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$}\raisebox{-4mm}{}$
12654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12657 \begin_layout Plain Layout
12664 \begin_layout Plain Layout
12679 \begin_layout Plain Layout
12693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12696 \begin_layout Plain Layout
12697 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12710 \begin_layout Plain Layout
12717 \begin_layout Plain Layout
12731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12734 \begin_layout Plain Layout
12735 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12748 \begin_layout Plain Layout
12755 \begin_layout Plain Layout
12765 \begin_inset Formula $\to$
12769 \begin_inset Formula $\to$
12782 \begin_layout Plain Layout
12792 \begin_inset Formula $\downarrow$
12800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12803 \begin_layout Plain Layout
12804 \begin_inset Formula $\raisebox{6mm}{}$
12808 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12812 \begin_inset Formula $\raisebox{-4mm}{}$
12833 \begin_layout Standard
12834 The frame thickness can also be adjusted.
12835 To do this the following commands have to be inserted in TeX-mode before
12839 \begin_layout Standard
12849 \begin_inset Quotes eld
12853 \begin_inset Quotes erd
12867 \begin_inset Quotes eld
12871 \begin_inset Quotes erd
12877 \begin_layout Standard
12878 \begin_inset Quotes eld
12882 \begin_inset Quotes erd
12885 specifies the minimal distance between the frame and the first character
12887 An example for this is the following framed formula:
12891 \begin_layout Plain Layout
12903 \begin_inset Formula \[
12908 Before this formula the commands
12911 \begin_layout Standard
12933 \begin_layout Standard
12934 were inserted in TeX-mode.
12935 The given values are used for all following boxes.
12938 \begin_layout Standard
12939 To return to the standard frame size, the command
12942 \begin_layout Standard
12967 \begin_layout Plain Layout
12981 \begin_layout Standard
12982 is inserted in TeX-mode before the next formula.
12985 \begin_layout Subsection
12986 Boxes without Frame
12987 \begin_inset CommandInset label
12989 name "sub:Boxes-without-Frame"
12997 \begin_layout Plain Layout
12998 Boxes ! without frame
13006 \begin_layout Standard
13007 For boxes without a frame there are the following box commands:
13017 \begin_layout Plain Layout
13035 \begin_layout Plain Layout
13053 \begin_layout Plain Layout
13064 \begin_layout Standard
13071 a box can be super- or subscripted.
13072 But in contrary to normal super- and subscripting, the characters in the
13073 box keep their font size.
13080 is used in the following scheme:
13083 \begin_layout Standard
13088 raisebox{height}{box content}
13091 \begin_layout Standard
13092 When the box should contain a formula, an extra formula is needed like for
13102 \begin_layout Standard
13104 \begin_inset Tabular
13105 <lyxtabular version="3" rows="4" columns="2">
13107 <column alignment="center" valignment="top" width="0">
13108 <column alignment="center" valignment="top" width="0">
13110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13113 \begin_layout Plain Layout
13119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13122 \begin_layout Plain Layout
13130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13133 \begin_layout Plain Layout
13137 \begin_inset Formula $\to$
13143 \begin_inset Formula $\to$
13151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13154 \begin_layout Plain Layout
13155 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13168 \begin_layout Plain Layout
13172 \begin_inset Formula $\to$
13178 \begin_inset Formula $\to$
13186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13189 \begin_layout Plain Layout
13190 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13203 \begin_layout Plain Layout
13207 \begin_inset Formula $\to$
13222 \begin_layout Plain Layout
13236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13239 \begin_layout Plain Layout
13243 \begin_layout Plain Layout
13267 \begin_layout Standard
13268 The last formula can currently only be created using TeX-mode because LyX
13269 inserts a box instead of the needed extra formula.
13273 \begin_layout Plain Layout
13275 \begin_inset CommandInset href
13277 name "LyX-bug #1435"
13278 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13290 \begin_layout Standard
13315 , with the difference that there is no frame.
13318 \begin_layout Subsection
13320 \begin_inset CommandInset label
13322 name "sub:Colored-Boxes"
13330 \begin_layout Plain Layout
13339 \begin_layout Standard
13340 To be able to use all commands explained in this section, the LaTeX-package
13349 \begin_layout Plain Layout
13354 is part of every LaTeX standard installation.
13363 \begin_layout Plain Layout
13369 has to be loaded in the LaTeX-preamble with the line
13373 \begin_layout Plain Layout
13374 When text is colored somewhere in the document with a predefined color,
13375 LyX loads the LaTeX-package
13380 Thus it is possible that the package is loaded twice, but this doesn't
13387 \begin_inset Note Note
13390 \begin_layout Plain Layout
13391 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13400 \begin_layout Standard
13408 \begin_layout Standard
13409 \begin_inset VSpace medskip
13412 To color boxes, the command
13422 \begin_layout Plain Layout
13430 is used in the following scheme:
13433 \begin_layout Standard
13438 colorbox{color}{box content}
13441 \begin_layout Standard
13442 The box content can also be a box and a
13448 can also be part of another box (see the 2nd and 3rd example).
13449 When the box should contain a formula, an extra formula has to be created,
13460 \begin_layout Plain Layout
13461 This also applies for the command
13469 \begin_inset CommandInset href
13471 name "LyX-bug #1435"
13472 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13484 \begin_layout Standard
13485 One of the following predefined colors can be chosen:
13488 \begin_layout Standard
13522 \begin_layout Standard
13524 \begin_inset Tabular
13525 <lyxtabular version="3" rows="4" columns="2">
13527 <column alignment="center" valignment="top" width="0">
13528 <column alignment="center" valignment="top" width="0">
13530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13533 \begin_layout Plain Layout
13539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13542 \begin_layout Plain Layout
13544 \begin_inset Note Note
13547 \begin_layout Plain Layout
13554 is only used as spacer.
13566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13569 \begin_layout Plain Layout
13573 \begin_inset Formula $\to$
13583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13586 \begin_layout Plain Layout
13587 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13600 \begin_layout Plain Layout
13604 \begin_inset Formula $\to$
13615 \begin_layout Plain Layout
13629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13632 \begin_layout Plain Layout
13633 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13646 \begin_layout Plain Layout
13653 \begin_layout Plain Layout
13665 \begin_inset Formula $\to$
13675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13678 \begin_layout Plain Layout
13679 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13695 \begin_layout Standard
13702 only colors the box but not the characters in the box.
13703 To color all characters, the whole formula is highlighted and the wanted
13704 color is chosen in the
13707 \begin_inset space ~
13713 The dialog can be called with the toolbar button
13714 \begin_inset Graphics
13715 filename ../images/dialog-show_character.png
13722 Edit\SpecialChar \menuseparator
13724 \begin_inset space ~
13727 Style\SpecialChar \menuseparator
13731 The formula number has then the same color as the formula.
13732 When the formula number should get another color than the formula characters,
13733 the color must be changed within the formula.
13736 \begin_layout Standard
13740 \begin_layout Standard
13743 \begin_inset Formula \begin{equation}
13744 \int A=B\label{eq:red}\end{equation}
13751 \begin_inset Formula \begin{equation}
13752 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13759 \begin_layout Standard
13761 \begin_inset CommandInset ref
13767 is completely colored red.
13768 \begin_inset Newline newline
13772 \begin_inset CommandInset ref
13774 reference "eq:redgreen"
13778 was first completely colored green to set the color for the formula number.
13779 Subsequently the formula characters were colored red.
13782 \begin_layout Standard
13783 \begin_inset VSpace bigskip
13786 To color the frame different than the rest of the box, the command
13796 \begin_layout Plain Layout
13804 is used in the following scheme:
13807 \begin_layout Standard
13812 fcolorbox{frame color}{color}{box content}
13815 \begin_layout Standard
13822 is an extension of the command
13829 The frame width is set, like for
13852 \begin_layout Plain Layout
13864 \begin_inset Formula \[
13865 \fcolorbox{cyan}{magenta}{A=B}\]
13873 \begin_layout Plain Layout
13887 \begin_layout Standard
13888 This formula was created with the command
13889 \begin_inset Newline newline
13897 \begin_inset Formula $\to$
13903 \begin_inset Formula $\to$
13913 \begin_layout Standard
13914 \begin_inset VSpace bigskip
13917 To use other colors than the predefined ones, they have to be defined first.
13920 \begin_layout Standard
13921 One can for example define the color
13922 \begin_inset Quotes eld
13930 \begin_inset Quotes erd
13933 with the LaTeX-preamble line:
13936 \begin_layout Standard
13941 definecolor{darkgreen}{cmyk}{0.5,
13959 \begin_layout Plain Layout
13970 \begin_layout Standard
13975 is the color space that denotes the colors
13992 The four comma separated numbers are the portion factor for the corresponding
13993 colors of the color space.
13994 The factors can be in the range of 0
13995 \begin_inset space \thinspace{}
13999 \begin_inset space \thinspace{}
14007 also the color space
14011 can be used for definitions.
14028 , so that there are in this case three portion factors for the corresponding
14030 Furthermore there is the color space
14034 with one portion factor for the gray value.
14037 \begin_layout Standard
14038 As example a framed box with the new defined color
14042 where the characters have been colored
14047 \begin_inset Formula \begin{equation}
14048 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14055 \begin_layout Standard
14056 Self-defined colors can also be used for text with the help of the command
14067 \begin_layout Plain Layout
14076 \begin_layout Standard
14080 \begin_layout Plain Layout
14084 textcolor{darkgreen}{
14090 \begin_inset Quotes eld
14094 \begin_inset Quotes erd
14101 \begin_layout Plain Layout
14111 \begin_layout Standard
14122 \begin_layout Plain Layout
14130 is used in the scheme
14134 textcolor{color}{characters to color}
14139 \begin_layout Subsection
14141 \begin_inset CommandInset label
14143 name "sub:Paragraph-Boxes"
14151 \begin_layout Plain Layout
14152 Boxes ! as paragraph
14160 \begin_layout Standard
14161 A box that can contain several lines and paragraphs, a so called paragraph
14162 box (parbox), can be created with the menu
14164 Insert\SpecialChar \menuseparator
14167 or the toolbar button
14168 \begin_inset Graphics
14169 filename ../images/box-insert.png
14177 \begin_layout Standard
14178 The following example shows a framed parbox in a line:
14181 \begin_layout Standard
14182 \begin_inset VSpace medskip
14186 \begin_inset Box Boxed
14195 height_special "totalheight"
14198 \begin_layout Plain Layout
14199 This is a paragraph box.
14201 \begin_inset space \thinspace{}
14204 cm long and can also contain formulas:
14205 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14216 \begin_layout Standard
14217 \begin_inset VSpace medskip
14223 \begin_layout Standard
14224 Such a box is created by right-clicking on the gray box inset.
14225 A dialog pops up showing the box properties.
14239 \begin_inset space \thinspace{}
14244 Vertical Box Alignment
14249 \begin_layout Standard
14250 \begin_inset VSpace medskip
14253 In LaTeX a parbox is created with the command
14263 \begin_layout Plain Layout
14271 that has the following scheme:
14274 \begin_layout Standard
14279 parbox[position]{width}{box content}
14282 \begin_layout Standard
14296 for bottom means that the box is aligned within the surrounding text with
14302 for top this is done with the first line.
14303 When no position is given, the box will be vertically centered, see section
14311 \begin_inset space ~
14316 manual for examples.
14319 \begin_layout Standard
14320 \begin_inset VSpace bigskip
14323 To frame formulas completely, including the formula number, the formula
14324 must be set into a parbox.
14325 To do this, the command
14339 is inserted in TeX-mode before the formula.
14348 \begin_layout Plain Layout
14358 is hereby the line width set for the document.
14359 Because the frame is outside the parbox, 2
14360 \begin_inset space \thinspace{}
14363 times the frame separation and the frame thickness must be subtracted from
14365 As this is not automatically done by LyX due to a bug
14369 \begin_layout Plain Layout
14370 \begin_inset CommandInset href
14372 name "LyX-bug #4483"
14373 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14382 , TeX-mode has to be used.
14383 To be able to multiply and subtract in arguments, the LaTeX-package
14391 \begin_layout Plain Layout
14396 is part of every LaTeX standard installation.
14405 \begin_layout Plain Layout
14411 must be loaded in the LaTeX-preamble with the line
14414 \begin_layout Standard
14422 \begin_layout Standard
14423 Behind the formula both boxes are closed by entering
14428 Here is an example:
14432 \begin_layout Plain Layout
14446 \begin_layout Standard
14450 \begin_layout Plain Layout
14468 \begin_inset Formula \begin{equation}
14469 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14477 \begin_layout Plain Layout
14488 \begin_layout Plain Layout
14502 \begin_layout Standard
14503 \begin_inset VSpace medskip
14506 As a parbox is used as argument of
14512 , there is in this case no difference between
14527 \begin_layout Standard
14528 \begin_inset VSpace bigskip
14531 Paragraph boxes are very useful to comment formulas directly.
14538 is used in combination with the command
14552 \begin_inset CommandInset ref
14554 reference "sub:User-defined-Numbering"
14561 \begin_layout Standard
14562 An example of a formula commented with
14571 \begin_layout Standard
14575 \begin_layout Plain Layout
14588 This is a description.
14589 It is distinctly separated from the formula and multiline.
14593 \begin_layout Plain Layout
14605 \begin_layout Standard
14606 Such a formula must be inserted completely in TeX-mode because LyX does
14607 not yet support the command
14614 The formula is created with the following command sequence:
14617 \begin_layout Standard
14630 is inserted in TeX-mode.
14634 \begin_layout Plain Layout
14635 When the formula style
14647 can also be replaced by
14654 (formula styles see
14655 \begin_inset CommandInset ref
14657 reference "sec:Formula-Styles"
14666 Then the description follows as normal text, and finally
14672 is inserted in TeX-mode.
14685 hereby create a displayed formula.
14688 \begin_layout Standard
14695 can be seen in this example that was
14696 \begin_inset Quotes eld
14700 \begin_inset Quotes erd
14703 using the mathematical textmode:
14704 \begin_inset Formula \[
14705 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14712 \begin_layout Section
14717 \begin_layout Plain Layout
14726 \begin_layout Subsection
14728 \begin_inset CommandInset label
14730 name "sub:Big-Operators"
14738 \begin_layout Plain Layout
14748 \begin_layout Plain Layout
14758 \begin_layout Plain Layout
14767 \begin_layout Standard
14768 To be able to use all integral operators listed here, the option
14770 Use esint package automatically
14772 must be set in the document settings under
14775 \begin_inset space ~
14783 \begin_layout Standard
14784 \begin_inset space \hfill{}
14788 \begin_inset Tabular
14789 <lyxtabular version="3" rows="11" columns="2">
14791 <column alignment="center" valignment="top" width="0pt">
14792 <column alignment="center" valignment="top" width="0pt">
14794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14797 \begin_layout Plain Layout
14803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14806 \begin_layout Plain Layout
14814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14817 \begin_layout Plain Layout
14824 \begin_layout Plain Layout
14837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14840 \begin_layout Plain Layout
14841 \begin_inset Formula $\sum$
14851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14854 \begin_layout Plain Layout
14861 \begin_layout Plain Layout
14874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14877 \begin_layout Plain Layout
14878 \begin_inset Formula $\int$
14888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14891 \begin_layout Plain Layout
14899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14902 \begin_layout Plain Layout
14903 \begin_inset Formula $\intop$
14913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14916 \begin_layout Plain Layout
14924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14927 \begin_layout Plain Layout
14928 \begin_inset Formula $\oint$
14938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14941 \begin_layout Plain Layout
14949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14952 \begin_layout Plain Layout
14953 \begin_inset Formula $\ointop$
14963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14966 \begin_layout Plain Layout
14974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14977 \begin_layout Plain Layout
14978 \begin_inset Formula $\ointctrclockwise$
14988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14991 \begin_layout Plain Layout
14999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15002 \begin_layout Plain Layout
15003 \begin_inset Formula $\ointclockwise$
15013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15016 \begin_layout Plain Layout
15024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15027 \begin_layout Plain Layout
15028 \begin_inset Formula $\sqint$
15038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15041 \begin_layout Plain Layout
15049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15052 \begin_layout Plain Layout
15053 \begin_inset Formula $\bigcap$
15063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15066 \begin_layout Plain Layout
15074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15077 \begin_layout Plain Layout
15078 \begin_inset Formula $\bigcup$
15092 \begin_inset space \hfill{}
15096 \begin_inset Tabular
15097 <lyxtabular version="3" rows="10" columns="2">
15099 <column alignment="center" valignment="top" width="0pt">
15100 <column alignment="center" valignment="top" width="0pt">
15102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15105 \begin_layout Plain Layout
15111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15114 \begin_layout Plain Layout
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15125 \begin_layout Plain Layout
15132 \begin_layout Plain Layout
15145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15148 \begin_layout Plain Layout
15149 \begin_inset Formula $\prod$
15159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15162 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15173 \begin_layout Plain Layout
15174 \begin_inset Formula $\coprod$
15184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15198 \begin_layout Plain Layout
15199 \begin_inset Formula $\bigodot$
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15212 \begin_layout Plain Layout
15220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15223 \begin_layout Plain Layout
15224 \begin_inset Formula $\bigotimes$
15234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15237 \begin_layout Plain Layout
15245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15248 \begin_layout Plain Layout
15249 \begin_inset Formula $\bigoplus$
15259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15262 \begin_layout Plain Layout
15270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15273 \begin_layout Plain Layout
15274 \begin_inset Formula $\bigwedge$
15284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15287 \begin_layout Plain Layout
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15298 \begin_layout Plain Layout
15299 \begin_inset Formula $\bigvee$
15309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15312 \begin_layout Plain Layout
15320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15323 \begin_layout Plain Layout
15324 \begin_inset Formula $\bigsqcup$
15334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15337 \begin_layout Plain Layout
15345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15348 \begin_layout Plain Layout
15349 \begin_inset Formula $\biguplus$
15363 \begin_inset space \hfill{}
15369 \begin_layout Standard
15370 All big operators can also be inserted via the math toolbar button
15371 \begin_inset Graphics
15372 filename ../images/math/intop.png
15380 \begin_layout Standard
15381 The operators are called big because they are bigger than the sometimes
15382 equal looking binary operators.
15383 All big operators can have limits as described in the next subsection.
15386 \begin_layout Standard
15412 \begin_inset space ~
15415 in the style the operator limits are displayed, see
15416 \begin_inset CommandInset ref
15418 reference "sub:Operator-Limits"
15426 \begin_layout Subsubsection*
15427 Advices for Integrals
15430 \begin_layout Standard
15435 in an integral is an operator, that therefore has to be set upright.
15436 This is done by highlighting the
15440 and using the keyboard shortcut
15443 \begin_inset space ~
15452 \begin_layout Plain Layout
15458 \begin_inset CommandInset ref
15460 reference "sub:Font-Styles"
15470 Finally the smallest space is inserted before the
15474 , as this is usual for operators.
15478 \begin_layout Standard
15480 \begin_inset Formula $\int A(x)dx$
15484 \begin_inset Newline newline
15491 \begin_layout Plain Layout
15501 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15507 \begin_layout Standard
15508 For multiple integrals there are the following commands:
15509 \begin_inset VSpace medskip
15515 \begin_layout Standard
15516 \begin_inset space \hfill{}
15520 \begin_inset Tabular
15521 <lyxtabular version="3" rows="4" columns="2">
15523 <column alignment="center" valignment="top" width="0">
15524 <column alignment="center" valignment="top" width="0">
15526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15529 \begin_layout Plain Layout
15535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15538 \begin_layout Plain Layout
15540 \begin_inset Note Note
15543 \begin_layout Plain Layout
15550 is only used as spacer.
15562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15565 \begin_layout Plain Layout
15573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15576 \begin_layout Plain Layout
15577 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15590 \begin_layout Plain Layout
15598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15601 \begin_layout Plain Layout
15602 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15615 \begin_layout Plain Layout
15623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15626 \begin_layout Plain Layout
15627 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15641 \begin_inset space \hfill{}
15645 \begin_inset Tabular
15646 <lyxtabular version="3" rows="4" columns="2">
15648 <column alignment="center" valignment="top" width="0">
15649 <column alignment="center" valignment="top" width="0">
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15654 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15663 \begin_layout Plain Layout
15671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15674 \begin_layout Plain Layout
15682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15685 \begin_layout Plain Layout
15686 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15699 \begin_layout Plain Layout
15707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15710 \begin_layout Plain Layout
15711 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15724 \begin_layout Plain Layout
15732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15735 \begin_layout Plain Layout
15736 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15750 \begin_inset space \hfill{}
15756 \begin_layout Subsection
15758 \begin_inset CommandInset label
15760 name "sub:Operator-Limits"
15768 \begin_layout Plain Layout
15777 \begin_layout Standard
15778 Limits are created by super- and subscripts:
15781 \begin_layout Standard
15783 \begin_inset Tabular
15784 <lyxtabular version="3" rows="2" columns="2">
15786 <column alignment="center" valignment="top" width="0pt">
15787 <column alignment="center" valignment="top" width="0pt">
15789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15792 \begin_layout Plain Layout
15798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15801 \begin_layout Plain Layout
15803 \begin_inset Note Note
15806 \begin_layout Plain Layout
15813 is only used as spacer.
15825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15828 \begin_layout Plain Layout
15837 \begin_layout Plain Layout
15847 \begin_inset Formula $\to$
15851 \begin_inset Formula $\to$
15859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15862 \begin_layout Plain Layout
15863 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15879 \begin_layout Standard
15880 Limits of inline formulas are set right beside the operator.
15881 Limits in displayed formulas are set above or below the operator, except
15882 of integral limits.
15885 \begin_layout Standard
15886 To force that the limits are set beside the operator, the cursor is set
15887 directly behind the operator and the limits type is changed with the menu
15890 Edit\SpecialChar \menuseparator
15891 Math\SpecialChar \menuseparator
15903 \begin_inset space ~
15912 \begin_layout Standard
15913 The default limits type is this:
15914 \begin_inset Formula \[
15915 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15919 This is how it looks when the limits type was changed to
15926 \begin_inset Formula \[
15927 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15931 For integrals, except of
15943 , the limits are by default set beside the operator.
15944 But for multiple integrals the limits are often set below the operator.
15945 In the following example the limits type was therefore set to
15949 and so set below the integrals:
15950 \begin_inset Formula \begin{equation}
15951 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15958 \begin_layout Standard
15959 \begin_inset VSpace medskip
15962 To specify conditions for limits, the commands
15972 \begin_layout Plain Layout
15990 \begin_layout Plain Layout
15999 To create for example this expression
16000 \begin_inset Formula \begin{equation}
16001 \sum_{\begin{subarray}{c}
16003 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16010 \begin_layout Standard
16011 the following has to be done:
16012 \begin_inset Newline newline
16027 \begin_layout Plain Layout
16039 One is now in a blue box under the summation operator and insert there
16048 \begin_layout Plain Layout
16060 The blue box is now within a purple box and now several lines can be written
16062 A new line is created by inserting a line break (
16068 \begin_inset Newline newline
16073 0<k<1000 Ctrl-Return
16074 \begin_inset Newline newline
16079 is typed in, a new box appears below for the new line.
16082 \begin_layout Standard
16083 The alignment of the lines can be changed to left aligned with the
16093 Edit\SpecialChar \menuseparator
16097 To get right alignment,
16105 \begin_layout Plain Layout
16116 is inserted at the beginning of the line.
16119 \begin_layout Standard
16132 with the difference that the lines are always centered.
16135 \begin_layout Standard
16136 \begin_inset VSpace bigskip
16140 \begin_inset CommandInset ref
16142 reference "eq:substack"
16146 there can be too much space beside an operator, because the characters
16147 following the operator are set beside the limits.
16150 \begin_layout Standard
16151 To avoid this, the following macro can be used in the LaTeX-preamble:
16154 \begin_layout Standard
16168 \begin_inset Newline newline
16180 \begin_inset Newline newline
16187 mathclapinternal #1#2{
16191 mathsurround =0pt #1{#2}$}}
16194 \begin_layout Standard
16195 This defines the command
16205 \begin_layout Plain Layout
16213 that sets the width of the limit to 0
16214 \begin_inset space \thinspace{}
16218 The command scheme is
16221 \begin_layout Standard
16229 \begin_layout Standard
16230 where the limit can consist of several conditions.
16233 \begin_layout Standard
16235 \begin_inset CommandInset ref
16237 reference "eq:substack"
16241 , one uses the command
16244 \begin_layout Standard
16257 \begin_layout Plain Layout
16266 0<k<1000 Ctrl-Enter
16269 \begin_layout Standard
16270 to create the lower limit.
16271 The summand is now directly behind the summation operator:
16272 \begin_inset Formula \[
16273 \sum_{\mathclap{\substack{0<k<1000\\
16274 \\k\,\in\,\mathbb{N}}
16282 \begin_layout Standard
16283 \begin_inset VSpace bigskip
16286 How to use one limit for several operators is described in
16287 \begin_inset CommandInset ref
16289 reference "sub:Self-defined-Operators"
16296 \begin_layout Standard
16297 \begin_inset Newpage newpage
16303 \begin_layout Subsection
16305 \begin_inset CommandInset label
16307 name "sub:Binary-Operators"
16315 \begin_layout Plain Layout
16324 \begin_layout Standard
16325 Binary operators are surrounded by space when there is a character before
16327 \begin_inset VSpace medskip
16333 \begin_layout Standard
16334 \begin_inset space \hfill{}
16338 \begin_inset Tabular
16339 <lyxtabular version="3" rows="13" columns="2">
16341 <column alignment="center" valignment="top" width="0pt">
16342 <column alignment="center" valignment="top" width="0pt">
16344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16347 \begin_layout Plain Layout
16349 \begin_inset Note Note
16352 \begin_layout Plain Layout
16359 is only used as spacer.
16369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16372 \begin_layout Plain Layout
16380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16383 \begin_layout Plain Layout
16389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16392 \begin_layout Plain Layout
16393 \begin_inset Formula $+$
16403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16406 \begin_layout Plain Layout
16412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16415 \begin_layout Plain Layout
16416 \begin_inset Formula $-$
16426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16429 \begin_layout Plain Layout
16437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16440 \begin_layout Plain Layout
16441 \begin_inset Formula $\pm$
16451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16454 \begin_layout Plain Layout
16462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16465 \begin_layout Plain Layout
16466 \begin_inset Formula $\mp$
16476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16479 \begin_layout Plain Layout
16487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16490 \begin_layout Plain Layout
16491 \begin_inset Formula $\cdot$
16501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16504 \begin_layout Plain Layout
16512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16515 \begin_layout Plain Layout
16516 \begin_inset Formula $\times$
16526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16529 \begin_layout Plain Layout
16537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16540 \begin_layout Plain Layout
16541 \begin_inset Formula $\div$
16551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16554 \begin_layout Plain Layout
16558 \begin_layout Plain Layout
16571 \begin_layout Plain Layout
16583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16586 \begin_layout Plain Layout
16587 \begin_inset Formula $*$
16597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16600 \begin_layout Plain Layout
16608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16611 \begin_layout Plain Layout
16612 \begin_inset Formula $\star$
16622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16625 \begin_layout Plain Layout
16633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16636 \begin_layout Plain Layout
16637 \begin_inset Formula $\circ$
16647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16650 \begin_layout Plain Layout
16658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16661 \begin_layout Plain Layout
16662 \begin_inset Formula $\diamond$
16672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16675 \begin_layout Plain Layout
16683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16686 \begin_layout Plain Layout
16687 \begin_inset Formula $\bullet$
16701 \begin_inset space \hfill{}
16705 \begin_inset Tabular
16706 <lyxtabular version="3" rows="13" columns="2">
16708 <column alignment="center" valignment="top" width="0pt">
16709 <column alignment="center" valignment="top" width="0pt">
16711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16714 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16723 \begin_layout Plain Layout
16731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16734 \begin_layout Plain Layout
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16745 \begin_layout Plain Layout
16746 \begin_inset Formula $\nabla$
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16759 \begin_layout Plain Layout
16767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16770 \begin_layout Plain Layout
16771 \begin_inset Formula $\bigtriangledown$
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16784 \begin_layout Plain Layout
16792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16795 \begin_layout Plain Layout
16796 \begin_inset Formula $\bigtriangleup$
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16809 \begin_layout Plain Layout
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16820 \begin_layout Plain Layout
16821 \begin_inset Formula $\Box$
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16834 \begin_layout Plain Layout
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16845 \begin_layout Plain Layout
16846 \begin_inset Formula $\cap$
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16859 \begin_layout Plain Layout
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16870 \begin_layout Plain Layout
16871 \begin_inset Formula $\cup$
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16884 \begin_layout Plain Layout
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16895 \begin_layout Plain Layout
16896 \begin_inset Formula $\dagger$
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16909 \begin_layout Plain Layout
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16920 \begin_layout Plain Layout
16921 \begin_inset Formula $\ddagger$
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16934 \begin_layout Plain Layout
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16945 \begin_layout Plain Layout
16946 \begin_inset Formula $\wr$
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16959 \begin_layout Plain Layout
16967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16970 \begin_layout Plain Layout
16971 \begin_inset Formula $\bigcirc$
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16984 \begin_layout Plain Layout
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16995 \begin_layout Plain Layout
16996 \begin_inset Formula $\wedge$
17006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17009 \begin_layout Plain Layout
17017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17020 \begin_layout Plain Layout
17021 \begin_inset Formula $\vee$
17035 \begin_inset space \hfill{}
17039 \begin_inset Tabular
17040 <lyxtabular version="3" rows="13" columns="2">
17042 <column alignment="center" valignment="top" width="0pt">
17043 <column alignment="center" valignment="top" width="0pt">
17045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17048 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17068 \begin_layout Plain Layout
17076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17079 \begin_layout Plain Layout
17080 \begin_inset Formula $\oplus$
17090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17093 \begin_layout Plain Layout
17101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17104 \begin_layout Plain Layout
17105 \begin_inset Formula $\ominus$
17115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17118 \begin_layout Plain Layout
17126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17129 \begin_layout Plain Layout
17130 \begin_inset Formula $\otimes$
17140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17143 \begin_layout Plain Layout
17151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17154 \begin_layout Plain Layout
17155 \begin_inset Formula $\oslash$
17165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17168 \begin_layout Plain Layout
17176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17179 \begin_layout Plain Layout
17180 \begin_inset Formula $\odot$
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17193 \begin_layout Plain Layout
17201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17204 \begin_layout Plain Layout
17205 \begin_inset Formula $\amalg$
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17218 \begin_layout Plain Layout
17226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17229 \begin_layout Plain Layout
17230 \begin_inset Formula $\uplus$
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17243 \begin_layout Plain Layout
17251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17254 \begin_layout Plain Layout
17255 \begin_inset Formula $\setminus$
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17268 \begin_layout Plain Layout
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17279 \begin_layout Plain Layout
17280 \begin_inset Formula $\sqcap$
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17293 \begin_layout Plain Layout
17301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17304 \begin_layout Plain Layout
17305 \begin_inset Formula $\sqcup$
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17318 \begin_layout Plain Layout
17326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17329 \begin_layout Plain Layout
17330 \begin_inset Formula $\triangleleft$
17340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17343 \begin_layout Plain Layout
17351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17354 \begin_layout Plain Layout
17355 \begin_inset Formula $\triangleright$
17369 \begin_inset space \hfill{}
17375 \begin_layout Standard
17376 All binary operators can also be inserted via the math toolbar button
17377 \begin_inset Graphics
17378 filename ../images/math/pm.png
17386 \begin_layout Standard
17387 To typeset the Laplace operator also
17404 \begin_inset Formula $\nabla^{2}$
17407 ) can be used instead of
17416 \begin_layout Standard
17423 Insert\SpecialChar \menuseparator
17435 \begin_layout Subsection
17436 Self-defined Operators
17437 \begin_inset CommandInset label
17439 name "sub:Self-defined-Operators"
17447 \begin_layout Plain Layout
17448 Operators ! self-defined
17456 \begin_layout Standard
17457 With the help of the command
17461 DeclareMathOperator
17467 \begin_layout Plain Layout
17472 DeclareMathOperator
17477 custom operators can be defined in the LaTeX-preamble.
17478 Its command scheme is:
17481 \begin_layout Standard
17486 DeclareMathOperator{new command}{display}
17489 \begin_layout Standard
17490 Display can be characters or symbols that define how the operator looks
17492 To define a big operator a * is set behind the command.
17493 All self-defined big operators can have limits as described in
17494 \begin_inset CommandInset ref
17496 reference "sub:Operator-Limits"
17503 \begin_layout Standard
17504 For example the LaTeX-preamble line
17507 \begin_layout Standard
17512 DeclareMathOperator*{
17519 \begin_layout Standard
17520 defines the command
17526 , that inserts a big operator consisting of the lozenge symbol from
17527 \begin_inset CommandInset ref
17529 reference "sub:Miscellaneous-Symbols"
17534 \begin_inset Formula \[
17535 \Lozenge_{n=1}^{\infty}\]
17539 The command for this formula is:
17550 \begin_inset Formula $\to$
17556 \begin_layout Standard
17557 \begin_inset VSpace bigskip
17560 When self-defined operators are not used several times in the document,
17561 they can also be defined with the commands
17571 \begin_layout Plain Layout
17589 \begin_layout Plain Layout
17597 , which have the following scheme:
17600 \begin_layout Standard
17614 \begin_layout Standard
17621 defines big operators,
17630 \begin_layout Standard
17638 \begin_inset space \thinspace{}
17642 \begin_inset space ~
17645 be used to use one limit for several operators:
17648 \begin_layout Standard
17649 \begin_inset Formula \[
17650 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17657 \begin_layout Standard
17658 The command for the formula above is:
17659 \begin_inset Newline newline
17678 \begin_layout Plain Layout
17690 \begin_inset Formula $\to$
17699 \begin_layout Plain Layout
17713 \begin_layout Section
17718 \begin_layout Plain Layout
17727 \begin_layout Subsection
17729 \begin_inset CommandInset label
17731 name "sub:Font-Styles"
17739 \begin_layout Plain Layout
17748 \begin_layout Standard
17749 Latin letters in formulas can be set in one of the following font styles:
17750 \begin_inset VSpace -2mm
17756 \begin_layout Standard
17758 \begin_inset Tabular
17759 <lyxtabular version="3" rows="6" columns="3">
17761 <column alignment="center" valignment="top" width="0">
17762 <column alignment="center" valignment="top" width="0">
17763 <column alignment="center" valignment="top" width="0">
17765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17768 \begin_layout Plain Layout
17774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17777 \begin_layout Plain Layout
17783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17786 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17797 \begin_layout Plain Layout
17806 \begin_layout Plain Layout
17822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17825 \begin_layout Plain Layout
17826 \begin_inset Formula $\mathbb{ABC}$
17834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17837 \begin_layout Plain Layout
17845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17848 \begin_layout Plain Layout
17857 \begin_layout Plain Layout
17873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17876 \begin_layout Plain Layout
17877 \begin_inset Formula $\mathbf{AbC}$
17885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17888 \begin_layout Plain Layout
17896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17899 \begin_layout Plain Layout
17908 \begin_layout Plain Layout
17924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17927 \begin_layout Plain Layout
17928 \begin_inset Formula $\boldsymbol{AbC}$
17936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17939 \begin_layout Plain Layout
17947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17950 \begin_layout Plain Layout
17959 \begin_layout Plain Layout
17975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17978 \begin_layout Plain Layout
17979 \begin_inset Formula $\mathcal{ABC}$
17987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17990 \begin_layout Plain Layout
17998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18001 \begin_layout Plain Layout
18010 \begin_layout Plain Layout
18026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18029 \begin_layout Plain Layout
18030 \begin_inset Formula $\mathfrak{AbC}$
18038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18041 \begin_layout Plain Layout
18055 \begin_layout Standard
18057 \begin_inset Tabular
18058 <lyxtabular version="3" rows="5" columns="3">
18060 <column alignment="center" valignment="top" width="0">
18061 <column alignment="center" valignment="top" width="0">
18062 <column alignment="center" valignment="top" width="0">
18064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18067 \begin_layout Plain Layout
18073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18076 \begin_layout Plain Layout
18082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18085 \begin_layout Plain Layout
18093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18096 \begin_layout Plain Layout
18105 \begin_layout Plain Layout
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18124 \begin_layout Plain Layout
18125 \begin_inset Formula $\mathit{AbC}$
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18136 \begin_layout Plain Layout
18144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18147 \begin_layout Plain Layout
18156 \begin_layout Plain Layout
18172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18175 \begin_layout Plain Layout
18176 \begin_inset Formula $\mathrm{AbC}$
18184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18187 \begin_layout Plain Layout
18195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18198 \begin_layout Plain Layout
18207 \begin_layout Plain Layout
18223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18226 \begin_layout Plain Layout
18227 \begin_inset Formula $\mathsf{AbC}$
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18238 \begin_layout Plain Layout
18246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18249 \begin_layout Plain Layout
18258 \begin_layout Plain Layout
18274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18277 \begin_layout Plain Layout
18278 \begin_inset Formula $\mathtt{AbC}$
18286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18289 \begin_layout Plain Layout
18303 \begin_layout Standard
18304 \begin_inset Note Greyedout
18307 \begin_layout Plain Layout
18324 can only be used for big letters.
18332 \begin_layout Standard
18333 Predefined is the style
18342 \begin_layout Standard
18343 The style commands work also for letters in mathematical constructs:
18344 \begin_inset Formula \[
18345 \mathfrak{A=\frac{b}{C}}\]
18352 \begin_layout Standard
18353 Characters in mathematical text don't appear in a math font style but in
18354 the text font style
18361 That their style can't be set correctly via the text style dialog is a
18366 \begin_layout Plain Layout
18367 \begin_inset CommandInset href
18369 name "LyX-bug #4091"
18370 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18382 \begin_layout Standard
18383 Instead of the style commands the dialog
18385 Edit\SpecialChar \menuseparator
18386 Math\SpecialChar \menuseparator
18389 or the toolbar button
18390 \begin_inset Graphics
18391 filename ../images/math/font.png
18399 \begin_layout Subsection
18401 \begin_inset CommandInset label
18403 name "sub:Bold-Formulas"
18411 \begin_layout Plain Layout
18420 \begin_layout Standard
18421 To make a complete formula bold, the command
18427 from the previous subsection cannot be used, because it doesn't work for
18428 small Greek letters.
18429 Furthermore it prints Latin letters always upright, like in the following
18433 \begin_layout Standard
18434 \begin_inset Formula \[
18435 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18442 \begin_layout Standard
18443 To display the formula correctly, the command
18450 \begin_inset Formula \[
18451 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18455 It is also possible to set the formula in a
18457 boldmath environment
18460 This environment is created by inserting the command
18468 \begin_layout Plain Layout
18479 To end the environment, the command
18487 \begin_layout Plain Layout
18497 is inserted in TeX-mode.
18501 \begin_layout Plain Layout
18511 \begin_inset Formula \[
18512 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18520 \begin_layout Plain Layout
18532 \begin_layout Subsection
18534 \begin_inset CommandInset label
18536 name "sub:Font-Sizes"
18544 \begin_layout Plain Layout
18553 \begin_layout Standard
18554 For characters in formulas there are, analog to characters in text, the
18555 following size commands:
18558 \begin_layout Standard
18602 \begin_inset Newline newline
18624 \begin_layout Standard
18625 The size produced by the commands depends on the document font size, that
18626 corresponds with the command
18633 The other commands produce smaller or larger sizes than
18640 The font size can however not exceed a certain value.
18641 Is for example the document font size 12
18642 \begin_inset space \thinspace{}
18651 switches to the same size as
18661 \begin_layout Standard
18662 A size command is inserted in TeX-mode before the formula and sets the size
18663 for all following formula and text characters.
18664 To switch back to the initial size, the command
18670 is inserted behind the formula in TeX-mode.
18673 \begin_layout Standard
18674 Within a formula the size can only be changed for symbols or letters in
18676 To do this, the size command is inserted in mathematical text.
18677 All following characters until the end of the mathematical text or until
18678 another size command will have the selected size.
18680 \begin_inset VSpace -2mm
18686 \begin_layout Standard
18690 \begin_layout Plain Layout
18700 \begin_inset Formula \[
18701 A=\frac{B}{c}\cdot\maltese\]
18706 \begin_inset Formula \[
18707 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18715 \begin_layout Plain Layout
18727 \begin_layout Standard
18728 \begin_inset VSpace medskip
18731 Before both formulas the command
18738 The command for the second formula is:
18739 \begin_inset Newline newline
18750 \begin_layout Plain Layout
18765 \begin_layout Plain Layout
18780 \begin_layout Plain Layout
18795 \begin_layout Plain Layout
18805 \begin_inset Formula $\to$
18809 \begin_inset Formula $\to$
18813 \begin_inset Newline newline
18817 \begin_inset space \hspace*{}
18831 \begin_layout Plain Layout
18846 \begin_layout Plain Layout
18861 \begin_layout Plain Layout
18873 \begin_layout Standard
18874 If a symbol cannot be displayed in different sizes, it will always be displayed
18875 in the default size.
18878 \begin_layout Section
18883 \begin_layout Plain Layout
18892 \begin_layout Standard
18893 All Greek letters can also be inserted via the toolbar button
18894 \begin_inset Graphics
18895 filename ../images/math/alpha.png
18903 \begin_layout Subsection
18905 \begin_inset CommandInset label
18907 name "sub:Small-Letters"
18915 \begin_layout Plain Layout
18916 Greek letters ! small
18924 \begin_layout Standard
18925 \begin_inset space \hfill{}
18929 \begin_inset Tabular
18930 <lyxtabular version="3" rows="11" columns="2">
18932 <column alignment="center" valignment="top" width="0pt">
18933 <column alignment="center" valignment="top" width="0pt">
18935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18938 \begin_layout Plain Layout
18944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18947 \begin_layout Plain Layout
18955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18958 \begin_layout Plain Layout
18966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18969 \begin_layout Plain Layout
18970 \begin_inset Formula $\alpha$
18980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18983 \begin_layout Plain Layout
18991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18994 \begin_layout Plain Layout
18995 \begin_inset Formula $\beta$
19005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19008 \begin_layout Plain Layout
19016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19019 \begin_layout Plain Layout
19020 \begin_inset Formula $\gamma$
19030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19033 \begin_layout Plain Layout
19041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19044 \begin_layout Plain Layout
19045 \begin_inset Formula $\delta$
19055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19058 \begin_layout Plain Layout
19066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19069 \begin_layout Plain Layout
19070 \begin_inset Formula $\epsilon$
19080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19083 \begin_layout Plain Layout
19091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19094 \begin_layout Plain Layout
19095 \begin_inset Formula $\varepsilon$
19105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19108 \begin_layout Plain Layout
19116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19119 \begin_layout Plain Layout
19120 \begin_inset Formula $\zeta$
19130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19133 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19144 \begin_layout Plain Layout
19145 \begin_inset Formula $\eta$
19155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19158 \begin_layout Plain Layout
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19169 \begin_layout Plain Layout
19170 \begin_inset Formula $\theta$
19180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19183 \begin_layout Plain Layout
19191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19194 \begin_layout Plain Layout
19195 \begin_inset Formula $\vartheta$
19209 \begin_inset space \hfill{}
19213 \begin_inset Tabular
19214 <lyxtabular version="3" rows="12" columns="2">
19216 <column alignment="center" valignment="top" width="0pt">
19217 <column alignment="center" valignment="top" width="0pt">
19219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19222 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19231 \begin_layout Plain Layout
19239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19242 \begin_layout Plain Layout
19250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19253 \begin_layout Plain Layout
19254 \begin_inset Formula $\iota$
19264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19267 \begin_layout Plain Layout
19275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19278 \begin_layout Plain Layout
19279 \begin_inset Formula $\kappa$
19289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19292 \begin_layout Plain Layout
19300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19303 \begin_layout Plain Layout
19304 \begin_inset Formula $\varkappa$
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19317 \begin_layout Plain Layout
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19328 \begin_layout Plain Layout
19329 \begin_inset Formula $\lambda$
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19342 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19353 \begin_layout Plain Layout
19354 \begin_inset Formula $\mu$
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19367 \begin_layout Plain Layout
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19378 \begin_layout Plain Layout
19379 \begin_inset Formula $\nu$
19389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19392 \begin_layout Plain Layout
19400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19403 \begin_layout Plain Layout
19404 \begin_inset Formula $\xi$
19414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19417 \begin_layout Plain Layout
19423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19426 \begin_layout Plain Layout
19427 \begin_inset Formula $o$
19437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19440 \begin_layout Plain Layout
19448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19451 \begin_layout Plain Layout
19452 \begin_inset Formula $\pi$
19462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19465 \begin_layout Plain Layout
19473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19476 \begin_layout Plain Layout
19477 \begin_inset Formula $\varpi$
19487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19490 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19502 \begin_inset Formula $\rho$
19516 \begin_inset space \hfill{}
19520 \begin_inset Tabular
19521 <lyxtabular version="3" rows="11" columns="2">
19523 <column alignment="center" valignment="top" width="0pt">
19524 <column alignment="center" valignment="top" width="0pt">
19526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19529 \begin_layout Plain Layout
19535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19538 \begin_layout Plain Layout
19546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19549 \begin_layout Plain Layout
19557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19560 \begin_layout Plain Layout
19561 \begin_inset Formula $\varrho$
19571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19574 \begin_layout Plain Layout
19582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19585 \begin_layout Plain Layout
19586 \begin_inset Formula $\sigma$
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19599 \begin_layout Plain Layout
19607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19610 \begin_layout Plain Layout
19611 \begin_inset Formula $\varsigma$
19621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\tau$
19646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\upsilon$
19671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\phi$
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\varphi$
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\chi$
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\psi$
19771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\omega$
19800 \begin_inset space \hfill{}
19806 \begin_layout Standard
19807 \begin_inset VSpace medskip
19813 \begin_layout Standard
19814 How to create upright Greek letters is explained in
19815 \begin_inset CommandInset ref
19817 reference "sub:Upright-small-Greek"
19824 \begin_layout Subsection
19829 \begin_layout Plain Layout
19830 Greek letters ! big
19838 \begin_layout Standard
19839 \begin_inset space \hfill{}
19843 \begin_inset Tabular
19844 <lyxtabular version="3" rows="7" columns="2">
19846 <column alignment="center" valignment="top" width="0pt">
19847 <column alignment="center" valignment="top" width="0pt">
19849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19852 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19872 \begin_layout Plain Layout
19880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Plain Layout
19884 \begin_inset Formula $\Gamma$
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $\Delta$
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\Theta$
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\Lambda$
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\Xi$
19994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\Pi$
20023 \begin_inset space \hfill{}
20027 \begin_inset Tabular
20028 <lyxtabular version="3" rows="6" columns="2">
20030 <column alignment="center" valignment="top" width="0pt">
20031 <column alignment="center" valignment="top" width="0pt">
20033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20036 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20056 \begin_layout Plain Layout
20064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20067 \begin_layout Plain Layout
20068 \begin_inset Formula $\Sigma$
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20081 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20093 \begin_inset Formula $\Upsilon$
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\Phi$
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20131 \begin_layout Plain Layout
20139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20142 \begin_layout Plain Layout
20143 \begin_inset Formula $\Psi$
20153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20156 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20167 \begin_layout Plain Layout
20168 \begin_inset Formula $\Omega$
20182 \begin_inset space \hfill{}
20188 \begin_layout Standard
20189 \begin_inset VSpace medskip
20192 That the big Greek letters appear upright is caused by a design bug when
20194 To get correct italic big letters, begin every command with
20199 For example the command
20206 \begin_inset Formula $\varGamma$
20212 \begin_layout Subsection
20217 \begin_layout Plain Layout
20218 Greek letters ! bold
20226 \begin_layout Standard
20227 Greek letters cannot be set with different font styles like Latin letters.
20228 They can only be made bold with the command
20238 \begin_layout Plain Layout
20249 \begin_layout Standard
20251 \begin_inset Tabular
20252 <lyxtabular version="3" rows="3" columns="2">
20254 <column alignment="center" valignment="top" width="0">
20255 <column alignment="center" valignment="top" width="0">
20257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20260 \begin_layout Plain Layout
20266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20269 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20280 \begin_layout Plain Layout
20292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20295 \begin_layout Plain Layout
20296 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20309 \begin_layout Plain Layout
20321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20324 \begin_layout Plain Layout
20325 \begin_inset Formula $\theta\boldsymbol{\theta}$
20341 \begin_layout Section
20346 \begin_layout Plain Layout
20359 \begin_layout Plain Layout
20360 A list with all symbols of most of the LaTeX-packages can be found in
20361 \begin_inset CommandInset citation
20376 \begin_layout Plain Layout
20384 \begin_inset Note Note
20387 \begin_layout Plain Layout
20390 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20393 \begin_layout Plain Layout
20396 texorpdfstring is in section
20397 \begin_inset CommandInset ref
20399 reference "sub:Formulas-in-Section"
20412 \begin_layout Plain Layout
20421 \begin_layout Standard
20422 Many of the symbols listed in this section can also be inserted via the
20424 \begin_inset Graphics
20425 filename ../images/math/nabla.png
20431 \begin_inset Graphics
20432 filename ../images/math/digamma.png
20440 \begin_layout Subsection
20441 Mathematical Symbols
20442 \begin_inset CommandInset label
20444 name "sub:Mathematical-Symbols"
20452 \begin_layout Plain Layout
20453 Symbols ! mathematical
20461 \begin_layout Standard
20462 \begin_inset space \hfill{}
20466 \begin_inset Tabular
20467 <lyxtabular version="3" rows="10" columns="2">
20469 <column alignment="center" valignment="top" width="0pt">
20470 <column alignment="center" valignment="top" width="0pt">
20472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20475 \begin_layout Plain Layout
20481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20484 \begin_layout Plain Layout
20492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20495 \begin_layout Plain Layout
20503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20506 \begin_layout Plain Layout
20507 \begin_inset Formula $\neg$
20517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20520 \begin_layout Plain Layout
20528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20531 \begin_layout Plain Layout
20532 \begin_inset Formula $\Im$
20542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20545 \begin_layout Plain Layout
20553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20556 \begin_layout Plain Layout
20557 \begin_inset Formula $\Re$
20567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20570 \begin_layout Plain Layout
20578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20581 \begin_layout Plain Layout
20582 \begin_inset Formula $\aleph$
20592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20595 \begin_layout Plain Layout
20603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20606 \begin_layout Plain Layout
20607 \begin_inset Formula $\partial$
20617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20620 \begin_layout Plain Layout
20628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20631 \begin_layout Plain Layout
20632 \begin_inset Formula $\infty$
20642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20645 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20657 \begin_inset Formula $\wp$
20667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20670 \begin_layout Plain Layout
20678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20681 \begin_layout Plain Layout
20682 \begin_inset Formula $\imath$
20692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20695 \begin_layout Plain Layout
20703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20706 \begin_layout Plain Layout
20707 \begin_inset Formula $\jmath$
20721 \begin_inset space \hfill{}
20725 \begin_inset Tabular
20726 <lyxtabular version="3" rows="10" columns="2">
20728 <column alignment="center" valignment="top" width="0pt">
20729 <column alignment="center" valignment="top" width="0pt">
20731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20743 \begin_layout Plain Layout
20745 \begin_inset Note Note
20748 \begin_layout Plain Layout
20755 is only used as spacer.
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\forall$
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20795 \begin_layout Plain Layout
20803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20806 \begin_layout Plain Layout
20807 \begin_inset Formula $\exists$
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20820 \begin_layout Plain Layout
20828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20831 \begin_layout Plain Layout
20832 \begin_inset Formula $\nexists$
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20845 \begin_layout Plain Layout
20853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20856 \begin_layout Plain Layout
20857 \begin_inset Formula $\emptyset$
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20870 \begin_layout Plain Layout
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20881 \begin_layout Plain Layout
20882 \begin_inset Formula $\varnothing$
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20895 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20906 \begin_layout Plain Layout
20907 \begin_inset Formula $\dag$
20917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20920 \begin_layout Plain Layout
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20931 \begin_layout Plain Layout
20932 \begin_inset Formula $\ddag$
20942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20960 \begin_layout Plain Layout
20970 \begin_inset Formula $\complement$
20977 \begin_layout Plain Layout
20991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20994 \begin_layout Plain Layout
21002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21005 \begin_layout Plain Layout
21006 \begin_inset Formula $\Bbbk$
21020 \begin_inset space \hfill{}
21024 \begin_inset Tabular
21025 <lyxtabular version="3" rows="10" columns="2">
21027 <column alignment="center" valignment="top" width="0pt">
21028 <column alignment="center" valignment="top" width="0pt">
21030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21033 \begin_layout Plain Layout
21039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21042 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21053 \begin_layout Plain Layout
21061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21064 \begin_layout Plain Layout
21065 \begin_inset Formula $\prime$
21075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21078 \begin_layout Plain Layout
21086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21089 \begin_layout Plain Layout
21090 \begin_inset Formula $\backprime$
21100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21103 \begin_layout Plain Layout
21111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21114 \begin_layout Plain Layout
21115 \begin_inset Formula $\mho$
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21128 \begin_layout Plain Layout
21136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21139 \begin_layout Plain Layout
21140 \begin_inset Formula $\triangle$
21150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21153 \begin_layout Plain Layout
21161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21164 \begin_layout Plain Layout
21165 \begin_inset Formula $\angle$
21175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21178 \begin_layout Plain Layout
21186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21189 \begin_layout Plain Layout
21190 \begin_inset Formula $\measuredangle$
21200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21203 \begin_layout Plain Layout
21211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21214 \begin_layout Plain Layout
21215 \begin_inset Formula $\sphericalangle$
21225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21228 \begin_layout Plain Layout
21236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21239 \begin_layout Plain Layout
21240 \begin_inset Formula $\top$
21250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21253 \begin_layout Plain Layout
21261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21264 \begin_layout Plain Layout
21265 \begin_inset Formula $\bot$
21279 \begin_inset space \hfill{}
21285 \begin_layout Standard
21286 \begin_inset Newpage newpage
21292 \begin_layout Subsection
21293 Miscellaneous Symbols
21294 \begin_inset CommandInset label
21296 name "sub:Miscellaneous-Symbols"
21304 \begin_layout Plain Layout
21305 Symbols ! miscellaneous
21313 \begin_layout Standard
21316 \begin_inset Tabular
21317 <lyxtabular version="3" rows="10" columns="2">
21319 <column alignment="center" valignment="top" width="0pt">
21320 <column alignment="center" valignment="top" width="0pt">
21322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21325 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\flat$
21367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\natural$
21392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Plain Layout
21407 \begin_inset Formula $\sharp$
21417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Plain Layout
21432 \begin_inset Formula $\surd$
21442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\checkmark$
21467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Plain Layout
21482 \begin_inset Formula $\yen$
21492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21495 \begin_layout Plain Layout
21503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Plain Layout
21507 \begin_inset Formula $\pounds$
21517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21520 \begin_layout Plain Layout
21526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21529 \begin_layout Plain Layout
21530 \begin_inset Formula $\$$
21540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21543 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $§$
21567 \begin_inset Tabular
21568 <lyxtabular version="3" rows="10" columns="2">
21570 <column alignment="center" valignment="top" width="0">
21571 <column alignment="center" valignment="top" width="0">
21573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21585 \begin_layout Plain Layout
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\hbar$
21618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\hslash$
21643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21658 \begin_inset Formula $\clubsuit$
21668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21671 \begin_layout Plain Layout
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21682 \begin_layout Plain Layout
21683 \begin_inset Formula $\spadesuit$
21693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21707 \begin_layout Plain Layout
21708 \begin_inset Formula $\bigstar$
21718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21721 \begin_layout Plain Layout
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21732 \begin_layout Plain Layout
21733 \begin_inset Formula $\blacklozenge$
21743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21746 \begin_layout Plain Layout
21754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21757 \begin_layout Plain Layout
21758 \begin_inset Formula $\blacktriangle$
21768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21771 \begin_layout Plain Layout
21779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21782 \begin_layout Plain Layout
21783 \begin_inset Formula $\blacktriangledown$
21793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21796 \begin_layout Plain Layout
21804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21807 \begin_layout Plain Layout
21808 \begin_inset Formula $\bullet$
21822 \begin_inset Tabular
21823 <lyxtabular version="3" rows="10" columns="2">
21825 <column alignment="center" valignment="top" width="0pt">
21826 <column alignment="center" valignment="top" width="0pt">
21828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21831 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21851 \begin_layout Plain Layout
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21862 \begin_layout Plain Layout
21863 \begin_inset Formula $\diamondsuit$
21873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21876 \begin_layout Plain Layout
21884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21887 \begin_layout Plain Layout
21888 \begin_inset Formula $\Diamond$
21898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21901 \begin_layout Plain Layout
21909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21912 \begin_layout Plain Layout
21913 \begin_inset Formula $\heartsuit$
21923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21926 \begin_layout Plain Layout
21934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21937 \begin_layout Plain Layout
21938 \begin_inset Formula $\P$
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21951 \begin_layout Plain Layout
21959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21962 \begin_layout Plain Layout
21963 \begin_inset Formula $\copyright$
21973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21976 \begin_layout Plain Layout
21984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21987 \begin_layout Plain Layout
21988 \begin_inset Formula $\circledR$
21998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22001 \begin_layout Plain Layout
22009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22012 \begin_layout Plain Layout
22013 \begin_inset Formula $\maltese$
22023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22026 \begin_layout Plain Layout
22034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22037 \begin_layout Plain Layout
22038 \begin_inset Formula $\diagup$
22048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22062 \begin_layout Plain Layout
22063 \begin_inset Formula $\diagdown$
22079 \begin_layout Standard
22080 \begin_inset VSpace medskip
22083 More symbols are listed in
22084 \begin_inset CommandInset ref
22086 reference "sub:Miscellaneous-special-Characters"
22093 \begin_layout Standard
22094 Some symbols can be displayed in different sizes, see
22095 \begin_inset CommandInset ref
22097 reference "sub:Font-Sizes"
22104 \begin_layout Subsection
22109 \begin_layout Plain Layout
22110 Symbols ! Euro-symbol
22119 \begin_layout Plain Layout
22126 \begin_layout Plain Layout
22143 \begin_layout Standard
22144 To use the Euro symbol in formulas, the LaTeX-package
22152 \begin_layout Plain Layout
22158 must be installed and loaded with the LaTeX-preamble line
22161 \begin_layout Standard
22166 usepackage[gennarrow]{eurosym}
22169 \begin_layout Standard
22170 The Euro symbol can now be inserted with the command
22180 \begin_layout Plain Layout
22191 \begin_layout Standard
22192 The Euro symbol can directly be inserted with the € key in mathematical
22193 text, without having
22208 can also be inserted in TeX-mode.
22209 The official currency symbol can then be inserted with the command
22219 \begin_layout Plain Layout
22227 , that is only available in TeX-mode.
22230 \begin_layout Standard
22234 \begin_layout Plain Layout
22244 \begin_inset Note Note
22247 \begin_layout Plain Layout
22248 The following table will only be displayed when the LaTeX-package
22260 \begin_layout Standard
22261 An overview about the different Euro symbols:
22264 \begin_layout Standard
22266 \begin_inset Tabular
22267 <lyxtabular version="3" rows="4" columns="3">
22269 <column alignment="center" valignment="top" width="0pt">
22270 <column alignment="center" valignment="top" width="0pt">
22271 <column alignment="center" valignment="top" width="0pt">
22273 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22276 \begin_layout Plain Layout
22282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22285 \begin_layout Plain Layout
22291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22305 \begin_layout Plain Layout
22311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22314 \begin_layout Plain Layout
22322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22325 \begin_layout Plain Layout
22326 \begin_inset Formula $\euro$
22336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22339 \begin_layout Plain Layout
22345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22348 \begin_layout Plain Layout
22354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22357 \begin_layout Plain Layout
22358 \begin_inset Formula $\mbox{€}$
22368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22371 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22380 \begin_layout Plain Layout
22388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22391 \begin_layout Plain Layout
22395 \begin_layout Plain Layout
22417 \begin_layout Standard
22421 \begin_layout Plain Layout
22431 \begin_inset Note Note
22434 \begin_layout Plain Layout
22435 The following will be displayed when the LaTeX-package
22447 \begin_layout Standard
22448 You need to install the LaTeX-package
22452 to see the rest of this subsection in the output.
22455 \begin_layout Standard
22459 \begin_layout Plain Layout
22471 \begin_layout Section
22473 \begin_inset CommandInset label
22475 name "sec:Relations"
22483 \begin_layout Plain Layout
22493 \begin_layout Plain Layout
22498 \begin_layout Plain Layout
22509 \begin_layout Plain Layout
22524 \begin_layout Standard
22525 All relations can also be inserted via the toolbar button
22526 \begin_inset Graphics
22527 filename ../images/math/leq.png
22535 \begin_layout Standard
22536 \begin_inset space \hfill{}
22540 \begin_inset Tabular
22541 <lyxtabular version="3" rows="17" columns="2">
22543 <column alignment="center" valignment="top" width="0pt">
22544 <column alignment="center" valignment="top" width="0pt">
22546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22549 \begin_layout Plain Layout
22555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22558 \begin_layout Plain Layout
22566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22569 \begin_layout Plain Layout
22575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22578 \begin_layout Plain Layout
22579 \begin_inset Formula $<$
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22592 \begin_layout Plain Layout
22600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22603 \begin_layout Plain Layout
22604 \begin_inset Formula $\le$
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22617 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22628 \begin_layout Plain Layout
22629 \begin_inset Formula $\ll$
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22654 \begin_inset Formula $\prec$
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22678 \begin_layout Plain Layout
22679 \begin_inset Formula $\preceq$
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22703 \begin_layout Plain Layout
22704 \begin_inset Formula $\subset$
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\subseteq$
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\sqsubseteq$
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\in$
22789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\vdash$
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\smile$
22839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\lhd$
22864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\unlhd$
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $\gtrless$
22914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\mid$
22939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22954 \begin_inset Formula $\nmid$
22968 \begin_inset space \hfill{}
22972 \begin_inset Tabular
22973 <lyxtabular version="3" rows="17" columns="2">
22975 <column alignment="center" valignment="top" width="0pt">
22976 <column alignment="center" valignment="top" width="0pt">
22978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22981 \begin_layout Plain Layout
22987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22990 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23001 \begin_layout Plain Layout
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23010 \begin_layout Plain Layout
23011 \begin_inset Formula $=$
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23024 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23035 \begin_layout Plain Layout
23036 \begin_inset Formula $\not=$
23046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23049 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23060 \begin_layout Plain Layout
23061 \begin_inset Formula $\equiv$
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23086 \begin_inset Formula $\sim$
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23099 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23110 \begin_layout Plain Layout
23111 \begin_inset Formula $\simeq$
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\approx$
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23161 \begin_inset Formula $\cong$
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23174 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\bowtie$
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\notin$
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23235 \begin_layout Plain Layout
23236 \begin_inset Formula $\perp$
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23261 \begin_inset Formula $\propto$
23271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23285 \begin_layout Plain Layout
23286 \begin_inset Formula $\asymp$
23296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23310 \begin_layout Plain Layout
23311 \begin_inset Formula $\doteq$
23321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23324 \begin_layout Plain Layout
23332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23335 \begin_layout Plain Layout
23336 \begin_inset Formula $\circeq$
23346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23349 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Plain Layout
23361 \begin_inset Formula $\models$
23371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23374 \begin_layout Plain Layout
23382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23385 \begin_layout Plain Layout
23386 \begin_inset Formula $\widehat{=}$
23400 \begin_inset space \hfill{}
23404 \begin_inset Tabular
23405 <lyxtabular version="3" rows="17" columns="2">
23407 <column alignment="center" valignment="top" width="0pt">
23408 <column alignment="center" valignment="top" width="0pt">
23410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23413 \begin_layout Plain Layout
23419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23433 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $>$
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\ge$
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\gg$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\succ$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\succeq$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\supset$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\supseteq$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\sqsupseteq$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\ni$
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\dashv$
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23693 \begin_inset Formula $\frown$
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23717 \begin_layout Plain Layout
23718 \begin_inset Formula $\rhd$
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23742 \begin_layout Plain Layout
23743 \begin_inset Formula $\unrhd$
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23756 \begin_layout Plain Layout
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23767 \begin_layout Plain Layout
23768 \begin_inset Formula $\lessgtr$
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23781 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23792 \begin_layout Plain Layout
23793 \begin_inset Formula $\parallel$
23803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23806 \begin_layout Plain Layout
23814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23817 \begin_layout Plain Layout
23818 \begin_inset Formula $\nparallel$
23832 \begin_inset space \hfill{}
23838 \begin_layout Standard
23839 \begin_inset VSpace medskip
23854 are bigger than the equal looking operators
23869 \begin_layout Standard
23870 Relations are, in contrary to symbols, always surrounded by space.
23873 \begin_layout Standard
23874 Relations with labels can be created with the command
23884 \begin_layout Plain Layout
23895 \begin_layout Standard
23897 \begin_inset Tabular
23898 <lyxtabular version="3" rows="2" columns="2">
23900 <column alignment="center" valignment="top" width="0">
23901 <column alignment="center" valignment="top" width="0">
23903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23906 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23917 \begin_inset Note Note
23920 \begin_layout Plain Layout
23927 is only used as spacer.
23939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23949 \begin_layout Plain Layout
23966 \begin_layout Plain Layout
23976 \begin_inset Formula $\downarrow$
23985 \begin_layout Plain Layout
23998 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24032 \begin_layout Section
24036 \begin_layout Subsection
24037 Predefined Functions
24038 \begin_inset CommandInset label
24040 name "sub:Predefined-Functions"
24048 \begin_layout Plain Layout
24049 Functions ! predefined
24057 \begin_layout Standard
24058 In general, variables are set
24062 in mathematical expressions, but not function names, because
24063 \begin_inset Formula $sin$
24066 could be misunderstood as
24067 \begin_inset Formula $s\cdot i\cdot n$
24071 Therefore there are predefined functions, that are additionally a bit separated
24073 They are inserted as commands starting with a backslash before their name.
24076 \begin_layout Standard
24078 \begin_inset Tabular
24079 <lyxtabular version="3" rows="2" columns="4">
24081 <column alignment="center" valignment="top" width="0pt">
24082 <column alignment="center" valignment="top" width="0pt">
24083 <column alignment="center" valignment="top" width="0pt">
24084 <column alignment="center" valignment="top" width="0pt">
24086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24089 \begin_layout Plain Layout
24095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24098 \begin_layout Plain Layout
24104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24107 \begin_layout Plain Layout
24113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24116 \begin_layout Plain Layout
24124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24127 \begin_layout Plain Layout
24133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24136 \begin_layout Plain Layout
24137 \begin_inset Formula $Asin(x)+B$
24145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24148 \begin_layout Plain Layout
24156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24159 \begin_layout Plain Layout
24160 \begin_inset Formula $A\sin(x)+B$
24174 \begin_inset Newpage pagebreak
24180 \begin_layout Standard
24181 The following functions are predefined:
24184 \begin_layout Standard
24185 \begin_inset VSpace -2mm
24191 \begin_layout Standard
24193 \begin_inset Tabular
24194 <lyxtabular version="3" rows="9" columns="4">
24196 <column alignment="center" valignment="top" width="0pt">
24197 <column alignment="center" valignment="top" width="0pt">
24198 <column alignment="center" valignment="top" width="0pt">
24199 <column alignment="center" valignment="top" width="0pt">
24201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24204 \begin_layout Plain Layout
24210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24213 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24231 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24253 \begin_layout Plain Layout
24261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24264 \begin_layout Plain Layout
24272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24275 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24288 \begin_layout Plain Layout
24296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24299 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24310 \begin_layout Plain Layout
24318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24321 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24334 \begin_layout Plain Layout
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24367 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24380 \begin_layout Plain Layout
24388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24391 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24402 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24413 \begin_layout Plain Layout
24423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24426 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24437 \begin_layout Plain Layout
24445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24448 \begin_layout Plain Layout
24456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24459 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Plain Layout
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24483 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24494 \begin_layout Plain Layout
24502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24505 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24518 \begin_layout Plain Layout
24526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24540 \begin_layout Plain Layout
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24551 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24564 \begin_layout Plain Layout
24572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24575 \begin_layout Plain Layout
24583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24586 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24597 \begin_layout Plain Layout
24613 \begin_layout Standard
24614 They can also be inserted with the math toolbar button
24615 \begin_inset Graphics
24616 filename ../images/math/functions.png
24624 \begin_layout Subsection
24625 Self-defined Functions
24629 \begin_layout Plain Layout
24630 Functions ! self-defined
24638 \begin_layout Standard
24639 To use a function that is not predefined, like for example the sign function
24640 sgn(x), there are two possibilities:
24643 \begin_layout Itemize
24644 Define the function by inserting the following line to the LaTeX-preamble
24648 \begin_layout Plain Layout
24653 DeclareMathOperator
24656 \begin_inset CommandInset ref
24658 reference "sub:Self-defined-Operators"
24668 \begin_inset Newline newline
24672 \begin_inset VSpace -3mm
24676 \begin_inset Newline newline
24683 DeclareMathOperator{
24691 \begin_layout Plain Layout
24696 DeclareMathOperator
24702 \begin_inset Newline newline
24706 \begin_inset VSpace -2mm
24710 \begin_inset Newline newline
24713 Now the new defined function can be called with the command
24722 \begin_layout Itemize
24723 Write the the formula as usual, mark the formula name, in our example the
24728 , and change it to mathematical text.
24729 At last a space is inserted between prefactor and function.
24732 \begin_layout Standard
24733 The result is the same with both methods as with a predefined function
24737 \begin_layout Plain Layout
24738 In LyX self-defined functions are displayed red, predefined ones black.
24746 \begin_layout Standard
24748 \begin_inset Tabular
24749 <lyxtabular version="3" rows="3" columns="2">
24751 <column alignment="center" valignment="top" width="0pt">
24752 <column alignment="center" valignment="top" width="0pt">
24754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24766 \begin_layout Plain Layout
24774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24777 \begin_layout Plain Layout
24785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24788 \begin_layout Plain Layout
24789 \begin_inset Formula $A\sgn(x)+B$
24799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24802 \begin_layout Plain Layout
24806 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24817 \begin_layout Plain Layout
24818 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24834 \begin_layout Standard
24835 The first method is more suitable when the self-defined function should
24836 be used several times.
24839 \begin_layout Subsection
24844 \begin_layout Plain Layout
24853 \begin_layout Standard
24854 For limits there are defined besides
24864 \begin_layout Plain Layout
24884 furthermore the following functions:
24887 \begin_layout Standard
24889 \begin_inset Tabular
24890 <lyxtabular version="3" rows="5" columns="2">
24892 <column alignment="center" valignment="top" width="0">
24893 <column alignment="center" valignment="top" width="0">
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24907 \begin_layout Plain Layout
24909 \begin_inset Note Note
24912 \begin_layout Plain Layout
24919 is only used as spacer.
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24946 \begin_inset Formula $\varliminf$
24956 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24970 \begin_layout Plain Layout
24971 \begin_inset Formula $\varlimsup$
24981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24995 \begin_layout Plain Layout
24996 \begin_inset Formula $\varprojlim$
25006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25020 \begin_layout Plain Layout
25021 \begin_inset Formula $\varinjlim$
25025 \begin_inset Formula $\raisebox{-2.5mm}{}$
25041 \begin_layout Standard
25042 \begin_inset VSpace medskip
25045 The limit is created by inserting a subscript.
25046 It is set right beside the function in an inline formula:
25049 \begin_layout Standard
25051 \begin_inset Tabular
25052 <lyxtabular version="3" rows="2" columns="2">
25054 <column alignment="center" valignment="top" width="0pt">
25055 <column alignment="center" valignment="top" width="0pt">
25057 <cell alignment="center" valignment="top" usebox="none">
25060 \begin_layout Plain Layout
25066 <cell alignment="center" valignment="top" usebox="none">
25069 \begin_layout Plain Layout
25070 \begin_inset space \hspace{}
25075 \begin_inset Note Note
25078 \begin_layout Plain Layout
25091 are used here as spacer.
25103 <cell alignment="center" valignment="top" usebox="none">
25106 \begin_layout Plain Layout
25115 \begin_layout Plain Layout
25128 \begin_layout Plain Layout
25142 <cell alignment="center" valignment="top" usebox="none">
25145 \begin_layout Plain Layout
25146 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25162 \begin_layout Standard
25163 In a displayed formula the limit is set below the formula, as usual:
25164 \begin_inset Formula \[
25172 \begin_layout Subsection
25177 \begin_layout Plain Layout
25178 Functions ! modulo-
25186 \begin_layout Standard
25187 The modulo-function is special, because it exists in four variants.
25190 \begin_layout Standard
25191 The variants in a displayed formula:
25192 \begin_inset Formula \begin{align*}
25193 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25194 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25195 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25196 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25197 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25204 \begin_layout Standard
25205 In an inline formula less space is set before the function names for all
25209 \begin_layout Section
25214 \begin_layout Plain Layout
25223 \begin_layout Subsection
25224 Special Characters in Mathematical Text
25227 \begin_layout Standard
25228 The following commands can only be used in mathematical text or in TeX-mode:
25231 \begin_layout Standard
25232 \begin_inset space \hfill{}
25236 \begin_inset Tabular
25237 <lyxtabular version="3" rows="8" columns="2">
25239 <column alignment="block" valignment="top" width="0">
25240 <column alignment="block" valignment="top" width="0">
25242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25245 \begin_layout Plain Layout
25251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25276 \begin_layout Plain Layout
25277 \begin_inset Formula $\textrm{œ}$
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25290 \begin_layout Plain Layout
25298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25301 \begin_layout Plain Layout
25302 \begin_inset Formula $\textrm{Œ}$
25312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25315 \begin_layout Plain Layout
25323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25326 \begin_layout Plain Layout
25327 \begin_inset Formula $\textrm{æ}$
25337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25340 \begin_layout Plain Layout
25348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25351 \begin_layout Plain Layout
25352 \begin_inset Formula $\textrm{Æ}$
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25365 \begin_layout Plain Layout
25373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25376 \begin_layout Plain Layout
25377 \begin_inset Formula $\textrm{\aa}$
25387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25390 \begin_layout Plain Layout
25397 \begin_layout Plain Layout
25404 \begin_layout Plain Layout
25425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25428 \begin_layout Plain Layout
25429 \begin_inset Formula $\textrm{Å}$
25439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25442 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25454 \begin_inset Formula $\textrm{ı}$
25468 \begin_inset space \hfill{}
25472 \begin_inset Tabular
25473 <lyxtabular version="3" rows="8" columns="2">
25475 <column alignment="block" valignment="top" width="0">
25476 <column alignment="center" valignment="top" width="0">
25478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25481 \begin_layout Plain Layout
25483 \begin_inset Note Note
25486 \begin_layout Plain Layout
25493 is used for separation, because otherwise the output will be ¡ and ¿ respective
25504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25507 \begin_layout Plain Layout
25515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25518 \begin_layout Plain Layout
25526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25529 \begin_layout Plain Layout
25530 \begin_inset Formula $\textrm{ø}$
25540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25543 \begin_layout Plain Layout
25551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25554 \begin_layout Plain Layout
25555 \begin_inset Formula $\textrm{Ø}$
25565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25568 \begin_layout Plain Layout
25576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25579 \begin_layout Plain Layout
25580 \begin_inset Formula $\textrm{ł}$
25590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25593 \begin_layout Plain Layout
25601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25604 \begin_layout Plain Layout
25605 \begin_inset Formula $\textrm{Ł}$
25615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25618 \begin_layout Plain Layout
25620 \begin_inset space \hspace{}
25628 \begin_layout Plain Layout
25642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25645 \begin_layout Plain Layout
25646 \begin_inset Formula $\textrm{!`}$
25656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25659 \begin_layout Plain Layout
25661 \begin_inset space \hspace{}
25669 \begin_layout Plain Layout
25683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25686 \begin_layout Plain Layout
25687 \begin_inset Formula $\textrm{?`}$
25697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25700 \begin_layout Plain Layout
25708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25711 \begin_layout Plain Layout
25712 \begin_inset Formula $\textrm{ȷ}$
25726 \begin_inset space \hfill{}
25732 \begin_layout Standard
25734 \begin_inset Formula $\textrm{\textrm{Å}}$
25738 \begin_inset Formula $\textrm{\textrm{Ø}}$
25741 can also be inserted via the math toolbar button
25742 \begin_inset Graphics
25743 filename ../images/math/digamma.png
25751 \begin_layout Standard
25752 An exception are the commands
25755 \begin_inset space \hspace{}
25764 \begin_inset space \hspace{}
25770 , because they can be inserted in LyX directly to text.
25773 \begin_layout Subsection
25775 \begin_inset CommandInset label
25777 name "sub:Accents-in-Text"
25785 \begin_layout Plain Layout
25794 \begin_layout Standard
25795 With the following commands all letters can be accented.
25796 The commands must be inserted in TeX-mode.
25799 \begin_layout Standard
25800 \begin_inset space \hfill{}
25804 \begin_inset Tabular
25805 <lyxtabular version="3" rows="8" columns="2">
25807 <column alignment="block" valignment="top" width="0">
25808 <column alignment="block" valignment="top" width="0">
25810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25813 \begin_layout Plain Layout
25819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25822 \begin_layout Plain Layout
25830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25833 \begin_layout Plain Layout
25837 \begin_inset Quotes grd
25845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25848 \begin_layout Plain Layout
25852 \begin_layout Plain Layout
25868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25871 \begin_layout Plain Layout
25879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25882 \begin_layout Plain Layout
25886 \begin_layout Plain Layout
25902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25905 \begin_layout Plain Layout
25912 \begin_layout Plain Layout
25926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25929 \begin_layout Plain Layout
25933 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25952 \begin_layout Plain Layout
25960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25963 \begin_layout Plain Layout
25967 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25986 \begin_layout Plain Layout
25993 \begin_layout Plain Layout
26007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26010 \begin_layout Plain Layout
26014 \begin_layout Plain Layout
26030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26033 \begin_layout Plain Layout
26040 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26061 \begin_layout Plain Layout
26077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26080 \begin_layout Plain Layout
26087 \begin_layout Plain Layout
26101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26108 \begin_layout Plain Layout
26128 \begin_inset space \hfill{}
26132 \begin_inset Tabular
26133 <lyxtabular version="3" rows="8" columns="2">
26135 <column alignment="block" valignment="top" width="0">
26136 <column alignment="center" valignment="top" width="0">
26138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26141 \begin_layout Plain Layout
26147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26150 \begin_layout Plain Layout
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26168 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26189 \begin_layout Plain Layout
26205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26219 \begin_layout Plain Layout
26223 \begin_layout Plain Layout
26239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26249 \begin_layout Plain Layout
26260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26263 \begin_layout Plain Layout
26267 \begin_layout Plain Layout
26283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26286 \begin_layout Plain Layout
26294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26297 \begin_layout Plain Layout
26301 \begin_layout Plain Layout
26317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26320 \begin_layout Plain Layout
26327 \begin_layout Plain Layout
26341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26344 \begin_layout Plain Layout
26348 \begin_layout Plain Layout
26364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26367 \begin_layout Plain Layout
26374 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26391 \begin_layout Plain Layout
26395 \begin_layout Plain Layout
26411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26414 \begin_layout Plain Layout
26421 \begin_layout Plain Layout
26435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26438 \begin_layout Plain Layout
26442 \begin_layout Plain Layout
26462 \begin_inset space \hfill{}
26468 \begin_layout Standard
26469 \begin_inset VSpace medskip
26478 also two different characters can be accented.
26487 \begin_layout Plain Layout
26502 \begin_layout Plain Layout
26514 \begin_layout Standard
26527 can in combination with vowels directly be inserted with the keyboard without
26529 The same applies for the tilde
26533 \begin_layout Plain Layout
26534 This only applies for keyboards where the tilde is defined as accent.
26543 in combination with
26558 \begin_layout Standard
26601 , and accents inserted directly with the keyboard are also available in
26603 For the other accents there are special math commands to be used in formulas,
26605 \begin_inset CommandInset ref
26607 reference "sub:Accents-for-one"
26614 \begin_layout Standard
26615 \begin_inset VSpace bigskip
26618 Furthermore, with the command
26628 \begin_layout Plain Layout
26636 all numbers and letters can be set into a circle, quasi accented with a
26637 circle, similar to the the copyright symbol.
26640 \begin_layout Standard
26642 \begin_inset Tabular
26643 <lyxtabular version="3" rows="3" columns="2">
26645 <column alignment="center" valignment="top" width="0">
26646 <column alignment="center" valignment="top" width="0">
26648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26651 \begin_layout Plain Layout
26657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26660 \begin_layout Plain Layout
26662 \begin_inset Note Note
26665 \begin_layout Plain Layout
26672 is only used as spacer.
26684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26687 \begin_layout Plain Layout
26695 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26698 \begin_layout Plain Layout
26702 \begin_layout Plain Layout
26718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26721 \begin_layout Plain Layout
26732 raisebox{-1.5pt}{W}}
26737 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26740 \begin_layout Plain Layout
26741 \begin_inset Formula $\raisebox{4.5mm}{}$
26748 \begin_layout Plain Layout
26766 \begin_inset Formula $\raisebox{-2mm}{}$
26782 \begin_layout Standard
26783 One has to take care that the character fits in the circle.
26794 \begin_layout Plain Layout
26796 \begin_inset CommandInset ref
26798 reference "sub:Font-Sizes"
26807 specifies thereby the size of the circle.
26818 \begin_layout Plain Layout
26820 \begin_inset CommandInset ref
26822 reference "sub:Boxes-without-Frame"
26831 the character can be centered.
26834 \begin_layout Subsection
26839 \begin_layout Plain Layout
26848 \begin_layout Standard
26849 Minuscule numbers are created with the command
26859 \begin_layout Plain Layout
26868 The command can be used in formulas and in TeX-mode.
26869 The command scheme is:
26872 \begin_layout Standard
26877 oldstylenums{number}
26880 \begin_layout Standard
26885 oldstylenums{0123456789
26888 \begin_inset Formula $\oldstylenums{0123456789}$
26894 \begin_layout Subsection
26895 Miscellaneous special Characters
26896 \begin_inset CommandInset label
26898 name "sub:Miscellaneous-special-Characters"
26906 \begin_layout Plain Layout
26907 Special characters ! miscellaneous
26915 \begin_layout Standard
26916 The following characters can only be inserted to formulas by using commands:
26919 \begin_layout Standard
26921 \begin_inset Tabular
26922 <lyxtabular version="3" rows="4" columns="2">
26924 <column alignment="center" valignment="top" width="0">
26925 <column alignment="center" valignment="top" width="0">
26927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26930 \begin_layout Plain Layout
26936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26939 \begin_layout Plain Layout
26947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26950 \begin_layout Plain Layout
26957 \begin_layout Plain Layout
26971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26974 \begin_layout Plain Layout
26975 \begin_inset Formula $\mathcircumflex$
26985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26988 \begin_layout Plain Layout
26996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26999 \begin_layout Plain Layout
27000 \begin_inset Formula $\_$
27010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27013 \begin_layout Plain Layout
27018 \begin_layout Plain Layout
27033 \begin_layout Plain Layout
27044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27047 \begin_layout Plain Layout
27048 \begin_inset Formula $^{\circ}$
27064 \begin_layout Standard
27065 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27066 contains the following line
27070 \begin_layout Plain Layout
27071 More about this is described in
27072 \begin_inset CommandInset ref
27074 reference "sub:Text-Characters-in"
27086 \begin_layout Standard
27091 DeclareInputtext{176}{
27104 \begin_layout Section
27106 \begin_inset CommandInset label
27108 name "sec:Formula-Styles"
27116 \begin_layout Plain Layout
27125 \begin_layout Itemize
27126 There are two different alignment styles:
27130 \begin_layout Description
27131 Centered is the predefined standard
27134 \begin_layout Description
27135 Indented for this the option
27139 must be inserted in the menu
27141 Document\SpecialChar \menuseparator
27147 \begin_inset space ~
27153 \begin_layout Standard
27158 is used, the indentation can be adjusted with the length
27168 \begin_layout Plain Layout
27177 Should the distance be 15
27178 \begin_inset space \thinspace{}
27181 mm, the following command line is inserted in the LaTeX-preamble
27184 \begin_layout Standard
27194 \begin_layout Standard
27195 When no length is specified, the predefined value of 30
27196 \begin_inset space \thinspace{}
27203 \begin_layout Itemize
27204 And two different numbering styles:
27208 \begin_layout Description
27209 Right is the predefined standard
27212 \begin_layout Description
27213 Left for this the option
27217 must be inserted in the menu
27219 Document\SpecialChar \menuseparator
27225 \begin_inset space ~
27232 \begin_layout Standard
27241 can also be used together.
27242 In this case both options are inserted, separated by a comma.
27245 \begin_layout Standard
27246 The chosen styles are used for all displayed formulas of the document.
27247 When both, centered and indented formulas should be created in a document,
27253 The indented formulas are then set in a flalign environment, see
27254 \begin_inset CommandInset ref
27256 reference "sub:Flalign-Environment"
27263 \begin_layout Section
27265 \begin_inset CommandInset label
27267 name "sec:Multiline-Formulas"
27275 \begin_layout Plain Layout
27276 Formula ! multiline
27284 \begin_layout Subsection
27288 \begin_layout Standard
27289 In LyX multiline formulas are created by pressing
27296 This creates either an
27298 eqnarray environment
27300 that is described in
27301 \begin_inset CommandInset ref
27303 reference "sub:Eqnarray-Environment"
27307 or, when the option
27309 Use AMS math package
27311 in the document settings is selected, an
27315 that is described in
27316 \begin_inset CommandInset ref
27318 reference "sub:Standard-align-Environment"
27325 \begin_layout Standard
27326 There are other multiline formula environments that can be created via the
27329 Insert\SpecialChar \menuseparator
27333 These environments are described in the following sections.
27336 \begin_layout Standard
27337 In all multiline formula environments a new line is created by pressing
27343 To add or delete lines, the math toolbar buttons
27344 \begin_inset Graphics
27345 filename ../images/tabular-feature_append-row.png
27351 \begin_inset Graphics
27352 filename ../images/tabular-feature_delete-row.png
27357 , respectively, or the menu
27359 Edit\SpecialChar \menuseparator
27365 \begin_layout Subsubsection
27367 \begin_inset CommandInset label
27369 name "sub:Line-Separation"
27377 \begin_layout Plain Layout
27378 Formula ! multiline ! Line separation
27386 \begin_layout Standard
27387 There is sometimes not enough space in multiline formulas between the lines:
27388 \begin_inset Formula \begin{eqnarray*}
27389 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}\\
27390 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*}
27397 \begin_layout Standard
27398 In LaTeX additional line space is specified as optional argument of the
27400 This is not yet possible in LyX
27404 \begin_layout Plain Layout
27406 \begin_inset CommandInset href
27408 name "LyX-bug #1505"
27409 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27418 , therefore the whole formula must be inserted in TeX-mode.
27419 To add in our example space, the command
27427 is inserted at the end of the first line.
27432 \begin_layout Plain Layout
27439 \begin_layout Plain Layout
27441 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27444 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27451 \begin_layout Plain Layout
27455 left(B^{2}+x_{0}^{2}
27463 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27468 \begin_layout Plain Layout
27480 \begin_layout Standard
27481 \begin_inset VSpace bigskip
27484 To set the the line separation for all lines in a formula, the length
27494 \begin_layout Plain Layout
27504 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27515 \begin_inset space \thinspace{}
27520 \begin_inset space \thinspace{}
27523 mm additional line separation as in the previous example, the command
27526 \begin_layout Standard
27536 \begin_layout Standard
27537 is inserted in TeX-mode before the formula.
27538 This requires that the LaTeX-package
27546 \begin_layout Plain Layout
27551 is part of every LaTeX standard installation.
27560 \begin_layout Plain Layout
27566 was loaded in LaTeX-preamble with the line
27569 \begin_layout Standard
27577 \begin_layout Standard
27582 \begin_layout Plain Layout
27594 \begin_inset Formula \begin{eqnarray*}
27595 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}\\
27596 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*}
27603 \begin_layout Standard
27607 \begin_layout Plain Layout
27618 To get back to the predefined distance,
27624 is set to the value 3
27625 \begin_inset space \thinspace{}
27631 \begin_layout Subsubsection
27633 \begin_inset CommandInset label
27635 name "sub:Column-Separation"
27643 \begin_layout Plain Layout
27644 Formula ! multiline ! Column separation
27652 \begin_layout Standard
27653 Multiline formulas form a matrix.
27654 A formula in the eqnarray environment is for example a matrix with three
27656 By changing the column separation in this environment, the space beside
27657 the relation sign can be changed.
27660 \begin_layout Standard
27661 The column separation is specified with the length
27671 \begin_layout Plain Layout
27680 \begin_inset Newline newline
27683 column separation = 2
27684 \begin_inset space \thinspace{}
27694 \begin_inset Newline newline
27700 \begin_layout Standard
27710 \begin_layout Standard
27711 inserted in TeX-mode, sets for all following formulas a column separation
27713 \begin_inset space \thinspace{}
27717 To get back to the predefined distance,
27724 \begin_inset space \thinspace{}
27730 \begin_layout Standard
27732 \begin_inset space \thinspace{}
27735 cm column separation:
27739 \begin_layout Plain Layout
27751 \begin_inset Formula \begin{eqnarray*}
27753 C & \ne & A\end{eqnarray*}
27757 A formula with the predefined column separation for matrices of 10
27758 \begin_inset space \thinspace{}
27765 \begin_layout Plain Layout
27777 \begin_inset Formula \begin{eqnarray*}
27779 C & \ne & A\end{eqnarray*}
27786 \begin_layout Subsubsection
27791 \begin_layout Plain Layout
27800 \begin_layout Standard
27801 Long formulas can be typeset using these methods:
27804 \begin_layout Itemize
27805 When one side of the equation is much shorther than the line width, this
27806 one is chosen for the left side and the right side is typeset over two
27811 \begin_layout Plain Layout
27821 \begin_inset Formula \begin{eqnarray}
27822 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 \\
27823 & & -\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}
27831 \begin_layout Plain Layout
27841 \begin_inset Newline newline
27844 The minus sign at the beginning of the second line does normally not appear
27845 as operator because it is the first character of the line.
27846 Thus it would not be surrounded by space and could not be distinguished
27847 from the fraction bar.
27848 To avoid this, space was inserted behind the minus sign with the command
27859 \begin_layout Plain Layout
27867 \begin_inset CommandInset ref
27869 reference "sub:Variable-Space"
27882 \begin_layout Plain Layout
27893 \begin_layout Itemize
27894 When both sides of the equation are too long, the command
27904 \begin_layout Plain Layout
27913 It is inserted to the first column of the first line and effects that all
27914 further insertions overwrite the following columns:
27918 \begin_layout Plain Layout
27928 \begin_inset Formula \begin{eqnarray}
27929 \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 \\
27930 & & -\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 \\
27931 & & =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}
27939 \begin_layout Plain Layout
27949 \begin_inset Newline newline
27952 After the insertion of
27958 , the cursor is in a purple box that is a bit shifted to the left from the
27960 In this the formula is inserted.
27964 \begin_layout Plain Layout
27974 \begin_inset Newline newline
27977 The content of the further lines is inserted to the second or another formula
27979 The greater the column number where it was inserted, the larger the indentation.
27983 \begin_layout Plain Layout
27993 \begin_inset Newline newline
27997 \begin_inset Note Greyedout
28000 \begin_layout Plain Layout
28001 Note the following when using
28010 \begin_layout Itemize
28011 The formula doesn't use the full page width.
28013 \begin_inset space \thinspace{}
28017 \begin_inset space ~
28021 \begin_inset Formula $-B^{2}$
28024 is added to the first line in the above example, it would have been outside
28026 To better use the width, negative space can be inserted at the beginning
28030 \begin_layout Itemize
28031 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28036 \begin_layout Plain Layout
28037 \begin_inset CommandInset href
28039 name "LyX-bug #1429"
28040 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28049 One can only set the cursor at the beginning of the line and move it with
28058 \begin_layout Itemize
28059 Other methods to set long formulas are offered by the environments described
28061 \begin_inset CommandInset ref
28063 reference "sub:Multline-Environment"
28068 \begin_inset CommandInset ref
28070 reference "sub:Multiline-Formula-Parts"
28077 \begin_layout Subsubsection
28079 \begin_inset CommandInset label
28081 name "sub:Multiline-Brackets"
28089 \begin_layout Plain Layout
28090 Brackets ! for multiline expressions
28098 \begin_layout Standard
28099 For brackets spanning multiple lines the following problem occurs:
28100 \begin_inset Formula \begin{eqnarray*}
28101 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28102 & & \left.\cdots+B-D\right]\end{eqnarray*}
28109 \begin_layout Standard
28110 The closing bracket is smaller than the opening bracket because brackets
28111 with variable size may not span multiple lines.
28114 \begin_layout Standard
28115 To set the bracket size for the second line correctly, the first line is
28126 \begin_layout Plain Layout
28134 and the second line with
28142 \begin_layout Plain Layout
28156 \begin_inset CommandInset ref
28158 reference "sub:Automatic-Bracket-Size"
28173 \begin_layout Plain Layout
28199 \begin_layout Plain Layout
28218 \begin_layout Plain Layout
28237 \begin_layout Plain Layout
28249 \begin_inset Formula $\downarrow$
28258 \begin_layout Plain Layout
28266 is inserted, because the multiplication operator with its limits is the
28267 largest symbol in the first line and this should be the size for the bracket
28268 in the second line.
28271 \begin_layout Standard
28272 The result is this:
28273 \begin_inset Formula \begin{eqnarray*}
28274 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28275 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28282 \begin_layout Subsection
28286 \begin_layout Standard
28287 Align environments can be used for every kind of multiline formulas.
28288 They are specially useful to set several formulas side by side.
28291 \begin_layout Standard
28292 Align environments consist of columns.
28293 The odd columns are right aligned, the even ones left aligned.
28294 Every line in an Align environment can be numbered.
28297 \begin_layout Standard
28298 Align environments are created via the menu
28300 Insert\SpecialChar \menuseparator
28306 Edit\SpecialChar \menuseparator
28307 Math\SpecialChar \menuseparator
28308 Change Formula Type
28310 already existing formulas can be converted to Align environments.
28313 \begin_layout Standard
28314 To add or delete columns, the math toolbar buttons
28315 \begin_inset Graphics
28316 filename ../images/tabular-feature_append-column.png
28322 \begin_inset Graphics
28323 filename ../images/tabular-feature_delete-column.png
28328 , respectively, or the menu
28330 Edit\SpecialChar \menuseparator
28336 \begin_layout Subsubsection
28337 Standard align Environment
28338 \begin_inset CommandInset label
28340 name "sub:Standard-align-Environment"
28348 \begin_layout Plain Layout
28349 Formula ! multiline ! align environment
28357 \begin_layout Standard
28358 This Align environment is created by presssing
28362 in a formula or by the menu
28364 Insert\SpecialChar \menuseparator
28365 Math\SpecialChar \menuseparator
28366 AMS align Environment
28371 \begin_layout Standard
28372 An example for two formulas set side by side, that are created with a four
28373 column align environment:
28374 \begin_inset Formula \begin{align*}
28375 A & =\sin(B) & C & =D\\
28376 C & \ne A & B & \ne D\end{align*}
28380 As it can be seen, the formulas in this environment are placed so as if
28389 \begin_layout Plain Layout
28397 \begin_inset CommandInset ref
28399 reference "sub:Variable-Space"
28410 before the first and after every even column.
28411 When the formula style
28417 \begin_layout Plain Layout
28419 \begin_inset CommandInset ref
28421 reference "sec:Formula-Styles"
28432 is used, the formula is set without the
28438 before the first column.
28441 \begin_layout Subsubsection
28442 Alignat Environment
28446 \begin_layout Plain Layout
28447 Formula ! multiline ! alignat environment
28455 \begin_layout Standard
28456 The alignat environment has no predefined column separation.
28457 It can be inserted manually with the spaces that are described
28458 \begin_inset CommandInset ref
28460 reference "sub:Space"
28467 \begin_layout Standard
28468 The above example in the alignat environment where 1
28469 \begin_inset space \thinspace{}
28472 cm space was inserted at the beginning of the second formula:
28473 \begin_inset Formula \begin{alignat*}{2}
28474 A & =\sin(B) & \hspace{1cm}C & =D\\
28475 C & \ne A & B & \ne D\end{alignat*}
28479 Because the column separation can be set separately for every column, this
28480 environment is especially suitable to set three and more formulas side
28484 \begin_layout Subsubsection
28485 Flalign Environment
28486 \begin_inset CommandInset label
28488 name "sub:Flalign-Environment"
28496 \begin_layout Plain Layout
28497 Formula ! multiline ! flalign environment
28505 \begin_layout Standard
28506 In this environment the first two columns are always set as much as possible
28507 to the left and the last two ones to the right.
28509 \begin_inset Formula \begin{flalign*}
28510 A & =1 & B & =2 & C & =3\\
28511 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28518 \begin_layout Standard
28519 By creating a flalign environment with an odd number of columns where an
28520 empty TeX-brace is inserted to the last column, several formulas in a document
28521 can be set to the left, although the formula style
28526 As example the indented formula
28527 \begin_inset CommandInset ref
28529 reference "eq:VolInt"
28534 \begin_inset Formula \begin{flalign}
28535 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28539 The first two columns contain the formula.
28540 To indent it as with the formula style
28545 \begin_inset space \thinspace{}
28548 pt space was inserted at the beginning of the first column.
28551 \begin_layout Subsection
28552 Eqnarray Environment
28553 \begin_inset CommandInset label
28555 name "sub:Eqnarray-Environment"
28563 \begin_layout Plain Layout
28564 Formula ! multiline ! eqnarray environment
28572 \begin_layout Standard
28573 When this environment has been created, three blue boxes appear.
28574 The content of the first box is right aligned, the content of the last
28576 The content of the middle box appears centered and a bit smaller, because
28577 it is designed to insert there only relation characters.
28578 \begin_inset Formula \begin{eqnarray*}
28579 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28581 A & = & A\end{eqnarray*}
28588 \begin_layout Subsection
28593 \begin_layout Plain Layout
28594 Formula ! multiline ! gather environment
28602 \begin_layout Standard
28603 This environment consists of only one centered column.
28604 Every line can be numbered.
28605 \begin_inset Formula \begin{gather}
28607 X=\textrm{-}1\end{gather}
28614 \begin_layout Subsection
28615 Multline Environment
28616 \begin_inset CommandInset label
28618 name "sub:Multline-Environment"
28626 \begin_layout Plain Layout
28627 Formula ! multiline ! multline environment
28635 \begin_layout Standard
28636 The multline environment consists, like the gather environment, of only
28638 But the first line is left aligned, the last one right aligned.
28639 All other lines are centered.
28640 Therefore this environment is suitable for long formulas.
28642 \begin_inset CommandInset ref
28644 reference "eq:lefteqn"
28648 in the multline environment:
28649 \begin_inset Formula \begin{multline}
28650 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}\\
28651 -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}\\
28652 =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}
28659 \begin_layout Standard
28660 In the output only the last (first) line of a multline environment appears
28661 numbered when the document numbering is right (left).
28665 \begin_layout Plain Layout
28666 numbering styles see
28667 \begin_inset CommandInset ref
28669 reference "sec:Formula-Styles"
28681 \begin_layout Standard
28690 \begin_layout Plain Layout
28708 \begin_layout Plain Layout
28718 a centered line can be right or left aligned, respectively.
28719 The commands are used as follows:
28722 \begin_layout Standard
28727 shoveright{line content}
28733 shoveleft{line content}
28736 \begin_layout Standard
28737 \begin_inset VSpace medskip
28748 \begin_layout Plain Layout
28758 specifies the distance of the first line from the left page margin.
28759 Predefined is the length 0
28760 \begin_inset space \thinspace{}
28766 \begin_layout Standard
28767 As example the above formula where the command
28770 \begin_layout Standard
28780 \begin_layout Standard
28781 was inserted in TeX-mode before:
28785 \begin_layout Plain Layout
28797 \begin_inset Formula \begin{multline}
28798 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}\\
28799 \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}}\\
28800 =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}
28808 \begin_layout Plain Layout
28819 The second line was left aligned using
28828 \begin_layout Subsection
28829 Multiline Formula Parts
28830 \begin_inset CommandInset label
28832 name "sub:Multiline-Formula-Parts"
28840 \begin_layout Plain Layout
28841 Formula ! multiline ! formula parts
28849 \begin_layout Standard
28850 To display only parts of a formula with multiple lines, one of the following
28851 environments are used:
28868 They can be inserted via the menu
28870 Insert\SpecialChar \menuseparator
28873 or by using the commands described in this section.
28876 \begin_layout Standard
28877 The first three have the same properties as the corresponding multiline
28878 formula environments, but it is possible to set further formula parts beside
28881 \begin_inset Formula \[
28882 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28883 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28884 \right\} \textrm{Uncertainty relations}\]
28891 \begin_layout Standard
28892 To get this formula, a displayed formula is created where the command
28900 \begin_layout Plain Layout
28911 A purple box appears around the blue formula box where now columns and
28912 lines can be added.
28913 Outside the multiline environment other formula parts can be set, like
28917 \begin_layout Standard
28918 The aligned environment is also suitable for long formulas whose lines are
28919 horizontally aligned.
28920 Using aligned in a displayed formula has the advantage that the formula
28921 number is vertically centered behind the lines.
28923 \begin_inset CommandInset ref
28925 reference "eq:kurzlang"
28929 in the aligned environment:
28930 \begin_inset Formula \begin{equation}
28931 \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}|}\\
28932 & -\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}
28940 \begin_layout Standard
28941 To use the environments
28963 \begin_layout Plain Layout
28981 \begin_layout Plain Layout
28999 \begin_layout Plain Layout
29007 are inserted, respectively.
29008 The split environment has the same properties as the aligned environment
29009 but it can only have two columns.
29012 \begin_layout Subsection
29013 Text in multiline Formulas
29014 \begin_inset CommandInset label
29016 name "sub:Text-in-multiline"
29024 \begin_layout Plain Layout
29034 \begin_layout Plain Layout
29035 Formula ! multiline ! text
29043 \begin_layout Standard
29044 In the Align environments, and the multline and gather environment, text
29045 can be inserted that will appear in a separate line and doesn't affect
29046 the column alignment.
29047 To do this, the command
29055 \begin_layout Plain Layout
29065 is used in the following scheme:
29068 \begin_layout Standard
29076 \begin_layout Standard
29077 The text should not be longer than a line because it cannot be hyphenated.
29078 As LyX doesn't yet support
29084 directly, the text is written as mathematical text.
29091 must hereby be at the beginning of a line and appears in the output above
29093 An example where the text was inserted at the beginning of the second line:
29094 \begin_inset Formula \begin{align}
29095 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29096 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29103 \begin_layout Section
29108 \begin_layout Plain Layout
29118 \begin_layout Plain Layout
29119 Formula ! numbering|see
29123 \begin_layout Plain Layout
29134 \begin_layout Plain Layout
29149 \begin_layout Subsection
29153 \begin_layout Standard
29154 Numbered formulas can be created with the menu
29156 Insert\SpecialChar \menuseparator
29157 Math\SpecialChar \menuseparator
29159 \begin_inset space ~
29167 \begin_inset space ~
29173 Existing formulas can be numbered with the menu
29175 Edit\SpecialChar \menuseparator
29176 Math\SpecialChar \menuseparator
29178 \begin_inset space ~
29186 \begin_inset space ~
29192 The formula number is displayed in LyX behind the formula as number sign
29194 The number sign is replaced in the output by the formula number.
29197 \begin_layout Standard
29198 When numbering is turned on in multiline formulas, all lines will be numbered.
29199 But the numbering can be controlled with the menu
29201 Edit\SpecialChar \menuseparator
29202 Math\SpecialChar \menuseparator
29204 \begin_inset space ~
29208 \begin_inset space ~
29212 \begin_inset space ~
29220 \begin_inset space ~
29228 \begin_layout Standard
29229 Except of inline formulas, all formulas can be numbered with two different
29231 \begin_inset CommandInset ref
29233 reference "sec:Formula-Styles"
29240 \begin_layout Subsection
29242 \begin_inset CommandInset label
29244 name "sub:Cross-References"
29252 \begin_layout Plain Layout
29253 Cross-references ! to formulas
29261 \begin_layout Standard
29262 All labeled formulas can be cross-referenced.
29263 A label is added by the menu
29265 Insert\SpecialChar \menuseparator
29268 or the toolbar button
29269 \begin_inset Graphics
29270 filename ../images/label-insert.png
29276 The cursor must hereby be inside a displayed formula.
29277 A dialog pops up displaying the prefix
29282 The label is inserted there behind the prefix.
29283 The predefined prefix means
29284 \begin_inset Quotes eld
29288 \begin_inset Quotes erd
29291 and makes it easier to find labels in large documents because it marks
29292 it as formula label to divide it from e.
29293 \begin_inset space \thinspace{}
29297 \begin_inset space ~
29301 To change a label, the menu
29303 Insert\SpecialChar \menuseparator
29309 \begin_layout Standard
29310 The name of the label is displayed in LyX within two parentheses behind
29312 A formula with a label is always numbered.
29315 \begin_layout Standard
29316 Cross-references are inserted via the menu
29318 Insert\SpecialChar \menuseparator
29321 or with the toolbar button
29322 \begin_inset Graphics
29323 filename ../images/dialog-show-new-inset_ref.png
29329 A formula cross-reference appears in the output as formula number.
29330 When in the cross-reference dialog window the format
29334 is chosen, the cross-reference appears in the output as formula number
29336 \begin_inset Newline newline
29339 By right-clicking on a cross-reference in LyX, one jumps to the formula
29340 that is referenced.
29343 \begin_layout Standard
29344 Here are as examples cross-references to formulas of the following subsections:
29345 \begin_inset Note Note
29348 \begin_layout Plain Layout
29349 Note the different cross-reference types.
29357 \begin_layout Standard
29359 \begin_inset CommandInset ref
29366 \begin_inset CommandInset ref
29374 \begin_inset CommandInset ref
29380 ) big Latin letters are used for the numbering in contrary to (
29381 \begin_inset CommandInset ref
29390 \begin_layout Standard
29391 \begin_inset VSpace medskip
29394 When the argument of
29402 \begin_layout Plain Layout
29410 \begin_inset CommandInset ref
29412 reference "sub:User-defined-Numbering"
29423 contains a box like in
29424 \begin_inset CommandInset ref
29426 reference "sub:Paragraph-Boxes"
29430 , the formula cannot be referenced.
29433 \begin_layout Subsection
29438 \begin_layout Plain Layout
29439 Formula numbering ! subnumbering
29447 \begin_layout Standard
29448 With the help of the commands
29452 begin{subequations}
29460 formulas can be subnumbered.
29461 Both commands are inserted in TeX-mode.
29464 \begin_layout Standard
29466 \begin_inset Formula \begin{equation}
29467 A=C-B\label{eq:a}\end{equation}
29475 \begin_layout Plain Layout
29479 addtocounter{equation}{-1}
29488 \begin_layout Plain Layout
29492 begin{subequations}
29498 \begin_inset VSpace -5mm
29502 \begin_inset Formula \begin{equation}
29503 B=C-A\label{eq:b}\end{equation}
29508 \begin_inset Formula \begin{equation}
29509 C=A+B\label{eq:c}\end{equation}
29516 \begin_layout Standard
29520 \begin_layout Plain Layout
29532 \begin_layout Standard
29533 To create the example, the following is done:
29536 \begin_layout Enumerate
29537 first formula is inserted
29540 \begin_layout Enumerate
29545 addtocounter{equation}{-1}
29547 begin{subequations}
29551 \begin_layout Plain Layout
29560 \begin_inset Newline newline
29565 is inserted after the first formula
29568 \begin_layout Enumerate
29569 second formula is inserted
29572 \begin_layout Enumerate
29573 third formula is inserted
29576 \begin_layout Enumerate
29583 is inserted after the third formula
29586 \begin_layout Standard
29587 Every formula between the commands
29599 is subnumbered as a, b,
29600 \begin_inset Newline linebreak
29603 c, \SpecialChar \ldots{}
29604 For multiline formulas every line will be subnumbered.
29605 All subnumbered formulas are treated as
29610 But as every numbered formula increases the counter
29614 by one, the command
29620 is needed to decrease it.
29621 Otherwise the formulas
29622 \begin_inset CommandInset ref
29629 \begin_inset CommandInset ref
29636 \begin_inset CommandInset ref
29642 would be numbered as
29643 \begin_inset CommandInset ref
29650 \begin_inset CommandInset ref
29657 \begin_inset CommandInset ref
29666 \begin_layout Standard
29667 By inserting the commands in TeX-mode, a space is created between the first
29670 \begin_inset space \thinspace{}
29673 mm vertical space is inserted after the command
29677 begin{subequations}
29680 When the formula style
29686 \begin_layout Plain Layout
29688 \begin_inset CommandInset ref
29690 reference "sec:Formula-Styles"
29702 \begin_inset space \thinspace{}
29705 mm space is inserted instead.
29708 \begin_layout Standard
29709 Here is an example for a multiline formula where the numbering was turned
29710 off for the second line:
29714 \begin_layout Plain Layout
29718 begin{subequations}
29724 \begin_inset Formula \begin{eqnarray}
29725 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29726 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29727 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29735 \begin_layout Plain Layout
29747 \begin_layout Subsection
29748 User-defined Numbering
29749 \begin_inset CommandInset label
29751 name "sub:User-defined-Numbering"
29759 \begin_layout Plain Layout
29760 Formula numbering ! user-defined
29768 \begin_layout Standard
29772 \begin_layout Plain Layout
29773 Formula numbering ! self-defined delimiters
29778 With the standard numbering parentheses are set around the formula number.
29779 To replace the parentheses for example by vertical bars, the following
29780 line is added to the LaTeX-preamble:
29783 \begin_layout Standard
29795 \begin_inset Note Note
29798 \begin_layout Plain Layout
29799 This macro is already declared in the LaTeX-preamble for testing.
29800 To activate it, remove the percent sign at the beginning.
29808 \begin_layout Standard
29809 To use other characters, the vertical bars besides the
29813 are replaced by one ore more characters.
29814 To get only the formula number the vertical bars are omitted.
29817 \begin_layout Standard
29818 \begin_inset VSpace bigskip
29821 When there should be an expression of your choice instead of the consecutive
29822 formula number in parentheses behind the formula, the command
29832 \begin_layout Plain Layout
29841 \begin_inset Formula \begin{equation}
29842 A+B=C\tag{something}\label{eq:tag}\end{equation}
29846 In this example the command
29854 \begin_layout Plain Layout
29865 was inserted to the formula.
29868 \begin_layout Standard
29877 \begin_layout Plain Layout
29888 is inserted instead, the star prevents the parentheses around the expression:
29889 \begin_inset Formula \[
29890 A+B=C\tag*{something}\]
29897 \begin_layout Standard
29898 \begin_inset VSpace bigskip
29901 To restart the formula numbering with new document parts or sections, the
29902 following command is used:
29905 \begin_layout Standard
29910 @addtoreset{equation}{part}
29916 \begin_layout Plain Layout
29921 \begin_layout Plain Layout
29932 \begin_layout Plain Layout
29945 \begin_layout Plain Layout
29956 \begin_layout Plain Layout
29969 \begin_inset Newline newline
29973 \begin_inset Newline newline
29980 @addtoreset{equation}{section}
29983 \begin_layout Standard
29984 To be able to use these commands in TeX-mode, the
29985 \begin_inset Quotes eld
29989 \begin_inset Quotes erd
29992 character has to be made
29993 \begin_inset Quotes eld
29997 \begin_inset Quotes erd
30000 for LaTeX using the command
30014 So the command sequence in TeX-mode is:
30017 \begin_layout Standard
30023 \begin_inset Newline newline
30028 @addtoreset{equation}{section}
30029 \begin_inset Newline newline
30037 \begin_layout Standard
30038 In the LaTeX-preamble
30050 can be omitted as they are automatically internally inserted by LyX.
30053 \begin_layout Standard
30068 \begin_layout Plain Layout
30073 is part of the LaTeX-package
30081 \begin_layout Plain Layout
30082 Packages ! carlisle
30087 that is part of every LaTeX standard installation.
30096 \begin_layout Plain Layout
30097 Packages ! remreset
30102 has to be loaded in the LaTeX-preamble with the line
30105 \begin_layout Standard
30110 usepackage{remreset}
30113 \begin_layout Standard
30124 \begin_layout Plain Layout
30129 \begin_layout Plain Layout
30140 \begin_layout Plain Layout
30153 \begin_layout Plain Layout
30164 \begin_layout Plain Layout
30176 can be used with the same scheme as
30185 \begin_layout Standard
30186 \begin_inset VSpace bigskip
30189 Sometimes formulas should be numbered in the following form:
30192 \begin_layout Standard
30195 (section number.formula number)
30198 \begin_layout Standard
30199 The formula number should start with every section with
30200 \begin_inset Quotes eld
30204 \begin_inset Quotes erd
30210 \begin_layout Standard
30211 For this case there is the command
30221 \begin_layout Plain Layout
30229 , which is used with the following scheme:
30232 \begin_layout Standard
30237 numberwithin{counter}{sectioning}
30240 \begin_layout Standard
30241 Counter denotes what kind of numbering is affected, sectioning denotes what
30242 number is before the dot.
30245 \begin_layout Standard
30246 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30249 \begin_layout Standard
30254 numberwithin{equation}{section}
30257 \begin_layout Standard
30258 This is the result:
30262 \begin_layout Plain Layout
30266 numberwithin{equation}{section}
30272 \begin_inset Formula \begin{equation}
30273 A+B=C\end{equation}
30280 \begin_layout Standard
30282 \begin_inset space \thinspace{}
30286 \begin_inset space ~
30289 tables so that the number of the part is the sectioning,
30290 \begin_inset Newline newline
30297 numberwithin{table}{part}
30302 \begin_layout Standard
30303 To go back to the standard numbering or to prevent this kind of numbering
30304 when it is defined by the document class, the following command is inserted
30305 as TeX-Code or to the LaTeX-preamble:
30308 \begin_layout Standard
30321 \begin_layout Plain Layout
30335 \begin_layout Plain Layout
30351 \begin_inset Newline newline
30359 \begin_inset Newline newline
30371 \begin_layout Standard
30378 uses internally the command
30384 , described above, that also needs to be reverted.
30388 \begin_layout Plain Layout
30395 \begin_layout Plain Layout
30399 @removefromreset{equation}{section}
30402 \begin_layout Plain Layout
30414 \begin_layout Subsection
30415 Numbering with Roman Numbers and Letters
30416 \begin_inset CommandInset label
30418 name "sub:Numbering-with-Roman"
30426 \begin_layout Plain Layout
30427 Formula numbering ! with letters
30436 \begin_layout Plain Layout
30437 Formula numbering ! with Roman numbers
30445 \begin_layout Standard
30446 Formulas can also be numbered with Roman numbers and Latin letters.
30447 To number for example with small Roman numbers, the command
30450 \begin_layout Standard
30462 \begin_layout Standard
30463 is inserted before the formula in TeX-mode.
30474 \begin_layout Plain Layout
30482 redefines the predefined command
30498 \begin_layout Plain Layout
30505 has the same scheme like the command
30511 that is described in
30512 \begin_inset CommandInset ref
30514 reference "sec:User-defined-Commands"
30528 is the formula counter.
30535 is used as prefix for a counter, the value of the counter is output as
30537 When a formula is numbered, LaTeX sets internally the command
30543 behind the formula.
30552 \begin_layout Plain Layout
30562 outputs the counter as small Roman number.
30565 \begin_layout Standard
30566 All formulas behind the command
30576 are now numbered Roman.
30577 To switch to numbering with big Roman numbers, the command is inserted
30594 \begin_layout Plain Layout
30606 \begin_inset Quotes eld
30610 \begin_inset Quotes erd
30613 with small Latin letters there is the command
30623 \begin_layout Plain Layout
30631 , for big ones there is the command
30641 \begin_layout Plain Layout
30654 \begin_layout Standard
30655 \begin_inset Note Greyedout
30658 \begin_layout Plain Layout
30663 Only maximal 26 formulas can be numbered with Latin letters in one document.
30671 \begin_layout Standard
30675 \begin_layout Plain Layout
30691 \begin_layout Standard
30692 \begin_inset Formula \begin{equation}
30693 A=\textrm{small roman}\label{eq:rom}\end{equation}
30701 \begin_layout Plain Layout
30715 \begin_inset Formula \begin{equation}
30716 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30724 \begin_layout Plain Layout
30738 \begin_inset Formula \begin{equation}
30739 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30747 \begin_layout Plain Layout
30761 \begin_inset Formula \begin{equation}
30762 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30769 \begin_layout Standard
30770 To switch back to the default numbering, insert the command:
30773 \begin_layout Standard
30786 \begin_layout Plain Layout
30797 \begin_layout Standard
30801 \begin_layout Plain Layout
30815 \begin_inset Formula \begin{equation}
30816 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30823 \begin_layout Standard
30824 \begin_inset VSpace medskip
30827 As you see, formulas are numbered serially independent from the numbering
30829 When then numbering should start with
30830 \begin_inset Quotes eld
30834 \begin_inset Quotes erd
30837 when the style is changed, new equation counters have to be defined.
30838 A description about this can be found in the file
30839 \begin_inset CommandInset href
30841 target "Formula-numbering.lyx"
30848 \begin_layout Section
30849 User-defined Commands
30850 \begin_inset CommandInset label
30852 name "sec:User-defined-Commands"
30860 \begin_layout Plain Layout
30861 User-defined commands
30869 \begin_layout Standard
30870 Many LaTeX-commands are too long to be used frequently.
30871 But it is possible to define with the command
30881 \begin_layout Plain Layout
30889 new shorter commands.
30892 \begin_layout Standard
30893 The command scheme of
30902 \begin_layout Standard
30907 newcommand{new command name}[number of arguments][optional
30912 \begin_inset Newline newline
30919 \begin_layout Plain Layout
30934 \begin_layout Plain Layout
30941 {command definition}
30944 \begin_layout Standard
30945 \begin_inset Note Greyedout
30948 \begin_layout Plain Layout
30953 Assure that the name of the new command is not already used in your document
30954 or by LaTeX-packages that you use.
30955 When you for example define the command
30967 , you get an error message because
30973 is already defined as command for
30974 \begin_inset Quotes eld
30978 \begin_inset Formula $\le$
30982 \begin_inset Quotes erd
30993 \begin_layout Standard
30994 \begin_inset Note Greyedout
30997 \begin_layout Plain Layout
31002 The names of user-defined commands may only consist of Latin letters.
31010 \begin_layout Standard
31011 The number of arguments is an integer in the range 0
31012 \begin_inset space \thinspace{}
31016 \begin_inset space \thinspace{}
31019 9 and specifies how many arguments the new command should have.
31020 With the optional value a value for an optional argument can be predefined.
31021 When this is done, the
31029 rgument of the new command is automatically an optional one.
31032 \begin_layout Standard
31033 Here are some examples:
31036 \begin_layout Itemize
31037 To define the command
31049 , the LaTeX-preamble line is:
31053 \begin_layout Plain Layout
31065 \begin_inset Newline newline
31077 \begin_layout Itemize
31078 To define the command
31090 , the argument (that should be underlined) must be taken into account.
31091 For this the preamble line is:
31095 \begin_layout Plain Layout
31107 \begin_inset Newline newline
31122 \begin_layout Plain Layout
31134 \begin_inset Newline newline
31143 acts as argument placeholder, the
31147 behind it denotes that it is the placeholder for the first argument.
31150 \begin_layout Itemize
31158 \begin_inset space \thinspace{}
31162 \begin_inset space ~
31175 \begin_layout Plain Layout
31187 \begin_inset Newline newline
31196 framebox#1#2{$#3$}}
31202 \begin_layout Plain Layout
31214 \begin_inset Newline newline
31219 The two Dollar signs creates the extra formula needed for
31226 \begin_inset CommandInset ref
31228 reference "sub:Boxes-with-Frame"
31235 \begin_layout Itemize
31236 To create a new command for
31242 where the color for the box needn't to be specified, the argument for the
31243 color is defined optional:
31247 \begin_layout Plain Layout
31259 \begin_inset Newline newline
31268 fcolorbox{#2}{#1}{$#3$}}
31274 \begin_layout Plain Layout
31284 \begin_inset Newline newline
31287 When the color is not specified when using
31293 , the predefined color
31300 \begin_layout Standard
31301 A test of the new defined commands:
31304 \begin_layout Standard
31306 \begin_inset Tabular
31307 <lyxtabular version="3" rows="6" columns="2">
31309 <column alignment="center" valignment="top" width="0">
31310 <column alignment="center" valignment="top" width="0">
31312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31315 \begin_layout Plain Layout
31321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31324 \begin_layout Plain Layout
31326 \begin_inset Note Note
31329 \begin_layout Plain Layout
31336 is only used as spacer.
31348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31351 \begin_layout Plain Layout
31358 \begin_layout Plain Layout
31372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31375 \begin_layout Plain Layout
31376 \begin_inset Formula $A\gr B$
31386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31389 \begin_layout Plain Layout
31397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31400 \begin_layout Plain Layout
31401 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31414 \begin_layout Plain Layout
31418 \begin_inset Formula $\to$
31424 \begin_inset Formula $\to$
31435 \begin_layout Plain Layout
31449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31452 \begin_layout Plain Layout
31453 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31466 \begin_layout Plain Layout
31470 \begin_inset Formula $\to$
31481 \begin_layout Plain Layout
31495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31498 \begin_layout Plain Layout
31499 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31512 \begin_layout Plain Layout
31518 \begin_inset Formula $\to$
31529 \begin_layout Plain Layout
31543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31546 \begin_layout Plain Layout
31547 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31563 \begin_layout Section
31567 \begin_layout Standard
31568 LyX supports two types of commutative diagrams:
31576 that are explained in the following.
31579 \begin_layout Subsection
31584 \begin_layout Plain Layout
31593 \begin_layout Standard
31594 Diagrams of this type visualize relations by vertical and horizontal lines
31596 \begin_inset Formula \[
31597 \begin{CD}A@>>>B@>>>C\\
31599 F@<<<E@<<<D\end{CD}\]
31606 \begin_layout Standard
31607 To get them, the command
31615 \begin_layout Plain Layout
31625 is inserted to a formula.
31626 A blue box appears with two dashed lines where further commands can be
31632 a new line is created.
31633 Horizontal relations are inserted in odd, vertical in even formula lines.
31636 \begin_layout Standard
31637 To create the relations there are the following commands:
31640 \begin_layout Itemize
31645 creates a left arrow,
31656 \begin_layout Itemize
31661 creates an up arrow,
31669 a vertical equal sign
31672 \begin_layout Itemize
31678 is a placeholder for non-existent relations
31681 \begin_layout Standard
31682 All arrows can be labeled as follows:
31685 \begin_layout Itemize
31686 Is text inserted between the first and second < or >, resp., it is placed
31688 When it is inserted between the second and third one, it appears under
31692 \begin_layout Itemize
31693 When text for vertical arrows is inserted between the first and second A
31694 or V, resp., it is placed left beside the arrow.
31695 When it is inserted between the second and third one, it appears right
31697 If the text contains an A or V, these letters must be set into a TeX-brace.
31700 \begin_layout Standard
31701 As example a diagram with all possible relations:
31704 \begin_layout Standard
31705 \begin_inset Formula \[
31706 \begin{CD}A@>j>>B@>>k>C@=F\\
31708 D@<<j<E@>k>>F@=C\end{CD}\]
31715 \begin_layout Standard
31716 The command for this is:
31717 \begin_inset Newline newline
31728 \begin_layout Plain Layout
31737 A@>j>>B@>>k>C@=F Ctrl-Enter
31738 \begin_inset Newline newline
31745 \begin_layout Plain Layout
31760 \begin_layout Plain Layout
31773 \begin_layout Plain Layout
31785 \begin_inset Formula $\to$
31791 \begin_inset Newline newline
31798 \begin_layout Plain Layout
31813 \begin_layout Plain Layout
31826 \begin_layout Plain Layout
31836 \begin_layout Subsection
31841 \begin_layout Plain Layout
31842 Diagrams ! xymatrix
31850 \begin_layout Standard
31851 To be able to use xymatrices, the LaTeX-package
31856 A xymatrix is created by inserting the command
31863 Then you are able to add new matrix columns and rows like for normal matrices,
31865 \begin_inset CommandInset ref
31867 reference "sec:Matrices"
31874 \begin_layout Standard
31875 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31877 All possibilities to create commutative diagrams and decorations are explained
31878 in detail in this manual:
31879 \begin_inset CommandInset href
31881 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31888 \begin_layout Standard
31889 \begin_inset Newpage newpage
31895 \begin_layout Section
31900 \begin_layout Plain Layout
31913 \begin_layout Plain Layout
31914 Other useful math tips can be found in
31915 \begin_inset CommandInset citation
31930 \begin_layout Plain Layout
31938 \begin_inset Note Note
31941 \begin_layout Plain Layout
31944 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31947 \begin_layout Plain Layout
31950 texorpdfstring is in section
31951 \begin_inset CommandInset ref
31953 reference "sub:Formulas-in-Section"
31966 \begin_layout Plain Layout
31976 \begin_layout Plain Layout
31981 \begin_layout Plain Layout
31988 Chemical characters
31992 \begin_layout Plain Layout
32007 \begin_layout Subsection
32008 Chemical Symbols and Equations
32009 \begin_inset CommandInset label
32011 name "sub:Chemical-Symbols-and"
32019 \begin_layout Plain Layout
32020 Chemical characters ! Symbols
32029 \begin_layout Plain Layout
32039 \begin_layout Plain Layout
32048 \begin_layout Standard
32049 An example text from chemistry:
32052 \begin_layout Quote
32054 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32057 -ion reacts with two
32058 \begin_inset Formula $\mathrm{Na^{+}}$
32061 -ions to sodium sulfate
32062 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32066 The chemical equation for this is:
32067 \begin_inset Formula \[
32068 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32075 \begin_layout Standard
32076 This chemical equation can directly be created as formula.
32077 To avoid that the symbols appear italic, everything is highlighted and
32078 changed by the shortcut
32081 \begin_inset space ~
32086 to the upright font style.
32090 \begin_layout Plain Layout
32096 \begin_inset CommandInset ref
32098 reference "sub:Font-Styles"
32110 \begin_layout Subsection
32115 \begin_layout Plain Layout
32124 \begin_layout Standard
32125 Negative numbers often look ugly in formulas because the minus sign before
32126 the number is set with the same length as the minus operator sign.
32127 When writing the negative number in normal text, the minus sign appears
32131 \begin_layout Standard
32132 Thus, the problem disappears when converting the minus sign to mathematical
32136 \begin_layout Standard
32137 An example to visualize the problem:
32140 \begin_layout Standard
32142 \begin_inset Tabular
32143 <lyxtabular version="3" rows="3" columns="2">
32145 <column alignment="right" valignment="top" width="0">
32146 <column alignment="left" valignment="top" width="0">
32148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32151 \begin_layout Plain Layout
32157 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32160 \begin_layout Plain Layout
32168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32171 \begin_layout Plain Layout
32177 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32180 \begin_layout Plain Layout
32181 \begin_inset Formula $x=-2$
32191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32194 \begin_layout Plain Layout
32200 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32203 \begin_layout Plain Layout
32204 \begin_inset Formula $x=\textrm{-}2$
32220 \begin_layout Subsection
32221 Comma as decimal Separator
32225 \begin_layout Plain Layout
32234 \begin_layout Standard
32235 In LaTeX a comma inside a formula is used, according to the English convention,
32236 as number group separator.
32237 So there will be space added behind all commas in formulas.
32240 \begin_layout Standard
32241 To avoid this, the comma is highlighted and changed to mathematical text
32245 \begin_inset space ~
32253 \begin_layout Standard
32254 To use all formula commas in the document as decimal separator, the file
32263 \begin_layout Plain Layout
32268 is part of the LaTeX-package
32276 \begin_layout Plain Layout
32281 \begin_layout Plain Layout
32304 \begin_layout Plain Layout
32310 is loaded with the LaTeX-preamble line
32313 \begin_layout Standard
32321 \begin_layout Subsection
32323 \begin_inset CommandInset label
32325 name "sub:Physical-Vectors"
32333 \begin_layout Plain Layout
32342 \begin_layout Standard
32343 Predefined vectors are offered by the LaTeX-package
32351 \begin_layout Plain Layout
32356 should be part of every LaTeX standard installation.
32365 \begin_layout Plain Layout
32371 that is loaded with the LaTeX-preamble line
32374 \begin_layout Standard
32382 \begin_layout Standard
32386 \begin_layout Plain Layout
32396 \begin_inset Note Note
32399 \begin_layout Plain Layout
32400 The following table will only be displayed when the LaTeX-package
32409 The following commands are defined:
32412 \begin_layout Standard
32414 \begin_inset Tabular
32415 <lyxtabular version="3" rows="4" columns="2">
32417 <column alignment="center" valignment="top" width="0">
32418 <column alignment="center" valignment="top" width="0">
32420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32423 \begin_layout Plain Layout
32429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32432 \begin_layout Plain Layout
32440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32443 \begin_layout Plain Layout
32453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32456 \begin_layout Plain Layout
32457 \begin_inset Formula $\Bra{\psi}$
32467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32470 \begin_layout Plain Layout
32480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32483 \begin_layout Plain Layout
32484 \begin_inset Formula $\Ket{\psi}$
32494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32497 \begin_layout Plain Layout
32509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32512 \begin_layout Plain Layout
32513 \begin_inset Formula $\Braket{\psi|\phi}$
32529 \begin_layout Standard
32536 assures that all vertical bars are set in the size of the surrounding brackets:
32537 \begin_inset Formula \[
32538 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32546 \begin_layout Plain Layout
32556 \begin_inset Note Note
32559 \begin_layout Plain Layout
32560 The following will be displayed when the LaTeX-package
32572 \begin_layout Standard
32573 You need to install the LaTeX-package
32577 to see the rest of this subsection in the output.
32580 \begin_layout Standard
32584 \begin_layout Plain Layout
32596 \begin_layout Standard
32603 can also be achieved using the command
32609 , that is described in
32610 \begin_inset CommandInset ref
32612 reference "sub:Automatic-Bracket-Size"
32619 \begin_layout Subsection
32620 Self-defined Fractions
32621 \begin_inset CommandInset label
32623 name "sub:Self-defined-Fractions"
32631 \begin_layout Plain Layout
32632 Fractions ! self-defined
32640 \begin_layout Standard
32641 To define custom commands for fractions, the command
32651 \begin_layout Plain Layout
32659 is used in the following scheme:
32662 \begin_layout Standard
32675 bracket}{fraction bar thickness}{style}
32676 \begin_inset Newline newline
32683 \begin_layout Plain Layout
32698 \begin_layout Plain Layout
32705 {numerator}{denominator}
32708 \begin_layout Standard
32709 The style is a number in the range of 0
32710 \begin_inset space \thinspace{}
32714 \begin_inset space \thinspace{}
32720 \begin_layout Standard
32722 \begin_inset Tabular
32723 <lyxtabular version="3" rows="5" columns="2">
32725 <column alignment="center" valignment="top" width="0">
32726 <column alignment="center" valignment="top" width="0">
32728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32731 \begin_layout Plain Layout
32737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32740 \begin_layout Plain Layout
32748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32751 \begin_layout Plain Layout
32757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32760 \begin_layout Plain Layout
32761 display style formula
32768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32771 \begin_layout Plain Layout
32777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32780 \begin_layout Plain Layout
32788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32791 \begin_layout Plain Layout
32797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32800 \begin_layout Plain Layout
32808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32811 \begin_layout Plain Layout
32817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32820 \begin_layout Plain Layout
32834 \begin_layout Standard
32835 When no style is given, the size is adjusted to the surrounding environment
32836 like for the command
32845 \begin_layout Standard
32846 When no fraction bar thickness is given, the predefined value of 0.4
32847 \begin_inset space \thinspace{}
32853 \begin_layout Standard
32854 \begin_inset VSpace medskip
32857 For example, the commands
32870 \begin_inset CommandInset ref
32872 reference "sub:Fractions"
32876 are defined with the commands
32879 \begin_layout Standard
32888 genfrac{}{}{}{0}{#1}{#2}}
32891 \begin_layout Standard
32895 \begin_layout Standard
32904 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32907 \begin_layout Standard
32908 \begin_inset VSpace medskip
32911 To define a fraction where the fraction bar thickness can be given as optional
32912 argument, the following line is inserted to the LaTeX-preamble:
32915 \begin_layout Standard
32924 genfrac{}{}{#1}{}{#2}{#3}}
32927 \begin_layout Standard
32929 \begin_inset Formula \begin{align*}
32930 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32931 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32935 As one can see, the distance of the numerator and the denominator to the
32936 fraction bar is round about three times the bar thickness.
32939 \begin_layout Subsection
32941 \begin_inset CommandInset label
32943 name "sub:Canceled-Formulas"
32951 \begin_layout Plain Layout
32960 \begin_layout Standard
32961 To cancel formulas or formula parts, the LaTeX-package
32969 \begin_layout Plain Layout
32974 is part of every LaTeX standard installation.
32983 \begin_layout Plain Layout
32989 has to be loaded with the LaTeX-preamble line
32992 \begin_layout Standard
32997 usepackage[samesize]{cancel}
33000 \begin_layout Standard
33001 There are four ways to cancel formulas:
33004 \begin_layout Standard
33006 \begin_inset Tabular
33007 <lyxtabular version="3" rows="5" columns="2">
33009 <column alignment="center" valignment="top" width="0">
33010 <column alignment="center" valignment="top" width="0">
33012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33015 \begin_layout Plain Layout
33021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33024 \begin_layout Plain Layout
33026 \begin_inset Note Note
33029 \begin_layout Plain Layout
33042 are used here as spacer.
33054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33057 \begin_layout Plain Layout
33066 \begin_layout Plain Layout
33080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33083 \begin_layout Plain Layout
33084 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33097 \begin_layout Plain Layout
33106 \begin_layout Plain Layout
33120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33123 \begin_layout Plain Layout
33124 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33137 \begin_layout Plain Layout
33146 \begin_layout Plain Layout
33160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33163 \begin_layout Plain Layout
33164 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33177 \begin_layout Plain Layout
33181 \begin_inset Formula $\to$
33192 \begin_layout Plain Layout
33206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33209 \begin_layout Plain Layout
33210 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33226 \begin_layout Standard
33233 is especially suitable to visualize the reduction of fractions within formulas:
33234 \begin_inset Formula \[
33235 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33242 \begin_layout Subsection
33243 Formulas in Section Headings
33244 \begin_inset CommandInset label
33246 name "sub:Formulas-in-Section"
33254 \begin_layout Plain Layout
33255 Formula ! in section headings
33263 \begin_layout Standard
33264 When formulas are used in section headings, the following has to be taken
33268 \begin_layout Standard
33269 \begin_inset Note Greyedout
33272 \begin_layout Plain Layout
33281 \begin_layout Plain Layout
33282 Packages ! hyperref
33287 support is enabled in the document settings dialog under
33290 \begin_inset space ~
33295 , PDF-bookmarks are created for every section heading in the table of contents.
33296 If a section heading contains formulas, they are incorrectly displayed
33297 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33306 \begin_layout Standard
33307 Both problems can be solved by inserting at the end of the section heading
33308 a short title with the menu
33310 Insert\SpecialChar \menuseparator
33312 \begin_inset space ~
33318 Short titles are used as alternative for multiline section headings to
33319 keep the table of contents clearly arranged.
33320 Only the short title appears in the table of contents and therefore also
33321 in the PDF-bookmark.
33324 \begin_layout Standard
33325 When formulas should be used in the table of contents but
33329 is used, one can use the following command in TeX-mode:
33332 \begin_layout Standard
33337 texorpdfstring{part}{alternative}
33341 \begin_layout Plain Layout
33352 \begin_layout Standard
33353 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33354 This can be characters, formulas, footnotes, but also cross-references.
33355 The alternative is used instead of the part for the bookmark.
33358 \begin_layout Standard
33359 Here are two example headings:
33360 \begin_inset VSpace -3mm
33367 \begin_layout Plain Layout
33379 \begin_layout Subsubsection
33380 Heading without formula in table of contents
33381 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33385 \begin_inset OptArg
33388 \begin_layout Plain Layout
33389 Heading without formula in table of contents
33397 \begin_layout Subsubsection
33398 Heading with formula in table of contents
33402 \begin_layout Plain Layout
33412 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33419 \begin_layout Plain Layout
33429 \begin_layout Standard
33433 \begin_layout Plain Layout
33442 In the first heading a short title was used, in the second one
33451 \begin_layout Standard
33452 To get the same formatting as for the other headings, the complete heading
33461 \begin_layout Plain Layout
33463 \begin_inset CommandInset ref
33465 reference "sub:Bold-Formulas"
33477 \begin_layout Subsection
33478 Formulas in multi-column Text
33482 \begin_layout Plain Layout
33483 Formula ! in multi-column text
33491 \begin_layout Standard
33492 Formulas in multi-column text are often too wide to fit into a column and
33493 thus need to be set over the whole page width.
33494 This is done by using the LaTeX-package
33502 \begin_layout Plain Layout
33507 is part of every LaTeX standard installation.
33516 \begin_layout Plain Layout
33517 Packages ! multicol
33522 , that is loaded with the LaTeX-preamble line
33525 \begin_layout Standard
33530 usepackage{multicol}
33533 \begin_layout Standard
33534 \begin_inset Note Greyedout
33537 \begin_layout Plain Layout
33538 Note herby that the setting
33541 \begin_inset space ~
33548 Document\SpecialChar \menuseparator
33554 \begin_inset space ~
33574 \begin_layout Standard
33575 Before the multi-column text the command
33578 \begin_layout Standard
33583 begin{multicols}{column number}
33586 \begin_layout Standard
33587 is written in TeX-mode.
33588 The column number is a number in the range of 2
33589 \begin_inset space \thinspace{}
33593 \begin_inset space \thinspace{}
33597 Before the formula the multi-column text is ended by inserting the command
33600 \begin_layout Standard
33608 \begin_layout Standard
33612 \begin_layout Standard
33613 Due to the command some space is automatically added before the formula.
33615 \begin_inset space \thinspace{}
33618 mm vertical space is inserted before the formula.
33619 When the formula style
33625 \begin_layout Plain Layout
33627 \begin_inset CommandInset ref
33629 reference "sec:Formula-Styles"
33641 \begin_inset space \thinspace{}
33644 mm space is inserted instead.
33647 \begin_layout Standard
33648 As example a multi-column text with a displayed formula:
33651 \begin_layout Standard
33655 \begin_layout Plain Layout
33659 begin{multicols}{2}
33664 Das Spektrum wird fouriertransformiert.
33665 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33666 , Lösungsmittel) zu trennen.
33667 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33668 nun das Aussehen des Ausgangssignals.
33669 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33670 über alle Phasen integrieren muss.
33672 \begin_inset Formula $S$
33675 unser normiertes Ausgangssignal and
33676 \begin_inset Formula $P$
33679 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33683 \begin_layout Plain Layout
33693 \begin_inset VSpace -6mm
33697 \begin_inset Formula \begin{equation}
33698 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33706 \begin_layout Plain Layout
33710 begin{multicols}{2}
33716 \begin_inset Formula $S_{0}$
33719 das Signal ohne Gradient ist and the Normierungsbedingung
33720 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33724 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33726 \begin_inset Formula $\nicefrac{\pi}{2}$
33730 \begin_inset space \thinspace{}
33733 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33734 das Signal zusätzlich abschwächt.
33735 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33737 \begin_inset Formula $T_{2}$
33743 \begin_layout Standard
33747 \begin_layout Plain Layout
33759 \begin_layout Subsection
33760 Formulas with Description of Variables
33764 \begin_layout Plain Layout
33765 Formula ! with description of variables
33773 \begin_layout Standard
33774 To describe variables within a formula, like in formula
33775 \begin_inset CommandInset ref
33777 reference "eq:within"
33786 \begin_inset Formula $n$
33790 \begin_inset space ~
33793 matrix is used with left aligned columns for the
33794 \begin_inset Formula $n$
33801 \begin_layout Plain Layout
33803 \begin_inset CommandInset ref
33805 reference "sec:Matrices"
33814 To set the description in a smaller size, before the matrix e.
33815 \begin_inset space \thinspace{}
33819 \begin_inset space ~
33832 \begin_layout Plain Layout
33834 \begin_inset CommandInset ref
33836 reference "sub:Font-Sizes"
33848 \begin_layout Standard
33849 When the formula style
33855 \begin_layout Plain Layout
33857 \begin_inset CommandInset ref
33859 reference "sec:Formula-Styles"
33880 \begin_layout Plain Layout
33887 only works in formulas with the style
33892 \begin_inset CommandInset ref
33894 reference "sub:Variable-Space"
33903 is inserted before and after the matrix to have the same separation of
33904 the matrix from the equation and the side margin.
33907 \begin_layout Standard
33908 When the formula style
33912 is used, the method described in
33913 \begin_inset CommandInset ref
33915 reference "sub:Flalign-Environment"
33919 is used to indent formulas.
33921 \begin_inset CommandInset ref
33923 reference "eq:within"
33927 consists of five columns whereas in the first two columns contain the equation,
33928 the third the matrix, and the last one an empty TeX-brace.
33929 \begin_inset Formula \begin{flalign}
33930 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33931 \rho & \textrm{density}\\
33932 V & \textrm{volume}\\
33933 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33940 \begin_layout Subsection
33941 Upright small Greek Letters
33942 \begin_inset CommandInset label
33944 name "sub:Upright-small-Greek"
33952 \begin_layout Plain Layout
33953 Greek letters ! upright
33961 \begin_layout Standard
33962 Most of the math fonts only provide italic small Greek letters.
33963 But for symbols of elementary particles like pions and neutrinos, upright
33964 Greek letters are needed.
33973 \begin_layout Plain Layout
33978 is part of the LaTeX-package
33986 \begin_layout Plain Layout
33991 \begin_layout Plain Layout
34014 \begin_layout Plain Layout
34020 that is loaded with the LaTeX-preamble line
34023 \begin_layout Standard
34028 usepackage{upgreek}
34031 \begin_layout Standard
34037 \begin_layout Plain Layout
34047 \begin_inset Note Note
34050 \begin_layout Plain Layout
34051 The following table will only be displayed when the LaTeX-package
34060 They are created when the command for a small Greek letters is started
34066 For example the command
34073 \begin_inset Formula $\uptau$
34079 \begin_layout Standard
34080 With these commands reactions of elementary particles can be typeset:
34081 \begin_inset Formula \[
34082 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34089 \begin_layout Standard
34090 The upright letters are more bold and wider than the italic ones.
34091 They should therefore not be used for units like
34092 \begin_inset Quotes eld
34096 \begin_inset Quotes erd
34102 \begin_layout Standard
34106 \begin_layout Plain Layout
34116 \begin_inset Note Note
34119 \begin_layout Plain Layout
34120 The following will be displayed when the LaTeX-package
34132 \begin_layout Standard
34133 You need to install the LaTeX-package
34137 to see the rest of this subsection in the output.
34140 \begin_layout Standard
34144 \begin_layout Plain Layout
34156 \begin_layout Subsection
34157 Text Characters in Formulas
34158 \begin_inset CommandInset label
34160 name "sub:Text-Characters-in"
34168 \begin_layout Plain Layout
34177 \begin_layout Standard
34178 In some cases you might want to insert text characters directly into formulas.
34179 When for example the centered dot · is often used in formulas like
34180 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34183 , one would have to insert the command
34193 \begin_layout Plain Layout
34195 \begin_inset CommandInset ref
34197 reference "sub:Binary-Operators"
34206 all the time, because this character is defined in all encodings as text
34208 But the encoding can be changed by this LaTeX-preamble line:
34211 \begin_layout Standard
34216 Declare Inputtext{183}{
34226 f\SpecialChar \textcompwordmark{}
34230 \begin_layout Standard
34231 The character encoding (menu
34233 Document\SpecialChar \menuseparator
34234 Settings\SpecialChar \menuseparator
34237 ) specifies what character appears when a keyboard key is pressed.
34238 When the key for the character '·' is pressed, internally the command
34245 But this command is not available in a formula so that you would get LaTeX-erro
34247 With the changed encoding the right command is chosen automatically, depending
34248 on if the character was inserted into a formula or not.
34251 \begin_layout Standard
34252 The encoding of several characters is saved in definition files.
34253 Fore example the encoding
34257 is defined in the file
34261 that is in the installation folder of LaTeX.
34262 Encodings should only be changed via the LaTeX-preamble and not in the
34264 Otherwise own documents could not be edited by other LyX users working
34265 on other computers.
34268 \begin_layout Standard
34269 \begin_inset VSpace medskip
34272 Besides the centered dot, in this document the degree sign ° is defined
34273 with the following LaTeX-preamble line so that it can directly be inserted
34277 \begin_layout Standard
34282 DeclareInputtext{176}{
34292 f\SpecialChar \textcompwordmark{}
34296 \begin_layout Standard
34297 \begin_inset Newpage newpage
34303 \begin_layout Section
34309 \begin_layout Plain Layout
34318 \begin_layout Standard
34319 This section is a summary of the most important typographic rules, listed
34324 \begin_layout Plain Layout
34325 This collection was partly taken from the German semi-official dictionary
34327 \begin_inset Quotes eld
34331 \begin_inset Quotes erd
34335 \begin_inset CommandInset citation
34341 that lists some of the ISO rules.
34349 \begin_layout Itemize
34358 \begin_layout Plain Layout
34359 done with font styles, see
34360 \begin_inset CommandInset ref
34362 reference "sub:Font-Styles"
34372 \begin_inset space \thinspace{}
34376 \begin_inset Newline newline
34379 Between the value and the unit is the smallest space, see
34380 \begin_inset CommandInset ref
34382 reference "sub:Predefined-Space"
34387 \begin_inset Newline newline
34390 This convention is automatically fulfilled when the command
34397 When it is entered to a formula, two boxes appear.
34398 In the first one the value is inserted, in the second one the unit, and
34400 \begin_inset Formula $\unit[30]{km/h}$
34404 \begin_inset space \thinspace{}
34414 is not a real LaTeX command but the command
34420 , therefore you cannot use it in TeX code.
34423 \begin_layout Itemize
34424 Percent and perthousand signs are set like physical units:
34425 \begin_inset Newline newline
34429 \begin_inset space \thinspace{}
34435 \begin_layout Itemize
34436 The degree sign follows directly on the value: 15°, but not when it is used
34438 \begin_inset space \thinspace{}
34444 \begin_layout Itemize
34445 In numbers with more than four digits the smallest space is inserted before
34446 every third digit to group them:
34456 \begin_inset space \thinspace{}
34460 \begin_inset space \thinspace{}
34466 \begin_layout Itemize
34467 For dimensions like 120×90×40
34468 \begin_inset space \thinspace{}
34471 cm the multiplication sign
34472 \begin_inset Quotes eld
34476 \begin_inset Quotes erd
34480 It is available with the LaTeX-command
34486 , but can also directly be inserted with some keyboard definitions.
34489 \begin_layout Itemize
34490 Functions with names consisting of several letters are set upright to avoid
34492 \begin_inset CommandInset ref
34494 reference "sub:Predefined-Functions"
34501 \begin_layout Itemize
34502 Indices consisting of several letters, are set upright:
34503 \begin_inset Formula $E_{\mathrm{kin}}$
34507 \begin_inset Newline newline
34510 Components of matrices are set italic:
34511 \begin_inset Formula $\hat{H}_{kl}$
34517 \begin_layout Itemize
34518 The differentiation/integration operator 'd', the Euler's number 'e', and
34519 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34523 \begin_layout Standard
34524 \begin_inset Newpage newpage
34530 \begin_layout Section
34535 \begin_layout Plain Layout
34544 \begin_layout Standard
34545 Some characters and symbols can be created with several commands.
34546 Here is a list of the synonym commands:
34549 \begin_layout Standard
34550 \begin_inset VSpace bigskip
34554 \begin_inset space \hfill{}
34558 \begin_inset Tabular
34559 <lyxtabular version="3" rows="12" columns="2">
34561 <column alignment="center" valignment="top" width="0pt">
34562 <column alignment="center" valignment="top" width="0pt">
34564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34567 \begin_layout Plain Layout
34573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34576 \begin_layout Plain Layout
34578 \begin_inset Note Note
34581 \begin_layout Plain Layout
34588 is only used as spacer.
34600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34603 \begin_layout Plain Layout
34611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34614 \begin_layout Plain Layout
34618 \begin_layout Plain Layout
34631 \begin_layout Plain Layout
34645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34648 \begin_layout Plain Layout
34656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34659 \begin_layout Plain Layout
34669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34672 \begin_layout Plain Layout
34680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34683 \begin_layout Plain Layout
34693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34696 \begin_layout Plain Layout
34704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34707 \begin_layout Plain Layout
34715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34718 \begin_layout Plain Layout
34726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34729 \begin_layout Plain Layout
34737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34740 \begin_layout Plain Layout
34748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34751 \begin_layout Plain Layout
34761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34764 \begin_layout Plain Layout
34772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34775 \begin_layout Plain Layout
34785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34788 \begin_layout Plain Layout
34796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34799 \begin_layout Plain Layout
34809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34812 \begin_layout Plain Layout
34820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34823 \begin_layout Plain Layout
34833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34836 \begin_layout Plain Layout
34844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34847 \begin_layout Plain Layout
34855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34858 \begin_layout Plain Layout
34866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34869 \begin_layout Plain Layout
34881 \begin_inset space \hfill{}
34885 \begin_inset Tabular
34886 <lyxtabular version="3" rows="12" columns="2">
34888 <column alignment="center" valignment="top" width="0pt">
34889 <column alignment="center" valignment="top" width="0pt">
34891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34894 \begin_layout Plain Layout
34900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34903 \begin_layout Plain Layout
34911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34914 \begin_layout Plain Layout
34922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34925 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34940 \begin_layout Plain Layout
34948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34951 \begin_layout Plain Layout
34961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34964 \begin_layout Plain Layout
34972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34975 \begin_layout Plain Layout
34985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34988 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34999 \begin_layout Plain Layout
35007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35010 \begin_layout Plain Layout
35018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35021 \begin_layout Plain Layout
35029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35032 \begin_layout Plain Layout
35040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35043 \begin_layout Plain Layout
35053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35056 \begin_layout Plain Layout
35064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35067 \begin_layout Plain Layout
35077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35080 \begin_layout Plain Layout
35088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35091 \begin_layout Plain Layout
35101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35104 \begin_layout Plain Layout
35112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35115 \begin_layout Plain Layout
35125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35128 \begin_layout Plain Layout
35136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35139 \begin_layout Plain Layout
35149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35152 \begin_layout Plain Layout
35160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35163 \begin_layout Plain Layout
35177 \begin_inset space \hfill{}
35183 \begin_layout Standard
35184 \begin_inset Newpage newpage
35190 \begin_layout Bibliography
35191 \begin_inset CommandInset bibitem
35192 LatexCommand bibitem
35204 The LaTeX Companion
35207 Addison Wesley, 2004
35210 \begin_layout Bibliography
35211 \begin_inset CommandInset bibitem
35212 LatexCommand bibitem
35218 \begin_inset CommandInset href
35221 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35225 of LaTeX's math abilities
35228 \begin_layout Bibliography
35229 \begin_inset CommandInset bibitem
35230 LatexCommand bibitem
35235 LaTeX tips and tricks-
35236 \begin_inset CommandInset href
35239 target "http://tug.org/TeXnik/"
35246 \begin_layout Bibliography
35247 \begin_inset CommandInset bibitem
35248 LatexCommand bibitem
35254 \begin_inset CommandInset href
35257 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35265 \begin_layout Plain Layout
35277 \begin_layout Bibliography
35278 \begin_inset CommandInset bibitem
35279 LatexCommand bibitem
35285 \begin_inset CommandInset href
35288 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35292 of all symbols available with LaTeX-packages
35295 \begin_layout Bibliography
35296 \begin_inset CommandInset bibitem
35297 LatexCommand bibitem
35303 \begin_inset CommandInset href
35305 name "Documentation"
35306 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35310 of the LaTeX-package
35318 \begin_layout Plain Layout
35319 Packages ! hyperref
35327 \begin_layout Bibliography
35328 \begin_inset CommandInset bibitem
35329 LatexCommand bibitem
35335 \begin_inset CommandInset href
35338 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35349 \begin_inset CommandInset ref
35351 reference "sub:Operator-Limits"
35359 \begin_layout Plain Layout
35370 \begin_layout Bibliography
35371 \begin_inset CommandInset bibitem
35372 LatexCommand bibitem
35383 Auflage, Duden 2001
35386 \begin_layout Subsubsection*
35387 \begin_inset CommandInset index_print
35388 LatexCommand printindex