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26947 \begin_layout Plain Layout
26954 \begin_layout Plain Layout
26968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26971 \begin_layout Plain Layout
26972 \begin_inset Formula $\mathcircumflex$
26982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26985 \begin_layout Plain Layout
26993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26996 \begin_layout Plain Layout
26997 \begin_inset Formula $\_$
27007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27010 \begin_layout Plain Layout
27015 \begin_layout Plain Layout
27030 \begin_layout Plain Layout
27041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27044 \begin_layout Plain Layout
27045 \begin_inset Formula $^{\circ}$
27061 \begin_layout Standard
27062 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27063 contains the following line
27067 \begin_layout Plain Layout
27068 More about this is described in
27069 \begin_inset CommandInset ref
27071 reference "sub:Text-Characters-in"
27083 \begin_layout Standard
27088 DeclareInputtext{176}{
27101 \begin_layout Section
27103 \begin_inset CommandInset label
27105 name "sec:Formula-Styles"
27113 \begin_layout Plain Layout
27122 \begin_layout Itemize
27123 There are two different alignment styles:
27127 \begin_layout Description
27128 Centered is the predefined standard
27131 \begin_layout Description
27132 Indented for this the option
27136 must be inserted in the menu
27138 Document\SpecialChar \menuseparator
27144 \begin_inset space ~
27150 \begin_layout Standard
27155 is used, the indentation can be adjusted with the length
27165 \begin_layout Plain Layout
27174 Should the distance be 15
27175 \begin_inset space \thinspace{}
27178 mm, the following command line is inserted in the LaTeX-preamble
27181 \begin_layout Standard
27191 \begin_layout Standard
27192 When no length is specified, the predefined value of 30
27193 \begin_inset space \thinspace{}
27200 \begin_layout Itemize
27201 And two different numbering styles:
27205 \begin_layout Description
27206 Right is the predefined standard
27209 \begin_layout Description
27210 Left for this the option
27214 must be inserted in the menu
27216 Document\SpecialChar \menuseparator
27222 \begin_inset space ~
27229 \begin_layout Standard
27238 can also be used together.
27239 In this case both options are inserted, separated by a comma.
27242 \begin_layout Standard
27243 The chosen styles are used for all displayed formulas of the document.
27244 When both, centered and indented formulas should be created in a document,
27250 The indented formulas are then set in a flalign environment, see
27251 \begin_inset CommandInset ref
27253 reference "sub:Flalign-Environment"
27260 \begin_layout Section
27262 \begin_inset CommandInset label
27264 name "sec:Multiline-Formulas"
27272 \begin_layout Plain Layout
27273 Formula ! multiline
27281 \begin_layout Subsection
27285 \begin_layout Standard
27286 In LyX multiline formulas are created by pressing
27293 This creates either an
27295 eqnarray environment
27297 that is described in
27298 \begin_inset CommandInset ref
27300 reference "sub:Eqnarray-Environment"
27304 or, when the option
27306 Use AMS math package
27308 in the document settings is selected, an
27312 that is described in
27313 \begin_inset CommandInset ref
27315 reference "sub:Standard-align-Environment"
27322 \begin_layout Standard
27323 There are other multiline formula environments that can be created via the
27326 Insert\SpecialChar \menuseparator
27330 These environments are described in the following sections.
27333 \begin_layout Standard
27334 In all multiline formula environments a new line is created by pressing
27340 To add or delete lines, the math toolbar buttons
27341 \begin_inset Graphics
27342 filename ../images/tabular-feature_append-row.png
27348 \begin_inset Graphics
27349 filename ../images/tabular-feature_delete-row.png
27354 , respectively, or the menu
27356 Edit\SpecialChar \menuseparator
27362 \begin_layout Subsubsection
27364 \begin_inset CommandInset label
27366 name "sub:Line-Separation"
27374 \begin_layout Plain Layout
27375 Formula ! multiline ! Line separation
27383 \begin_layout Standard
27384 There is sometimes not enough space in multiline formulas between the lines:
27385 \begin_inset Formula \begin{eqnarray*}
27386 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}\\
27387 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\end{eqnarray*}
27394 \begin_layout Standard
27395 In LaTeX additional line space is specified as optional argument of the
27397 This is not yet possible in LyX
27401 \begin_layout Plain Layout
27403 \begin_inset CommandInset href
27405 name "LyX-bug #1505"
27406 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27415 , therefore the whole formula must be inserted in TeX-mode.
27416 To add in our example space, the command
27424 is inserted at the end of the first line.
27429 \begin_layout Plain Layout
27436 \begin_layout Plain Layout
27438 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27441 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27448 \begin_layout Plain Layout
27452 left(B^{2}+x_{0}^{2}
27460 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27465 \begin_layout Plain Layout
27477 \begin_layout Standard
27478 \begin_inset VSpace bigskip
27481 To set the the line separation for all lines in a formula, the length
27491 \begin_layout Plain Layout
27501 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27512 \begin_inset space \thinspace{}
27517 \begin_inset space \thinspace{}
27520 mm additional line separation as in the previous example, the command
27523 \begin_layout Standard
27533 \begin_layout Standard
27534 is inserted in TeX-mode before the formula.
27535 This requires that the LaTeX-package
27543 \begin_layout Plain Layout
27548 is part of every LaTeX standard installation.
27557 \begin_layout Plain Layout
27563 was loaded in LaTeX-preamble with the line
27566 \begin_layout Standard
27574 \begin_layout Standard
27579 \begin_layout Plain Layout
27591 \begin_inset Formula \begin{eqnarray*}
27592 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}\\
27593 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\end{eqnarray*}
27600 \begin_layout Standard
27604 \begin_layout Plain Layout
27615 To get back to the predefined distance,
27621 is set to the value 3
27622 \begin_inset space \thinspace{}
27628 \begin_layout Subsubsection
27630 \begin_inset CommandInset label
27632 name "sub:Column-Separation"
27640 \begin_layout Plain Layout
27641 Formula ! multiline ! Column separation
27649 \begin_layout Standard
27650 Multiline formulas form a matrix.
27651 A formula in the eqnarray environment is for example a matrix with three
27653 By changing the column separation in this environment, the space beside
27654 the relation sign can be changed.
27657 \begin_layout Standard
27658 The column separation is specified with the length
27668 \begin_layout Plain Layout
27677 \begin_inset Newline newline
27680 column separation = 2
27681 \begin_inset space \thinspace{}
27691 \begin_inset Newline newline
27697 \begin_layout Standard
27707 \begin_layout Standard
27708 inserted in TeX-mode, sets for all following formulas a column separation
27710 \begin_inset space \thinspace{}
27714 To get back to the predefined distance,
27721 \begin_inset space \thinspace{}
27727 \begin_layout Standard
27729 \begin_inset space \thinspace{}
27732 cm column separation:
27736 \begin_layout Plain Layout
27748 \begin_inset Formula \begin{eqnarray*}
27750 C & \ne & A\end{eqnarray*}
27754 A formula with the predefined column separation for matrices of 10
27755 \begin_inset space \thinspace{}
27762 \begin_layout Plain Layout
27774 \begin_inset Formula \begin{eqnarray*}
27776 C & \ne & A\end{eqnarray*}
27783 \begin_layout Subsubsection
27788 \begin_layout Plain Layout
27797 \begin_layout Standard
27798 Long formulas can be typeset using these methods:
27801 \begin_layout Itemize
27802 When one side of the equation is much shorther than the line width, this
27803 one is chosen for the left side and the right side is typeset over two
27808 \begin_layout Plain Layout
27818 \begin_inset Formula \begin{eqnarray}
27819 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 \\
27820 & & -\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:kurzlang}\end{eqnarray}
27828 \begin_layout Plain Layout
27838 \begin_inset Newline newline
27841 The minus sign at the beginning of the second line does normally not appear
27842 as operator because it is the first character of the line.
27843 Thus it would not be surrounded by space and could not be distinguished
27844 from the fraction bar.
27845 To avoid this, space was inserted behind the minus sign with the command
27856 \begin_layout Plain Layout
27864 \begin_inset CommandInset ref
27866 reference "sub:Variable-Space"
27879 \begin_layout Plain Layout
27890 \begin_layout Itemize
27891 When both sides of the equation are too long, the command
27901 \begin_layout Plain Layout
27910 It is inserted to the first column of the first line and effects that all
27911 further insertions overwrite the following columns:
27915 \begin_layout Plain Layout
27925 \begin_inset Formula \begin{eqnarray}
27926 \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 \\
27927 & & -\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 \\
27928 & & =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}\end{eqnarray}
27936 \begin_layout Plain Layout
27946 \begin_inset Newline newline
27949 After the insertion of
27955 , the cursor is in a purple box that is a bit shifted to the left from the
27957 In this the formula is inserted.
27961 \begin_layout Plain Layout
27971 \begin_inset Newline newline
27974 The content of the further lines is inserted to the second or another formula
27976 The greater the column number where it was inserted, the larger the indentation.
27980 \begin_layout Plain Layout
27990 \begin_inset Newline newline
27994 \begin_inset Note Greyedout
27997 \begin_layout Plain Layout
27998 Note the following when using
28007 \begin_layout Itemize
28008 The formula doesn't use the full page width.
28010 \begin_inset space \thinspace{}
28014 \begin_inset space ~
28018 \begin_inset Formula $-B^{2}$
28021 is added to the first line in the above example, it would have been outside
28023 To better use the width, negative space can be inserted at the beginning
28027 \begin_layout Itemize
28028 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28033 \begin_layout Plain Layout
28034 \begin_inset CommandInset href
28036 name "LyX-bug #1429"
28037 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28046 One can only set the cursor at the beginning of the line and move it with
28055 \begin_layout Itemize
28056 Other methods to set long formulas are offered by the environments described
28058 \begin_inset CommandInset ref
28060 reference "sub:Multline-Environment"
28065 \begin_inset CommandInset ref
28067 reference "sub:Multiline-Formula-Parts"
28074 \begin_layout Subsubsection
28076 \begin_inset CommandInset label
28078 name "sub:Multiline-Brackets"
28086 \begin_layout Plain Layout
28087 Brackets ! for multiline expressions
28095 \begin_layout Standard
28096 For brackets spanning multiple lines the following problem occurs:
28097 \begin_inset Formula \begin{eqnarray*}
28098 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28099 & & \left.\cdots+B-D\right]\end{eqnarray*}
28106 \begin_layout Standard
28107 The closing bracket is smaller than the opening bracket because brackets
28108 with variable size may not span multiple lines.
28111 \begin_layout Standard
28112 To set the bracket size for the second line correctly, the first line is
28123 \begin_layout Plain Layout
28131 and the second line with
28139 \begin_layout Plain Layout
28153 \begin_inset CommandInset ref
28155 reference "sub:Automatic-Bracket-Size"
28170 \begin_layout Plain Layout
28196 \begin_layout Plain Layout
28215 \begin_layout Plain Layout
28234 \begin_layout Plain Layout
28246 \begin_inset Formula $\downarrow$
28255 \begin_layout Plain Layout
28263 is inserted, because the multiplication operator with its limits is the
28264 largest symbol in the first line and this should be the size for the bracket
28265 in the second line.
28268 \begin_layout Standard
28269 The result is this:
28270 \begin_inset Formula \begin{eqnarray*}
28271 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28272 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28279 \begin_layout Subsection
28283 \begin_layout Standard
28284 Align environments can be used for every kind of multiline formulas.
28285 They are specially useful to set several formulas side by side.
28288 \begin_layout Standard
28289 Align environments consist of columns.
28290 The odd columns are right aligned, the even ones left aligned.
28291 Every line in an Align environment can be numbered.
28294 \begin_layout Standard
28295 Align environments are created via the menu
28297 Insert\SpecialChar \menuseparator
28303 Edit\SpecialChar \menuseparator
28304 Math\SpecialChar \menuseparator
28305 Change Formula Type
28307 already existing formulas can be converted to Align environments.
28310 \begin_layout Standard
28311 To add or delete columns, the math toolbar buttons
28312 \begin_inset Graphics
28313 filename ../images/tabular-feature_append-column.png
28319 \begin_inset Graphics
28320 filename ../images/tabular-feature_delete-column.png
28325 , respectively, or the menu
28327 Edit\SpecialChar \menuseparator
28333 \begin_layout Subsubsection
28334 Standard align Environment
28335 \begin_inset CommandInset label
28337 name "sub:Standard-align-Environment"
28345 \begin_layout Plain Layout
28346 Formula ! multiline ! align environment
28354 \begin_layout Standard
28355 This Align environment is created by presssing
28359 in a formula or by the menu
28361 Insert\SpecialChar \menuseparator
28362 Math\SpecialChar \menuseparator
28363 AMS align Environment
28368 \begin_layout Standard
28369 An example for two formulas set side by side, that are created with a four
28370 column align environment:
28371 \begin_inset Formula \begin{align*}
28372 A & =\sin(B) & C & =D\\
28373 C & \ne A & B & \ne D\end{align*}
28377 As it can be seen, the formulas in this environment are placed so as if
28386 \begin_layout Plain Layout
28394 \begin_inset CommandInset ref
28396 reference "sub:Variable-Space"
28407 before the first and after every even column.
28408 When the formula style
28414 \begin_layout Plain Layout
28416 \begin_inset CommandInset ref
28418 reference "sec:Formula-Styles"
28429 is used, the formula is set without the
28435 before the first column.
28438 \begin_layout Subsubsection
28439 Alignat Environment
28443 \begin_layout Plain Layout
28444 Formula ! multiline ! alignat environment
28452 \begin_layout Standard
28453 The alignat environment has no predefined column separation.
28454 It can be inserted manually with the spaces that are described
28455 \begin_inset CommandInset ref
28457 reference "sub:Space"
28464 \begin_layout Standard
28465 The above example in the alignat environment where 1
28466 \begin_inset space \thinspace{}
28469 cm space was inserted at the beginning of the second formula:
28470 \begin_inset Formula \begin{alignat*}{2}
28471 A & =\sin(B) & \hspace{1cm}C & =D\\
28472 C & \ne A & B & \ne D\end{alignat*}
28476 Because the column separation can be set separately for every column, this
28477 environment is especially suitable to set three and more formulas side
28481 \begin_layout Subsubsection
28482 Flalign Environment
28483 \begin_inset CommandInset label
28485 name "sub:Flalign-Environment"
28493 \begin_layout Plain Layout
28494 Formula ! multiline ! flalign environment
28502 \begin_layout Standard
28503 In this environment the first two columns are always set as much as possible
28504 to the left and the last two ones to the right.
28506 \begin_inset Formula \begin{flalign*}
28507 A & =1 & B & =2 & C & =3\\
28508 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28515 \begin_layout Standard
28516 By creating a flalign environment with an odd number of columns where an
28517 empty TeX-brace is inserted to the last column, several formulas in a document
28518 can be set to the left, although the formula style
28523 As example the indented formula
28524 \begin_inset CommandInset ref
28526 reference "eq:VolInt"
28531 \begin_inset Formula \begin{flalign}
28532 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28536 The first two columns contain the formula.
28537 To indent it as with the formula style
28542 \begin_inset space \thinspace{}
28545 pt space was inserted at the beginning of the first column.
28548 \begin_layout Subsection
28549 Eqnarray Environment
28550 \begin_inset CommandInset label
28552 name "sub:Eqnarray-Environment"
28560 \begin_layout Plain Layout
28561 Formula ! multiline ! eqnarray environment
28569 \begin_layout Standard
28570 When this environment has been created, three blue boxes appear.
28571 The content of the first box is right aligned, the content of the last
28573 The content of the middle box appears centered and a bit smaller, because
28574 it is designed to insert there only relation characters.
28575 \begin_inset Formula \begin{eqnarray*}
28576 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28578 A & = & A\end{eqnarray*}
28585 \begin_layout Subsection
28590 \begin_layout Plain Layout
28591 Formula ! multiline ! gather environment
28599 \begin_layout Standard
28600 This environment consists of only one centered column.
28601 Every line can be numbered.
28602 \begin_inset Formula \begin{gather}
28604 X=\textrm{-}1\end{gather}
28611 \begin_layout Subsection
28612 Multline Environment
28613 \begin_inset CommandInset label
28615 name "sub:Multline-Environment"
28623 \begin_layout Plain Layout
28624 Formula ! multiline ! multline environment
28632 \begin_layout Standard
28633 The multline environment consists, like the gather environment, of only
28635 But the first line is left aligned, the last one right aligned.
28636 All other lines are centered.
28637 Therefore this environment is suitable for long formulas.
28639 \begin_inset CommandInset ref
28641 reference "eq:lefteqn"
28645 in the multline environment:
28646 \begin_inset Formula \begin{multline}
28647 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}\\
28648 -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}\\
28649 =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}}\end{multline}
28656 \begin_layout Standard
28657 In the output only the last (first) line of a multline environment appears
28658 numbered when the document numbering is right (left).
28662 \begin_layout Plain Layout
28663 numbering styles see
28664 \begin_inset CommandInset ref
28666 reference "sec:Formula-Styles"
28678 \begin_layout Standard
28687 \begin_layout Plain Layout
28705 \begin_layout Plain Layout
28715 a centered line can be right or left aligned, respectively.
28716 The commands are used as follows:
28719 \begin_layout Standard
28724 shoveright{line content}
28730 shoveleft{line content}
28733 \begin_layout Standard
28734 \begin_inset VSpace medskip
28745 \begin_layout Plain Layout
28755 specifies the distance of the first line from the left page margin.
28756 Predefined is the length 0
28757 \begin_inset space \thinspace{}
28763 \begin_layout Standard
28764 As example the above formula where the command
28767 \begin_layout Standard
28777 \begin_layout Standard
28778 was inserted in TeX-mode before:
28782 \begin_layout Plain Layout
28794 \begin_inset Formula \begin{multline}
28795 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}\\
28796 \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}}\\
28797 =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}}\end{multline}
28805 \begin_layout Plain Layout
28816 The second line was left aligned using
28825 \begin_layout Subsection
28826 Multiline Formula Parts
28827 \begin_inset CommandInset label
28829 name "sub:Multiline-Formula-Parts"
28837 \begin_layout Plain Layout
28838 Formula ! multiline ! formula parts
28846 \begin_layout Standard
28847 To display only parts of a formula with multiple lines, one of the following
28848 environments are used:
28865 They can be inserted via the menu
28867 Insert\SpecialChar \menuseparator
28870 or by using the commands described in this section.
28873 \begin_layout Standard
28874 The first three have the same properties as the corresponding multiline
28875 formula environments, but it is possible to set further formula parts beside
28878 \begin_inset Formula \[
28879 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28880 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28881 \right\} \textrm{Uncertainty relations}\]
28888 \begin_layout Standard
28889 To get this formula, a displayed formula is created where the command
28897 \begin_layout Plain Layout
28908 A purple box appears around the blue formula box where now columns and
28909 lines can be added.
28910 Outside the multiline environment other formula parts can be set, like
28914 \begin_layout Standard
28915 The aligned environment is also suitable for long formulas whose lines are
28916 horizontally aligned.
28917 Using aligned in a displayed formula has the advantage that the formula
28918 number is vertically centered behind the lines.
28920 \begin_inset CommandInset ref
28922 reference "eq:kurzlang"
28926 in the aligned environment:
28927 \begin_inset Formula \begin{equation}
28928 \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}|}\\
28929 & -\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}|}\end{aligned}
28937 \begin_layout Standard
28938 To use the environments
28960 \begin_layout Plain Layout
28978 \begin_layout Plain Layout
28996 \begin_layout Plain Layout
29004 are inserted, respectively.
29005 The split environment has the same properties as the aligned environment
29006 but it can only have two columns.
29009 \begin_layout Subsection
29010 Text in multiline Formulas
29011 \begin_inset CommandInset label
29013 name "sub:Text-in-multiline"
29021 \begin_layout Plain Layout
29031 \begin_layout Plain Layout
29032 Formula ! multiline ! text
29040 \begin_layout Standard
29041 In the Align environments, and the multline and gather environment, text
29042 can be inserted that will appear in a separate line and doesn't affect
29043 the column alignment.
29044 To do this, the command
29052 \begin_layout Plain Layout
29062 is used in the following scheme:
29065 \begin_layout Standard
29073 \begin_layout Standard
29074 The text should not be longer than a line because it cannot be hyphenated.
29075 As LyX doesn't yet support
29081 directly, the text is written as mathematical text.
29088 must hereby be at the beginning of a line and appears in the output above
29090 An example where the text was inserted at the beginning of the second line:
29091 \begin_inset Formula \begin{align}
29092 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29093 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29100 \begin_layout Section
29105 \begin_layout Plain Layout
29115 \begin_layout Plain Layout
29116 Formula ! numbering|see
29120 \begin_layout Plain Layout
29131 \begin_layout Plain Layout
29146 \begin_layout Subsection
29150 \begin_layout Standard
29151 Numbered formulas can be created with the menu
29153 Insert\SpecialChar \menuseparator
29154 Math\SpecialChar \menuseparator
29156 \begin_inset space ~
29164 \begin_inset space ~
29170 Existing formulas can be numbered with the menu
29172 Edit\SpecialChar \menuseparator
29173 Math\SpecialChar \menuseparator
29175 \begin_inset space ~
29183 \begin_inset space ~
29189 The formula number is displayed in LyX behind the formula as number sign
29191 The number sign is replaced in the output by the formula number.
29194 \begin_layout Standard
29195 When numbering is turned on in multiline formulas, all lines will be numbered.
29196 But the numbering can be controlled with the menu
29198 Edit\SpecialChar \menuseparator
29199 Math\SpecialChar \menuseparator
29201 \begin_inset space ~
29205 \begin_inset space ~
29209 \begin_inset space ~
29217 \begin_inset space ~
29225 \begin_layout Standard
29226 Except of inline formulas, all formulas can be numbered with two different
29228 \begin_inset CommandInset ref
29230 reference "sec:Formula-Styles"
29237 \begin_layout Subsection
29239 \begin_inset CommandInset label
29241 name "sub:Cross-References"
29249 \begin_layout Plain Layout
29250 Cross-references ! to formulas
29258 \begin_layout Standard
29259 All labeled formulas can be cross-referenced.
29260 A label is added by the menu
29262 Insert\SpecialChar \menuseparator
29265 or the toolbar button
29266 \begin_inset Graphics
29267 filename ../images/label-insert.png
29273 The cursor must hereby be inside a displayed formula.
29274 A dialog pops up displaying the prefix
29279 The label is inserted there behind the prefix.
29280 The predefined prefix means
29281 \begin_inset Quotes eld
29285 \begin_inset Quotes erd
29288 and makes it easier to find labels in large documents because it marks
29289 it as formula label to divide it from e.
29290 \begin_inset space \thinspace{}
29294 \begin_inset space ~
29298 To change a label, the menu
29300 Insert\SpecialChar \menuseparator
29306 \begin_layout Standard
29307 The name of the label is displayed in LyX within two parentheses behind
29309 A formula with a label is always numbered.
29312 \begin_layout Standard
29313 Cross-references are inserted via the menu
29315 Insert\SpecialChar \menuseparator
29318 or with the toolbar button
29319 \begin_inset Graphics
29320 filename ../images/dialog-show-new-inset_ref.png
29326 A formula cross-reference appears in the output as formula number.
29327 When in the cross-reference dialog window the format
29331 is chosen, the cross-reference appears in the output as formula number
29333 \begin_inset Newline newline
29336 By right-clicking on a cross-reference in LyX, one jumps to the formula
29337 that is referenced.
29340 \begin_layout Standard
29341 Here are as examples cross-references to formulas of the following subsections:
29342 \begin_inset Note Note
29345 \begin_layout Plain Layout
29346 Note the different cross-reference types.
29354 \begin_layout Standard
29356 \begin_inset CommandInset ref
29363 \begin_inset CommandInset ref
29371 \begin_inset CommandInset ref
29377 ) big Latin letters are used for the numbering in contrary to (
29378 \begin_inset CommandInset ref
29387 \begin_layout Standard
29388 \begin_inset VSpace medskip
29391 When the argument of
29399 \begin_layout Plain Layout
29407 \begin_inset CommandInset ref
29409 reference "sub:User-defined-Numbering"
29420 contains a box like in
29421 \begin_inset CommandInset ref
29423 reference "sub:Paragraph-Boxes"
29427 , the formula cannot be referenced.
29430 \begin_layout Subsection
29435 \begin_layout Plain Layout
29436 Formula numbering ! subnumbering
29444 \begin_layout Standard
29445 With the help of the commands
29449 begin{subequations}
29457 formulas can be subnumbered.
29458 Both commands are inserted in TeX-mode.
29461 \begin_layout Standard
29463 \begin_inset Formula \begin{equation}
29464 A=C-B\label{eq:a}\end{equation}
29472 \begin_layout Plain Layout
29476 addtocounter{equation}{-1}
29485 \begin_layout Plain Layout
29489 begin{subequations}
29495 \begin_inset VSpace -5mm
29499 \begin_inset Formula \begin{equation}
29500 B=C-A\label{eq:b}\end{equation}
29505 \begin_inset Formula \begin{equation}
29506 C=A+B\label{eq:c}\end{equation}
29513 \begin_layout Standard
29517 \begin_layout Plain Layout
29529 \begin_layout Standard
29530 To create the example, the following is done:
29533 \begin_layout Enumerate
29534 first formula is inserted
29537 \begin_layout Enumerate
29542 addtocounter{equation}{-1}
29544 begin{subequations}
29548 \begin_layout Plain Layout
29557 \begin_inset Newline newline
29562 is inserted after the first formula
29565 \begin_layout Enumerate
29566 second formula is inserted
29569 \begin_layout Enumerate
29570 third formula is inserted
29573 \begin_layout Enumerate
29580 is inserted after the third formula
29583 \begin_layout Standard
29584 Every formula between the commands
29596 is subnumbered as a, b,
29597 \begin_inset Newline linebreak
29600 c, \SpecialChar \ldots{}
29601 For multiline formulas every line will be subnumbered.
29602 All subnumbered formulas are treated as
29607 But as every numbered formula increases the counter
29611 by one, the command
29617 is needed to decrease it.
29618 Otherwise the formulas
29619 \begin_inset CommandInset ref
29626 \begin_inset CommandInset ref
29633 \begin_inset CommandInset ref
29639 would be numbered as
29640 \begin_inset CommandInset ref
29647 \begin_inset CommandInset ref
29654 \begin_inset CommandInset ref
29663 \begin_layout Standard
29664 By inserting the commands in TeX-mode, a space is created between the first
29667 \begin_inset space \thinspace{}
29670 mm vertical space is inserted after the command
29674 begin{subequations}
29677 When the formula style
29683 \begin_layout Plain Layout
29685 \begin_inset CommandInset ref
29687 reference "sec:Formula-Styles"
29699 \begin_inset space \thinspace{}
29702 mm space is inserted instead.
29705 \begin_layout Standard
29706 Here is an example for a multiline formula where the numbering was turned
29707 off for the second line:
29711 \begin_layout Plain Layout
29715 begin{subequations}
29721 \begin_inset Formula \begin{eqnarray}
29722 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29723 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29724 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29732 \begin_layout Plain Layout
29744 \begin_layout Subsection
29745 User-defined Numbering
29746 \begin_inset CommandInset label
29748 name "sub:User-defined-Numbering"
29756 \begin_layout Plain Layout
29757 Formula numbering ! user-defined
29765 \begin_layout Standard
29769 \begin_layout Plain Layout
29770 Formula numbering ! self-defined delimiters
29775 With the standard numbering parentheses are set around the formula number.
29776 To replace the parentheses for example by vertical bars, the following
29777 line is added to the LaTeX-preamble:
29780 \begin_layout Standard
29792 \begin_inset Note Note
29795 \begin_layout Plain Layout
29796 This macro is already declared in the LaTeX-preamble for testing.
29797 To activate it, remove the percent sign at the beginning.
29805 \begin_layout Standard
29806 To use other characters, the vertical bars besides the
29810 are replaced by one ore more characters.
29811 To get only the formula number the vertical bars are omitted.
29814 \begin_layout Standard
29815 \begin_inset VSpace bigskip
29818 When there should be an expression of your choice instead of the consecutive
29819 formula number in parentheses behind the formula, the command
29829 \begin_layout Plain Layout
29838 \begin_inset Formula \begin{equation}
29839 A+B=C\tag{something}\label{eq:tag}\end{equation}
29843 In this example the command
29851 \begin_layout Plain Layout
29862 was inserted to the formula.
29865 \begin_layout Standard
29874 \begin_layout Plain Layout
29885 is inserted instead, the star prevents the parentheses around the expression:
29886 \begin_inset Formula \[
29887 A+B=C\tag*{something}\]
29894 \begin_layout Standard
29895 \begin_inset VSpace bigskip
29898 To restart the formula numbering with new document parts or sections, the
29899 following command is used:
29902 \begin_layout Standard
29907 @addtoreset{equation}{part}
29913 \begin_layout Plain Layout
29918 \begin_layout Plain Layout
29929 \begin_layout Plain Layout
29942 \begin_layout Plain Layout
29953 \begin_layout Plain Layout
29966 \begin_inset Newline newline
29970 \begin_inset Newline newline
29977 @addtoreset{equation}{section}
29980 \begin_layout Standard
29981 To be able to use these commands in TeX-mode, the
29982 \begin_inset Quotes eld
29986 \begin_inset Quotes erd
29989 character has to be made
29990 \begin_inset Quotes eld
29994 \begin_inset Quotes erd
29997 for LaTeX using the command
30011 So the command sequence in TeX-mode is:
30014 \begin_layout Standard
30020 \begin_inset Newline newline
30025 @addtoreset{equation}{section}
30026 \begin_inset Newline newline
30034 \begin_layout Standard
30035 In the LaTeX-preamble
30047 can be omitted as they are automatically internally inserted by LyX.
30050 \begin_layout Standard
30065 \begin_layout Plain Layout
30070 is part of the LaTeX-package
30078 \begin_layout Plain Layout
30079 Packages ! carlisle
30084 that is part of every LaTeX standard installation.
30093 \begin_layout Plain Layout
30094 Packages ! remreset
30099 has to be loaded in the LaTeX-preamble with the line
30102 \begin_layout Standard
30107 usepackage{remreset}
30110 \begin_layout Standard
30121 \begin_layout Plain Layout
30126 \begin_layout Plain Layout
30137 \begin_layout Plain Layout
30150 \begin_layout Plain Layout
30161 \begin_layout Plain Layout
30173 can be used with the same scheme as
30182 \begin_layout Standard
30183 \begin_inset VSpace bigskip
30186 Sometimes formulas should be numbered in the following form:
30189 \begin_layout Standard
30192 (section number.formula number)
30195 \begin_layout Standard
30196 The formula number should start with every section with
30197 \begin_inset Quotes eld
30201 \begin_inset Quotes erd
30207 \begin_layout Standard
30208 For this case there is the command
30218 \begin_layout Plain Layout
30226 , which is used with the following scheme:
30229 \begin_layout Standard
30234 numberwithin{counter}{sectioning}
30237 \begin_layout Standard
30238 Counter denotes what kind of numbering is affected, sectioning denotes what
30239 number is before the dot.
30242 \begin_layout Standard
30243 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30246 \begin_layout Standard
30251 numberwithin{equation}{section}
30254 \begin_layout Standard
30255 This is the result:
30259 \begin_layout Plain Layout
30263 numberwithin{equation}{section}
30269 \begin_inset Formula \begin{equation}
30270 A+B=C\end{equation}
30277 \begin_layout Standard
30279 \begin_inset space \thinspace{}
30283 \begin_inset space ~
30286 tables so that the number of the part is the sectioning,
30287 \begin_inset Newline newline
30294 numberwithin{table}{part}
30299 \begin_layout Standard
30300 To go back to the standard numbering or to prevent this kind of numbering
30301 when it is defined by the document class, the following command is inserted
30302 as TeX-Code or to the LaTeX-preamble:
30305 \begin_layout Standard
30318 \begin_layout Plain Layout
30332 \begin_layout Plain Layout
30348 \begin_inset Newline newline
30356 \begin_inset Newline newline
30368 \begin_layout Standard
30375 uses internally the command
30381 , described above, that also needs to be reverted.
30385 \begin_layout Plain Layout
30392 \begin_layout Plain Layout
30396 @removefromreset{equation}{section}
30399 \begin_layout Plain Layout
30411 \begin_layout Subsection
30412 Numbering with Roman Numbers and Letters
30413 \begin_inset CommandInset label
30415 name "sub:Numbering-with-Roman"
30423 \begin_layout Plain Layout
30424 Formula numbering ! with letters
30433 \begin_layout Plain Layout
30434 Formula numbering ! with Roman numbers
30442 \begin_layout Standard
30443 Formulas can also be numbered with Roman numbers and Latin letters.
30444 To number for example with small Roman numbers, the command
30447 \begin_layout Standard
30459 \begin_layout Standard
30460 is inserted before the formula in TeX-mode.
30471 \begin_layout Plain Layout
30479 redefines the predefined command
30495 \begin_layout Plain Layout
30502 has the same scheme like the command
30508 that is described in
30509 \begin_inset CommandInset ref
30511 reference "sec:User-defined-Commands"
30525 is the formula counter.
30532 is used as prefix for a counter, the value of the counter is output as
30534 When a formula is numbered, LaTeX sets internally the command
30540 behind the formula.
30549 \begin_layout Plain Layout
30559 outputs the counter as small Roman number.
30562 \begin_layout Standard
30563 All formulas behind the command
30573 are now numbered Roman.
30574 To switch to numbering with big Roman numbers, the command is inserted
30591 \begin_layout Plain Layout
30603 \begin_inset Quotes eld
30607 \begin_inset Quotes erd
30610 with small Latin letters there is the command
30620 \begin_layout Plain Layout
30628 , for big ones there is the command
30638 \begin_layout Plain Layout
30651 \begin_layout Standard
30652 \begin_inset Note Greyedout
30655 \begin_layout Plain Layout
30660 Only maximal 26 formulas can be numbered with Latin letters in one document.
30668 \begin_layout Standard
30672 \begin_layout Plain Layout
30688 \begin_layout Standard
30689 \begin_inset Formula \begin{equation}
30690 A=\textrm{small roman}\label{eq:rom}\end{equation}
30698 \begin_layout Plain Layout
30712 \begin_inset Formula \begin{equation}
30713 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30721 \begin_layout Plain Layout
30735 \begin_inset Formula \begin{equation}
30736 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30744 \begin_layout Plain Layout
30758 \begin_inset Formula \begin{equation}
30759 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30766 \begin_layout Standard
30767 To switch back to the default numbering, insert the command:
30770 \begin_layout Standard
30783 \begin_layout Plain Layout
30794 \begin_layout Standard
30798 \begin_layout Plain Layout
30812 \begin_inset Formula \begin{equation}
30813 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30820 \begin_layout Standard
30821 \begin_inset VSpace medskip
30824 As you see, formulas are numbered serially independent from the numbering
30826 When then numbering should start with
30827 \begin_inset Quotes eld
30831 \begin_inset Quotes erd
30834 when the style is changed, new equation counters have to be defined.
30835 A description about this can be found in the file
30836 \begin_inset CommandInset href
30838 target "Formula-numbering.lyx"
30845 \begin_layout Section
30846 User-defined Commands
30847 \begin_inset CommandInset label
30849 name "sec:User-defined-Commands"
30857 \begin_layout Plain Layout
30858 User-defined commands
30866 \begin_layout Standard
30867 Many LaTeX-commands are too long to be used frequently.
30868 But it is possible to define with the command
30878 \begin_layout Plain Layout
30886 new shorter commands.
30889 \begin_layout Standard
30890 The command scheme of
30899 \begin_layout Standard
30904 newcommand{new command name}[number of arguments][optional
30909 \begin_inset Newline newline
30916 \begin_layout Plain Layout
30931 \begin_layout Plain Layout
30938 {command definition}
30941 \begin_layout Standard
30942 \begin_inset Note Greyedout
30945 \begin_layout Plain Layout
30950 Assure that the name of the new command is not already used in your document
30951 or by LaTeX-packages that you use.
30952 When you for example define the command
30964 , you get an error message because
30970 is already defined as command for
30971 \begin_inset Quotes eld
30975 \begin_inset Formula $\le$
30979 \begin_inset Quotes erd
30990 \begin_layout Standard
30991 \begin_inset Note Greyedout
30994 \begin_layout Plain Layout
30999 The names of user-defined commands may only consist of Latin letters.
31007 \begin_layout Standard
31008 The number of arguments is an integer in the range 0
31009 \begin_inset space \thinspace{}
31013 \begin_inset space \thinspace{}
31016 9 and specifies how many arguments the new command should have.
31017 With the optional value a value for an optional argument can be predefined.
31018 When this is done, the
31026 rgument of the new command is automatically an optional one.
31029 \begin_layout Standard
31030 Here are some examples:
31033 \begin_layout Itemize
31034 To define the command
31046 , the LaTeX-preamble line is:
31050 \begin_layout Plain Layout
31062 \begin_inset Newline newline
31074 \begin_layout Itemize
31075 To define the command
31087 , the argument (that should be underlined) must be taken into account.
31088 For this the preamble line is:
31092 \begin_layout Plain Layout
31104 \begin_inset Newline newline
31119 \begin_layout Plain Layout
31131 \begin_inset Newline newline
31140 acts as argument placeholder, the
31144 behind it denotes that it is the placeholder for the first argument.
31147 \begin_layout Itemize
31155 \begin_inset space \thinspace{}
31159 \begin_inset space ~
31172 \begin_layout Plain Layout
31184 \begin_inset Newline newline
31193 framebox#1#2{$#3$}}
31199 \begin_layout Plain Layout
31211 \begin_inset Newline newline
31216 The two Dollar signs creates the extra formula needed for
31223 \begin_inset CommandInset ref
31225 reference "sub:Boxes-with-Frame"
31232 \begin_layout Itemize
31233 To create a new command for
31239 where the color for the box needn't to be specified, the argument for the
31240 color is defined optional:
31244 \begin_layout Plain Layout
31256 \begin_inset Newline newline
31265 fcolorbox{#2}{#1}{$#3$}}
31271 \begin_layout Plain Layout
31281 \begin_inset Newline newline
31284 When the color is not specified when using
31290 , the predefined color
31297 \begin_layout Standard
31298 A test of the new defined commands:
31301 \begin_layout Standard
31303 \begin_inset Tabular
31304 <lyxtabular version="3" rows="6" columns="2">
31306 <column alignment="center" valignment="top" width="0">
31307 <column alignment="center" valignment="top" width="0">
31309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31312 \begin_layout Plain Layout
31318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31321 \begin_layout Plain Layout
31323 \begin_inset Note Note
31326 \begin_layout Plain Layout
31333 is only used as spacer.
31345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31348 \begin_layout Plain Layout
31355 \begin_layout Plain Layout
31369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31372 \begin_layout Plain Layout
31373 \begin_inset Formula $A\gr B$
31383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31386 \begin_layout Plain Layout
31394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31397 \begin_layout Plain Layout
31398 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31411 \begin_layout Plain Layout
31415 \begin_inset Formula $\to$
31421 \begin_inset Formula $\to$
31432 \begin_layout Plain Layout
31446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31449 \begin_layout Plain Layout
31450 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31463 \begin_layout Plain Layout
31467 \begin_inset Formula $\to$
31478 \begin_layout Plain Layout
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31495 \begin_layout Plain Layout
31496 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31509 \begin_layout Plain Layout
31515 \begin_inset Formula $\to$
31526 \begin_layout Plain Layout
31540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31543 \begin_layout Plain Layout
31544 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31560 \begin_layout Section
31564 \begin_layout Standard
31565 LyX supports two types of commutative diagrams:
31573 that are explained in the following.
31576 \begin_layout Subsection
31581 \begin_layout Plain Layout
31590 \begin_layout Standard
31591 Diagrams of this type visualize relations by vertical and horizontal lines
31593 \begin_inset Formula \[
31594 \begin{CD}A@>>>B@>>>C\\
31596 F@<<<E@<<<D\end{CD}\]
31603 \begin_layout Standard
31604 To get them, the command
31612 \begin_layout Plain Layout
31622 is inserted to a formula.
31623 A blue box appears with two dashed lines where further commands can be
31629 a new line is created.
31630 Horizontal relations are inserted in odd, vertical in even formula lines.
31633 \begin_layout Standard
31634 To create the relations there are the following commands:
31637 \begin_layout Itemize
31642 creates a left arrow,
31653 \begin_layout Itemize
31658 creates an up arrow,
31666 a vertical equal sign
31669 \begin_layout Itemize
31675 is a placeholder for non-existent relations
31678 \begin_layout Standard
31679 All arrows can be labeled as follows:
31682 \begin_layout Itemize
31683 Is text inserted between the first and second < or >, resp., it is placed
31685 When it is inserted between the second and third one, it appears under
31689 \begin_layout Itemize
31690 When text for vertical arrows is inserted between the first and second A
31691 or V, resp., it is placed left beside the arrow.
31692 When it is inserted between the second and third one, it appears right
31694 If the text contains an A or V, these letters must be set into a TeX-brace.
31697 \begin_layout Standard
31698 As example a diagram with all possible relations:
31701 \begin_layout Standard
31702 \begin_inset Formula \[
31703 \begin{CD}A@>j>>B@>>k>C@=F\\
31705 D@<<j<E@>k>>F@=C\end{CD}\]
31712 \begin_layout Standard
31713 The command for this is:
31714 \begin_inset Newline newline
31725 \begin_layout Plain Layout
31734 A@>j>>B@>>k>C@=F Ctrl-Enter
31735 \begin_inset Newline newline
31742 \begin_layout Plain Layout
31757 \begin_layout Plain Layout
31770 \begin_layout Plain Layout
31782 \begin_inset Formula $\to$
31788 \begin_inset Newline newline
31795 \begin_layout Plain Layout
31810 \begin_layout Plain Layout
31823 \begin_layout Plain Layout
31833 \begin_layout Subsection
31838 \begin_layout Plain Layout
31839 Diagrams ! xymatrix
31847 \begin_layout Standard
31848 To be able to use xymatrices, the LaTeX-package
31853 A xymatrix is created by inserting the command
31860 Then you are able to add new matrix columns and rows like for normal matrices,
31862 \begin_inset CommandInset ref
31864 reference "sec:Matrices"
31871 \begin_layout Standard
31872 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31874 All possibilities to create commutative diagrams and decorations are explained
31875 in detail in this manual:
31876 \begin_inset CommandInset href
31878 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31885 \begin_layout Standard
31886 \begin_inset Newpage newpage
31892 \begin_layout Section
31897 \begin_layout Plain Layout
31910 \begin_layout Plain Layout
31911 Other useful math tips can be found in
31912 \begin_inset CommandInset citation
31927 \begin_layout Plain Layout
31935 \begin_inset Note Note
31938 \begin_layout Plain Layout
31941 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31944 \begin_layout Plain Layout
31947 texorpdfstring is in section
31948 \begin_inset CommandInset ref
31950 reference "sub:Formulas-in-Section"
31963 \begin_layout Plain Layout
31973 \begin_layout Plain Layout
31978 \begin_layout Plain Layout
31985 Chemical characters
31989 \begin_layout Plain Layout
32004 \begin_layout Subsection
32005 Chemical Symbols and Equations
32006 \begin_inset CommandInset label
32008 name "sub:Chemical-Symbols-and"
32016 \begin_layout Plain Layout
32017 Chemical characters ! Symbols
32026 \begin_layout Plain Layout
32036 \begin_layout Plain Layout
32045 \begin_layout Standard
32046 An example text from chemistry:
32049 \begin_layout Quote
32051 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32054 -ion reacts with two
32055 \begin_inset Formula $\mathrm{Na^{+}}$
32058 -ions to sodium sulfate
32059 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32063 The chemical equation for this is:
32064 \begin_inset Formula \[
32065 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32072 \begin_layout Standard
32073 This chemical equation can directly be created as formula.
32074 To avoid that the symbols appear italic, everything is highlighted and
32075 changed by the shortcut
32078 \begin_inset space ~
32083 to the upright font style.
32087 \begin_layout Plain Layout
32093 \begin_inset CommandInset ref
32095 reference "sub:Font-Styles"
32107 \begin_layout Subsection
32112 \begin_layout Plain Layout
32121 \begin_layout Standard
32122 Negative numbers often look ugly in formulas because the minus sign before
32123 the number is set with the same length as the minus operator sign.
32124 When writing the negative number in normal text, the minus sign appears
32128 \begin_layout Standard
32129 Thus, the problem disappears when converting the minus sign to mathematical
32133 \begin_layout Standard
32134 An example to visualize the problem:
32137 \begin_layout Standard
32139 \begin_inset Tabular
32140 <lyxtabular version="3" rows="3" columns="2">
32142 <column alignment="right" valignment="top" width="0">
32143 <column alignment="left" valignment="top" width="0">
32145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32148 \begin_layout Plain Layout
32154 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32157 \begin_layout Plain Layout
32165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32168 \begin_layout Plain Layout
32174 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32177 \begin_layout Plain Layout
32178 \begin_inset Formula $x=-2$
32188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32191 \begin_layout Plain Layout
32197 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32200 \begin_layout Plain Layout
32201 \begin_inset Formula $x=\textrm{-}2$
32217 \begin_layout Subsection
32218 Comma as decimal Separator
32222 \begin_layout Plain Layout
32231 \begin_layout Standard
32232 In LaTeX a comma inside a formula is used, according to the English convention,
32233 as number group separator.
32234 So there will be space added behind all commas in formulas.
32237 \begin_layout Standard
32238 To avoid this, the comma is highlighted and changed to mathematical text
32242 \begin_inset space ~
32250 \begin_layout Standard
32251 To use all formula commas in the document as decimal separator, the file
32260 \begin_layout Plain Layout
32265 is part of the LaTeX-package
32273 \begin_layout Plain Layout
32278 \begin_layout Plain Layout
32301 \begin_layout Plain Layout
32307 is loaded with the LaTeX-preamble line
32310 \begin_layout Standard
32318 \begin_layout Subsection
32320 \begin_inset CommandInset label
32322 name "sub:Physical-Vectors"
32330 \begin_layout Plain Layout
32339 \begin_layout Standard
32340 Predefined vectors are offered by the LaTeX-package
32348 \begin_layout Plain Layout
32353 should be part of every LaTeX standard installation.
32362 \begin_layout Plain Layout
32368 that is loaded with the LaTeX-preamble line
32371 \begin_layout Standard
32379 \begin_layout Standard
32383 \begin_layout Plain Layout
32393 \begin_inset Note Note
32396 \begin_layout Plain Layout
32397 The following table will only be displayed when the LaTeX-package
32406 The following commands are defined:
32409 \begin_layout Standard
32411 \begin_inset Tabular
32412 <lyxtabular version="3" rows="4" columns="2">
32414 <column alignment="center" valignment="top" width="0">
32415 <column alignment="center" valignment="top" width="0">
32417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32420 \begin_layout Plain Layout
32426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32429 \begin_layout Plain Layout
32437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32440 \begin_layout Plain Layout
32450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32453 \begin_layout Plain Layout
32454 \begin_inset Formula $\Bra{\psi}$
32464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32467 \begin_layout Plain Layout
32477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32480 \begin_layout Plain Layout
32481 \begin_inset Formula $\Ket{\psi}$
32491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32494 \begin_layout Plain Layout
32506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32509 \begin_layout Plain Layout
32510 \begin_inset Formula $\Braket{\psi|\phi}$
32526 \begin_layout Standard
32533 assures that all vertical bars are set in the size of the surrounding brackets:
32534 \begin_inset Formula \[
32535 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32543 \begin_layout Plain Layout
32553 \begin_inset Note Note
32556 \begin_layout Plain Layout
32557 The following will be displayed when the LaTeX-package
32569 \begin_layout Standard
32570 You need to install the LaTeX-package
32574 to see the rest of this subsection in the output.
32577 \begin_layout Standard
32581 \begin_layout Plain Layout
32593 \begin_layout Standard
32600 can also be achieved using the command
32606 , that is described in
32607 \begin_inset CommandInset ref
32609 reference "sub:Automatic-Bracket-Size"
32616 \begin_layout Subsection
32617 Self-defined Fractions
32618 \begin_inset CommandInset label
32620 name "sub:Self-defined-Fractions"
32628 \begin_layout Plain Layout
32629 Fractions ! self-defined
32637 \begin_layout Standard
32638 To define custom commands for fractions, the command
32648 \begin_layout Plain Layout
32656 is used in the following scheme:
32659 \begin_layout Standard
32672 bracket}{fraction bar thickness}{style}
32673 \begin_inset Newline newline
32680 \begin_layout Plain Layout
32695 \begin_layout Plain Layout
32702 {numerator}{denominator}
32705 \begin_layout Standard
32706 The style is a number in the range of 0
32707 \begin_inset space \thinspace{}
32711 \begin_inset space \thinspace{}
32717 \begin_layout Standard
32719 \begin_inset Tabular
32720 <lyxtabular version="3" rows="5" columns="2">
32722 <column alignment="center" valignment="top" width="0">
32723 <column alignment="center" valignment="top" width="0">
32725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32728 \begin_layout Plain Layout
32734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32737 \begin_layout Plain Layout
32745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32748 \begin_layout Plain Layout
32754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32757 \begin_layout Plain Layout
32758 display style formula
32765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32768 \begin_layout Plain Layout
32774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32777 \begin_layout Plain Layout
32785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32788 \begin_layout Plain Layout
32794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32797 \begin_layout Plain Layout
32805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32808 \begin_layout Plain Layout
32814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32817 \begin_layout Plain Layout
32831 \begin_layout Standard
32832 When no style is given, the size is adjusted to the surrounding environment
32833 like for the command
32842 \begin_layout Standard
32843 When no fraction bar thickness is given, the predefined value of 0.4
32844 \begin_inset space \thinspace{}
32850 \begin_layout Standard
32851 \begin_inset VSpace medskip
32854 For example, the commands
32867 \begin_inset CommandInset ref
32869 reference "sub:Fractions"
32873 are defined with the commands
32876 \begin_layout Standard
32885 genfrac{}{}{}{0}{#1}{#2}}
32888 \begin_layout Standard
32892 \begin_layout Standard
32901 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32904 \begin_layout Standard
32905 \begin_inset VSpace medskip
32908 To define a fraction where the fraction bar thickness can be given as optional
32909 argument, the following line is inserted to the LaTeX-preamble:
32912 \begin_layout Standard
32921 genfrac{}{}{#1}{}{#2}{#3}}
32924 \begin_layout Standard
32926 \begin_inset Formula \begin{align*}
32927 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32928 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32932 As one can see, the distance of the numerator and the denominator to the
32933 fraction bar is round about three times the bar thickness.
32936 \begin_layout Subsection
32938 \begin_inset CommandInset label
32940 name "sub:Canceled-Formulas"
32948 \begin_layout Plain Layout
32957 \begin_layout Standard
32958 To cancel formulas or formula parts, the LaTeX-package
32966 \begin_layout Plain Layout
32971 is part of every LaTeX standard installation.
32980 \begin_layout Plain Layout
32986 has to be loaded with the LaTeX-preamble line
32989 \begin_layout Standard
32994 usepackage[samesize]{cancel}
32997 \begin_layout Standard
32998 There are four ways to cancel formulas:
33001 \begin_layout Standard
33003 \begin_inset Tabular
33004 <lyxtabular version="3" rows="5" columns="2">
33006 <column alignment="center" valignment="top" width="0">
33007 <column alignment="center" valignment="top" width="0">
33009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33012 \begin_layout Plain Layout
33018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33021 \begin_layout Plain Layout
33023 \begin_inset Note Note
33026 \begin_layout Plain Layout
33039 are used here as spacer.
33051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33054 \begin_layout Plain Layout
33063 \begin_layout Plain Layout
33077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33080 \begin_layout Plain Layout
33081 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33094 \begin_layout Plain Layout
33103 \begin_layout Plain Layout
33117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33120 \begin_layout Plain Layout
33121 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33134 \begin_layout Plain Layout
33143 \begin_layout Plain Layout
33157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33160 \begin_layout Plain Layout
33161 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33174 \begin_layout Plain Layout
33178 \begin_inset Formula $\to$
33189 \begin_layout Plain Layout
33203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33206 \begin_layout Plain Layout
33207 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33223 \begin_layout Standard
33230 is especially suitable to visualize the reduction of fractions within formulas:
33231 \begin_inset Formula \[
33232 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33239 \begin_layout Subsection
33240 Formulas in Section Headings
33241 \begin_inset CommandInset label
33243 name "sub:Formulas-in-Section"
33251 \begin_layout Plain Layout
33252 Formula ! in section headings
33260 \begin_layout Standard
33261 When formulas are used in section headings, the following has to be taken
33265 \begin_layout Standard
33266 \begin_inset Note Greyedout
33269 \begin_layout Plain Layout
33278 \begin_layout Plain Layout
33279 Packages ! hyperref
33284 support is enabled in the document settings dialog under
33287 \begin_inset space ~
33292 , PDF-bookmarks are created for every section heading in the table of contents.
33293 If a section heading contains formulas, they are incorrectly displayed
33294 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33303 \begin_layout Standard
33304 Both problems can be solved by inserting at the end of the section heading
33305 a short title with the menu
33307 Insert\SpecialChar \menuseparator
33309 \begin_inset space ~
33315 Short titles are used as alternative for multiline section headings to
33316 keep the table of contents clearly arranged.
33317 Only the short title appears in the table of contents and therefore also
33318 in the PDF-bookmark.
33321 \begin_layout Standard
33322 When formulas should be used in the table of contents but
33326 is used, one can use the following command in TeX-mode:
33329 \begin_layout Standard
33334 texorpdfstring{part}{alternative}
33338 \begin_layout Plain Layout
33349 \begin_layout Standard
33350 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33351 This can be characters, formulas, footnotes, but also cross-references.
33352 The alternative is used instead of the part for the bookmark.
33355 \begin_layout Standard
33356 Here are two example headings:
33357 \begin_inset VSpace -3mm
33364 \begin_layout Plain Layout
33376 \begin_layout Subsubsection
33377 Heading without formula in table of contents
33378 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33382 \begin_inset OptArg
33385 \begin_layout Plain Layout
33386 Heading without formula in table of contents
33394 \begin_layout Subsubsection
33395 Heading with formula in table of contents
33399 \begin_layout Plain Layout
33409 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33416 \begin_layout Plain Layout
33426 \begin_layout Standard
33430 \begin_layout Plain Layout
33439 In the first heading a short title was used, in the second one
33448 \begin_layout Standard
33449 To get the same formatting as for the other headings, the complete heading
33458 \begin_layout Plain Layout
33460 \begin_inset CommandInset ref
33462 reference "sub:Bold-Formulas"
33474 \begin_layout Subsection
33475 Formulas in multi-column Text
33479 \begin_layout Plain Layout
33480 Formula ! in multi-column text
33488 \begin_layout Standard
33489 Formulas in multi-column text are often too wide to fit into a column and
33490 thus need to be set over the whole page width.
33491 This is done by using the LaTeX-package
33499 \begin_layout Plain Layout
33504 is part of every LaTeX standard installation.
33513 \begin_layout Plain Layout
33514 Packages ! multicol
33519 , that is loaded with the LaTeX-preamble line
33522 \begin_layout Standard
33527 usepackage{multicol}
33530 \begin_layout Standard
33531 \begin_inset Note Greyedout
33534 \begin_layout Plain Layout
33535 Note herby that the setting
33538 \begin_inset space ~
33545 Document\SpecialChar \menuseparator
33551 \begin_inset space ~
33571 \begin_layout Standard
33572 Before the multi-column text the command
33575 \begin_layout Standard
33580 begin{multicols}{column number}
33583 \begin_layout Standard
33584 is written in TeX-mode.
33585 The column number is a number in the range of 2
33586 \begin_inset space \thinspace{}
33590 \begin_inset space \thinspace{}
33594 Before the formula the multi-column text is ended by inserting the command
33597 \begin_layout Standard
33605 \begin_layout Standard
33609 \begin_layout Standard
33610 Due to the command some space is automatically added before the formula.
33612 \begin_inset space \thinspace{}
33615 mm vertical space is inserted before the formula.
33616 When the formula style
33622 \begin_layout Plain Layout
33624 \begin_inset CommandInset ref
33626 reference "sec:Formula-Styles"
33638 \begin_inset space \thinspace{}
33641 mm space is inserted instead.
33644 \begin_layout Standard
33645 As example a multi-column text with a displayed formula:
33648 \begin_layout Standard
33652 \begin_layout Plain Layout
33656 begin{multicols}{2}
33661 Das Spektrum wird fouriertransformiert.
33662 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33663 , Lösungsmittel) zu trennen.
33664 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33665 nun das Aussehen des Ausgangssignals.
33666 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33667 über alle Phasen integrieren muss.
33669 \begin_inset Formula $S$
33672 unser normiertes Ausgangssignal and
33673 \begin_inset Formula $P$
33676 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33680 \begin_layout Plain Layout
33690 \begin_inset VSpace -6mm
33694 \begin_inset Formula \begin{equation}
33695 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33703 \begin_layout Plain Layout
33707 begin{multicols}{2}
33713 \begin_inset Formula $S_{0}$
33716 das Signal ohne Gradient ist and the Normierungsbedingung
33717 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33721 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33723 \begin_inset Formula $\nicefrac{\pi}{2}$
33727 \begin_inset space \thinspace{}
33730 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33731 das Signal zusätzlich abschwächt.
33732 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33734 \begin_inset Formula $T_{2}$
33740 \begin_layout Standard
33744 \begin_layout Plain Layout
33756 \begin_layout Subsection
33757 Formulas with Description of Variables
33761 \begin_layout Plain Layout
33762 Formula ! with description of variables
33770 \begin_layout Standard
33771 To describe variables within a formula, like in formula
33772 \begin_inset CommandInset ref
33774 reference "eq:within"
33783 \begin_inset Formula $n$
33787 \begin_inset space ~
33790 matrix is used with left aligned columns for the
33791 \begin_inset Formula $n$
33798 \begin_layout Plain Layout
33800 \begin_inset CommandInset ref
33802 reference "sec:Matrices"
33811 To set the description in a smaller size, before the matrix e.
33812 \begin_inset space \thinspace{}
33816 \begin_inset space ~
33829 \begin_layout Plain Layout
33831 \begin_inset CommandInset ref
33833 reference "sub:Font-Sizes"
33845 \begin_layout Standard
33846 When the formula style
33852 \begin_layout Plain Layout
33854 \begin_inset CommandInset ref
33856 reference "sec:Formula-Styles"
33877 \begin_layout Plain Layout
33884 only works in formulas with the style
33889 \begin_inset CommandInset ref
33891 reference "sub:Variable-Space"
33900 is inserted before and after the matrix to have the same separation of
33901 the matrix from the equation and the side margin.
33904 \begin_layout Standard
33905 When the formula style
33909 is used, the method described in
33910 \begin_inset CommandInset ref
33912 reference "sub:Flalign-Environment"
33916 is used to indent formulas.
33918 \begin_inset CommandInset ref
33920 reference "eq:within"
33924 consists of five columns whereas in the first two columns contain the equation,
33925 the third the matrix, and the last one an empty TeX-brace.
33926 \begin_inset Formula \begin{flalign}
33927 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33928 \rho & \textrm{density}\\
33929 V & \textrm{volume}\\
33930 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33937 \begin_layout Subsection
33938 Upright small Greek Letters
33939 \begin_inset CommandInset label
33941 name "sub:Upright-small-Greek"
33949 \begin_layout Plain Layout
33950 Greek letters ! upright
33958 \begin_layout Standard
33959 Most of the math fonts only provide italic small Greek letters.
33960 But for symbols of elementary particles like pions and neutrinos, upright
33961 Greek letters are needed.
33970 \begin_layout Plain Layout
33975 is part of the LaTeX-package
33983 \begin_layout Plain Layout
33988 \begin_layout Plain Layout
34011 \begin_layout Plain Layout
34017 that is loaded with the LaTeX-preamble line
34020 \begin_layout Standard
34025 usepackage{upgreek}
34028 \begin_layout Standard
34034 \begin_layout Plain Layout
34044 \begin_inset Note Note
34047 \begin_layout Plain Layout
34048 The following table will only be displayed when the LaTeX-package
34057 They are created when the command for a small Greek letters is started
34063 For example the command
34070 \begin_inset Formula $\uptau$
34076 \begin_layout Standard
34077 With these commands reactions of elementary particles can be typeset:
34078 \begin_inset Formula \[
34079 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34086 \begin_layout Standard
34087 The upright letters are more bold and wider than the italic ones.
34088 They should therefore not be used for units like
34089 \begin_inset Quotes eld
34093 \begin_inset Quotes erd
34099 \begin_layout Standard
34103 \begin_layout Plain Layout
34113 \begin_inset Note Note
34116 \begin_layout Plain Layout
34117 The following will be displayed when the LaTeX-package
34129 \begin_layout Standard
34130 You need to install the LaTeX-package
34134 to see the rest of this subsection in the output.
34137 \begin_layout Standard
34141 \begin_layout Plain Layout
34153 \begin_layout Subsection
34154 Text Characters in Formulas
34155 \begin_inset CommandInset label
34157 name "sub:Text-Characters-in"
34165 \begin_layout Plain Layout
34174 \begin_layout Standard
34175 In some cases you might want to insert text characters directly into formulas.
34176 When for example the centered dot · is often used in formulas like
34177 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34180 , one would have to insert the command
34190 \begin_layout Plain Layout
34192 \begin_inset CommandInset ref
34194 reference "sub:Binary-Operators"
34203 all the time, because this character is defined in all encodings as text
34205 But the encoding can be changed by this LaTeX-preamble line:
34208 \begin_layout Standard
34213 Declare Inputtext{183}{
34223 f\SpecialChar \textcompwordmark{}
34227 \begin_layout Standard
34228 The character encoding (menu
34230 Document\SpecialChar \menuseparator
34231 Settings\SpecialChar \menuseparator
34234 ) specifies what character appears when a keyboard key is pressed.
34235 When the key for the character '·' is pressed, internally the command
34242 But this command is not available in a formula so that you would get LaTeX-erro
34244 With the changed encoding the right command is chosen automatically, depending
34245 on if the character was inserted into a formula or not.
34248 \begin_layout Standard
34249 The encoding of several characters is saved in definition files.
34250 Fore example the encoding
34254 is defined in the file
34258 that is in the installation folder of LaTeX.
34259 Encodings should only be changed via the LaTeX-preamble and not in the
34261 Otherwise own documents could not be edited by other LyX users working
34262 on other computers.
34265 \begin_layout Standard
34266 \begin_inset VSpace medskip
34269 Besides the centered dot, in this document the degree sign ° is defined
34270 with the following LaTeX-preamble line so that it can directly be inserted
34274 \begin_layout Standard
34279 DeclareInputtext{176}{
34289 f\SpecialChar \textcompwordmark{}
34293 \begin_layout Standard
34294 \begin_inset Newpage newpage
34300 \begin_layout Section
34306 \begin_layout Plain Layout
34315 \begin_layout Standard
34316 This section is a summary of the most important typographic rules, listed
34321 \begin_layout Plain Layout
34322 This collection was partly taken from the German semi-official dictionary
34324 \begin_inset Quotes eld
34328 \begin_inset Quotes erd
34332 \begin_inset CommandInset citation
34338 that lists some of the ISO rules.
34346 \begin_layout Itemize
34355 \begin_layout Plain Layout
34356 done with font styles, see
34357 \begin_inset CommandInset ref
34359 reference "sub:Font-Styles"
34369 \begin_inset space \thinspace{}
34373 \begin_inset Newline newline
34376 Between the value and the unit is the smallest space, see
34377 \begin_inset CommandInset ref
34379 reference "sub:Predefined-Space"
34384 \begin_inset Newline newline
34387 This convention is automatically fulfilled when the command
34394 When it is entered to a formula, two boxes appear.
34395 In the first one the value is inserted, in the second one the unit, and
34397 \begin_inset Formula $\unit[30]{km/h}$
34401 \begin_inset space \thinspace{}
34411 is not a real LaTeX command but the command
34417 , therefore you cannot use it in TeX code.
34420 \begin_layout Itemize
34421 Percent and perthousand signs are set like physical units:
34422 \begin_inset Newline newline
34426 \begin_inset space \thinspace{}
34432 \begin_layout Itemize
34433 The degree sign follows directly on the value: 15°, but not when it is used
34435 \begin_inset space \thinspace{}
34441 \begin_layout Itemize
34442 In numbers with more than four digits the smallest space is inserted before
34443 every third digit to group them:
34453 \begin_inset space \thinspace{}
34457 \begin_inset space \thinspace{}
34463 \begin_layout Itemize
34464 For dimensions like 120×90×40
34465 \begin_inset space \thinspace{}
34468 cm the multiplication sign
34469 \begin_inset Quotes eld
34473 \begin_inset Quotes erd
34477 It is available with the LaTeX-command
34483 , but can also directly be inserted with some keyboard definitions.
34486 \begin_layout Itemize
34487 Functions with names consisting of several letters are set upright to avoid
34489 \begin_inset CommandInset ref
34491 reference "sub:Predefined-Functions"
34498 \begin_layout Itemize
34499 Indices consisting of several letters, are set upright:
34500 \begin_inset Formula $E_{\mathrm{kin}}$
34504 \begin_inset Newline newline
34507 Components of matrices are set italic:
34508 \begin_inset Formula $\hat{H}_{kl}$
34514 \begin_layout Itemize
34515 The differentiation/integration operator 'd', the Euler's number 'e', and
34516 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34520 \begin_layout Standard
34521 \begin_inset Newpage newpage
34527 \begin_layout Section
34532 \begin_layout Plain Layout
34541 \begin_layout Standard
34542 Some characters and symbols can be created with several commands.
34543 Here is a list of the synonym commands:
34546 \begin_layout Standard
34547 \begin_inset VSpace bigskip
34551 \begin_inset space \hfill{}
34555 \begin_inset Tabular
34556 <lyxtabular version="3" rows="12" columns="2">
34558 <column alignment="center" valignment="top" width="0pt">
34559 <column alignment="center" valignment="top" width="0pt">
34561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34564 \begin_layout Plain Layout
34570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34573 \begin_layout Plain Layout
34575 \begin_inset Note Note
34578 \begin_layout Plain Layout
34585 is only used as spacer.
34597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34600 \begin_layout Plain Layout
34608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34611 \begin_layout Plain Layout
34615 \begin_layout Plain Layout
34628 \begin_layout Plain Layout
34642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34645 \begin_layout Plain Layout
34653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34656 \begin_layout Plain Layout
34666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34669 \begin_layout Plain Layout
34677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34680 \begin_layout Plain Layout
34690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34693 \begin_layout Plain Layout
34701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34704 \begin_layout Plain Layout
34712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34715 \begin_layout Plain Layout
34723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34726 \begin_layout Plain Layout
34734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34737 \begin_layout Plain Layout
34745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34748 \begin_layout Plain Layout
34758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34761 \begin_layout Plain Layout
34769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34772 \begin_layout Plain Layout
34782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34785 \begin_layout Plain Layout
34793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34796 \begin_layout Plain Layout
34806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34809 \begin_layout Plain Layout
34817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34820 \begin_layout Plain Layout
34830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34833 \begin_layout Plain Layout
34841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34844 \begin_layout Plain Layout
34852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34855 \begin_layout Plain Layout
34863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34866 \begin_layout Plain Layout
34878 \begin_inset space \hfill{}
34882 \begin_inset Tabular
34883 <lyxtabular version="3" rows="12" columns="2">
34885 <column alignment="center" valignment="top" width="0pt">
34886 <column alignment="center" valignment="top" width="0pt">
34888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34891 \begin_layout Plain Layout
34897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34900 \begin_layout Plain Layout
34908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34911 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34922 \begin_layout Plain Layout
34934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34937 \begin_layout Plain Layout
34945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34948 \begin_layout Plain Layout
34958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34961 \begin_layout Plain Layout
34969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34972 \begin_layout Plain Layout
34982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34985 \begin_layout Plain Layout
34993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34996 \begin_layout Plain Layout
35004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35007 \begin_layout Plain Layout
35015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35018 \begin_layout Plain Layout
35026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35029 \begin_layout Plain Layout
35037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35040 \begin_layout Plain Layout
35050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35053 \begin_layout Plain Layout
35061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35064 \begin_layout Plain Layout
35074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35077 \begin_layout Plain Layout
35085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35088 \begin_layout Plain Layout
35098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35101 \begin_layout Plain Layout
35109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35112 \begin_layout Plain Layout
35122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35125 \begin_layout Plain Layout
35133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35136 \begin_layout Plain Layout
35146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35149 \begin_layout Plain Layout
35157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35160 \begin_layout Plain Layout
35174 \begin_inset space \hfill{}
35180 \begin_layout Standard
35181 \begin_inset Newpage newpage
35187 \begin_layout Bibliography
35188 \begin_inset CommandInset bibitem
35189 LatexCommand bibitem
35201 The LaTeX Companion
35204 Addison Wesley, 2004
35207 \begin_layout Bibliography
35208 \begin_inset CommandInset bibitem
35209 LatexCommand bibitem
35215 \begin_inset CommandInset href
35218 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35222 of LaTeX's math abilities
35225 \begin_layout Bibliography
35226 \begin_inset CommandInset bibitem
35227 LatexCommand bibitem
35232 LaTeX tips and tricks-
35233 \begin_inset CommandInset href
35236 target "http://tug.org/TeXnik/"
35243 \begin_layout Bibliography
35244 \begin_inset CommandInset bibitem
35245 LatexCommand bibitem
35251 \begin_inset CommandInset href
35254 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35262 \begin_layout Plain Layout
35274 \begin_layout Bibliography
35275 \begin_inset CommandInset bibitem
35276 LatexCommand bibitem
35282 \begin_inset CommandInset href
35285 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35289 of all symbols available with LaTeX-packages
35292 \begin_layout Bibliography
35293 \begin_inset CommandInset bibitem
35294 LatexCommand bibitem
35300 \begin_inset CommandInset href
35302 name "Documentation"
35303 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35307 of the LaTeX-package
35315 \begin_layout Plain Layout
35316 Packages ! hyperref
35324 \begin_layout Bibliography
35325 \begin_inset CommandInset bibitem
35326 LatexCommand bibitem
35332 \begin_inset CommandInset href
35335 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35346 \begin_inset CommandInset ref
35348 reference "sub:Operator-Limits"
35356 \begin_layout Plain Layout
35367 \begin_layout Bibliography
35368 \begin_inset CommandInset bibitem
35369 LatexCommand bibitem
35380 Auflage, Duden 2001
35383 \begin_layout Subsubsection*
35384 \begin_inset CommandInset index_print
35385 LatexCommand printindex