1 #LyX 1.6.0svn 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
177 \pdf_pdfusetitle false
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
22127 \begin_layout Plain Layout
22144 \begin_layout Standard
22145 To use the Euro symbol in formulas, the LaTeX-package
22153 \begin_layout Plain Layout
22159 must be installed and loaded with the LaTeX-preamble line
22162 \begin_layout Standard
22167 usepackage[gennarrow]{eurosym}
22170 \begin_layout Standard
22171 The Euro symbol can now be inserted with the command
22181 \begin_layout Plain Layout
22192 \begin_layout Standard
22193 The Euro symbol can directly be inserted with the € key in mathematical
22194 text, without having
22209 can also be inserted in TeX-mode.
22210 The official currency symbol can then be inserted with the command
22220 \begin_layout Plain Layout
22228 , that is only available in TeX-mode.
22231 \begin_layout Standard
22235 \begin_layout Plain Layout
22245 \begin_inset Note Note
22248 \begin_layout Plain Layout
22249 The following table will only be displayed when the LaTeX-package
22261 \begin_layout Standard
22262 An overview about the different Euro symbols:
22265 \begin_layout Standard
22267 \begin_inset Tabular
22268 <lyxtabular version="3" rows="4" columns="3">
22270 <column alignment="center" valignment="top" width="0pt">
22271 <column alignment="center" valignment="top" width="0pt">
22272 <column alignment="center" valignment="top" width="0pt">
22274 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22277 \begin_layout Plain Layout
22283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22295 \begin_layout Plain Layout
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22306 \begin_layout Plain Layout
22312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22315 \begin_layout Plain Layout
22323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22326 \begin_layout Plain Layout
22327 \begin_inset Formula $\euro$
22337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22340 \begin_layout Plain Layout
22346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22349 \begin_layout Plain Layout
22355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22358 \begin_layout Plain Layout
22359 \begin_inset Formula $\mbox{€}$
22369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22372 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22381 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22396 \begin_layout Plain Layout
22418 \begin_layout Standard
22422 \begin_layout Plain Layout
22432 \begin_inset Note Note
22435 \begin_layout Plain Layout
22436 The following will be displayed when the LaTeX-package
22448 \begin_layout Standard
22449 You need to install the LaTeX-package
22453 to see the rest of this subsection in the output.
22456 \begin_layout Standard
22460 \begin_layout Plain Layout
22472 \begin_layout Section
22474 \begin_inset CommandInset label
22476 name "sec:Relations"
22484 \begin_layout Plain Layout
22494 \begin_layout Plain Layout
22499 \begin_layout Plain Layout
22510 \begin_layout Plain Layout
22525 \begin_layout Standard
22526 All relations can also be inserted via the toolbar button
22527 \begin_inset Graphics
22528 filename ../images/math/leq.png
22536 \begin_layout Standard
22537 \begin_inset space \hfill{}
22541 \begin_inset Tabular
22542 <lyxtabular version="3" rows="17" columns="2">
22544 <column alignment="center" valignment="top" width="0pt">
22545 <column alignment="center" valignment="top" width="0pt">
22547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22550 \begin_layout Plain Layout
22556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22559 \begin_layout Plain Layout
22567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22570 \begin_layout Plain Layout
22576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22579 \begin_layout Plain Layout
22580 \begin_inset Formula $<$
22590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22593 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22604 \begin_layout Plain Layout
22605 \begin_inset Formula $\le$
22615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22618 \begin_layout Plain Layout
22626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22629 \begin_layout Plain Layout
22630 \begin_inset Formula $\ll$
22640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22643 \begin_layout Plain Layout
22651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22654 \begin_layout Plain Layout
22655 \begin_inset Formula $\prec$
22665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22668 \begin_layout Plain Layout
22676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22679 \begin_layout Plain Layout
22680 \begin_inset Formula $\preceq$
22690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22693 \begin_layout Plain Layout
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Plain Layout
22705 \begin_inset Formula $\subset$
22715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22718 \begin_layout Plain Layout
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22729 \begin_layout Plain Layout
22730 \begin_inset Formula $\subseteq$
22740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22743 \begin_layout Plain Layout
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22754 \begin_layout Plain Layout
22755 \begin_inset Formula $\sqsubseteq$
22765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22768 \begin_layout Plain Layout
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22779 \begin_layout Plain Layout
22780 \begin_inset Formula $\in$
22790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22793 \begin_layout Plain Layout
22801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22804 \begin_layout Plain Layout
22805 \begin_inset Formula $\vdash$
22815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22818 \begin_layout Plain Layout
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22829 \begin_layout Plain Layout
22830 \begin_inset Formula $\smile$
22840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22843 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22854 \begin_layout Plain Layout
22855 \begin_inset Formula $\lhd$
22865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22868 \begin_layout Plain Layout
22876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22879 \begin_layout Plain Layout
22880 \begin_inset Formula $\unlhd$
22890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22893 \begin_layout Plain Layout
22901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22904 \begin_layout Plain Layout
22905 \begin_inset Formula $\gtrless$
22915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22918 \begin_layout Plain Layout
22926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22929 \begin_layout Plain Layout
22930 \begin_inset Formula $\mid$
22940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22943 \begin_layout Plain Layout
22951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22954 \begin_layout Plain Layout
22955 \begin_inset Formula $\nmid$
22969 \begin_inset space \hfill{}
22973 \begin_inset Tabular
22974 <lyxtabular version="3" rows="17" columns="2">
22976 <column alignment="center" valignment="top" width="0pt">
22977 <column alignment="center" valignment="top" width="0pt">
22979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22982 \begin_layout Plain Layout
22988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22991 \begin_layout Plain Layout
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23002 \begin_layout Plain Layout
23008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23011 \begin_layout Plain Layout
23012 \begin_inset Formula $=$
23022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23025 \begin_layout Plain Layout
23033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23036 \begin_layout Plain Layout
23037 \begin_inset Formula $\not=$
23047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23050 \begin_layout Plain Layout
23058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23061 \begin_layout Plain Layout
23062 \begin_inset Formula $\equiv$
23072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23075 \begin_layout Plain Layout
23083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23086 \begin_layout Plain Layout
23087 \begin_inset Formula $\sim$
23097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23100 \begin_layout Plain Layout
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23111 \begin_layout Plain Layout
23112 \begin_inset Formula $\simeq$
23122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23125 \begin_layout Plain Layout
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23136 \begin_layout Plain Layout
23137 \begin_inset Formula $\approx$
23147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23150 \begin_layout Plain Layout
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23161 \begin_layout Plain Layout
23162 \begin_inset Formula $\cong$
23172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23175 \begin_layout Plain Layout
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23186 \begin_layout Plain Layout
23187 \begin_inset Formula $\bowtie$
23197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23200 \begin_layout Plain Layout
23208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23211 \begin_layout Plain Layout
23212 \begin_inset Formula $\notin$
23222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23225 \begin_layout Plain Layout
23233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23236 \begin_layout Plain Layout
23237 \begin_inset Formula $\perp$
23247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23250 \begin_layout Plain Layout
23258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23261 \begin_layout Plain Layout
23262 \begin_inset Formula $\propto$
23272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23275 \begin_layout Plain Layout
23283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23286 \begin_layout Plain Layout
23287 \begin_inset Formula $\asymp$
23297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23300 \begin_layout Plain Layout
23308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23311 \begin_layout Plain Layout
23312 \begin_inset Formula $\doteq$
23322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23325 \begin_layout Plain Layout
23333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23336 \begin_layout Plain Layout
23337 \begin_inset Formula $\circeq$
23347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23350 \begin_layout Plain Layout
23358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23361 \begin_layout Plain Layout
23362 \begin_inset Formula $\models$
23372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23375 \begin_layout Plain Layout
23383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23386 \begin_layout Plain Layout
23387 \begin_inset Formula $\widehat{=}$
23401 \begin_inset space \hfill{}
23405 \begin_inset Tabular
23406 <lyxtabular version="3" rows="17" columns="2">
23408 <column alignment="center" valignment="top" width="0pt">
23409 <column alignment="center" valignment="top" width="0pt">
23411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23414 \begin_layout Plain Layout
23420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23423 \begin_layout Plain Layout
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23443 \begin_layout Plain Layout
23444 \begin_inset Formula $>$
23454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23457 \begin_layout Plain Layout
23465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23468 \begin_layout Plain Layout
23469 \begin_inset Formula $\ge$
23479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23482 \begin_layout Plain Layout
23490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23493 \begin_layout Plain Layout
23494 \begin_inset Formula $\gg$
23504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23507 \begin_layout Plain Layout
23515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23518 \begin_layout Plain Layout
23519 \begin_inset Formula $\succ$
23529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23532 \begin_layout Plain Layout
23540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23543 \begin_layout Plain Layout
23544 \begin_inset Formula $\succeq$
23554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23557 \begin_layout Plain Layout
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23568 \begin_layout Plain Layout
23569 \begin_inset Formula $\supset$
23579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23582 \begin_layout Plain Layout
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23593 \begin_layout Plain Layout
23594 \begin_inset Formula $\supseteq$
23604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23607 \begin_layout Plain Layout
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23618 \begin_layout Plain Layout
23619 \begin_inset Formula $\sqsupseteq$
23629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23632 \begin_layout Plain Layout
23640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23643 \begin_layout Plain Layout
23644 \begin_inset Formula $\ni$
23654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23657 \begin_layout Plain Layout
23665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23668 \begin_layout Plain Layout
23669 \begin_inset Formula $\dashv$
23679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23682 \begin_layout Plain Layout
23690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23693 \begin_layout Plain Layout
23694 \begin_inset Formula $\frown$
23704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23707 \begin_layout Plain Layout
23715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23718 \begin_layout Plain Layout
23719 \begin_inset Formula $\rhd$
23729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23732 \begin_layout Plain Layout
23740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23743 \begin_layout Plain Layout
23744 \begin_inset Formula $\unrhd$
23754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23757 \begin_layout Plain Layout
23765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23768 \begin_layout Plain Layout
23769 \begin_inset Formula $\lessgtr$
23779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23782 \begin_layout Plain Layout
23790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23793 \begin_layout Plain Layout
23794 \begin_inset Formula $\parallel$
23804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23807 \begin_layout Plain Layout
23815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23818 \begin_layout Plain Layout
23819 \begin_inset Formula $\nparallel$
23833 \begin_inset space \hfill{}
23839 \begin_layout Standard
23840 \begin_inset VSpace medskip
23855 are bigger than the equal looking operators
23870 \begin_layout Standard
23871 Relations are, in contrary to symbols, always surrounded by space.
23874 \begin_layout Standard
23875 Relations with labels can be created with the command
23885 \begin_layout Plain Layout
23896 \begin_layout Standard
23898 \begin_inset Tabular
23899 <lyxtabular version="3" rows="2" columns="2">
23901 <column alignment="center" valignment="top" width="0">
23902 <column alignment="center" valignment="top" width="0">
23904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23907 \begin_layout Plain Layout
23913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23916 \begin_layout Plain Layout
23918 \begin_inset Note Note
23921 \begin_layout Plain Layout
23928 is only used as spacer.
23940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23950 \begin_layout Plain Layout
23967 \begin_layout Plain Layout
23977 \begin_inset Formula $\downarrow$
23986 \begin_layout Plain Layout
23999 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24017 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24033 \begin_layout Section
24037 \begin_layout Subsection
24038 Predefined Functions
24039 \begin_inset CommandInset label
24041 name "sub:Predefined-Functions"
24049 \begin_layout Plain Layout
24050 Functions ! predefined
24058 \begin_layout Standard
24059 In general, variables are set
24063 in mathematical expressions, but not function names, because
24064 \begin_inset Formula $sin$
24067 could be misunderstood as
24068 \begin_inset Formula $s\cdot i\cdot n$
24072 Therefore there are predefined functions, that are additionally a bit separated
24074 They are inserted as commands starting with a backslash before their name.
24077 \begin_layout Standard
24079 \begin_inset Tabular
24080 <lyxtabular version="3" rows="2" columns="4">
24082 <column alignment="center" valignment="top" width="0pt">
24083 <column alignment="center" valignment="top" width="0pt">
24084 <column alignment="center" valignment="top" width="0pt">
24085 <column alignment="center" valignment="top" width="0pt">
24087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24090 \begin_layout Plain Layout
24096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24099 \begin_layout Plain Layout
24105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24108 \begin_layout Plain Layout
24114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24128 \begin_layout Plain Layout
24134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24137 \begin_layout Plain Layout
24138 \begin_inset Formula $Asin(x)+B$
24146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24149 \begin_layout Plain Layout
24157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24160 \begin_layout Plain Layout
24161 \begin_inset Formula $A\sin(x)+B$
24175 \begin_inset Newpage pagebreak
24181 \begin_layout Standard
24182 The following functions are predefined:
24185 \begin_layout Standard
24186 \begin_inset VSpace -2mm
24192 \begin_layout Standard
24194 \begin_inset Tabular
24195 <lyxtabular version="3" rows="9" columns="4">
24197 <column alignment="center" valignment="top" width="0pt">
24198 <column alignment="center" valignment="top" width="0pt">
24199 <column alignment="center" valignment="top" width="0pt">
24200 <column alignment="center" valignment="top" width="0pt">
24202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24205 \begin_layout Plain Layout
24211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24214 \begin_layout Plain Layout
24220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24223 \begin_layout Plain Layout
24229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24232 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24243 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24276 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24289 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24335 \begin_layout Plain Layout
24343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24346 \begin_layout Plain Layout
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24392 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24414 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24438 \begin_layout Plain Layout
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24473 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24519 \begin_layout Plain Layout
24527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24530 \begin_layout Plain Layout
24538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24541 \begin_layout Plain Layout
24549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24552 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24565 \begin_layout Plain Layout
24573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24576 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24587 \begin_layout Plain Layout
24595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24598 \begin_layout Plain Layout
24614 \begin_layout Standard
24615 They can also be inserted with the math toolbar button
24616 \begin_inset Graphics
24617 filename ../images/math/functions.png
24625 \begin_layout Subsection
24626 Self-defined Functions
24630 \begin_layout Plain Layout
24631 Functions ! self-defined
24639 \begin_layout Standard
24640 To use a function that is not predefined, like for example the sign function
24641 sgn(x), there are two possibilities:
24644 \begin_layout Itemize
24645 Define the function by inserting the following line to the LaTeX-preamble
24649 \begin_layout Plain Layout
24654 DeclareMathOperator
24657 \begin_inset CommandInset ref
24659 reference "sub:Self-defined-Operators"
24669 \begin_inset Newline newline
24673 \begin_inset VSpace -3mm
24677 \begin_inset Newline newline
24684 DeclareMathOperator{
24692 \begin_layout Plain Layout
24697 DeclareMathOperator
24703 \begin_inset Newline newline
24707 \begin_inset VSpace -2mm
24711 \begin_inset Newline newline
24714 Now the new defined function can be called with the command
24723 \begin_layout Itemize
24724 Write the the formula as usual, mark the formula name, in our example the
24729 , and change it to mathematical text.
24730 At last a space is inserted between prefactor and function.
24733 \begin_layout Standard
24734 The result is the same with both methods as with a predefined function
24738 \begin_layout Plain Layout
24739 In LyX self-defined functions are displayed red, predefined ones black.
24747 \begin_layout Standard
24749 \begin_inset Tabular
24750 <lyxtabular version="3" rows="3" columns="2">
24752 <column alignment="center" valignment="top" width="0pt">
24753 <column alignment="center" valignment="top" width="0pt">
24755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24778 \begin_layout Plain Layout
24786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24789 \begin_layout Plain Layout
24790 \begin_inset Formula $A\sgn(x)+B$
24800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24803 \begin_layout Plain Layout
24807 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24818 \begin_layout Plain Layout
24819 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24835 \begin_layout Standard
24836 The first method is more suitable when the self-defined function should
24837 be used several times.
24840 \begin_layout Subsection
24845 \begin_layout Plain Layout
24854 \begin_layout Standard
24855 For limits there are defined besides
24865 \begin_layout Plain Layout
24885 furthermore the following functions:
24888 \begin_layout Standard
24890 \begin_inset Tabular
24891 <lyxtabular version="3" rows="5" columns="2">
24893 <column alignment="center" valignment="top" width="0">
24894 <column alignment="center" valignment="top" width="0">
24896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24899 \begin_layout Plain Layout
24905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24908 \begin_layout Plain Layout
24910 \begin_inset Note Note
24913 \begin_layout Plain Layout
24920 is only used as spacer.
24932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24935 \begin_layout Plain Layout
24943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24946 \begin_layout Plain Layout
24947 \begin_inset Formula $\varliminf$
24957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24960 \begin_layout Plain Layout
24968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24971 \begin_layout Plain Layout
24972 \begin_inset Formula $\varlimsup$
24982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24985 \begin_layout Plain Layout
24993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24996 \begin_layout Plain Layout
24997 \begin_inset Formula $\varprojlim$
25007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25010 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25021 \begin_layout Plain Layout
25022 \begin_inset Formula $\varinjlim$
25026 \begin_inset Formula $\raisebox{-2.5mm}{}$
25042 \begin_layout Standard
25043 \begin_inset VSpace medskip
25046 The limit is created by inserting a subscript.
25047 It is set right beside the function in an inline formula:
25050 \begin_layout Standard
25052 \begin_inset Tabular
25053 <lyxtabular version="3" rows="2" columns="2">
25055 <column alignment="center" valignment="top" width="0pt">
25056 <column alignment="center" valignment="top" width="0pt">
25058 <cell alignment="center" valignment="top" usebox="none">
25061 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" usebox="none">
25070 \begin_layout Plain Layout
25071 \begin_inset space \hspace{}
25076 \begin_inset Note Note
25079 \begin_layout Plain Layout
25092 are used here as spacer.
25104 <cell alignment="center" valignment="top" usebox="none">
25107 \begin_layout Plain Layout
25116 \begin_layout Plain Layout
25129 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" usebox="none">
25146 \begin_layout Plain Layout
25147 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25163 \begin_layout Standard
25164 In a displayed formula the limit is set below the formula, as usual:
25165 \begin_inset Formula \[
25173 \begin_layout Subsection
25178 \begin_layout Plain Layout
25179 Functions ! modulo-
25187 \begin_layout Standard
25188 The modulo-function is special, because it exists in four variants.
25191 \begin_layout Standard
25192 The variants in a displayed formula:
25193 \begin_inset Formula \begin{align*}
25194 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25195 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25196 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25197 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25198 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25205 \begin_layout Standard
25206 In an inline formula less space is set before the function names for all
25210 \begin_layout Section
25215 \begin_layout Plain Layout
25224 \begin_layout Subsection
25225 Special Characters in Mathematical Text
25228 \begin_layout Standard
25229 The following commands can only be used in mathematical text or in TeX-mode:
25232 \begin_layout Standard
25233 \begin_inset space \hfill{}
25237 \begin_inset Tabular
25238 <lyxtabular version="3" rows="8" columns="2">
25240 <column alignment="block" valignment="top" width="0">
25241 <column alignment="block" valignment="top" width="0">
25243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25255 \begin_layout Plain Layout
25263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25266 \begin_layout Plain Layout
25274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25277 \begin_layout Plain Layout
25278 \begin_inset Formula $\textrm{œ}$
25288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25291 \begin_layout Plain Layout
25299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25302 \begin_layout Plain Layout
25303 \begin_inset Formula $\textrm{Œ}$
25313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25327 \begin_layout Plain Layout
25328 \begin_inset Formula $\textrm{æ}$
25338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25341 \begin_layout Plain Layout
25349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25352 \begin_layout Plain Layout
25353 \begin_inset Formula $\textrm{Æ}$
25363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25366 \begin_layout Plain Layout
25374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25377 \begin_layout Plain Layout
25378 \begin_inset Formula $\textrm{\aa}$
25388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25391 \begin_layout Plain Layout
25398 \begin_layout Plain Layout
25405 \begin_layout Plain Layout
25426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25429 \begin_layout Plain Layout
25430 \begin_inset Formula $\textrm{Å}$
25440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25451 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25454 \begin_layout Plain Layout
25455 \begin_inset Formula $\textrm{ı}$
25469 \begin_inset space \hfill{}
25473 \begin_inset Tabular
25474 <lyxtabular version="3" rows="8" columns="2">
25476 <column alignment="block" valignment="top" width="0">
25477 <column alignment="center" valignment="top" width="0">
25479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25482 \begin_layout Plain Layout
25484 \begin_inset Note Note
25487 \begin_layout Plain Layout
25494 is used for separation, because otherwise the output will be ¡ and ¿ respective
25505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25508 \begin_layout Plain Layout
25516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25519 \begin_layout Plain Layout
25527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25530 \begin_layout Plain Layout
25531 \begin_inset Formula $\textrm{ø}$
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25555 \begin_layout Plain Layout
25556 \begin_inset Formula $\textrm{Ø}$
25566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25569 \begin_layout Plain Layout
25577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25580 \begin_layout Plain Layout
25581 \begin_inset Formula $\textrm{ł}$
25591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25594 \begin_layout Plain Layout
25602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25605 \begin_layout Plain Layout
25606 \begin_inset Formula $\textrm{Ł}$
25616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25619 \begin_layout Plain Layout
25621 \begin_inset space \hspace{}
25629 \begin_layout Plain Layout
25643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25646 \begin_layout Plain Layout
25647 \begin_inset Formula $\textrm{!`}$
25657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25662 \begin_inset space \hspace{}
25670 \begin_layout Plain Layout
25684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25687 \begin_layout Plain Layout
25688 \begin_inset Formula $\textrm{?`}$
25698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25701 \begin_layout Plain Layout
25709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25712 \begin_layout Plain Layout
25713 \begin_inset Formula $\textrm{ȷ}$
25727 \begin_inset space \hfill{}
25733 \begin_layout Standard
25735 \begin_inset Formula $\textrm{\textrm{Å}}$
25739 \begin_inset Formula $\textrm{\textrm{Ø}}$
25742 can also be inserted via the math toolbar button
25743 \begin_inset Graphics
25744 filename ../images/math/digamma.png
25752 \begin_layout Standard
25753 An exception are the commands
25756 \begin_inset space \hspace{}
25765 \begin_inset space \hspace{}
25771 , because they can be inserted in LyX directly to text.
25774 \begin_layout Subsection
25776 \begin_inset CommandInset label
25778 name "sub:Accents-in-Text"
25786 \begin_layout Plain Layout
25795 \begin_layout Standard
25796 With the following commands all letters can be accented.
25797 The commands must be inserted in TeX-mode.
25800 \begin_layout Standard
25801 \begin_inset space \hfill{}
25805 \begin_inset Tabular
25806 <lyxtabular version="3" rows="8" columns="2">
25808 <column alignment="block" valignment="top" width="0">
25809 <column alignment="block" valignment="top" width="0">
25811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25814 \begin_layout Plain Layout
25820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25823 \begin_layout Plain Layout
25831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25834 \begin_layout Plain Layout
25838 \begin_inset Quotes grd
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25849 \begin_layout Plain Layout
25853 \begin_layout Plain Layout
25869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25872 \begin_layout Plain Layout
25880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25883 \begin_layout Plain Layout
25887 \begin_layout Plain Layout
25903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25906 \begin_layout Plain Layout
25913 \begin_layout Plain Layout
25927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25930 \begin_layout Plain Layout
25934 \begin_layout Plain Layout
25950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25953 \begin_layout Plain Layout
25961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25964 \begin_layout Plain Layout
25968 \begin_layout Plain Layout
25984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25987 \begin_layout Plain Layout
25994 \begin_layout Plain Layout
26008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26011 \begin_layout Plain Layout
26015 \begin_layout Plain Layout
26031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26034 \begin_layout Plain Layout
26041 \begin_layout Plain Layout
26055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26058 \begin_layout Plain Layout
26062 \begin_layout Plain Layout
26078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26081 \begin_layout Plain Layout
26088 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26105 \begin_layout Plain Layout
26109 \begin_layout Plain Layout
26129 \begin_inset space \hfill{}
26133 \begin_inset Tabular
26134 <lyxtabular version="3" rows="8" columns="2">
26136 <column alignment="block" valignment="top" width="0">
26137 <column alignment="center" valignment="top" width="0">
26139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26142 \begin_layout Plain Layout
26148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26151 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26162 \begin_layout Plain Layout
26169 \begin_layout Plain Layout
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26186 \begin_layout Plain Layout
26190 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26209 \begin_layout Plain Layout
26217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26220 \begin_layout Plain Layout
26224 \begin_layout Plain Layout
26240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26250 \begin_layout Plain Layout
26261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26264 \begin_layout Plain Layout
26268 \begin_layout Plain Layout
26284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26287 \begin_layout Plain Layout
26295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26298 \begin_layout Plain Layout
26302 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26321 \begin_layout Plain Layout
26328 \begin_layout Plain Layout
26342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26345 \begin_layout Plain Layout
26349 \begin_layout Plain Layout
26365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26368 \begin_layout Plain Layout
26375 \begin_layout Plain Layout
26389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26392 \begin_layout Plain Layout
26396 \begin_layout Plain Layout
26412 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26415 \begin_layout Plain Layout
26422 \begin_layout Plain Layout
26436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26439 \begin_layout Plain Layout
26443 \begin_layout Plain Layout
26463 \begin_inset space \hfill{}
26469 \begin_layout Standard
26470 \begin_inset VSpace medskip
26479 also two different characters can be accented.
26488 \begin_layout Plain Layout
26503 \begin_layout Plain Layout
26515 \begin_layout Standard
26528 can in combination with vowels directly be inserted with the keyboard without
26530 The same applies for the tilde
26534 \begin_layout Plain Layout
26535 This only applies for keyboards where the tilde is defined as accent.
26544 in combination with
26559 \begin_layout Standard
26602 , and accents inserted directly with the keyboard are also available in
26604 For the other accents there are special math commands to be used in formulas,
26606 \begin_inset CommandInset ref
26608 reference "sub:Accents-for-one"
26615 \begin_layout Standard
26616 \begin_inset VSpace bigskip
26619 Furthermore, with the command
26629 \begin_layout Plain Layout
26637 all numbers and letters can be set into a circle, quasi accented with a
26638 circle, similar to the the copyright symbol.
26641 \begin_layout Standard
26643 \begin_inset Tabular
26644 <lyxtabular version="3" rows="3" columns="2">
26646 <column alignment="center" valignment="top" width="0">
26647 <column alignment="center" valignment="top" width="0">
26649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26652 \begin_layout Plain Layout
26658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26661 \begin_layout Plain Layout
26663 \begin_inset Note Note
26666 \begin_layout Plain Layout
26673 is only used as spacer.
26685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26688 \begin_layout Plain Layout
26696 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26699 \begin_layout Plain Layout
26703 \begin_layout Plain Layout
26719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26722 \begin_layout Plain Layout
26733 raisebox{-1.5pt}{W}}
26738 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26741 \begin_layout Plain Layout
26742 \begin_inset Formula $\raisebox{4.5mm}{}$
26749 \begin_layout Plain Layout
26767 \begin_inset Formula $\raisebox{-2mm}{}$
26783 \begin_layout Standard
26784 One has to take care that the character fits in the circle.
26795 \begin_layout Plain Layout
26797 \begin_inset CommandInset ref
26799 reference "sub:Font-Sizes"
26808 specifies thereby the size of the circle.
26819 \begin_layout Plain Layout
26821 \begin_inset CommandInset ref
26823 reference "sub:Boxes-without-Frame"
26832 the character can be centered.
26835 \begin_layout Subsection
26840 \begin_layout Plain Layout
26849 \begin_layout Standard
26850 Minuscule numbers are created with the command
26860 \begin_layout Plain Layout
26869 The command can be used in formulas and in TeX-mode.
26870 The command scheme is:
26873 \begin_layout Standard
26878 oldstylenums{number}
26881 \begin_layout Standard
26886 oldstylenums{0123456789
26889 \begin_inset Formula $\oldstylenums{0123456789}$
26895 \begin_layout Subsection
26896 Miscellaneous special Characters
26897 \begin_inset CommandInset label
26899 name "sub:Miscellaneous-special-Characters"
26907 \begin_layout Plain Layout
26908 Special characters ! miscellaneous
26916 \begin_layout Standard
26917 The following characters can only be inserted to formulas by using commands:
26920 \begin_layout Standard
26922 \begin_inset Tabular
26923 <lyxtabular version="3" rows="4" columns="2">
26925 <column alignment="center" valignment="top" width="0">
26926 <column alignment="center" valignment="top" width="0">
26928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26931 \begin_layout Plain Layout
26937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26940 \begin_layout Plain Layout
26948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26951 \begin_layout Plain Layout
26958 \begin_layout Plain Layout
26972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26975 \begin_layout Plain Layout
26976 \begin_inset Formula $\mathcircumflex$
26986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26989 \begin_layout Plain Layout
26997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27000 \begin_layout Plain Layout
27001 \begin_inset Formula $\_$
27011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27014 \begin_layout Plain Layout
27019 \begin_layout Plain Layout
27034 \begin_layout Plain Layout
27045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27048 \begin_layout Plain Layout
27049 \begin_inset Formula $^{\circ}$
27065 \begin_layout Standard
27066 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27067 contains the following line
27071 \begin_layout Plain Layout
27072 More about this is described in
27073 \begin_inset CommandInset ref
27075 reference "sub:Text-Characters-in"
27087 \begin_layout Standard
27092 DeclareInputtext{176}{
27105 \begin_layout Section
27107 \begin_inset CommandInset label
27109 name "sec:Formula-Styles"
27117 \begin_layout Plain Layout
27126 \begin_layout Itemize
27127 There are two different alignment styles:
27131 \begin_layout Description
27132 Centered is the predefined standard
27135 \begin_layout Description
27136 Indented for this the option
27140 must be inserted in the menu
27142 Document\SpecialChar \menuseparator
27148 \begin_inset space ~
27154 \begin_layout Standard
27159 is used, the indentation can be adjusted with the length
27169 \begin_layout Plain Layout
27178 Should the distance be 15
27179 \begin_inset space \thinspace{}
27182 mm, the following command line is inserted in the LaTeX-preamble
27185 \begin_layout Standard
27195 \begin_layout Standard
27196 When no length is specified, the predefined value of 30
27197 \begin_inset space \thinspace{}
27204 \begin_layout Itemize
27205 And two different numbering styles:
27209 \begin_layout Description
27210 Right is the predefined standard
27213 \begin_layout Description
27214 Left for this the option
27218 must be inserted in the menu
27220 Document\SpecialChar \menuseparator
27226 \begin_inset space ~
27233 \begin_layout Standard
27242 can also be used together.
27243 In this case both options are inserted, separated by a comma.
27246 \begin_layout Standard
27247 The chosen styles are used for all displayed formulas of the document.
27248 When both, centered and indented formulas should be created in a document,
27254 The indented formulas are then set in a flalign environment, see
27255 \begin_inset CommandInset ref
27257 reference "sub:Flalign-Environment"
27264 \begin_layout Section
27266 \begin_inset CommandInset label
27268 name "sec:Multiline-Formulas"
27276 \begin_layout Plain Layout
27277 Formula ! multiline
27285 \begin_layout Subsection
27289 \begin_layout Standard
27290 In LyX multiline formulas are created by pressing
27297 This creates either an
27299 eqnarray environment
27301 that is described in
27302 \begin_inset CommandInset ref
27304 reference "sub:Eqnarray-Environment"
27308 or, when the option
27310 Use AMS math package
27312 in the document settings is selected, an
27316 that is described in
27317 \begin_inset CommandInset ref
27319 reference "sub:Standard-align-Environment"
27326 \begin_layout Standard
27327 There are other multiline formula environments that can be created via the
27330 Insert\SpecialChar \menuseparator
27334 These environments are described in the following sections.
27337 \begin_layout Standard
27338 In all multiline formula environments a new line is created by pressing
27344 To add or delete lines, the math toolbar buttons
27345 \begin_inset Graphics
27346 filename ../images/tabular-feature_append-row.png
27352 \begin_inset Graphics
27353 filename ../images/tabular-feature_delete-row.png
27358 , respectively, or the menu
27360 Edit\SpecialChar \menuseparator
27366 \begin_layout Subsubsection
27368 \begin_inset CommandInset label
27370 name "sub:Line-Separation"
27378 \begin_layout Plain Layout
27379 Formula ! multiline ! Line separation
27387 \begin_layout Standard
27388 There is sometimes not enough space in multiline formulas between the lines:
27389 \begin_inset Formula \begin{eqnarray*}
27390 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}\\
27391 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*}
27398 \begin_layout Standard
27399 In LaTeX additional line space is specified as optional argument of the
27401 This is not yet possible in LyX
27405 \begin_layout Plain Layout
27407 \begin_inset CommandInset href
27409 name "LyX-bug #1505"
27410 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27419 , therefore the whole formula must be inserted in TeX-mode.
27420 To add in our example space, the command
27428 is inserted at the end of the first line.
27433 \begin_layout Plain Layout
27440 \begin_layout Plain Layout
27442 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27445 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27452 \begin_layout Plain Layout
27456 left(B^{2}+x_{0}^{2}
27464 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27469 \begin_layout Plain Layout
27481 \begin_layout Standard
27482 \begin_inset VSpace bigskip
27485 To set the the line separation for all lines in a formula, the length
27495 \begin_layout Plain Layout
27505 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27516 \begin_inset space \thinspace{}
27521 \begin_inset space \thinspace{}
27524 mm additional line separation as in the previous example, the command
27527 \begin_layout Standard
27537 \begin_layout Standard
27538 is inserted in TeX-mode before the formula.
27539 This requires that the LaTeX-package
27547 \begin_layout Plain Layout
27552 is part of every LaTeX standard installation.
27561 \begin_layout Plain Layout
27567 was loaded in LaTeX-preamble with the line
27570 \begin_layout Standard
27578 \begin_layout Standard
27583 \begin_layout Plain Layout
27595 \begin_inset Formula \begin{eqnarray*}
27596 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}\\
27597 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*}
27604 \begin_layout Standard
27608 \begin_layout Plain Layout
27619 To get back to the predefined distance,
27625 is set to the value 3
27626 \begin_inset space \thinspace{}
27632 \begin_layout Subsubsection
27634 \begin_inset CommandInset label
27636 name "sub:Column-Separation"
27644 \begin_layout Plain Layout
27645 Formula ! multiline ! Column separation
27653 \begin_layout Standard
27654 Multiline formulas form a matrix.
27655 A formula in the eqnarray environment is for example a matrix with three
27657 By changing the column separation in this environment, the space beside
27658 the relation sign can be changed.
27661 \begin_layout Standard
27662 The column separation is specified with the length
27672 \begin_layout Plain Layout
27681 \begin_inset Newline newline
27684 column separation = 2
27685 \begin_inset space \thinspace{}
27695 \begin_inset Newline newline
27701 \begin_layout Standard
27711 \begin_layout Standard
27712 inserted in TeX-mode, sets for all following formulas a column separation
27714 \begin_inset space \thinspace{}
27718 To get back to the predefined distance,
27725 \begin_inset space \thinspace{}
27731 \begin_layout Standard
27733 \begin_inset space \thinspace{}
27736 cm column separation:
27740 \begin_layout Plain Layout
27752 \begin_inset Formula \begin{eqnarray*}
27754 C & \ne & A\end{eqnarray*}
27758 A formula with the predefined column separation for matrices of 10
27759 \begin_inset space \thinspace{}
27766 \begin_layout Plain Layout
27778 \begin_inset Formula \begin{eqnarray*}
27780 C & \ne & A\end{eqnarray*}
27787 \begin_layout Subsubsection
27792 \begin_layout Plain Layout
27801 \begin_layout Standard
27802 Long formulas can be typeset using these methods:
27805 \begin_layout Itemize
27806 When one side of the equation is much shorther than the line width, this
27807 one is chosen for the left side and the right side is typeset over two
27812 \begin_layout Plain Layout
27822 \begin_inset Formula \begin{eqnarray}
27823 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 \\
27824 & & -\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}
27832 \begin_layout Plain Layout
27842 \begin_inset Newline newline
27845 The minus sign at the beginning of the second line does normally not appear
27846 as operator because it is the first character of the line.
27847 Thus it would not be surrounded by space and could not be distinguished
27848 from the fraction bar.
27849 To avoid this, space was inserted behind the minus sign with the command
27860 \begin_layout Plain Layout
27868 \begin_inset CommandInset ref
27870 reference "sub:Variable-Space"
27883 \begin_layout Plain Layout
27894 \begin_layout Itemize
27895 When both sides of the equation are too long, the command
27905 \begin_layout Plain Layout
27914 It is inserted to the first column of the first line and effects that all
27915 further insertions overwrite the following columns:
27919 \begin_layout Plain Layout
27929 \begin_inset Formula \begin{eqnarray}
27930 \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 \\
27931 & & -\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 \\
27932 & & =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}
27940 \begin_layout Plain Layout
27950 \begin_inset Newline newline
27953 After the insertion of
27959 , the cursor is in a purple box that is a bit shifted to the left from the
27961 In this the formula is inserted.
27965 \begin_layout Plain Layout
27975 \begin_inset Newline newline
27978 The content of the further lines is inserted to the second or another formula
27980 The greater the column number where it was inserted, the larger the indentation.
27984 \begin_layout Plain Layout
27994 \begin_inset Newline newline
27998 \begin_inset Note Greyedout
28001 \begin_layout Plain Layout
28002 Note the following when using
28011 \begin_layout Itemize
28012 The formula doesn't use the full page width.
28014 \begin_inset space \thinspace{}
28018 \begin_inset space ~
28022 \begin_inset Formula $-B^{2}$
28025 is added to the first line in the above example, it would have been outside
28027 To better use the width, negative space can be inserted at the beginning
28031 \begin_layout Itemize
28032 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28037 \begin_layout Plain Layout
28038 \begin_inset CommandInset href
28040 name "LyX-bug #1429"
28041 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28050 One can only set the cursor at the beginning of the line and move it with
28059 \begin_layout Itemize
28060 Other methods to set long formulas are offered by the environments described
28062 \begin_inset CommandInset ref
28064 reference "sub:Multline-Environment"
28069 \begin_inset CommandInset ref
28071 reference "sub:Multiline-Formula-Parts"
28078 \begin_layout Subsubsection
28080 \begin_inset CommandInset label
28082 name "sub:Multiline-Brackets"
28090 \begin_layout Plain Layout
28091 Brackets ! for multiline expressions
28099 \begin_layout Standard
28100 For brackets spanning multiple lines the following problem occurs:
28101 \begin_inset Formula \begin{eqnarray*}
28102 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28103 & & \left.\cdots+B-D\right]\end{eqnarray*}
28110 \begin_layout Standard
28111 The closing bracket is smaller than the opening bracket because brackets
28112 with variable size may not span multiple lines.
28115 \begin_layout Standard
28116 To set the bracket size for the second line correctly, the first line is
28127 \begin_layout Plain Layout
28135 and the second line with
28143 \begin_layout Plain Layout
28157 \begin_inset CommandInset ref
28159 reference "sub:Automatic-Bracket-Size"
28174 \begin_layout Plain Layout
28200 \begin_layout Plain Layout
28219 \begin_layout Plain Layout
28238 \begin_layout Plain Layout
28250 \begin_inset Formula $\downarrow$
28259 \begin_layout Plain Layout
28267 is inserted, because the multiplication operator with its limits is the
28268 largest symbol in the first line and this should be the size for the bracket
28269 in the second line.
28272 \begin_layout Standard
28273 The result is this:
28274 \begin_inset Formula \begin{eqnarray*}
28275 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28276 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28283 \begin_layout Subsection
28287 \begin_layout Standard
28288 Align environments can be used for every kind of multiline formulas.
28289 They are specially useful to set several formulas side by side.
28292 \begin_layout Standard
28293 Align environments consist of columns.
28294 The odd columns are right aligned, the even ones left aligned.
28295 Every line in an Align environment can be numbered.
28298 \begin_layout Standard
28299 Align environments are created via the menu
28301 Insert\SpecialChar \menuseparator
28307 Edit\SpecialChar \menuseparator
28308 Math\SpecialChar \menuseparator
28309 Change Formula Type
28311 already existing formulas can be converted to Align environments.
28314 \begin_layout Standard
28315 To add or delete columns, the math toolbar buttons
28316 \begin_inset Graphics
28317 filename ../images/tabular-feature_append-column.png
28323 \begin_inset Graphics
28324 filename ../images/tabular-feature_delete-column.png
28329 , respectively, or the menu
28331 Edit\SpecialChar \menuseparator
28337 \begin_layout Subsubsection
28338 Standard align Environment
28339 \begin_inset CommandInset label
28341 name "sub:Standard-align-Environment"
28349 \begin_layout Plain Layout
28350 Formula ! multiline ! align environment
28358 \begin_layout Standard
28359 This Align environment is created by presssing
28363 in a formula or by the menu
28365 Insert\SpecialChar \menuseparator
28366 Math\SpecialChar \menuseparator
28367 AMS align Environment
28372 \begin_layout Standard
28373 An example for two formulas set side by side, that are created with a four
28374 column align environment:
28375 \begin_inset Formula \begin{align*}
28376 A & =\sin(B) & C & =D\\
28377 C & \ne A & B & \ne D\end{align*}
28381 As it can be seen, the formulas in this environment are placed so as if
28390 \begin_layout Plain Layout
28398 \begin_inset CommandInset ref
28400 reference "sub:Variable-Space"
28411 before the first and after every even column.
28412 When the formula style
28418 \begin_layout Plain Layout
28420 \begin_inset CommandInset ref
28422 reference "sec:Formula-Styles"
28433 is used, the formula is set without the
28439 before the first column.
28442 \begin_layout Subsubsection
28443 Alignat Environment
28447 \begin_layout Plain Layout
28448 Formula ! multiline ! alignat environment
28456 \begin_layout Standard
28457 The alignat environment has no predefined column separation.
28458 It can be inserted manually with the spaces that are described
28459 \begin_inset CommandInset ref
28461 reference "sub:Space"
28468 \begin_layout Standard
28469 The above example in the alignat environment where 1
28470 \begin_inset space \thinspace{}
28473 cm space was inserted at the beginning of the second formula:
28474 \begin_inset Formula \begin{alignat*}{2}
28475 A & =\sin(B) & \hspace{1cm}C & =D\\
28476 C & \ne A & B & \ne D\end{alignat*}
28480 Because the column separation can be set separately for every column, this
28481 environment is especially suitable to set three and more formulas side
28485 \begin_layout Subsubsection
28486 Flalign Environment
28487 \begin_inset CommandInset label
28489 name "sub:Flalign-Environment"
28497 \begin_layout Plain Layout
28498 Formula ! multiline ! flalign environment
28506 \begin_layout Standard
28507 In this environment the first two columns are always set as much as possible
28508 to the left and the last two ones to the right.
28510 \begin_inset Formula \begin{flalign*}
28511 A & =1 & B & =2 & C & =3\\
28512 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28519 \begin_layout Standard
28520 By creating a flalign environment with an odd number of columns where an
28521 empty TeX-brace is inserted to the last column, several formulas in a document
28522 can be set to the left, although the formula style
28527 As example the indented formula
28528 \begin_inset CommandInset ref
28530 reference "eq:VolInt"
28535 \begin_inset Formula \begin{flalign}
28536 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28540 The first two columns contain the formula.
28541 To indent it as with the formula style
28546 \begin_inset space \thinspace{}
28549 pt space was inserted at the beginning of the first column.
28552 \begin_layout Subsection
28553 Eqnarray Environment
28554 \begin_inset CommandInset label
28556 name "sub:Eqnarray-Environment"
28564 \begin_layout Plain Layout
28565 Formula ! multiline ! eqnarray environment
28573 \begin_layout Standard
28574 When this environment has been created, three blue boxes appear.
28575 The content of the first box is right aligned, the content of the last
28577 The content of the middle box appears centered and a bit smaller, because
28578 it is designed to insert there only relation characters.
28579 \begin_inset Formula \begin{eqnarray*}
28580 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28582 A & = & A\end{eqnarray*}
28589 \begin_layout Subsection
28594 \begin_layout Plain Layout
28595 Formula ! multiline ! gather environment
28603 \begin_layout Standard
28604 This environment consists of only one centered column.
28605 Every line can be numbered.
28606 \begin_inset Formula \begin{gather}
28608 X=\textrm{-}1\end{gather}
28615 \begin_layout Subsection
28616 Multline Environment
28617 \begin_inset CommandInset label
28619 name "sub:Multline-Environment"
28627 \begin_layout Plain Layout
28628 Formula ! multiline ! multline environment
28636 \begin_layout Standard
28637 The multline environment consists, like the gather environment, of only
28639 But the first line is left aligned, the last one right aligned.
28640 All other lines are centered.
28641 Therefore this environment is suitable for long formulas.
28643 \begin_inset CommandInset ref
28645 reference "eq:lefteqn"
28649 in the multline environment:
28650 \begin_inset Formula \begin{multline}
28651 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}\\
28652 -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}\\
28653 =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}
28660 \begin_layout Standard
28661 In the output only the last (first) line of a multline environment appears
28662 numbered when the document numbering is right (left).
28666 \begin_layout Plain Layout
28667 numbering styles see
28668 \begin_inset CommandInset ref
28670 reference "sec:Formula-Styles"
28682 \begin_layout Standard
28691 \begin_layout Plain Layout
28709 \begin_layout Plain Layout
28719 a centered line can be right or left aligned, respectively.
28720 The commands are used as follows:
28723 \begin_layout Standard
28728 shoveright{line content}
28734 shoveleft{line content}
28737 \begin_layout Standard
28738 \begin_inset VSpace medskip
28749 \begin_layout Plain Layout
28759 specifies the distance of the first line from the left page margin.
28760 Predefined is the length 0
28761 \begin_inset space \thinspace{}
28767 \begin_layout Standard
28768 As example the above formula where the command
28771 \begin_layout Standard
28781 \begin_layout Standard
28782 was inserted in TeX-mode before:
28786 \begin_layout Plain Layout
28798 \begin_inset Formula \begin{multline}
28799 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}\\
28800 \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}}\\
28801 =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}
28809 \begin_layout Plain Layout
28820 The second line was left aligned using
28829 \begin_layout Subsection
28830 Multiline Formula Parts
28831 \begin_inset CommandInset label
28833 name "sub:Multiline-Formula-Parts"
28841 \begin_layout Plain Layout
28842 Formula ! multiline ! formula parts
28850 \begin_layout Standard
28851 To display only parts of a formula with multiple lines, one of the following
28852 environments are used:
28869 They can be inserted via the menu
28871 Insert\SpecialChar \menuseparator
28874 or by using the commands described in this section.
28877 \begin_layout Standard
28878 The first three have the same properties as the corresponding multiline
28879 formula environments, but it is possible to set further formula parts beside
28882 \begin_inset Formula \[
28883 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28884 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28885 \right\} \textrm{Uncertainty relations}\]
28892 \begin_layout Standard
28893 To get this formula, a displayed formula is created where the command
28901 \begin_layout Plain Layout
28912 A purple box appears around the blue formula box where now columns and
28913 lines can be added.
28914 Outside the multiline environment other formula parts can be set, like
28918 \begin_layout Standard
28919 The aligned environment is also suitable for long formulas whose lines are
28920 horizontally aligned.
28921 Using aligned in a displayed formula has the advantage that the formula
28922 number is vertically centered behind the lines.
28924 \begin_inset CommandInset ref
28926 reference "eq:kurzlang"
28930 in the aligned environment:
28931 \begin_inset Formula \begin{equation}
28932 \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}|}\\
28933 & -\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}
28941 \begin_layout Standard
28942 To use the environments
28964 \begin_layout Plain Layout
28982 \begin_layout Plain Layout
29000 \begin_layout Plain Layout
29008 are inserted, respectively.
29009 The split environment has the same properties as the aligned environment
29010 but it can only have two columns.
29013 \begin_layout Subsection
29014 Text in multiline Formulas
29015 \begin_inset CommandInset label
29017 name "sub:Text-in-multiline"
29025 \begin_layout Plain Layout
29035 \begin_layout Plain Layout
29036 Formula ! multiline ! text
29044 \begin_layout Standard
29045 In the Align environments, and the multline and gather environment, text
29046 can be inserted that will appear in a separate line and doesn't affect
29047 the column alignment.
29048 To do this, the command
29056 \begin_layout Plain Layout
29066 is used in the following scheme:
29069 \begin_layout Standard
29077 \begin_layout Standard
29078 The text should not be longer than a line because it cannot be hyphenated.
29079 As LyX doesn't yet support
29085 directly, the text is written as mathematical text.
29092 must hereby be at the beginning of a line and appears in the output above
29094 An example where the text was inserted at the beginning of the second line:
29095 \begin_inset Formula \begin{align}
29096 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29097 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29104 \begin_layout Section
29109 \begin_layout Plain Layout
29119 \begin_layout Plain Layout
29120 Formula ! numbering|see
29124 \begin_layout Plain Layout
29135 \begin_layout Plain Layout
29150 \begin_layout Subsection
29154 \begin_layout Standard
29155 Numbered formulas can be created with the menu
29157 Insert\SpecialChar \menuseparator
29158 Math\SpecialChar \menuseparator
29160 \begin_inset space ~
29168 \begin_inset space ~
29174 Existing formulas can be numbered with the menu
29176 Edit\SpecialChar \menuseparator
29177 Math\SpecialChar \menuseparator
29179 \begin_inset space ~
29187 \begin_inset space ~
29193 The formula number is displayed in LyX behind the formula as number sign
29195 The number sign is replaced in the output by the formula number.
29198 \begin_layout Standard
29199 When numbering is turned on in multiline formulas, all lines will be numbered.
29200 But the numbering can be controlled with the menu
29202 Edit\SpecialChar \menuseparator
29203 Math\SpecialChar \menuseparator
29205 \begin_inset space ~
29209 \begin_inset space ~
29213 \begin_inset space ~
29221 \begin_inset space ~
29229 \begin_layout Standard
29230 Except of inline formulas, all formulas can be numbered with two different
29232 \begin_inset CommandInset ref
29234 reference "sec:Formula-Styles"
29241 \begin_layout Subsection
29243 \begin_inset CommandInset label
29245 name "sub:Cross-References"
29253 \begin_layout Plain Layout
29254 Cross-references ! to formulas
29262 \begin_layout Standard
29263 All labeled formulas can be cross-referenced.
29264 A label is added by the menu
29266 Insert\SpecialChar \menuseparator
29269 or the toolbar button
29270 \begin_inset Graphics
29271 filename ../images/label-insert.png
29277 The cursor must hereby be inside a displayed formula.
29278 A dialog pops up displaying the prefix
29283 The label is inserted there behind the prefix.
29284 The predefined prefix means
29285 \begin_inset Quotes eld
29289 \begin_inset Quotes erd
29292 and makes it easier to find labels in large documents because it marks
29293 it as formula label to divide it from e.
29294 \begin_inset space \thinspace{}
29298 \begin_inset space ~
29302 To change a label, the menu
29304 Insert\SpecialChar \menuseparator
29310 \begin_layout Standard
29311 The name of the label is displayed in LyX within two parentheses behind
29313 A formula with a label is always numbered.
29316 \begin_layout Standard
29317 Cross-references are inserted via the menu
29319 Insert\SpecialChar \menuseparator
29322 or with the toolbar button
29323 \begin_inset Graphics
29324 filename ../images/dialog-show-new-inset_ref.png
29330 A formula cross-reference appears in the output as formula number.
29331 When in the cross-reference dialog window the format
29335 is chosen, the cross-reference appears in the output as formula number
29337 \begin_inset Newline newline
29340 By right-clicking on a cross-reference in LyX, one jumps to the formula
29341 that is referenced.
29344 \begin_layout Standard
29345 Here are as examples cross-references to formulas of the following subsections:
29346 \begin_inset Note Note
29349 \begin_layout Plain Layout
29350 Note the different cross-reference types.
29358 \begin_layout Standard
29360 \begin_inset CommandInset ref
29367 \begin_inset CommandInset ref
29375 \begin_inset CommandInset ref
29381 ) big Latin letters are used for the numbering in contrary to (
29382 \begin_inset CommandInset ref
29391 \begin_layout Standard
29392 \begin_inset VSpace medskip
29395 When the argument of
29403 \begin_layout Plain Layout
29411 \begin_inset CommandInset ref
29413 reference "sub:User-defined-Numbering"
29424 contains a box like in
29425 \begin_inset CommandInset ref
29427 reference "sub:Paragraph-Boxes"
29431 , the formula cannot be referenced.
29434 \begin_layout Subsection
29439 \begin_layout Plain Layout
29440 Formula numbering ! subnumbering
29448 \begin_layout Standard
29449 With the help of the commands
29453 begin{subequations}
29461 formulas can be subnumbered.
29462 Both commands are inserted in TeX-mode.
29465 \begin_layout Standard
29467 \begin_inset Formula \begin{equation}
29468 A=C-B\label{eq:a}\end{equation}
29476 \begin_layout Plain Layout
29480 addtocounter{equation}{-1}
29489 \begin_layout Plain Layout
29493 begin{subequations}
29499 \begin_inset VSpace -5mm
29503 \begin_inset Formula \begin{equation}
29504 B=C-A\label{eq:b}\end{equation}
29509 \begin_inset Formula \begin{equation}
29510 C=A+B\label{eq:c}\end{equation}
29517 \begin_layout Standard
29521 \begin_layout Plain Layout
29533 \begin_layout Standard
29534 To create the example, the following is done:
29537 \begin_layout Enumerate
29538 first formula is inserted
29541 \begin_layout Enumerate
29546 addtocounter{equation}{-1}
29548 begin{subequations}
29552 \begin_layout Plain Layout
29561 \begin_inset Newline newline
29566 is inserted after the first formula
29569 \begin_layout Enumerate
29570 second formula is inserted
29573 \begin_layout Enumerate
29574 third formula is inserted
29577 \begin_layout Enumerate
29584 is inserted after the third formula
29587 \begin_layout Standard
29588 Every formula between the commands
29600 is subnumbered as a, b,
29601 \begin_inset Newline linebreak
29604 c, \SpecialChar \ldots{}
29605 For multiline formulas every line will be subnumbered.
29606 All subnumbered formulas are treated as
29611 But as every numbered formula increases the counter
29615 by one, the command
29621 is needed to decrease it.
29622 Otherwise the formulas
29623 \begin_inset CommandInset ref
29630 \begin_inset CommandInset ref
29637 \begin_inset CommandInset ref
29643 would be numbered as
29644 \begin_inset CommandInset ref
29651 \begin_inset CommandInset ref
29658 \begin_inset CommandInset ref
29667 \begin_layout Standard
29668 By inserting the commands in TeX-mode, a space is created between the first
29671 \begin_inset space \thinspace{}
29674 mm vertical space is inserted after the command
29678 begin{subequations}
29681 When the formula style
29687 \begin_layout Plain Layout
29689 \begin_inset CommandInset ref
29691 reference "sec:Formula-Styles"
29703 \begin_inset space \thinspace{}
29706 mm space is inserted instead.
29709 \begin_layout Standard
29710 Here is an example for a multiline formula where the numbering was turned
29711 off for the second line:
29715 \begin_layout Plain Layout
29719 begin{subequations}
29725 \begin_inset Formula \begin{eqnarray}
29726 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29727 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29728 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29736 \begin_layout Plain Layout
29748 \begin_layout Subsection
29749 User-defined Numbering
29750 \begin_inset CommandInset label
29752 name "sub:User-defined-Numbering"
29760 \begin_layout Plain Layout
29761 Formula numbering ! user-defined
29769 \begin_layout Standard
29773 \begin_layout Plain Layout
29774 Formula numbering ! self-defined delimiters
29779 With the standard numbering parentheses are set around the formula number.
29780 To replace the parentheses for example by vertical bars, the following
29781 line is added to the LaTeX-preamble:
29784 \begin_layout Standard
29796 \begin_inset Note Note
29799 \begin_layout Plain Layout
29800 This macro is already declared in the LaTeX-preamble for testing.
29801 To activate it, remove the percent sign at the beginning.
29809 \begin_layout Standard
29810 To use other characters, the vertical bars besides the
29814 are replaced by one ore more characters.
29815 To get only the formula number the vertical bars are omitted.
29818 \begin_layout Standard
29819 \begin_inset VSpace bigskip
29822 When there should be an expression of your choice instead of the consecutive
29823 formula number in parentheses behind the formula, the command
29833 \begin_layout Plain Layout
29842 \begin_inset Formula \begin{equation}
29843 A+B=C\tag{something}\label{eq:tag}\end{equation}
29847 In this example the command
29855 \begin_layout Plain Layout
29866 was inserted to the formula.
29869 \begin_layout Standard
29878 \begin_layout Plain Layout
29889 is inserted instead, the star prevents the parentheses around the expression:
29890 \begin_inset Formula \[
29891 A+B=C\tag*{something}\]
29898 \begin_layout Standard
29899 \begin_inset VSpace bigskip
29902 To restart the formula numbering with new document parts or sections, the
29903 following command is used:
29906 \begin_layout Standard
29911 @addtoreset{equation}{part}
29917 \begin_layout Plain Layout
29922 \begin_layout Plain Layout
29933 \begin_layout Plain Layout
29946 \begin_layout Plain Layout
29957 \begin_layout Plain Layout
29970 \begin_inset Newline newline
29974 \begin_inset Newline newline
29981 @addtoreset{equation}{section}
29984 \begin_layout Standard
29985 To be able to use these commands in TeX-mode, the
29986 \begin_inset Quotes eld
29990 \begin_inset Quotes erd
29993 character has to be made
29994 \begin_inset Quotes eld
29998 \begin_inset Quotes erd
30001 for LaTeX using the command
30015 So the command sequence in TeX-mode is:
30018 \begin_layout Standard
30024 \begin_inset Newline newline
30029 @addtoreset{equation}{section}
30030 \begin_inset Newline newline
30038 \begin_layout Standard
30039 In the LaTeX-preamble
30051 can be omitted as they are automatically internally inserted by LyX.
30054 \begin_layout Standard
30069 \begin_layout Plain Layout
30074 is part of the LaTeX-package
30082 \begin_layout Plain Layout
30083 Packages ! carlisle
30088 that is part of every LaTeX standard installation.
30097 \begin_layout Plain Layout
30098 Packages ! remreset
30103 has to be loaded in the LaTeX-preamble with the line
30106 \begin_layout Standard
30111 usepackage{remreset}
30114 \begin_layout Standard
30125 \begin_layout Plain Layout
30130 \begin_layout Plain Layout
30141 \begin_layout Plain Layout
30154 \begin_layout Plain Layout
30165 \begin_layout Plain Layout
30177 can be used with the same scheme as
30186 \begin_layout Standard
30187 \begin_inset VSpace bigskip
30190 Sometimes formulas should be numbered in the following form:
30193 \begin_layout Standard
30196 (section number.formula number)
30199 \begin_layout Standard
30200 The formula number should start with every section with
30201 \begin_inset Quotes eld
30205 \begin_inset Quotes erd
30211 \begin_layout Standard
30212 For this case there is the command
30222 \begin_layout Plain Layout
30230 , which is used with the following scheme:
30233 \begin_layout Standard
30238 numberwithin{counter}{sectioning}
30241 \begin_layout Standard
30242 Counter denotes what kind of numbering is affected, sectioning denotes what
30243 number is before the dot.
30246 \begin_layout Standard
30247 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30250 \begin_layout Standard
30255 numberwithin{equation}{section}
30258 \begin_layout Standard
30259 This is the result:
30263 \begin_layout Plain Layout
30267 numberwithin{equation}{section}
30273 \begin_inset Formula \begin{equation}
30274 A+B=C\end{equation}
30281 \begin_layout Standard
30283 \begin_inset space \thinspace{}
30287 \begin_inset space ~
30290 tables so that the number of the part is the sectioning,
30291 \begin_inset Newline newline
30298 numberwithin{table}{part}
30303 \begin_layout Standard
30304 To go back to the standard numbering or to prevent this kind of numbering
30305 when it is defined by the document class, the following command is inserted
30306 as TeX-Code or to the LaTeX-preamble:
30309 \begin_layout Standard
30322 \begin_layout Plain Layout
30336 \begin_layout Plain Layout
30352 \begin_inset Newline newline
30360 \begin_inset Newline newline
30372 \begin_layout Standard
30379 uses internally the command
30385 , described above, that also needs to be reverted.
30389 \begin_layout Plain Layout
30396 \begin_layout Plain Layout
30400 @removefromreset{equation}{section}
30403 \begin_layout Plain Layout
30415 \begin_layout Subsection
30416 Numbering with Roman Numbers and Letters
30417 \begin_inset CommandInset label
30419 name "sub:Numbering-with-Roman"
30427 \begin_layout Plain Layout
30428 Formula numbering ! with letters
30437 \begin_layout Plain Layout
30438 Formula numbering ! with Roman numbers
30446 \begin_layout Standard
30447 Formulas can also be numbered with Roman numbers and Latin letters.
30448 To number for example with small Roman numbers, the command
30451 \begin_layout Standard
30463 \begin_layout Standard
30464 is inserted before the formula in TeX-mode.
30475 \begin_layout Plain Layout
30483 redefines the predefined command
30499 \begin_layout Plain Layout
30506 has the same scheme like the command
30512 that is described in
30513 \begin_inset CommandInset ref
30515 reference "sec:User-defined-Commands"
30529 is the formula counter.
30536 is used as prefix for a counter, the value of the counter is output as
30538 When a formula is numbered, LaTeX sets internally the command
30544 behind the formula.
30553 \begin_layout Plain Layout
30563 outputs the counter as small Roman number.
30566 \begin_layout Standard
30567 All formulas behind the command
30577 are now numbered Roman.
30578 To switch to numbering with big Roman numbers, the command is inserted
30595 \begin_layout Plain Layout
30607 \begin_inset Quotes eld
30611 \begin_inset Quotes erd
30614 with small Latin letters there is the command
30624 \begin_layout Plain Layout
30632 , for big ones there is the command
30642 \begin_layout Plain Layout
30655 \begin_layout Standard
30656 \begin_inset Note Greyedout
30659 \begin_layout Plain Layout
30664 Only maximal 26 formulas can be numbered with Latin letters in one document.
30672 \begin_layout Standard
30676 \begin_layout Plain Layout
30692 \begin_layout Standard
30693 \begin_inset Formula \begin{equation}
30694 A=\textrm{small roman}\label{eq:rom}\end{equation}
30702 \begin_layout Plain Layout
30716 \begin_inset Formula \begin{equation}
30717 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30725 \begin_layout Plain Layout
30739 \begin_inset Formula \begin{equation}
30740 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30748 \begin_layout Plain Layout
30762 \begin_inset Formula \begin{equation}
30763 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30770 \begin_layout Standard
30771 To switch back to the default numbering, insert the command:
30774 \begin_layout Standard
30787 \begin_layout Plain Layout
30798 \begin_layout Standard
30802 \begin_layout Plain Layout
30816 \begin_inset Formula \begin{equation}
30817 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30824 \begin_layout Standard
30825 \begin_inset VSpace medskip
30828 As you see, formulas are numbered serially independent from the numbering
30830 When then numbering should start with
30831 \begin_inset Quotes eld
30835 \begin_inset Quotes erd
30838 when the style is changed, new equation counters have to be defined.
30839 A description about this can be found in the file
30840 \begin_inset CommandInset href
30842 target "Formula-numbering.lyx"
30849 \begin_layout Section
30850 User-defined Commands
30851 \begin_inset CommandInset label
30853 name "sec:User-defined-Commands"
30861 \begin_layout Plain Layout
30862 User-defined commands
30870 \begin_layout Standard
30871 Many LaTeX-commands are too long to be used frequently.
30872 But it is possible to define with the command
30882 \begin_layout Plain Layout
30890 new shorter commands.
30893 \begin_layout Standard
30894 The command scheme of
30903 \begin_layout Standard
30908 newcommand{new command name}[number of arguments][optional
30913 \begin_inset Newline newline
30920 \begin_layout Plain Layout
30935 \begin_layout Plain Layout
30942 {command definition}
30945 \begin_layout Standard
30946 \begin_inset Note Greyedout
30949 \begin_layout Plain Layout
30954 Assure that the name of the new command is not already used in your document
30955 or by LaTeX-packages that you use.
30956 When you for example define the command
30968 , you get an error message because
30974 is already defined as command for
30975 \begin_inset Quotes eld
30979 \begin_inset Formula $\le$
30983 \begin_inset Quotes erd
30994 \begin_layout Standard
30995 \begin_inset Note Greyedout
30998 \begin_layout Plain Layout
31003 The names of user-defined commands may only consist of Latin letters.
31011 \begin_layout Standard
31012 The number of arguments is an integer in the range 0
31013 \begin_inset space \thinspace{}
31017 \begin_inset space \thinspace{}
31020 9 and specifies how many arguments the new command should have.
31021 With the optional value a value for an optional argument can be predefined.
31022 When this is done, the
31030 rgument of the new command is automatically an optional one.
31033 \begin_layout Standard
31034 Here are some examples:
31037 \begin_layout Itemize
31038 To define the command
31050 , the LaTeX-preamble line is:
31054 \begin_layout Plain Layout
31066 \begin_inset Newline newline
31078 \begin_layout Itemize
31079 To define the command
31091 , the argument (that should be underlined) must be taken into account.
31092 For this the preamble line is:
31096 \begin_layout Plain Layout
31108 \begin_inset Newline newline
31123 \begin_layout Plain Layout
31135 \begin_inset Newline newline
31144 acts as argument placeholder, the
31148 behind it denotes that it is the placeholder for the first argument.
31151 \begin_layout Itemize
31159 \begin_inset space \thinspace{}
31163 \begin_inset space ~
31176 \begin_layout Plain Layout
31188 \begin_inset Newline newline
31197 framebox#1#2{$#3$}}
31203 \begin_layout Plain Layout
31215 \begin_inset Newline newline
31220 The two Dollar signs creates the extra formula needed for
31227 \begin_inset CommandInset ref
31229 reference "sub:Boxes-with-Frame"
31236 \begin_layout Itemize
31237 To create a new command for
31243 where the color for the box needn't to be specified, the argument for the
31244 color is defined optional:
31248 \begin_layout Plain Layout
31260 \begin_inset Newline newline
31269 fcolorbox{#2}{#1}{$#3$}}
31275 \begin_layout Plain Layout
31285 \begin_inset Newline newline
31288 When the color is not specified when using
31294 , the predefined color
31301 \begin_layout Standard
31302 A test of the new defined commands:
31305 \begin_layout Standard
31307 \begin_inset Tabular
31308 <lyxtabular version="3" rows="6" columns="2">
31310 <column alignment="center" valignment="top" width="0">
31311 <column alignment="center" valignment="top" width="0">
31313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31316 \begin_layout Plain Layout
31322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31325 \begin_layout Plain Layout
31327 \begin_inset Note Note
31330 \begin_layout Plain Layout
31337 is only used as spacer.
31349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31352 \begin_layout Plain Layout
31359 \begin_layout Plain Layout
31373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31376 \begin_layout Plain Layout
31377 \begin_inset Formula $A\gr B$
31387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31390 \begin_layout Plain Layout
31398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31401 \begin_layout Plain Layout
31402 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31415 \begin_layout Plain Layout
31419 \begin_inset Formula $\to$
31425 \begin_inset Formula $\to$
31436 \begin_layout Plain Layout
31450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31453 \begin_layout Plain Layout
31454 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31467 \begin_layout Plain Layout
31471 \begin_inset Formula $\to$
31482 \begin_layout Plain Layout
31496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31499 \begin_layout Plain Layout
31500 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31513 \begin_layout Plain Layout
31519 \begin_inset Formula $\to$
31530 \begin_layout Plain Layout
31544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31547 \begin_layout Plain Layout
31548 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31564 \begin_layout Section
31568 \begin_layout Standard
31569 LyX supports two types of commutative diagrams:
31577 that are explained in the following.
31580 \begin_layout Subsection
31585 \begin_layout Plain Layout
31594 \begin_layout Standard
31595 Diagrams of this type visualize relations by vertical and horizontal lines
31597 \begin_inset Formula \[
31598 \begin{CD}A@>>>B@>>>C\\
31600 F@<<<E@<<<D\end{CD}\]
31607 \begin_layout Standard
31608 To get them, the command
31616 \begin_layout Plain Layout
31626 is inserted to a formula.
31627 A blue box appears with two dashed lines where further commands can be
31633 a new line is created.
31634 Horizontal relations are inserted in odd, vertical in even formula lines.
31637 \begin_layout Standard
31638 To create the relations there are the following commands:
31641 \begin_layout Itemize
31646 creates a left arrow,
31657 \begin_layout Itemize
31662 creates an up arrow,
31670 a vertical equal sign
31673 \begin_layout Itemize
31679 is a placeholder for non-existent relations
31682 \begin_layout Standard
31683 All arrows can be labeled as follows:
31686 \begin_layout Itemize
31687 Is text inserted between the first and second < or >, resp., it is placed
31689 When it is inserted between the second and third one, it appears under
31693 \begin_layout Itemize
31694 When text for vertical arrows is inserted between the first and second A
31695 or V, resp., it is placed left beside the arrow.
31696 When it is inserted between the second and third one, it appears right
31698 If the text contains an A or V, these letters must be set into a TeX-brace.
31701 \begin_layout Standard
31702 As example a diagram with all possible relations:
31705 \begin_layout Standard
31706 \begin_inset Formula \[
31707 \begin{CD}A@>j>>B@>>k>C@=F\\
31709 D@<<j<E@>k>>F@=C\end{CD}\]
31716 \begin_layout Standard
31717 The command for this is:
31718 \begin_inset Newline newline
31729 \begin_layout Plain Layout
31738 A@>j>>B@>>k>C@=F Ctrl-Enter
31739 \begin_inset Newline newline
31746 \begin_layout Plain Layout
31761 \begin_layout Plain Layout
31774 \begin_layout Plain Layout
31786 \begin_inset Formula $\to$
31792 \begin_inset Newline newline
31799 \begin_layout Plain Layout
31814 \begin_layout Plain Layout
31827 \begin_layout Plain Layout
31837 \begin_layout Subsection
31842 \begin_layout Plain Layout
31843 Diagrams ! xymatrix
31851 \begin_layout Standard
31852 To be able to use xymatrices, the LaTeX-package
31857 A xymatrix is created by inserting the command
31864 Then you are able to add new matrix columns and rows like for normal matrices,
31866 \begin_inset CommandInset ref
31868 reference "sec:Matrices"
31875 \begin_layout Standard
31876 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31878 All possibilities to create commutative diagrams and decorations are explained
31879 in detail in this manual:
31880 \begin_inset CommandInset href
31882 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31889 \begin_layout Standard
31890 \begin_inset Newpage newpage
31896 \begin_layout Section
31901 \begin_layout Plain Layout
31914 \begin_layout Plain Layout
31915 Other useful math tips can be found in
31916 \begin_inset CommandInset citation
31931 \begin_layout Plain Layout
31939 \begin_inset Note Note
31942 \begin_layout Plain Layout
31945 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31948 \begin_layout Plain Layout
31951 texorpdfstring is in section
31952 \begin_inset CommandInset ref
31954 reference "sub:Formulas-in-Section"
31967 \begin_layout Plain Layout
31977 \begin_layout Plain Layout
31982 \begin_layout Plain Layout
31989 Chemical characters
31993 \begin_layout Plain Layout
32008 \begin_layout Subsection
32009 Chemical Symbols and Equations
32010 \begin_inset CommandInset label
32012 name "sub:Chemical-Symbols-and"
32020 \begin_layout Plain Layout
32021 Chemical characters ! Symbols
32030 \begin_layout Plain Layout
32040 \begin_layout Plain Layout
32049 \begin_layout Standard
32050 An example text from chemistry:
32053 \begin_layout Quote
32055 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32058 -ion reacts with two
32059 \begin_inset Formula $\mathrm{Na^{+}}$
32062 -ions to sodium sulfate
32063 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32067 The chemical equation for this is:
32068 \begin_inset Formula \[
32069 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32076 \begin_layout Standard
32077 This chemical equation can directly be created as formula.
32078 To avoid that the symbols appear italic, everything is highlighted and
32079 changed by the shortcut
32082 \begin_inset space ~
32087 to the upright font style.
32091 \begin_layout Plain Layout
32097 \begin_inset CommandInset ref
32099 reference "sub:Font-Styles"
32111 \begin_layout Subsection
32116 \begin_layout Plain Layout
32125 \begin_layout Standard
32126 Negative numbers often look ugly in formulas because the minus sign before
32127 the number is set with the same length as the minus operator sign.
32128 When writing the negative number in normal text, the minus sign appears
32132 \begin_layout Standard
32133 Thus, the problem disappears when converting the minus sign to mathematical
32137 \begin_layout Standard
32138 An example to visualize the problem:
32141 \begin_layout Standard
32143 \begin_inset Tabular
32144 <lyxtabular version="3" rows="3" columns="2">
32146 <column alignment="right" valignment="top" width="0">
32147 <column alignment="left" valignment="top" width="0">
32149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32152 \begin_layout Plain Layout
32158 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32161 \begin_layout Plain Layout
32169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32172 \begin_layout Plain Layout
32178 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32181 \begin_layout Plain Layout
32182 \begin_inset Formula $x=-2$
32192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32195 \begin_layout Plain Layout
32201 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32204 \begin_layout Plain Layout
32205 \begin_inset Formula $x=\textrm{-}2$
32221 \begin_layout Subsection
32222 Comma as decimal Separator
32226 \begin_layout Plain Layout
32235 \begin_layout Standard
32236 In LaTeX a comma inside a formula is used, according to the English convention,
32237 as number group separator.
32238 So there will be space added behind all commas in formulas.
32241 \begin_layout Standard
32242 To avoid this, the comma is highlighted and changed to mathematical text
32246 \begin_inset space ~
32254 \begin_layout Standard
32255 To use all formula commas in the document as decimal separator, the file
32264 \begin_layout Plain Layout
32269 is part of the LaTeX-package
32277 \begin_layout Plain Layout
32282 \begin_layout Plain Layout
32305 \begin_layout Plain Layout
32311 is loaded with the LaTeX-preamble line
32314 \begin_layout Standard
32322 \begin_layout Subsection
32324 \begin_inset CommandInset label
32326 name "sub:Physical-Vectors"
32334 \begin_layout Plain Layout
32343 \begin_layout Standard
32344 Predefined vectors are offered by the LaTeX-package
32352 \begin_layout Plain Layout
32357 should be part of every LaTeX standard installation.
32366 \begin_layout Plain Layout
32372 that is loaded with the LaTeX-preamble line
32375 \begin_layout Standard
32383 \begin_layout Standard
32387 \begin_layout Plain Layout
32397 \begin_inset Note Note
32400 \begin_layout Plain Layout
32401 The following table will only be displayed when the LaTeX-package
32410 The following commands are defined:
32413 \begin_layout Standard
32415 \begin_inset Tabular
32416 <lyxtabular version="3" rows="4" columns="2">
32418 <column alignment="center" valignment="top" width="0">
32419 <column alignment="center" valignment="top" width="0">
32421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32424 \begin_layout Plain Layout
32430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32433 \begin_layout Plain Layout
32441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32444 \begin_layout Plain Layout
32454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32457 \begin_layout Plain Layout
32458 \begin_inset Formula $\Bra{\psi}$
32468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32471 \begin_layout Plain Layout
32481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32484 \begin_layout Plain Layout
32485 \begin_inset Formula $\Ket{\psi}$
32495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32498 \begin_layout Plain Layout
32510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32513 \begin_layout Plain Layout
32514 \begin_inset Formula $\Braket{\psi|\phi}$
32530 \begin_layout Standard
32537 assures that all vertical bars are set in the size of the surrounding brackets:
32538 \begin_inset Formula \[
32539 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32547 \begin_layout Plain Layout
32557 \begin_inset Note Note
32560 \begin_layout Plain Layout
32561 The following will be displayed when the LaTeX-package
32573 \begin_layout Standard
32574 You need to install the LaTeX-package
32578 to see the rest of this subsection in the output.
32581 \begin_layout Standard
32585 \begin_layout Plain Layout
32597 \begin_layout Standard
32604 can also be achieved using the command
32610 , that is described in
32611 \begin_inset CommandInset ref
32613 reference "sub:Automatic-Bracket-Size"
32620 \begin_layout Subsection
32621 Self-defined Fractions
32622 \begin_inset CommandInset label
32624 name "sub:Self-defined-Fractions"
32632 \begin_layout Plain Layout
32633 Fractions ! self-defined
32641 \begin_layout Standard
32642 To define custom commands for fractions, the command
32652 \begin_layout Plain Layout
32660 is used in the following scheme:
32663 \begin_layout Standard
32676 bracket}{fraction bar thickness}{style}
32677 \begin_inset Newline newline
32684 \begin_layout Plain Layout
32699 \begin_layout Plain Layout
32706 {numerator}{denominator}
32709 \begin_layout Standard
32710 The style is a number in the range of 0
32711 \begin_inset space \thinspace{}
32715 \begin_inset space \thinspace{}
32721 \begin_layout Standard
32723 \begin_inset Tabular
32724 <lyxtabular version="3" rows="5" columns="2">
32726 <column alignment="center" valignment="top" width="0">
32727 <column alignment="center" valignment="top" width="0">
32729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32732 \begin_layout Plain Layout
32738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32741 \begin_layout Plain Layout
32749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32752 \begin_layout Plain Layout
32758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32761 \begin_layout Plain Layout
32762 display style formula
32769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32772 \begin_layout Plain Layout
32778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32781 \begin_layout Plain Layout
32789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32792 \begin_layout Plain Layout
32798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32801 \begin_layout Plain Layout
32809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32812 \begin_layout Plain Layout
32818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32821 \begin_layout Plain Layout
32835 \begin_layout Standard
32836 When no style is given, the size is adjusted to the surrounding environment
32837 like for the command
32846 \begin_layout Standard
32847 When no fraction bar thickness is given, the predefined value of 0.4
32848 \begin_inset space \thinspace{}
32854 \begin_layout Standard
32855 \begin_inset VSpace medskip
32858 For example, the commands
32871 \begin_inset CommandInset ref
32873 reference "sub:Fractions"
32877 are defined with the commands
32880 \begin_layout Standard
32889 genfrac{}{}{}{0}{#1}{#2}}
32892 \begin_layout Standard
32896 \begin_layout Standard
32905 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32908 \begin_layout Standard
32909 \begin_inset VSpace medskip
32912 To define a fraction where the fraction bar thickness can be given as optional
32913 argument, the following line is inserted to the LaTeX-preamble:
32916 \begin_layout Standard
32925 genfrac{}{}{#1}{}{#2}{#3}}
32928 \begin_layout Standard
32930 \begin_inset Formula \begin{align*}
32931 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32932 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32936 As one can see, the distance of the numerator and the denominator to the
32937 fraction bar is round about three times the bar thickness.
32940 \begin_layout Subsection
32942 \begin_inset CommandInset label
32944 name "sub:Canceled-Formulas"
32952 \begin_layout Plain Layout
32961 \begin_layout Standard
32962 To cancel formulas or formula parts, the LaTeX-package
32970 \begin_layout Plain Layout
32975 is part of every LaTeX standard installation.
32984 \begin_layout Plain Layout
32990 has to be loaded with the LaTeX-preamble line
32993 \begin_layout Standard
32998 usepackage[samesize]{cancel}
33001 \begin_layout Standard
33002 There are four ways to cancel formulas:
33005 \begin_layout Standard
33007 \begin_inset Tabular
33008 <lyxtabular version="3" rows="5" columns="2">
33010 <column alignment="center" valignment="top" width="0">
33011 <column alignment="center" valignment="top" width="0">
33013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33016 \begin_layout Plain Layout
33022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33025 \begin_layout Plain Layout
33027 \begin_inset Note Note
33030 \begin_layout Plain Layout
33043 are used here as spacer.
33055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33058 \begin_layout Plain Layout
33067 \begin_layout Plain Layout
33081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33084 \begin_layout Plain Layout
33085 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33098 \begin_layout Plain Layout
33107 \begin_layout Plain Layout
33121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33124 \begin_layout Plain Layout
33125 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33138 \begin_layout Plain Layout
33147 \begin_layout Plain Layout
33161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33164 \begin_layout Plain Layout
33165 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33178 \begin_layout Plain Layout
33182 \begin_inset Formula $\to$
33193 \begin_layout Plain Layout
33207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33210 \begin_layout Plain Layout
33211 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33227 \begin_layout Standard
33234 is especially suitable to visualize the reduction of fractions within formulas:
33235 \begin_inset Formula \[
33236 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33243 \begin_layout Subsection
33244 Formulas in Section Headings
33245 \begin_inset CommandInset label
33247 name "sub:Formulas-in-Section"
33255 \begin_layout Plain Layout
33256 Formula ! in section headings
33264 \begin_layout Standard
33265 When formulas are used in section headings, the following has to be taken
33269 \begin_layout Standard
33270 \begin_inset Note Greyedout
33273 \begin_layout Plain Layout
33282 \begin_layout Plain Layout
33283 Packages ! hyperref
33288 support is enabled in the document settings dialog under
33291 \begin_inset space ~
33296 , PDF-bookmarks are created for every section heading in the table of contents.
33297 If a section heading contains formulas, they are incorrectly displayed
33298 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33307 \begin_layout Standard
33308 Both problems can be solved by inserting at the end of the section heading
33309 a short title with the menu
33311 Insert\SpecialChar \menuseparator
33313 \begin_inset space ~
33319 Short titles are used as alternative for multiline section headings to
33320 keep the table of contents clearly arranged.
33321 Only the short title appears in the table of contents and therefore also
33322 in the PDF-bookmark.
33325 \begin_layout Standard
33326 When formulas should be used in the table of contents but
33330 is used, one can use the following command in TeX-mode:
33333 \begin_layout Standard
33338 texorpdfstring{part}{alternative}
33342 \begin_layout Plain Layout
33353 \begin_layout Standard
33354 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33355 This can be characters, formulas, footnotes, but also cross-references.
33356 The alternative is used instead of the part for the bookmark.
33359 \begin_layout Standard
33360 Here are two example headings:
33361 \begin_inset VSpace -3mm
33368 \begin_layout Plain Layout
33380 \begin_layout Subsubsection
33381 Heading without formula in table of contents
33382 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33386 \begin_inset OptArg
33389 \begin_layout Plain Layout
33390 Heading without formula in table of contents
33398 \begin_layout Subsubsection
33399 Heading with formula in table of contents
33403 \begin_layout Plain Layout
33413 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33420 \begin_layout Plain Layout
33430 \begin_layout Standard
33434 \begin_layout Plain Layout
33443 In the first heading a short title was used, in the second one
33452 \begin_layout Standard
33453 To get the same formatting as for the other headings, the complete heading
33462 \begin_layout Plain Layout
33464 \begin_inset CommandInset ref
33466 reference "sub:Bold-Formulas"
33478 \begin_layout Subsection
33479 Formulas in multi-column Text
33483 \begin_layout Plain Layout
33484 Formula ! in multi-column text
33492 \begin_layout Standard
33493 Formulas in multi-column text are often too wide to fit into a column and
33494 thus need to be set over the whole page width.
33495 This is done by using the LaTeX-package
33503 \begin_layout Plain Layout
33508 is part of every LaTeX standard installation.
33517 \begin_layout Plain Layout
33518 Packages ! multicol
33523 , that is loaded with the LaTeX-preamble line
33526 \begin_layout Standard
33531 usepackage{multicol}
33534 \begin_layout Standard
33535 \begin_inset Note Greyedout
33538 \begin_layout Plain Layout
33539 Note herby that the setting
33542 \begin_inset space ~
33549 Document\SpecialChar \menuseparator
33555 \begin_inset space ~
33575 \begin_layout Standard
33576 Before the multi-column text the command
33579 \begin_layout Standard
33584 begin{multicols}{column number}
33587 \begin_layout Standard
33588 is written in TeX-mode.
33589 The column number is a number in the range of 2
33590 \begin_inset space \thinspace{}
33594 \begin_inset space \thinspace{}
33598 Before the formula the multi-column text is ended by inserting the command
33601 \begin_layout Standard
33609 \begin_layout Standard
33613 \begin_layout Standard
33614 Due to the command some space is automatically added before the formula.
33616 \begin_inset space \thinspace{}
33619 mm vertical space is inserted before the formula.
33620 When the formula style
33626 \begin_layout Plain Layout
33628 \begin_inset CommandInset ref
33630 reference "sec:Formula-Styles"
33642 \begin_inset space \thinspace{}
33645 mm space is inserted instead.
33648 \begin_layout Standard
33649 As example a multi-column text with a displayed formula:
33652 \begin_layout Standard
33656 \begin_layout Plain Layout
33660 begin{multicols}{2}
33665 Das Spektrum wird fouriertransformiert.
33666 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33667 , Lösungsmittel) zu trennen.
33668 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33669 nun das Aussehen des Ausgangssignals.
33670 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33671 über alle Phasen integrieren muss.
33673 \begin_inset Formula $S$
33676 unser normiertes Ausgangssignal and
33677 \begin_inset Formula $P$
33680 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33684 \begin_layout Plain Layout
33694 \begin_inset VSpace -6mm
33698 \begin_inset Formula \begin{equation}
33699 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33707 \begin_layout Plain Layout
33711 begin{multicols}{2}
33717 \begin_inset Formula $S_{0}$
33720 das Signal ohne Gradient ist and the Normierungsbedingung
33721 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33725 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33727 \begin_inset Formula $\nicefrac{\pi}{2}$
33731 \begin_inset space \thinspace{}
33734 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33735 das Signal zusätzlich abschwächt.
33736 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33738 \begin_inset Formula $T_{2}$
33744 \begin_layout Standard
33748 \begin_layout Plain Layout
33760 \begin_layout Subsection
33761 Formulas with Description of Variables
33765 \begin_layout Plain Layout
33766 Formula ! with description of variables
33774 \begin_layout Standard
33775 To describe variables within a formula, like in formula
33776 \begin_inset CommandInset ref
33778 reference "eq:within"
33787 \begin_inset Formula $n$
33791 \begin_inset space ~
33794 matrix is used with left aligned columns for the
33795 \begin_inset Formula $n$
33802 \begin_layout Plain Layout
33804 \begin_inset CommandInset ref
33806 reference "sec:Matrices"
33815 To set the description in a smaller size, before the matrix e.
33816 \begin_inset space \thinspace{}
33820 \begin_inset space ~
33833 \begin_layout Plain Layout
33835 \begin_inset CommandInset ref
33837 reference "sub:Font-Sizes"
33849 \begin_layout Standard
33850 When the formula style
33856 \begin_layout Plain Layout
33858 \begin_inset CommandInset ref
33860 reference "sec:Formula-Styles"
33881 \begin_layout Plain Layout
33888 only works in formulas with the style
33893 \begin_inset CommandInset ref
33895 reference "sub:Variable-Space"
33904 is inserted before and after the matrix to have the same separation of
33905 the matrix from the equation and the side margin.
33908 \begin_layout Standard
33909 When the formula style
33913 is used, the method described in
33914 \begin_inset CommandInset ref
33916 reference "sub:Flalign-Environment"
33920 is used to indent formulas.
33922 \begin_inset CommandInset ref
33924 reference "eq:within"
33928 consists of five columns whereas in the first two columns contain the equation,
33929 the third the matrix, and the last one an empty TeX-brace.
33930 \begin_inset Formula \begin{flalign}
33931 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33932 \rho & \textrm{density}\\
33933 V & \textrm{volume}\\
33934 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33941 \begin_layout Subsection
33942 Upright small Greek Letters
33943 \begin_inset CommandInset label
33945 name "sub:Upright-small-Greek"
33953 \begin_layout Plain Layout
33954 Greek letters ! upright
33962 \begin_layout Standard
33963 Most of the math fonts only provide italic small Greek letters.
33964 But for symbols of elementary particles like pions and neutrinos, upright
33965 Greek letters are needed.
33974 \begin_layout Plain Layout
33979 is part of the LaTeX-package
33987 \begin_layout Plain Layout
33992 \begin_layout Plain Layout
34015 \begin_layout Plain Layout
34021 that is loaded with the LaTeX-preamble line
34024 \begin_layout Standard
34029 usepackage{upgreek}
34032 \begin_layout Standard
34038 \begin_layout Plain Layout
34048 \begin_inset Note Note
34051 \begin_layout Plain Layout
34052 The following table will only be displayed when the LaTeX-package
34061 They are created when the command for a small Greek letters is started
34067 For example the command
34074 \begin_inset Formula $\uptau$
34080 \begin_layout Standard
34081 With these commands reactions of elementary particles can be typeset:
34082 \begin_inset Formula \[
34083 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34090 \begin_layout Standard
34091 The upright letters are more bold and wider than the italic ones.
34092 They should therefore not be used for units like
34093 \begin_inset Quotes eld
34097 \begin_inset Quotes erd
34103 \begin_layout Standard
34107 \begin_layout Plain Layout
34117 \begin_inset Note Note
34120 \begin_layout Plain Layout
34121 The following will be displayed when the LaTeX-package
34133 \begin_layout Standard
34134 You need to install the LaTeX-package
34138 to see the rest of this subsection in the output.
34141 \begin_layout Standard
34145 \begin_layout Plain Layout
34157 \begin_layout Subsection
34158 Text Characters in Formulas
34159 \begin_inset CommandInset label
34161 name "sub:Text-Characters-in"
34169 \begin_layout Plain Layout
34178 \begin_layout Standard
34179 In some cases you might want to insert text characters directly into formulas.
34180 When for example the centered dot · is often used in formulas like
34181 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34184 , one would have to insert the command
34194 \begin_layout Plain Layout
34196 \begin_inset CommandInset ref
34198 reference "sub:Binary-Operators"
34207 all the time, because this character is defined in all encodings as text
34209 But the encoding can be changed by this LaTeX-preamble line:
34212 \begin_layout Standard
34217 Declare Inputtext{183}{
34227 f\SpecialChar \textcompwordmark{}
34231 \begin_layout Standard
34232 The character encoding (menu
34234 Document\SpecialChar \menuseparator
34235 Settings\SpecialChar \menuseparator
34238 ) specifies what character appears when a keyboard key is pressed.
34239 When the key for the character '·' is pressed, internally the command
34246 But this command is not available in a formula so that you would get LaTeX-erro
34248 With the changed encoding the right command is chosen automatically, depending
34249 on if the character was inserted into a formula or not.
34252 \begin_layout Standard
34253 The encoding of several characters is saved in definition files.
34254 Fore example the encoding
34258 is defined in the file
34262 that is in the installation folder of LaTeX.
34263 Encodings should only be changed via the LaTeX-preamble and not in the
34265 Otherwise own documents could not be edited by other LyX users working
34266 on other computers.
34269 \begin_layout Standard
34270 \begin_inset VSpace medskip
34273 Besides the centered dot, in this document the degree sign ° is defined
34274 with the following LaTeX-preamble line so that it can directly be inserted
34278 \begin_layout Standard
34283 DeclareInputtext{176}{
34293 f\SpecialChar \textcompwordmark{}
34297 \begin_layout Standard
34298 \begin_inset Newpage newpage
34304 \begin_layout Section
34310 \begin_layout Plain Layout
34319 \begin_layout Standard
34320 This section is a summary of the most important typographic rules, listed
34325 \begin_layout Plain Layout
34326 This collection was partly taken from the German semi-official dictionary
34328 \begin_inset Quotes eld
34332 \begin_inset Quotes erd
34336 \begin_inset CommandInset citation
34342 that lists some of the ISO rules.
34350 \begin_layout Itemize
34359 \begin_layout Plain Layout
34360 done with font styles, see
34361 \begin_inset CommandInset ref
34363 reference "sub:Font-Styles"
34373 \begin_inset space \thinspace{}
34377 \begin_inset Newline newline
34380 Between the value and the unit is the smallest space, see
34381 \begin_inset CommandInset ref
34383 reference "sub:Predefined-Space"
34388 \begin_inset Newline newline
34391 This convention is automatically fulfilled when the command
34398 When it is entered to a formula, two boxes appear.
34399 In the first one the value is inserted, in the second one the unit, and
34401 \begin_inset Formula $\unit[30]{km/h}$
34405 \begin_inset space \thinspace{}
34415 is not a real LaTeX command but the command
34421 , therefore you cannot use it in TeX code.
34424 \begin_layout Itemize
34425 Percent and perthousand signs are set like physical units:
34426 \begin_inset Newline newline
34430 \begin_inset space \thinspace{}
34436 \begin_layout Itemize
34437 The degree sign follows directly on the value: 15°, but not when it is used
34439 \begin_inset space \thinspace{}
34445 \begin_layout Itemize
34446 In numbers with more than four digits the smallest space is inserted before
34447 every third digit to group them:
34457 \begin_inset space \thinspace{}
34461 \begin_inset space \thinspace{}
34467 \begin_layout Itemize
34468 For dimensions like 120×90×40
34469 \begin_inset space \thinspace{}
34472 cm the multiplication sign
34473 \begin_inset Quotes eld
34477 \begin_inset Quotes erd
34481 It is available with the LaTeX-command
34487 , but can also directly be inserted with some keyboard definitions.
34490 \begin_layout Itemize
34491 Functions with names consisting of several letters are set upright to avoid
34493 \begin_inset CommandInset ref
34495 reference "sub:Predefined-Functions"
34502 \begin_layout Itemize
34503 Indices consisting of several letters, are set upright:
34504 \begin_inset Formula $E_{\mathrm{kin}}$
34508 \begin_inset Newline newline
34511 Components of matrices are set italic:
34512 \begin_inset Formula $\hat{H}_{kl}$
34518 \begin_layout Itemize
34519 The differentiation/integration operator 'd', the Euler's number 'e', and
34520 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34524 \begin_layout Standard
34525 \begin_inset Newpage newpage
34531 \begin_layout Section
34536 \begin_layout Plain Layout
34545 \begin_layout Standard
34546 Some characters and symbols can be created with several commands.
34547 Here is a list of the synonym commands:
34550 \begin_layout Standard
34551 \begin_inset VSpace bigskip
34555 \begin_inset space \hfill{}
34559 \begin_inset Tabular
34560 <lyxtabular version="3" rows="12" columns="2">
34562 <column alignment="center" valignment="top" width="0pt">
34563 <column alignment="center" valignment="top" width="0pt">
34565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34568 \begin_layout Plain Layout
34574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34577 \begin_layout Plain Layout
34579 \begin_inset Note Note
34582 \begin_layout Plain Layout
34589 is only used as spacer.
34601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34604 \begin_layout Plain Layout
34612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34615 \begin_layout Plain Layout
34619 \begin_layout Plain Layout
34632 \begin_layout Plain Layout
34646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34649 \begin_layout Plain Layout
34657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34660 \begin_layout Plain Layout
34670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34673 \begin_layout Plain Layout
34681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34684 \begin_layout Plain Layout
34694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34697 \begin_layout Plain Layout
34705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34708 \begin_layout Plain Layout
34716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34719 \begin_layout Plain Layout
34727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34730 \begin_layout Plain Layout
34738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34741 \begin_layout Plain Layout
34749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34752 \begin_layout Plain Layout
34762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34765 \begin_layout Plain Layout
34773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34776 \begin_layout Plain Layout
34786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34789 \begin_layout Plain Layout
34797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34800 \begin_layout Plain Layout
34810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34813 \begin_layout Plain Layout
34821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34824 \begin_layout Plain Layout
34834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34837 \begin_layout Plain Layout
34845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34848 \begin_layout Plain Layout
34856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34859 \begin_layout Plain Layout
34867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34870 \begin_layout Plain Layout
34882 \begin_inset space \hfill{}
34886 \begin_inset Tabular
34887 <lyxtabular version="3" rows="12" columns="2">
34889 <column alignment="center" valignment="top" width="0pt">
34890 <column alignment="center" valignment="top" width="0pt">
34892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34895 \begin_layout Plain Layout
34901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34904 \begin_layout Plain Layout
34912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34915 \begin_layout Plain Layout
34923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34926 \begin_layout Plain Layout
34938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34941 \begin_layout Plain Layout
34949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34952 \begin_layout Plain Layout
34962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34965 \begin_layout Plain Layout
34973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34976 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35000 \begin_layout Plain Layout
35008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35011 \begin_layout Plain Layout
35019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35022 \begin_layout Plain Layout
35030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35033 \begin_layout Plain Layout
35041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35044 \begin_layout Plain Layout
35054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35057 \begin_layout Plain Layout
35065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35068 \begin_layout Plain Layout
35078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35081 \begin_layout Plain Layout
35089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35092 \begin_layout Plain Layout
35102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35105 \begin_layout Plain Layout
35113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35116 \begin_layout Plain Layout
35126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35129 \begin_layout Plain Layout
35137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35140 \begin_layout Plain Layout
35150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35153 \begin_layout Plain Layout
35161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35164 \begin_layout Plain Layout
35178 \begin_inset space \hfill{}
35184 \begin_layout Standard
35185 \begin_inset Newpage newpage
35191 \begin_layout Bibliography
35192 \begin_inset CommandInset bibitem
35193 LatexCommand bibitem
35205 The LaTeX Companion
35208 Addison Wesley, 2004
35211 \begin_layout Bibliography
35212 \begin_inset CommandInset bibitem
35213 LatexCommand bibitem
35219 \begin_inset CommandInset href
35222 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35226 of LaTeX's math abilities
35229 \begin_layout Bibliography
35230 \begin_inset CommandInset bibitem
35231 LatexCommand bibitem
35236 LaTeX tips and tricks-
35237 \begin_inset CommandInset href
35240 target "http://tug.org/TeXnik/"
35247 \begin_layout Bibliography
35248 \begin_inset CommandInset bibitem
35249 LatexCommand bibitem
35255 \begin_inset CommandInset href
35258 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35266 \begin_layout Plain Layout
35278 \begin_layout Bibliography
35279 \begin_inset CommandInset bibitem
35280 LatexCommand bibitem
35286 \begin_inset CommandInset href
35289 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35293 of all symbols available with LaTeX-packages
35296 \begin_layout Bibliography
35297 \begin_inset CommandInset bibitem
35298 LatexCommand bibitem
35304 \begin_inset CommandInset href
35306 name "Documentation"
35307 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35311 of the LaTeX-package
35319 \begin_layout Plain Layout
35320 Packages ! hyperref
35328 \begin_layout Bibliography
35329 \begin_inset CommandInset bibitem
35330 LatexCommand bibitem
35336 \begin_inset CommandInset href
35339 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35350 \begin_inset CommandInset ref
35352 reference "sub:Operator-Limits"
35360 \begin_layout Plain Layout
35371 \begin_layout Bibliography
35372 \begin_inset CommandInset bibitem
35373 LatexCommand bibitem
35384 Auflage, Duden 2001
35387 \begin_layout Subsubsection*
35388 \begin_inset CommandInset index_print
35389 LatexCommand printindex