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 coefficient s
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
4270 which has the following scheme:
4273 \begin_layout Standard
4278 rule[vertical offset]{length}{thickness}
4281 \begin_layout Standard
4282 The optional vertical offset shifts the line upwards (or downwards, when
4283 the value is negative).
4285 \begin_inset CommandInset ref
4287 reference "tab:Available-units"
4291 can be used for the values.
4292 Here are two example lines created with the commands
4293 \begin_inset Newline newline
4300 rule[-2ex]{3cm}{2pt}
4311 \begin_layout Standard
4313 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4319 \begin_layout Standard
4326 can also be used for text when it is inserted in TeX-mode.
4329 \begin_layout Subsection
4331 \begin_inset CommandInset label
4341 \begin_layout Plain Layout
4350 \begin_layout Standard
4351 There are different types of ellipses available.
4355 \begin_layout Plain Layout
4356 In the math toolbar in the submenu of the button
4357 \begin_inset Graphics
4358 filename ../images/math/ldots.png
4368 For listings dots at the baseline are used (
4378 \begin_layout Plain Layout
4386 ), while for operations dots are needed that are on the same height as the
4397 \begin_layout Plain Layout
4406 When using the command
4416 \begin_layout Plain Layout
4424 , LaTeX decides on the basis of the next character what type is used.
4427 \begin_layout Standard
4429 \begin_inset Tabular
4430 <lyxtabular version="3" rows="8" columns="2">
4432 <column alignment="center" valignment="top" width="0pt">
4433 <column alignment="center" valignment="top" width="0pt">
4435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4438 \begin_layout Plain Layout
4444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4447 \begin_layout Plain Layout
4455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4458 \begin_layout Plain Layout
4463 \begin_layout Plain Layout
4478 \begin_layout Plain Layout
4492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4495 \begin_layout Plain Layout
4496 \begin_inset Formula $A_{1},\dots,A_{n}$
4506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4509 \begin_layout Plain Layout
4514 \begin_layout Plain Layout
4529 \begin_layout Plain Layout
4543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4546 \begin_layout Plain Layout
4547 \begin_inset Formula $A_{1}+\dots+A_{n}$
4557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4560 \begin_layout Plain Layout
4565 \begin_layout Plain Layout
4580 \begin_layout Plain Layout
4594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4597 \begin_layout Plain Layout
4598 \begin_inset Formula $A_{1},\ldots,A_{n}$
4608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4611 \begin_layout Plain Layout
4616 \begin_layout Plain Layout
4631 \begin_layout Plain Layout
4645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4648 \begin_layout Plain Layout
4649 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4662 \begin_layout Plain Layout
4670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4673 \begin_layout Plain Layout
4674 \begin_inset Formula $\vdots$
4684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4687 \begin_layout Plain Layout
4695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4698 \begin_layout Plain Layout
4699 \begin_inset Formula $\ddots$
4709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4712 \begin_layout Plain Layout
4714 \begin_inset space \thinspace{}
4717 matrix with the different dots
4722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4725 \begin_layout Plain Layout
4726 \begin_inset Formula $\begin{array}{ccc}
4727 A_{11} & \cdots & A_{1m}\\
4728 \vdots & \ddots & \vdots\\
4729 A_{n1} & \cdots & A_{nm}\end{array}$
4745 \begin_layout Standard
4746 The ellipses available in menu
4748 Insert\SpecialChar \menuseparator
4750 \begin_inset space ~
4764 \begin_layout Standard
4765 \begin_inset VSpace medskip
4768 Specially for matrices there are ellipses that span over several columns.
4769 They are created with the command
4779 \begin_layout Plain Layout
4787 , that has the following scheme:
4790 \begin_layout Standard
4795 hdotsfor[distance]{number of columns}
4798 \begin_layout Standard
4799 The number of columns specifies how many columns should be spanned.
4800 Distance is a factor for the distance between the dots.
4803 \begin_layout Standard
4804 In the following matrix the command
4810 was inserted in the first box of the second line, to get an ellipsis with
4811 a dot distance twice as long as with the command
4818 \begin_inset Formula \[
4819 \left(\begin{array}{cccc}
4822 q & w & e & r\end{array}\right)\]
4826 Note that the matrix fields that should be spanned must be empty, otherwise
4827 you get LaTeX-errors.
4830 \begin_layout Standard
4831 \begin_inset VSpace bigskip
4834 Furthermore you can fill with the command
4844 \begin_layout Plain Layout
4852 the rest of a line with dots.
4853 The effect of these commands is the same like with
4860 \begin_inset CommandInset ref
4862 reference "sub:Variable-Space"
4869 \begin_layout Standard
4870 For example the command
4878 \begin_layout Plain Layout
4892 \begin_layout Standard
4893 \begin_inset Formula $A\dotfill B$
4899 \begin_layout Standard
4906 there is for a line the command
4916 \begin_layout Plain Layout
4927 \begin_layout Standard
4928 \begin_inset Formula $A\hrulefill B$
4934 \begin_layout Standard
4935 To use the commands for text, they have to be inserted in TeX-mode.
4938 \begin_layout Section
4940 \begin_inset CommandInset label
4950 \begin_layout Plain Layout
4959 \begin_layout Standard
4960 Matrices can be inserted via the math toolbar button
4961 \begin_inset Graphics
4962 filename ../images/dialog-show_mathmatrix.png
4969 Insert\SpecialChar \menuseparator
4970 Math\SpecialChar \menuseparator
4974 You will be asked for the number of matrix columns and rows, and the alignment.
4975 The vertical alignment is hereby only of importance for matrices in inline
4979 \begin_layout Standard
4980 The first matrix is top
4981 \begin_inset Formula $\begin{array}[t]{cccc}
4984 C & F & I & L\end{array}$
4988 \begin_inset Formula $\begin{array}{cccc}
4991 C & F & I & L\end{array}$
4994 , and the third bottom
4995 \begin_inset Formula $\begin{array}[b]{cccc}
4998 C & F & I & L\end{array}$
5004 \begin_layout Standard
5005 The horizontal alignment specifies how the column entries should be aligned.
5006 It is set by entering a letter for every column.
5011 denotes left aligned,
5020 To create for example a 4
5025 \begin_inset space ~
5028 matrix where the first column is left aligned, the second and third are
5029 centered, and the last one is right aligned, one enters for the horizontal
5035 Normally are in a matrix all columns centered, therefore the default is
5036 for every column is a
5043 \begin_layout Standard
5044 Horizontal alignment:
5047 \begin_layout Standard
5053 \begin_inset Formula $\begin{array}{lll}
5056 C & F & 10000\end{array}$
5064 \begin_inset Formula $\begin{array}{ccc}
5067 C & F & 10000\end{array}$
5075 \begin_inset Formula $\begin{array}{rrr}
5078 C & F & 10000\end{array}$
5084 \begin_layout Standard
5085 To add or delete rows and columns subsequently, the math toolbar buttons
5087 \begin_inset Graphics
5088 filename ../images/tabular-feature_append-row.png
5094 \begin_inset Graphics
5095 filename ../images/tabular-feature_delete-row.png
5101 \begin_inset space \thinspace{}
5106 Edit\SpecialChar \menuseparator
5110 New rows can also be created with
5117 \begin_layout Standard
5118 \begin_inset VSpace bigskip
5121 Parentheses around a matrix can can either be created with the commands
5132 \begin_layout Plain Layout
5150 \begin_layout Plain Layout
5161 \begin_inset space ~
5167 \begin_inset CommandInset ref
5169 reference "sub:Automatic-Bracket-Size"
5173 , or by using the following commands:
5174 \begin_inset VSpace medskip
5180 \begin_layout Standard
5181 \begin_inset space \hfill{}
5185 \begin_inset Tabular
5186 <lyxtabular version="3" rows="4" columns="2">
5188 <column alignment="center" valignment="top" width="0">
5189 <column alignment="center" valignment="top" width="0">
5191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5194 \begin_layout Plain Layout
5200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5203 \begin_layout Plain Layout
5205 \begin_inset Note Note
5208 \begin_layout Plain Layout
5215 is only used as spacer.
5227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5230 \begin_layout Plain Layout
5237 \begin_layout Plain Layout
5251 \begin_inset space \thinspace{}
5259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5262 \begin_layout Plain Layout
5263 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5264 0 & \textrm{-}\mathrm{i}\\
5265 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5278 \begin_layout Plain Layout
5285 \begin_layout Plain Layout
5299 \begin_inset space \thinspace{}
5307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5310 \begin_layout Plain Layout
5311 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5312 0 & \textrm{-}\mathrm{i}\\
5313 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5326 \begin_layout Plain Layout
5333 \begin_layout Plain Layout
5347 \begin_inset space \thinspace{}
5355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5358 \begin_layout Plain Layout
5359 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5360 0 & \textrm{-}\mathrm{i}\\
5361 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5375 \begin_inset space \hfill{}
5379 \begin_inset Tabular
5380 <lyxtabular version="3" rows="4" columns="2">
5382 <column alignment="center" valignment="top" width="0">
5383 <column alignment="center" valignment="top" width="0">
5385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5388 \begin_layout Plain Layout
5394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5397 \begin_layout Plain Layout
5405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5408 \begin_layout Plain Layout
5415 \begin_layout Plain Layout
5429 \begin_inset space \thinspace{}
5437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5440 \begin_layout Plain Layout
5441 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5442 0 & \textrm{-}\mathrm{i}\\
5443 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5456 \begin_layout Plain Layout
5463 \begin_layout Plain Layout
5477 \begin_inset space \thinspace{}
5485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5488 \begin_layout Plain Layout
5489 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5490 0 & \textrm{-}\mathrm{i}\\
5491 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5504 \begin_layout Plain Layout
5511 \begin_layout Plain Layout
5525 \begin_inset space \thinspace{}
5533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5536 \begin_layout Plain Layout
5537 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5538 0 & \textrm{-}\mathrm{i}\\
5539 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5553 \begin_inset space \hfill{}
5559 \begin_layout Standard
5560 \begin_inset VSpace medskip
5564 \begin_inset space \thinspace{}
5568 \begin_inset space ~
5577 is inserted, a blue box appears between two vertical lines where the matrix
5581 \begin_layout Standard
5582 \begin_inset VSpace bigskip
5585 As all multiline formulas are matrices, the length
5595 \begin_layout Plain Layout
5603 that is described in
5604 \begin_inset CommandInset ref
5606 reference "sub:Column-Separation"
5610 can also be used to change the column separation of matrices.
5613 \begin_layout Standard
5614 To change the row separation, the command
5624 \begin_layout Plain Layout
5633 It is used as follows:
5636 \begin_layout Standard
5643 arraystretch}{stretch factor}
5647 \begin_layout Plain Layout
5658 \begin_layout Standard
5665 assigns the stretch factor to the predefined command
5673 \begin_inset space \thinspace{}
5677 \begin_inset space ~
5680 the row separation, use the factor 2.
5681 This is then used for all following matrices.
5682 To go back to the original separation, assign the factor 1 to
5691 \begin_layout Standard
5692 To set matrices into a text line, the command
5702 \begin_layout Plain Layout
5711 When it is inserted a blue box with two dashed lines appears.
5712 In this box the matrix is inserted.
5715 \begin_layout Standard
5717 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5718 C & D\end{smallmatrix}\right)$
5724 \begin_layout Section
5725 Brackets and Delimiters
5729 \begin_layout Plain Layout
5739 \begin_layout Plain Layout
5748 \begin_layout Subsection
5749 Vertical Brackets and Delimiters
5753 \begin_layout Plain Layout
5762 \begin_layout Standard
5763 \begin_inset space \hfill{}
5767 \begin_inset Tabular
5768 <lyxtabular version="3" rows="9" columns="2">
5770 <column alignment="center" valignment="top" width="0pt">
5771 <column alignment="center" valignment="top" width="0pt">
5773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5776 \begin_layout Plain Layout
5782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5785 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5796 \begin_layout Plain Layout
5802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5805 \begin_layout Plain Layout
5806 \begin_inset Formula $($
5816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5819 \begin_layout Plain Layout
5825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5828 \begin_layout Plain Layout
5829 \begin_inset Formula $\{$
5839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5842 \begin_layout Plain Layout
5848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5851 \begin_layout Plain Layout
5852 \begin_inset Formula $[$
5862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5865 \begin_layout Plain Layout
5873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5876 \begin_layout Plain Layout
5877 \begin_inset Formula $\langle$
5887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5890 \begin_layout Plain Layout
5898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5901 \begin_layout Plain Layout
5902 \begin_inset Formula $\lceil$
5912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5915 \begin_layout Plain Layout
5923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5926 \begin_layout Plain Layout
5927 \begin_inset Formula $\lfloor$
5937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5940 \begin_layout Plain Layout
5946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5949 \begin_layout Plain Layout
5950 \begin_inset Formula $/$
5960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5963 \begin_layout Plain Layout
5969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5972 \begin_layout Plain Layout
5973 \begin_inset Formula $|$
5987 \begin_inset space \hfill{}
5991 \begin_inset Tabular
5992 <lyxtabular version="3" rows="9" columns="2">
5994 <column alignment="center" valignment="top" width="0pt">
5995 <column alignment="center" valignment="top" width="0pt">
5997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6000 \begin_layout Plain Layout
6006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6009 \begin_layout Plain Layout
6017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6020 \begin_layout Plain Layout
6026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6029 \begin_layout Plain Layout
6030 \begin_inset Formula $)$
6040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6043 \begin_layout Plain Layout
6049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6052 \begin_layout Plain Layout
6053 \begin_inset Formula $\}$
6063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6066 \begin_layout Plain Layout
6072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6075 \begin_layout Plain Layout
6076 \begin_inset Formula $]$
6086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6089 \begin_layout Plain Layout
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6100 \begin_layout Plain Layout
6101 \begin_inset Formula $\rangle$
6111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6114 \begin_layout Plain Layout
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6125 \begin_layout Plain Layout
6126 \begin_inset Formula $\rceil$
6136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6139 \begin_layout Plain Layout
6147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6150 \begin_layout Plain Layout
6151 \begin_inset Formula $\rfloor$
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6164 \begin_layout Plain Layout
6174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6177 \begin_layout Plain Layout
6178 \begin_inset Formula $\backslash$
6188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6191 \begin_layout Plain Layout
6199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6202 \begin_layout Plain Layout
6203 \begin_inset Formula $\|$
6217 \begin_inset space \hfill{}
6223 \begin_layout Standard
6226 \begin_inset Note Greyedout
6229 \begin_layout Plain Layout
6234 In TeX-mode the command
6244 \begin_layout Plain Layout
6252 must be used for the backslash, because the command
6260 produces there a line break.
6268 \begin_layout Standard
6269 For all characters listed above the size can be adjusted with the commands
6270 described in the following two subsections.
6271 When using these commands, the characters < and > can directly be used
6272 instead of the commands
6287 \begin_layout Subsubsection
6289 \begin_inset CommandInset label
6291 name "sub:Manual-Bracket-Size"
6299 \begin_layout Plain Layout
6300 Bracket size ! manual
6308 \begin_layout Standard
6309 The bracket size can be specified manually by the LaTeX-commands
6319 \begin_layout Plain Layout
6352 denotes the smallest and
6358 the largest bracket size.
6361 \begin_layout Standard
6362 These commands are used to emphasize levels of brackets:
6365 \begin_layout Standard
6367 \begin_inset Tabular
6368 <lyxtabular version="3" rows="2" columns="2">
6370 <column alignment="center" valignment="top" width="0pt">
6371 <column alignment="center" valignment="top" width="0pt">
6373 <cell alignment="center" valignment="top" usebox="none">
6376 \begin_layout Plain Layout
6377 all brackets in the same size:
6382 <cell alignment="center" valignment="top" usebox="none">
6385 \begin_layout Plain Layout
6386 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6396 <cell alignment="center" valignment="top" usebox="none">
6399 \begin_layout Plain Layout
6405 <cell alignment="center" valignment="top" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6423 \begin_inset Note Note
6426 \begin_layout Plain Layout
6433 is only used as spacer.
6441 \begin_layout Standard
6442 For the second formula the command
6452 \begin_layout Plain Layout
6466 \begin_layout Standard
6467 Here is an overview about all bracket sizes:
6470 \begin_layout Standard
6490 \begin_layout Plain Layout
6507 \begin_layout Plain Layout
6520 \begin_layout Plain Layout
6536 \begin_layout Standard
6538 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6544 \begin_layout Standard
6551 -commands there is the variant
6561 \begin_layout Plain Layout
6569 that adds a bit more space between the bracket and its content, and the
6586 \begin_layout Plain Layout
6596 , that don't add additional space.
6601 at the end of the command
6607 is for a left bracket; for a right bracket this will be replaced by an
6613 A left or right bracket can each be an opening or closing bracket.
6616 \begin_layout Standard
6617 In the following table is a comparison of the variants:
6620 \begin_layout Standard
6622 \begin_inset Tabular
6623 <lyxtabular version="3" rows="5" columns="2">
6625 <column alignment="center" valignment="middle" width="0">
6626 <column alignment="center" valignment="middle" width="0">
6628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6631 \begin_layout Plain Layout
6637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6640 \begin_layout Plain Layout
6642 \begin_inset Note Note
6645 \begin_layout Plain Layout
6652 is only used as spacer.
6664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6667 \begin_layout Plain Layout
6682 \begin_layout Plain Layout
6700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6703 \begin_layout Plain Layout
6704 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6717 \begin_layout Plain Layout
6732 \begin_layout Plain Layout
6750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6753 \begin_layout Plain Layout
6754 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6767 \begin_layout Plain Layout
6782 \begin_layout Plain Layout
6800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6803 \begin_layout Plain Layout
6804 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6817 \begin_layout Plain Layout
6829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6832 \begin_layout Plain Layout
6833 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6849 \begin_layout Subsubsection
6850 Automatic Bracket Size
6851 \begin_inset CommandInset label
6853 name "sub:Automatic-Bracket-Size"
6861 \begin_layout Plain Layout
6862 Bracket size ! automatic
6870 \begin_layout Standard
6871 Brackets with variable size can be inserted with the commands
6881 \begin_layout Plain Layout
6899 \begin_layout Plain Layout
6907 or via the math toolbar button
6908 \begin_inset Graphics
6909 filename ../images/dialog-show_mathdelimiter.png
6927 the wanted bracket must be inserted.
6928 The bracket size will then automatically be calculated for the output.
6931 \begin_layout Standard
6933 normal bracket: The command
6943 \begin_layout Plain Layout
6953 \begin_inset Formula $\downarrow$
6960 \begin_layout Plain Layout
6972 \begin_inset Formula \[
6980 \begin_layout Standard
6982 multiline bracket: The command
6994 \begin_layout Plain Layout
7004 \begin_inset Formula $\downarrow$
7011 \begin_layout Plain Layout
7025 \begin_inset Formula \[
7026 \ln\left(\frac{A}{C}\right)\]
7033 \begin_layout Standard
7049 \begin_inset space ~
7055 This has the advantage that you can see in LyX immediately the real bracket
7056 size and that the matching right bracket will be created too.
7057 \begin_inset Newline newline
7060 The command for the last example would then be:
7074 \begin_layout Plain Layout
7084 \begin_inset Formula $\downarrow$
7090 \begin_layout Standard
7091 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7092 For example the command
7102 \begin_layout Plain Layout
7112 \begin_inset Formula $\downarrow$
7119 \begin_layout Plain Layout
7135 \begin_inset Formula \[
7136 \left.\frac{A}{B}\right\} \]
7154 will be converted by LyX to brackets in the right size when the document
7155 is reloaded and an omitted bracket will appear as dashed line.
7158 \begin_layout Standard
7159 \begin_inset VSpace bigskip
7162 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7173 \begin_layout Plain Layout
7181 is additionally available for all brackets and limits.
7182 With this command the height of the following character is adapted to the
7183 one of the surrounding brackets, what is e.
7184 \begin_inset space \thinspace{}
7188 \begin_inset space ~
7191 needed for physical vectors:
7192 \begin_inset Formula \[
7193 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7197 For physical vectors there is a special LaTeX-package, described in
7198 \begin_inset CommandInset ref
7200 reference "sub:Physical-Vectors"
7207 \begin_layout Subsection
7212 \begin_layout Plain Layout
7213 Brackets ! horizontal
7221 \begin_layout Standard
7223 \begin_inset Tabular
7224 <lyxtabular version="3" rows="4" columns="2">
7226 <column alignment="center" valignment="top" width="0pt">
7227 <column alignment="center" valignment="top" width="0pt">
7229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7232 \begin_layout Plain Layout
7234 \begin_inset Note Note
7237 \begin_layout Plain Layout
7244 is only used as spacer.
7254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7257 \begin_layout Plain Layout
7265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7268 \begin_layout Plain Layout
7272 \begin_layout Plain Layout
7287 \begin_layout Plain Layout
7300 \begin_layout Plain Layout
7313 \begin_layout Plain Layout
7326 \begin_layout Plain Layout
7337 \begin_layout Plain Layout
7350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7353 \begin_layout Plain Layout
7354 \begin_inset Formula $\overbrace{A+B}^{3}$
7364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7367 \begin_layout Plain Layout
7371 \begin_layout Plain Layout
7386 \begin_layout Plain Layout
7399 \begin_layout Plain Layout
7412 \begin_layout Plain Layout
7423 \begin_layout Plain Layout
7436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7439 \begin_layout Plain Layout
7440 \begin_inset Formula $\underbrace{A+B}_{5}$
7450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7453 \begin_layout Plain Layout
7460 \begin_layout Plain Layout
7475 \begin_layout Plain Layout
7488 \begin_layout Plain Layout
7501 \begin_layout Plain Layout
7514 \begin_layout Plain Layout
7527 \begin_layout Plain Layout
7540 \begin_layout Plain Layout
7554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7557 \begin_layout Plain Layout
7558 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7574 \begin_layout Standard
7575 In the last example it doesn't matter if
7587 is inserted at first.
7590 \begin_layout Standard
7591 \begin_inset VSpace bigskip
7594 When brackets are needed that overlap each other, multiline formulas, as
7596 \begin_inset CommandInset ref
7598 reference "sec:Multiline-Formulas"
7603 \begin_inset Formula \begin{eqnarray*}
7604 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7605 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7609 In the first row the formula is inserted together with the first brace.
7610 It is hereby important that the space command
7614 \begin_layout Plain Layout
7615 Space commands are explained in
7616 \begin_inset CommandInset ref
7618 reference "sub:Predefined-Space"
7633 is inserted before the first
7634 \begin_inset Formula $d$
7637 , because the brace that ends behind the
7638 \begin_inset Formula $q$
7641 prevents that the following
7642 \begin_inset Quotes eld
7646 \begin_inset Quotes erd
7649 is surrounded by space.
7653 \begin_layout Plain Layout
7654 because a bracket is not handled as character, see
7655 \begin_inset CommandInset ref
7657 reference "sub:Binary-Operators"
7666 In the second row the second brace is inserted.
7667 As it should begin before the
7668 \begin_inset Formula $b$
7683 \begin_layout Plain Layout
7691 \begin_inset CommandInset ref
7693 reference "sub:Placeholders"
7702 This space is needed because the
7703 \begin_inset Quotes eld
7707 \begin_inset Quotes erd
7710 is also surrounded by space in the formula.
7711 The brace is placed under the command
7720 \begin_layout Standard
7721 It gets more complicated when brackets overlap each other, like in the following
7726 \begin_layout Plain Layout
7738 \begin_inset Formula \begin{eqnarray*}
7739 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7740 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7748 \begin_layout Plain Layout
7759 The first formula row is the same as the second row of the previous example,
7760 with the difference that the brace is above.
7761 The second row contains the formula together with the second brace.
7762 To avoid that there is space between the upper brace in the first row and
7763 the formula, the row spacing need to be reduced.
7764 This is not easily possible due to a bug in LyX
7768 \begin_layout Plain Layout
7769 \begin_inset CommandInset href
7771 name "LyX-bug #1505"
7772 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7782 As solution for the problem, the global formula row separation
7792 \begin_layout Plain Layout
7800 must be changed to -6
7801 \begin_inset space \thinspace{}
7804 pt before the formula with the command
7819 is set back after the formula to the standard value of 3
7820 \begin_inset space \thinspace{}
7823 pt using the same command.
7824 More about the row separation in formulas is explained in
7825 \begin_inset CommandInset ref
7827 reference "sub:Line-Separation"
7834 \begin_layout Section
7839 \begin_layout Plain Layout
7848 \begin_layout Standard
7849 Arrows can be inserted via the math toolbar button
7850 \begin_inset Graphics
7851 filename ../images/math/leftarrow.png
7856 or the commands listed in the following subsections.
7859 \begin_layout Standard
7860 \begin_inset Newpage newpage
7866 \begin_layout Subsection
7871 \begin_layout Plain Layout
7880 \begin_layout Standard
7881 \begin_inset space \hfill{}
7885 \begin_inset Tabular
7886 <lyxtabular version="3" rows="8" columns="2">
7888 <column alignment="center" valignment="top" width="0pt">
7889 <column alignment="center" valignment="top" width="0pt">
7891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7894 \begin_layout Plain Layout
7900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7903 \begin_layout Plain Layout
7911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7914 \begin_layout Plain Layout
7922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7925 \begin_layout Plain Layout
7926 \begin_inset Formula $\gets$
7936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7939 \begin_layout Plain Layout
7947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7950 \begin_layout Plain Layout
7951 \begin_inset Formula $\Leftarrow$
7961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7964 \begin_layout Plain Layout
7972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7975 \begin_layout Plain Layout
7976 \begin_inset Formula $\longleftarrow$
7986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7989 \begin_layout Plain Layout
7997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8000 \begin_layout Plain Layout
8001 \begin_inset Formula $\Longleftarrow$
8011 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8014 \begin_layout Plain Layout
8022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8025 \begin_layout Plain Layout
8026 \begin_inset Formula $\leftharpoonup$
8036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8039 \begin_layout Plain Layout
8047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8050 \begin_layout Plain Layout
8051 \begin_inset Formula $\leftharpoondown$
8061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8064 \begin_layout Plain Layout
8072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8075 \begin_layout Plain Layout
8076 \begin_inset Formula $\hookleftarrow$
8090 \begin_inset space \hfill{}
8094 \begin_inset Tabular
8095 <lyxtabular version="3" rows="8" columns="2">
8097 <column alignment="center" valignment="top" width="0pt">
8098 <column alignment="center" valignment="top" width="0pt">
8100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8103 \begin_layout Plain Layout
8109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8123 \begin_layout Plain Layout
8131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8134 \begin_layout Plain Layout
8135 \begin_inset Formula $\to$
8145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8148 \begin_layout Plain Layout
8156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8159 \begin_layout Plain Layout
8160 \begin_inset Formula $\Rightarrow$
8170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8173 \begin_layout Plain Layout
8181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8184 \begin_layout Plain Layout
8185 \begin_inset Formula $\longrightarrow$
8195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8198 \begin_layout Plain Layout
8206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8209 \begin_layout Plain Layout
8210 \begin_inset Formula $\Longrightarrow$
8220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8223 \begin_layout Plain Layout
8231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8234 \begin_layout Plain Layout
8235 \begin_inset Formula $\rightharpoonup$
8245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8248 \begin_layout Plain Layout
8256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8259 \begin_layout Plain Layout
8260 \begin_inset Formula $\rightharpoondown$
8270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8273 \begin_layout Plain Layout
8281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8284 \begin_layout Plain Layout
8285 \begin_inset Formula $\hookrightarrow$
8299 \begin_inset space \hfill{}
8305 \begin_layout Standard
8306 \begin_inset space \hfill{}
8310 \begin_inset Tabular
8311 <lyxtabular version="3" rows="6" columns="2">
8313 <column alignment="center" valignment="top" width="0pt">
8314 <column alignment="center" valignment="top" width="0pt">
8316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8319 \begin_layout Plain Layout
8325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8328 \begin_layout Plain Layout
8336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8339 \begin_layout Plain Layout
8347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8350 \begin_layout Plain Layout
8351 \begin_inset Formula $\leftrightarrow$
8361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8364 \begin_layout Plain Layout
8372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8375 \begin_layout Plain Layout
8376 \begin_inset Formula $\Leftrightarrow$
8386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8389 \begin_layout Plain Layout
8397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8400 \begin_layout Plain Layout
8401 \begin_inset Formula $\longleftrightarrow$
8411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8414 \begin_layout Plain Layout
8422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8425 \begin_layout Plain Layout
8426 \begin_inset Formula $\Longleftrightarrow$
8436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8439 \begin_layout Plain Layout
8447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8450 \begin_layout Plain Layout
8451 \begin_inset Formula $\rightleftharpoons$
8465 \begin_inset space \hspace{}
8470 \begin_inset space \hfill{}
8474 \begin_inset Tabular
8475 <lyxtabular version="3" rows="5" columns="2">
8477 <column alignment="center" valignment="top" width="0pt">
8478 <column alignment="center" valignment="top" width="0pt">
8480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8483 \begin_layout Plain Layout
8489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8492 \begin_layout Plain Layout
8500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8503 \begin_layout Plain Layout
8511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8514 \begin_layout Plain Layout
8515 \begin_inset Formula $\mapsto$
8525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8528 \begin_layout Plain Layout
8536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8539 \begin_layout Plain Layout
8540 \begin_inset Formula $\longmapsto$
8550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8553 \begin_layout Plain Layout
8561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8564 \begin_layout Plain Layout
8565 \begin_inset Formula $\leadsto$
8575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8578 \begin_layout Plain Layout
8586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8589 \begin_layout Plain Layout
8590 \begin_inset Formula $\dasharrow$
8604 \begin_inset space \hfill{}
8610 \begin_layout Standard
8611 \begin_inset VSpace medskip
8614 Arrows used as accent like e.
8615 \begin_inset space \thinspace{}
8619 \begin_inset space ~
8622 vector arrows are listed in
8623 \begin_inset CommandInset ref
8625 reference "sec:Accents"
8632 \begin_layout Standard
8633 \begin_inset VSpace bigskip
8636 Furthermore there are the labeled arrows
8640 \begin_layout Plain Layout
8656 \begin_layout Plain Layout
8674 \begin_layout Plain Layout
8681 \begin_layout Plain Layout
8696 When inserting one of these commands in a formula, an arrow with two blue
8697 boxes appear where the label can be inserted.
8698 The length of the arrow adapts to the label width.
8701 \begin_layout Standard
8703 \begin_inset Tabular
8704 <lyxtabular version="3" rows="3" columns="2">
8706 <column alignment="center" valignment="top" width="0pt">
8707 <column alignment="center" valignment="top" width="0pt">
8709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8712 \begin_layout Plain Layout
8718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8721 \begin_layout Plain Layout
8723 \begin_inset Note Note
8726 \begin_layout Plain Layout
8733 is only used as spacer.
8745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8748 \begin_layout Plain Layout
8755 \begin_layout Plain Layout
8765 \begin_inset Formula $\downarrow$
8769 \begin_inset Formula $\to$
8777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8780 \begin_layout Plain Layout
8781 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8794 \begin_layout Plain Layout
8801 \begin_layout Plain Layout
8811 \begin_inset Formula $\downarrow$
8815 \begin_inset Formula $\to$
8823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8826 \begin_layout Plain Layout
8827 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8843 \begin_layout Subsection
8844 Vertical and diagonal Arrows
8848 \begin_layout Plain Layout
8858 \begin_layout Plain Layout
8867 \begin_layout Standard
8868 \begin_inset space \hfill{}
8872 \begin_inset Tabular
8873 <lyxtabular version="3" rows="7" columns="2">
8875 <column alignment="center" valignment="top" width="0pt">
8876 <column alignment="center" valignment="top" width="0pt">
8878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8881 \begin_layout Plain Layout
8887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8890 \begin_layout Plain Layout
8898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8901 \begin_layout Plain Layout
8909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8912 \begin_layout Plain Layout
8913 \begin_inset Formula $\uparrow$
8923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8926 \begin_layout Plain Layout
8934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8937 \begin_layout Plain Layout
8938 \begin_inset Formula $\Uparrow$
8948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8951 \begin_layout Plain Layout
8959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8962 \begin_layout Plain Layout
8963 \begin_inset Formula $\updownarrow$
8973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8976 \begin_layout Plain Layout
8984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8987 \begin_layout Plain Layout
8988 \begin_inset Formula $\Updownarrow$
8998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9001 \begin_layout Plain Layout
9009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9012 \begin_layout Plain Layout
9013 \begin_inset Formula $\Downarrow$
9023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9026 \begin_layout Plain Layout
9034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9037 \begin_layout Plain Layout
9038 \begin_inset Formula $\downarrow$
9052 \begin_inset space \hfill{}
9056 \begin_inset Tabular
9057 <lyxtabular version="3" rows="5" columns="2">
9059 <column alignment="center" valignment="top" width="0pt">
9060 <column alignment="center" valignment="top" width="0pt">
9062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9065 \begin_layout Plain Layout
9071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9074 \begin_layout Plain Layout
9082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9085 \begin_layout Plain Layout
9093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9096 \begin_layout Plain Layout
9097 \begin_inset Formula $\nearrow$
9107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9110 \begin_layout Plain Layout
9118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9121 \begin_layout Plain Layout
9122 \begin_inset Formula $\searrow$
9132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9135 \begin_layout Plain Layout
9143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9146 \begin_layout Plain Layout
9147 \begin_inset Formula $\swarrow$
9157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9160 \begin_layout Plain Layout
9168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9171 \begin_layout Plain Layout
9172 \begin_inset Formula $\nwarrow$
9186 \begin_inset space \hfill{}
9192 \begin_layout Standard
9193 \begin_inset VSpace medskip
9196 Vertical arrows can be used also as delimiter together with the commands
9198 \begin_inset CommandInset ref
9200 reference "sub:Manual-Bracket-Size"
9205 \begin_inset CommandInset ref
9207 reference "sub:Automatic-Bracket-Size"
9214 \begin_layout Standard
9215 \begin_inset Newpage newpage
9221 \begin_layout Section
9223 \begin_inset CommandInset label
9233 \begin_layout Plain Layout
9242 \begin_layout Standard
9243 Accents can be inserted via the math toolbar button
9244 \begin_inset Graphics
9245 filename ../images/math/hat.png
9250 or the commands listed in the following subsections.
9253 \begin_layout Subsection
9254 Accents for one Character
9258 \begin_layout Plain Layout
9271 \begin_layout Plain Layout
9273 \begin_inset CommandInset ref
9275 reference "sub:Accents-in-Text"
9288 \begin_layout Plain Layout
9296 \begin_inset Note Note
9299 \begin_layout Plain Layout
9302 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9305 \begin_layout Plain Layout
9308 texorpdfstring is in section
9309 \begin_inset CommandInset ref
9311 reference "sub:Formulas-in-Section"
9321 \begin_inset CommandInset label
9323 name "sub:Accents-for-one"
9331 \begin_layout Plain Layout
9332 Accents ! for one character
9340 \begin_layout Standard
9341 \begin_inset space \hfill{}
9345 \begin_inset Tabular
9346 <lyxtabular version="3" rows="8" columns="2">
9348 <column alignment="center" valignment="top" width="0pt">
9349 <column alignment="center" valignment="top" width="0pt">
9351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9354 \begin_layout Plain Layout
9360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9363 \begin_layout Plain Layout
9365 \begin_inset Note Note
9368 \begin_layout Plain Layout
9375 is only used as spacer.
9387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9390 \begin_layout Plain Layout
9397 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9414 \begin_layout Plain Layout
9415 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9425 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9428 \begin_layout Plain Layout
9435 \begin_layout Plain Layout
9449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9452 \begin_layout Plain Layout
9453 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9466 \begin_layout Plain Layout
9473 \begin_layout Plain Layout
9487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9504 \begin_layout Plain Layout
9512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9515 \begin_layout Plain Layout
9516 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9529 \begin_layout Plain Layout
9536 \begin_layout Plain Layout
9549 \begin_layout Plain Layout
9560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9563 \begin_layout Plain Layout
9564 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9577 \begin_layout Plain Layout
9584 \begin_layout Plain Layout
9598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9601 \begin_layout Plain Layout
9602 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9615 \begin_layout Plain Layout
9622 \begin_layout Plain Layout
9636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9639 \begin_layout Plain Layout
9640 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9654 \begin_inset space \hfill{}
9658 \begin_inset Tabular
9659 <lyxtabular version="3" rows="7" columns="2">
9661 <column alignment="center" valignment="top" width="0pt">
9662 <column alignment="center" valignment="top" width="0pt">
9664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9667 \begin_layout Plain Layout
9673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9676 \begin_layout Plain Layout
9684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9687 \begin_layout Plain Layout
9694 \begin_layout Plain Layout
9708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9711 \begin_layout Plain Layout
9712 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9725 \begin_layout Plain Layout
9732 \begin_layout Plain Layout
9746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9749 \begin_layout Plain Layout
9750 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9763 \begin_layout Plain Layout
9770 \begin_layout Plain Layout
9784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9787 \begin_layout Plain Layout
9788 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9801 \begin_layout Plain Layout
9808 \begin_layout Plain Layout
9822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9839 \begin_layout Plain Layout
9846 \begin_layout Plain Layout
9860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9863 \begin_layout Plain Layout
9864 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9877 \begin_layout Plain Layout
9884 \begin_layout Plain Layout
9898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9901 \begin_layout Plain Layout
9902 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9916 \begin_inset space \hfill{}
9922 \begin_layout Standard
9923 \begin_inset VSpace bigskip
9930 \begin_layout Plain Layout
9936 in formulas, a quotation mark is inserted before the vowel.
9937 These two characters are then treated by LaTeX as
9941 character when the formula part with the umlaut is marked as German.
9949 \begin_inset Quotes eld
9953 \begin_inset Quotes erd
9956 umlauts are created as demonstrated in the following example:
9959 \begin_layout Standard
9960 \begin_inset VSpace -2mm
9966 \begin_layout Standard
9968 \begin_inset Tabular
9969 <lyxtabular version="3" rows="3" columns="2">
9971 <column alignment="center" valignment="top" width="0">
9972 <column alignment="center" valignment="top" width="0">
9974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9977 \begin_layout Plain Layout
9983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9986 \begin_layout Plain Layout
9988 \begin_inset Note Note
9991 \begin_layout Plain Layout
9998 is only used as spacer.
10010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10013 \begin_layout Plain Layout
10016 \begin_inset Quotes grd
10024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10027 \begin_layout Plain Layout
10030 \begin_inset Formula $"i$
10040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10043 \begin_layout Plain Layout
10050 \begin_layout Plain Layout
10064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10067 \begin_layout Plain Layout
10068 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10084 \begin_layout Standard
10085 Another advantage to
10091 is that umlauts can directly be converted to mathematical text because
10092 the accent commands above are
10098 in mathematical text
10101 To convert an accented character to mathematical text, only the character
10102 under the accent may be converted.
10103 This applies also for all other conversions, e.
10104 \begin_inset space \thinspace{}
10108 \begin_inset space ~
10114 \begin_layout Standard
10115 In mathematical text, umlauts and other accented characters can directly
10119 \begin_layout Subsection
10120 Accents for Operators
10124 \begin_layout Plain Layout
10125 Accents ! for operators
10133 \begin_layout Standard
10144 \begin_layout Plain Layout
10162 \begin_layout Plain Layout
10170 characters can be placed above or below an operator, respectively, to accent
10182 \begin_layout Plain Layout
10190 characters can be set before and behind an operator.
10191 The command scheme is:
10194 \begin_layout Standard
10210 \begin_layout Standard
10217 must always be before the operator that should be accented.
10218 You can accent with several characters and even with other operators and
10226 for example only characters behind an operator, write nothing between the
10227 first braces but don't omit the braces.
10230 \begin_layout Standard
10231 For example the command
10236 \begin_inset Formula $\to$
10246 \begin_inset Formula $\to$
10255 \begin_layout Plain Layout
10271 \begin_inset Formula \[
10272 \sideset{}{'}\sum_{k=1}^{n}\]
10279 \begin_layout Standard
10288 \begin_layout Plain Layout
10303 \begin_layout Plain Layout
10315 \begin_inset Formula $\uparrow$
10323 \begin_inset Formula \[
10324 \overset{a}{\maltese}\]
10328 As seen in the last example, with
10340 also symbols and characters can be accented; with
10346 this is not possible.
10349 \begin_layout Subsection
10350 Accents for several Characters
10351 \begin_inset CommandInset label
10353 name "sub:Accents-for-several"
10361 \begin_layout Plain Layout
10362 Accents ! for several characters
10370 \begin_layout Standard
10371 \begin_inset space \hfill{}
10375 \begin_inset Tabular
10376 <lyxtabular version="3" rows="5" columns="2">
10378 <column alignment="center" valignment="top" width="0pt">
10379 <column alignment="center" valignment="top" width="0pt">
10381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10384 \begin_layout Plain Layout
10390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10393 \begin_layout Plain Layout
10395 \begin_inset Note Note
10398 \begin_layout Plain Layout
10405 is only used as spacer.
10417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10420 \begin_layout Plain Layout
10427 \begin_layout Plain Layout
10441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10444 \begin_layout Plain Layout
10445 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10458 \begin_layout Plain Layout
10465 \begin_layout Plain Layout
10479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10482 \begin_layout Plain Layout
10483 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10496 \begin_layout Plain Layout
10503 \begin_layout Plain Layout
10517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10520 \begin_layout Plain Layout
10521 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10534 \begin_layout Plain Layout
10537 underleftrightarrow
10541 \begin_layout Plain Layout
10555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10558 \begin_layout Plain Layout
10559 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10573 \begin_inset space \hfill{}
10577 \begin_inset Tabular
10578 <lyxtabular version="3" rows="5" columns="2">
10580 <column alignment="center" valignment="top" width="0pt">
10581 <column alignment="center" valignment="top" width="0pt">
10583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10586 \begin_layout Plain Layout
10592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10595 \begin_layout Plain Layout
10603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10606 \begin_layout Plain Layout
10613 \begin_layout Plain Layout
10627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10630 \begin_layout Plain Layout
10631 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10644 \begin_layout Plain Layout
10651 \begin_layout Plain Layout
10665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10668 \begin_layout Plain Layout
10669 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10682 \begin_layout Plain Layout
10689 \begin_layout Plain Layout
10703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10706 \begin_layout Plain Layout
10707 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10720 \begin_layout Plain Layout
10727 \begin_layout Plain Layout
10741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10744 \begin_layout Plain Layout
10745 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10759 \begin_inset space \hfill{}
10765 \begin_layout Standard
10766 \begin_inset VSpace medskip
10769 With these commands as many characters as you like can be accented.
10782 will only be set in the output with a length of three characters, as shown
10783 in the following example:
10784 \begin_inset Formula \[
10785 \widetilde{A+B=C-D}\]
10792 \begin_layout Standard
10803 \begin_layout Plain Layout
10821 \begin_layout Plain Layout
10829 described in the previous subsection it is also possible to accent several
10839 \begin_layout Plain Layout
10849 \begin_inset Formula $\downarrow$
10855 \begin_inset Formula \[
10856 \underset{***}{A=B}\]
10863 \begin_layout Section
10865 \begin_inset CommandInset label
10875 \begin_layout Plain Layout
10884 \begin_layout Subsection
10886 \begin_inset CommandInset label
10888 name "sub:Predefined-Space"
10896 \begin_layout Plain Layout
10897 Space ! horizontal ! predefined
10905 \begin_layout Standard
10906 Sometimes it is necessary to insert horizontal space to a formula.
10907 This is done by inserting a protected space (shortcut
10913 \begin_inset Quotes eld
10923 \begin_layout Plain Layout
10936 \begin_inset Quotes erd
10939 appears and by pressing
10943 several times one can select one of eight different space sizes.
10944 The spaces can also be inserted using the math toolbar button
10945 \begin_inset Graphics
10946 filename ../images/math/space.png
10951 or special commands.
10952 Independent from the inserted command, one can select the size again by
10960 \begin_layout Standard
10963 \begin_inset VSpace -5mm
10967 \begin_inset Tabular
10968 <lyxtabular version="3" rows="3" columns="7">
10970 <column alignment="center" valignment="middle" width="6.8cm">
10971 <column alignment="center" valignment="top" width="0">
10972 <column alignment="center" valignment="top" width="0">
10973 <column alignment="center" valignment="top" width="0">
10974 <column alignment="center" valignment="top" width="0">
10975 <column alignment="center" valignment="top" width="0">
10976 <column alignment="center" valignment="top" width="0">
10978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10981 \begin_layout Plain Layout
10987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10990 \begin_layout Plain Layout
10998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11012 \begin_layout Plain Layout
11020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11023 \begin_layout Plain Layout
11031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11034 \begin_layout Plain Layout
11042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11045 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11058 \begin_layout Plain Layout
11063 keystrokes after inserting the protected space
11068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11071 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11089 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11116 \begin_layout Plain Layout
11124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11127 \begin_layout Plain Layout
11133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11136 \begin_layout Plain Layout
11137 \begin_inset Formula $A\, B$
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 $A\quad B$
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11185 \begin_inset Formula $A\qquad B$
11193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11196 \begin_layout Plain Layout
11197 \begin_inset Formula $A\! B$
11213 \begin_layout Standard
11214 The last size seem to produce no space.
11215 It is displayed red in LyX contrary to the other sizes, because it is a
11217 There are two more negative spaces:
11220 \begin_layout Standard
11222 \begin_inset Tabular
11223 <lyxtabular version="3" rows="3" columns="3">
11225 <column alignment="center" valignment="middle" width="6.8cm">
11226 <column alignment="center" valignment="top" width="0pt">
11227 <column alignment="center" valignment="top" width="0pt">
11229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11232 \begin_layout Plain Layout
11238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11241 \begin_layout Plain Layout
11249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11252 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11270 keystrokes after inserting the protected space
11275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11278 \begin_layout Plain Layout
11284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11287 \begin_layout Plain Layout
11295 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11308 \begin_inset Formula $A\negmedspace B$
11316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11319 \begin_layout Plain Layout
11320 \begin_inset Formula $A\negthickspace B$
11336 \begin_layout Standard
11337 Negative spaces can lead to characters overlapping each other.
11338 Thus they can be used to enforce ligatures, what is e.
11339 \begin_inset space \thinspace{}
11343 \begin_inset space ~
11346 useful for summation operators:
11349 \begin_layout Standard
11351 \begin_inset Tabular
11352 <lyxtabular version="3" rows="3" columns="2">
11354 <column alignment="center" valignment="top" width="0">
11355 <column alignment="center" valignment="top" width="0">
11357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11360 \begin_layout Plain Layout
11366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11369 \begin_layout Plain Layout
11371 \begin_inset Note Note
11374 \begin_layout Plain Layout
11381 is only used as spacer.
11393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11405 \begin_layout Plain Layout
11419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11422 \begin_layout Plain Layout
11423 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11436 \begin_layout Plain Layout
11447 \begin_layout Plain Layout
11461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11464 \begin_layout Plain Layout
11465 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11481 \begin_layout Standard
11482 Relations like for example equal signs, are always surrounded by space.
11483 To suppress this, the equal sign is placed into a TeX-brace.
11484 The following example demonstrates this:
11487 \begin_layout Standard
11489 \begin_inset Tabular
11490 <lyxtabular version="3" rows="2" columns="2">
11492 <column alignment="center" valignment="top" width="0pt">
11493 <column alignment="center" valignment="top" width="0pt">
11495 <cell alignment="center" valignment="top" usebox="none">
11498 \begin_layout Plain Layout
11504 <cell alignment="center" valignment="top" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A=B$
11518 <cell alignment="center" valignment="top" usebox="none">
11521 \begin_layout Plain Layout
11522 \begin_inset Note Note
11525 \begin_layout Plain Layout
11532 is only used as spacer.
11538 \begin_inset Formula $\raisebox{5mm}{}$
11541 equation without space
11546 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11549 \begin_layout Plain Layout
11550 \begin_inset Formula $A{=}B$
11566 \begin_layout Standard
11568 The command for the last formula is:
11573 \begin_inset Formula $\to$
11579 \begin_layout Standard
11580 \begin_inset VSpace bigskip
11583 Spaces are needed for physical units, because the space between the value
11584 and the unit is the smallest one and not a normal space.
11585 For units in text, the smallest space is inserted via the menu
11587 Insert\SpecialChar \menuseparator
11588 Formatting\SpecialChar \menuseparator
11590 \begin_inset space ~
11602 \begin_layout Standard
11603 An example to visualize the difference:
11606 \begin_layout Standard
11607 \begin_inset Tabular
11608 <lyxtabular version="3" rows="2" columns="2">
11610 <column alignment="left" valignment="top" width="0">
11611 <column alignment="left" valignment="top" width="0">
11613 <cell alignment="center" valignment="top" usebox="none">
11616 \begin_layout Plain Layout
11618 \begin_inset Formula $\cdot$
11626 <cell alignment="center" valignment="top" usebox="none">
11629 \begin_layout Plain Layout
11630 space between value and unit
11637 <cell alignment="center" valignment="top" usebox="none">
11640 \begin_layout Plain Layout
11642 \begin_inset space \thinspace{}
11646 \begin_inset Formula $\cdot$
11654 <cell alignment="center" valignment="top" usebox="none">
11657 \begin_layout Plain Layout
11658 smallest space between value and unit
11671 \begin_layout Subsection
11676 \begin_layout Plain Layout
11689 \begin_layout Plain Layout
11690 for vertical space in formulas see
11691 \begin_inset CommandInset ref
11693 reference "sub:Line-Separation"
11706 \begin_layout Plain Layout
11714 \begin_inset Note Note
11717 \begin_layout Plain Layout
11720 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11723 \begin_layout Plain Layout
11726 texorpdfstring is in section
11727 \begin_inset CommandInset ref
11729 reference "sub:Formulas-in-Section"
11739 \begin_inset CommandInset label
11741 name "sub:Variable-Space"
11749 \begin_layout Plain Layout
11750 Space ! horizontal ! variable
11758 \begin_layout Standard
11759 Space with a defined length can be inserted in LyX with the command
11760 \begin_inset Newline newline
11773 \begin_layout Plain Layout
11782 For the length all units listed in
11783 \begin_inset CommandInset ref
11785 reference "tab:Available-units"
11789 are allowed, except of the unit
11790 \begin_inset Quotes eld
11794 \begin_inset Quotes erd
11798 The length may also be negative.
11799 To insert so many space that the formula uses all available space, the
11810 \begin_layout Plain Layout
11821 \begin_layout Standard
11822 \begin_inset VSpace -1mm
11828 \begin_layout Standard
11830 \begin_inset Tabular
11831 <lyxtabular version="3" rows="4" columns="2">
11833 <column alignment="center" valignment="top" width="0">
11834 <column alignment="center" valignment="top" width="0">
11836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11839 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11848 \begin_layout Plain Layout
11856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11859 \begin_layout Plain Layout
11863 \begin_inset Formula $\to$
11873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11876 \begin_layout Plain Layout
11877 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11890 \begin_layout Plain Layout
11894 \begin_inset Formula $\to$
11904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11907 \begin_layout Plain Layout
11908 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11921 \begin_layout Plain Layout
11928 \begin_layout Plain Layout
11942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11945 \begin_layout Plain Layout
11946 \begin_inset Formula $A=A\hfill B=B$
11962 \begin_layout Standard
11963 In the last example the available space is given by the longest column entry
11965 In an inline formula the space depends on the length of the line in which
11973 Thus, when the line uses the full width, no space will be created.
11980 only has an effect on displayed formulas when the formula style
11985 (Formula styles are explained in
11986 \begin_inset CommandInset ref
11988 reference "sec:Formula-Styles"
11995 \begin_layout Standard
12002 , there are the commands
12014 that fill the space with a pattern, see
12015 \begin_inset CommandInset ref
12017 reference "sub:Ellipses"
12024 \begin_layout Standard
12025 For text, variable space can be inserted via the menu
12027 Insert\SpecialChar \menuseparator
12028 Formatting\SpecialChar \menuseparator
12030 \begin_inset space ~
12035 , what is not possible in formulas:
12038 \begin_layout Standard
12039 This is a line with
12040 \begin_inset space \hspace{}
12045 \begin_inset space \thinspace{}
12051 \begin_layout Standard
12052 This is a line with
12053 \begin_inset space \hfill{}
12059 \begin_layout Subsection
12060 Space besides inline Formulas
12064 \begin_layout Plain Layout
12065 Space ! besides inline formulas
12073 \begin_layout Standard
12074 The space that surrounds inline formulas can be adjusted with the length
12083 \begin_layout Plain Layout
12094 The value of a length is set with the command
12102 \begin_layout Plain Layout
12112 that has the following scheme:
12115 \begin_layout Standard
12120 setlength{length name}{value}
12123 \begin_layout Standard
12131 \begin_inset space \thinspace{}
12137 \begin_layout Standard
12147 \begin_layout Standard
12148 is inserted in TeX-mode.
12150 \begin_inset space \thinspace{}
12153 mm space will now be set around all inline formulas:
12157 \begin_layout Plain Layout
12171 \begin_layout Standard
12172 This is a line with an inline formula
12173 \begin_inset Formula $A=B$
12177 \begin_inset space \thinspace{}
12180 mm surrounding space.
12184 \begin_layout Plain Layout
12198 \begin_layout Standard
12199 To return to the predefined value,
12205 is set to the value 0
12206 \begin_inset space \thinspace{}
12212 \begin_layout Section
12217 \begin_layout Plain Layout
12227 \begin_layout Plain Layout
12232 \begin_layout Plain Layout
12243 \begin_layout Plain Layout
12258 \begin_layout Standard
12259 Boxes for text are described in chapter
12266 \begin_inset space ~
12274 \begin_layout Subsection
12276 \begin_inset CommandInset label
12278 name "sub:Boxes-with-Frame"
12286 \begin_layout Plain Layout
12295 \begin_layout Standard
12296 It is possible to frame formulas or parts of it with the commands
12306 \begin_layout Plain Layout
12324 \begin_layout Plain Layout
12335 \begin_layout Standard
12336 When one of these commands is inserted to a formula, a blue box appears
12337 within a frame to enter formula parts.
12344 an additional formula has to be created by
12352 \begin_layout Plain Layout
12353 Due to a bug in LyX it is not possible to create a new formula with
12358 \begin_inset CommandInset href
12360 name "LyX-bug #1435"
12361 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12370 , because the box content will otherwise be treated as mathematical text.
12377 is used, a new formula is automatically created inside the frame.
12380 \begin_layout Standard
12387 is not suitable to frame displayed formulas, because the formula will always
12388 be set in the size of the text.
12395 is in contrary not suitable to frame inline formulas, because the formula
12396 will always be set in the size of a displayed formula.
12399 \begin_layout Standard
12406 there is the command
12416 \begin_layout Plain Layout
12424 where additionally the frame width and the alignment can be specified.
12431 is used in the following scheme:
12434 \begin_layout Standard
12439 framebox[frame width][position]{box content}
12442 \begin_layout Standard
12443 The position can either be
12460 right aligns the formula in the box.
12461 When no position is given, the formula will be centered.
12462 \begin_inset Newline newline
12465 Is no width given, also no position can be given.
12466 In this case the frame width is adjusted to the box content like for
12475 \begin_layout Standard
12482 is inserted, a box appears containing three blue boxes.
12483 The first two boxes are surrounded by brackets and denote the two optional
12485 The third box is for formula parts like for
12494 \begin_layout Standard
12496 \begin_inset Note Note
12499 \begin_layout Plain Layout
12500 The table has been set into a minipage to make the footnote appearing.
12501 Otherwise the footnote text would not be displayed.
12507 \begin_inset Box Frameless
12516 height_special "totalheight"
12519 \begin_layout Plain Layout
12521 \begin_inset Tabular
12522 <lyxtabular version="3" rows="5" columns="2">
12524 <column alignment="center" valignment="top" width="0">
12525 <column alignment="center" valignment="top" width="0">
12527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12530 \begin_layout Plain Layout
12535 \begin_layout Plain Layout
12536 Due to a bug in LyX it is not possible to create a new formula with
12541 \begin_inset CommandInset href
12543 name "LyX-bug #1435"
12544 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12561 \begin_layout Plain Layout
12563 \begin_inset Note Note
12566 \begin_layout Plain Layout
12573 is only used as spacer.
12585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12588 \begin_layout Plain Layout
12595 \begin_layout Plain Layout
12614 \begin_layout Plain Layout
12628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12631 \begin_layout Plain Layout
12632 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12646 \begin_layout Plain Layout
12653 \begin_layout Plain Layout
12668 \begin_layout Plain Layout
12682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12685 \begin_layout Plain Layout
12686 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12699 \begin_layout Plain Layout
12706 \begin_layout Plain Layout
12720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12723 \begin_layout Plain Layout
12724 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12737 \begin_layout Plain Layout
12744 \begin_layout Plain Layout
12754 \begin_inset Formula $\to$
12758 \begin_inset Formula $\to$
12771 \begin_layout Plain Layout
12781 \begin_inset Formula $\downarrow$
12789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12792 \begin_layout Plain Layout
12793 \begin_inset Formula $\raisebox{6mm}{}$
12797 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12801 \begin_inset Formula $\raisebox{-4mm}{}$
12822 \begin_layout Standard
12823 The frame thickness can also be adjusted.
12824 To do this the following commands have to be inserted in TeX-mode before
12828 \begin_layout Standard
12838 \begin_inset Quotes eld
12842 \begin_inset Quotes erd
12856 \begin_inset Quotes eld
12860 \begin_inset Quotes erd
12866 \begin_layout Standard
12867 \begin_inset Quotes eld
12871 \begin_inset Quotes erd
12874 specifies the minimal distance between the frame and the first character
12876 An example for this is the following framed formula:
12880 \begin_layout Plain Layout
12892 \begin_inset Formula \[
12897 Before this formula the commands
12900 \begin_layout Standard
12922 \begin_layout Standard
12923 were inserted in TeX-mode.
12924 The given values are used for all following boxes.
12927 \begin_layout Standard
12928 To return to the standard frame size, the command
12931 \begin_layout Standard
12956 \begin_layout Plain Layout
12970 \begin_layout Standard
12971 is inserted in TeX-mode before the next formula.
12974 \begin_layout Subsection
12975 Boxes without Frame
12976 \begin_inset CommandInset label
12978 name "sub:Boxes-without-Frame"
12986 \begin_layout Plain Layout
12987 Boxes ! without frame
12995 \begin_layout Standard
12996 For boxes without a frame there are the following box commands:
13006 \begin_layout Plain Layout
13024 \begin_layout Plain Layout
13042 \begin_layout Plain Layout
13053 \begin_layout Standard
13060 a box can be super- or subscripted.
13061 But in contrary to normal super- and subscripting, the characters in the
13062 box keep their font size.
13069 is used in the following scheme:
13072 \begin_layout Standard
13077 raisebox{height}{box content}
13080 \begin_layout Standard
13081 When the box should contain a formula, an extra formula is needed like for
13091 \begin_layout Standard
13093 \begin_inset Tabular
13094 <lyxtabular version="3" rows="4" columns="2">
13096 <column alignment="center" valignment="top" width="0">
13097 <column alignment="center" valignment="top" width="0">
13099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13102 \begin_layout Plain Layout
13108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13111 \begin_layout Plain Layout
13119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13122 \begin_layout Plain Layout
13126 \begin_inset Formula $\to$
13132 \begin_inset Formula $\to$
13140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13143 \begin_layout Plain Layout
13144 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13157 \begin_layout Plain Layout
13161 \begin_inset Formula $\to$
13167 \begin_inset Formula $\to$
13175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13178 \begin_layout Plain Layout
13179 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13192 \begin_layout Plain Layout
13196 \begin_inset Formula $\to$
13211 \begin_layout Plain Layout
13225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13228 \begin_layout Plain Layout
13232 \begin_layout Plain Layout
13256 \begin_layout Standard
13257 The last formula can currently only be created using TeX-mode because LyX
13258 inserts a box instead of the needed extra formula.
13262 \begin_layout Plain Layout
13264 \begin_inset CommandInset href
13266 name "LyX-bug #1435"
13267 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13279 \begin_layout Standard
13304 , with the difference that there is no frame.
13307 \begin_layout Subsection
13309 \begin_inset CommandInset label
13311 name "sub:Colored-Boxes"
13319 \begin_layout Plain Layout
13328 \begin_layout Standard
13329 To be able to use all commands explained in this section, the LaTeX-package
13338 \begin_layout Plain Layout
13343 is part of every LaTeX standard installation.
13352 \begin_layout Plain Layout
13358 has to be loaded in the LaTeX-preamble with the line
13362 \begin_layout Plain Layout
13363 When text is colored somewhere in the document with a predefined color,
13364 LyX loads the LaTeX-package
13369 Thus it is possible that the package is loaded twice, but this doesn't
13376 \begin_inset Note Note
13379 \begin_layout Plain Layout
13380 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13389 \begin_layout Standard
13397 \begin_layout Standard
13398 \begin_inset VSpace medskip
13401 To color boxes, the command
13411 \begin_layout Plain Layout
13419 is used in the following scheme:
13422 \begin_layout Standard
13427 colorbox{color}{box content}
13430 \begin_layout Standard
13431 The box content can also be a box and a
13437 can also be part of another box (see the 2nd and 3rd example).
13438 When the box should contain a formula, an extra formula has to be created,
13449 \begin_layout Plain Layout
13450 This also applies for the command
13458 \begin_inset CommandInset href
13460 name "LyX-bug #1435"
13461 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13473 \begin_layout Standard
13474 One of the following predefined colors can be chosen:
13477 \begin_layout Standard
13511 \begin_layout Standard
13513 \begin_inset Tabular
13514 <lyxtabular version="3" rows="4" columns="2">
13516 <column alignment="center" valignment="top" width="0">
13517 <column alignment="center" valignment="top" width="0">
13519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13522 \begin_layout Plain Layout
13528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13531 \begin_layout Plain Layout
13533 \begin_inset Note Note
13536 \begin_layout Plain Layout
13543 is only used as spacer.
13555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13558 \begin_layout Plain Layout
13562 \begin_inset Formula $\to$
13572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13575 \begin_layout Plain Layout
13576 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13589 \begin_layout Plain Layout
13593 \begin_inset Formula $\to$
13604 \begin_layout Plain Layout
13618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13621 \begin_layout Plain Layout
13622 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13635 \begin_layout Plain Layout
13642 \begin_layout Plain Layout
13654 \begin_inset Formula $\to$
13664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13667 \begin_layout Plain Layout
13668 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13684 \begin_layout Standard
13691 only colors the box but not the characters in the box.
13692 To color all characters, the whole formula is highlighted and the wanted
13693 color is chosen in the
13696 \begin_inset space ~
13702 The dialog can be called with the toolbar button
13703 \begin_inset Graphics
13704 filename ../images/dialog-show_character.png
13711 Edit\SpecialChar \menuseparator
13713 \begin_inset space ~
13716 Style\SpecialChar \menuseparator
13720 The formula number has then the same color as the formula.
13721 When the formula number should get another color than the formula characters,
13722 the color must be changed within the formula.
13725 \begin_layout Standard
13729 \begin_layout Standard
13732 \begin_inset Formula \begin{equation}
13733 \int A=B\label{eq:red}\end{equation}
13740 \begin_inset Formula \begin{equation}
13741 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13748 \begin_layout Standard
13750 \begin_inset CommandInset ref
13756 is completely colored red.
13757 \begin_inset Newline newline
13761 \begin_inset CommandInset ref
13763 reference "eq:redgreen"
13767 was first completely colored green to set the color for the formula number.
13768 Subsequently the formula characters were colored red.
13771 \begin_layout Standard
13772 \begin_inset VSpace bigskip
13775 To color the frame different than the rest of the box, the command
13785 \begin_layout Plain Layout
13793 is used in the following scheme:
13796 \begin_layout Standard
13801 fcolorbox{frame color}{color}{box content}
13804 \begin_layout Standard
13811 is an extension of the command
13818 The frame width is set, like for
13841 \begin_layout Plain Layout
13853 \begin_inset Formula \[
13854 \fcolorbox{cyan}{magenta}{A=B}\]
13862 \begin_layout Plain Layout
13876 \begin_layout Standard
13877 This formula was created with the command
13878 \begin_inset Newline newline
13886 \begin_inset Formula $\to$
13892 \begin_inset Formula $\to$
13902 \begin_layout Standard
13903 \begin_inset VSpace bigskip
13906 To use other colors than the predefined ones, they have to be defined first.
13909 \begin_layout Standard
13910 One can for example define the color
13911 \begin_inset Quotes eld
13919 \begin_inset Quotes erd
13922 with the LaTeX-preamble line:
13925 \begin_layout Standard
13930 definecolor{darkgreen}{cmyk}{0.5,
13948 \begin_layout Plain Layout
13959 \begin_layout Standard
13964 is the color space that denotes the colors
13981 The four comma separated numbers are the portion factor for the corresponding
13982 colors of the color space.
13983 The factors can be in the range of 0
13984 \begin_inset space \thinspace{}
13988 \begin_inset space \thinspace{}
13996 also the color space
14000 can be used for definitions.
14017 , so that there are in this case three portion factors for the corresponding
14019 Furthermore there is the color space
14023 with one portion factor for the gray value.
14026 \begin_layout Standard
14027 As example a framed box with the new defined color
14031 where the characters have been colored
14036 \begin_inset Formula \begin{equation}
14037 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14044 \begin_layout Standard
14045 Self-defined colors can also be used for text with the help of the command
14056 \begin_layout Plain Layout
14065 \begin_layout Standard
14069 \begin_layout Plain Layout
14073 textcolor{darkgreen}{
14079 \begin_inset Quotes eld
14083 \begin_inset Quotes erd
14090 \begin_layout Plain Layout
14100 \begin_layout Standard
14111 \begin_layout Plain Layout
14119 is used in the scheme
14123 textcolor{color}{characters to color}
14128 \begin_layout Subsection
14130 \begin_inset CommandInset label
14132 name "sub:Paragraph-Boxes"
14140 \begin_layout Plain Layout
14141 Boxes ! as paragraph
14149 \begin_layout Standard
14150 A box that can contain several lines and paragraphs, a so called paragraph
14151 box (parbox), can be created with the menu
14153 Insert\SpecialChar \menuseparator
14156 or the toolbar button
14157 \begin_inset Graphics
14158 filename ../images/box-insert.png
14166 \begin_layout Standard
14167 The following example shows a framed parbox in a line:
14170 \begin_layout Standard
14171 \begin_inset VSpace medskip
14175 \begin_inset Box Boxed
14184 height_special "totalheight"
14187 \begin_layout Plain Layout
14188 This is a paragraph box.
14190 \begin_inset space \thinspace{}
14193 cm long and can also contain formulas:
14194 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14205 \begin_layout Standard
14206 \begin_inset VSpace medskip
14212 \begin_layout Standard
14213 Such a box is created by right-clicking on the gray box inset.
14214 A dialog pops up showing the box properties.
14228 \begin_inset space \thinspace{}
14233 Vertical Box Alignment
14238 \begin_layout Standard
14239 \begin_inset VSpace medskip
14242 In LaTeX a parbox is created with the command
14252 \begin_layout Plain Layout
14260 that has the following scheme:
14263 \begin_layout Standard
14268 parbox[position]{width}{box content}
14271 \begin_layout Standard
14285 for bottom means that the box is aligned within the surrounding text with
14291 for top this is done with the first line.
14292 When no position is given, the box will be vertically centered, see section
14300 \begin_inset space ~
14305 manual for examples.
14308 \begin_layout Standard
14309 \begin_inset VSpace bigskip
14312 To frame formulas completely, including the formula number, the formula
14313 must be set into a parbox.
14314 To do this, the command
14328 is inserted in TeX-mode before the formula.
14337 \begin_layout Plain Layout
14347 is hereby the line width set for the document.
14348 Because the frame is outside the parbox, 2
14349 \begin_inset space \thinspace{}
14352 times the frame separation and the frame thickness must be subtracted from
14354 As this is not automatically done by LyX due to a bug
14358 \begin_layout Plain Layout
14359 \begin_inset CommandInset href
14361 name "LyX-bug #4483"
14362 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14371 , TeX-mode has to be used.
14372 To be able to multiply and subtract in arguments, the LaTeX-package
14380 \begin_layout Plain Layout
14385 is part of every LaTeX standard installation.
14394 \begin_layout Plain Layout
14400 must be loaded in the LaTeX-preamble with the line
14403 \begin_layout Standard
14411 \begin_layout Standard
14412 Behind the formula both boxes are closed by entering
14417 Here is an example:
14421 \begin_layout Plain Layout
14435 \begin_layout Standard
14439 \begin_layout Plain Layout
14457 \begin_inset Formula \begin{equation}
14458 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14466 \begin_layout Plain Layout
14477 \begin_layout Plain Layout
14491 \begin_layout Standard
14492 \begin_inset VSpace medskip
14495 As a parbox is used as argument of
14501 , there is in this case no difference between
14516 \begin_layout Standard
14517 \begin_inset VSpace bigskip
14520 Paragraph boxes are very useful to comment formulas directly.
14527 is used in combination with the command
14541 \begin_inset CommandInset ref
14543 reference "sub:User-defined-Numbering"
14550 \begin_layout Standard
14551 An example of a formula commented with
14560 \begin_layout Standard
14564 \begin_layout Plain Layout
14577 This is a description.
14578 It is distinctly separated from the formula and multiline.
14582 \begin_layout Plain Layout
14594 \begin_layout Standard
14595 Such a formula must be inserted completely in TeX-mode because LyX does
14596 not yet support the command
14603 The formula is created with the following command sequence:
14606 \begin_layout Standard
14619 is inserted in TeX-mode.
14623 \begin_layout Plain Layout
14624 When the formula style
14636 can also be replaced by
14643 (formula styles see
14644 \begin_inset CommandInset ref
14646 reference "sec:Formula-Styles"
14655 Then the description follows as normal text, and finally
14661 is inserted in TeX-mode.
14674 hereby create a displayed formula.
14677 \begin_layout Standard
14684 can be seen in this example that was
14685 \begin_inset Quotes eld
14689 \begin_inset Quotes erd
14692 using the mathematical textmode:
14693 \begin_inset Formula \[
14694 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14701 \begin_layout Section
14706 \begin_layout Plain Layout
14715 \begin_layout Subsection
14717 \begin_inset CommandInset label
14719 name "sub:Big-Operators"
14727 \begin_layout Plain Layout
14737 \begin_layout Plain Layout
14747 \begin_layout Plain Layout
14756 \begin_layout Standard
14757 To be able to use all integral operators listed here, the option
14759 Use esint package automatically
14761 must be set in the document settings under
14764 \begin_inset space ~
14772 \begin_layout Standard
14773 \begin_inset space \hfill{}
14777 \begin_inset Tabular
14778 <lyxtabular version="3" rows="11" columns="2">
14780 <column alignment="center" valignment="top" width="0pt">
14781 <column alignment="center" valignment="top" width="0pt">
14783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14786 \begin_layout Plain Layout
14792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14795 \begin_layout Plain Layout
14803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14806 \begin_layout Plain Layout
14813 \begin_layout Plain Layout
14826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14829 \begin_layout Plain Layout
14830 \begin_inset Formula $\sum$
14840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14843 \begin_layout Plain Layout
14850 \begin_layout Plain Layout
14863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14866 \begin_layout Plain Layout
14867 \begin_inset Formula $\int$
14877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14880 \begin_layout Plain Layout
14888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14891 \begin_layout Plain Layout
14892 \begin_inset Formula $\intop$
14902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14905 \begin_layout Plain Layout
14913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14916 \begin_layout Plain Layout
14917 \begin_inset Formula $\oint$
14927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14930 \begin_layout Plain Layout
14938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14941 \begin_layout Plain Layout
14942 \begin_inset Formula $\ointop$
14952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14955 \begin_layout Plain Layout
14963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14966 \begin_layout Plain Layout
14967 \begin_inset Formula $\ointctrclockwise$
14977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14980 \begin_layout Plain Layout
14988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14991 \begin_layout Plain Layout
14992 \begin_inset Formula $\ointclockwise$
15002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15005 \begin_layout Plain Layout
15013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15016 \begin_layout Plain Layout
15017 \begin_inset Formula $\sqint$
15027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15030 \begin_layout Plain Layout
15038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15041 \begin_layout Plain Layout
15042 \begin_inset Formula $\bigcap$
15052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15055 \begin_layout Plain Layout
15063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15066 \begin_layout Plain Layout
15067 \begin_inset Formula $\bigcup$
15081 \begin_inset space \hfill{}
15085 \begin_inset Tabular
15086 <lyxtabular version="3" rows="10" columns="2">
15088 <column alignment="center" valignment="top" width="0pt">
15089 <column alignment="center" valignment="top" width="0pt">
15091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15094 \begin_layout Plain Layout
15100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15103 \begin_layout Plain Layout
15111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15114 \begin_layout Plain Layout
15121 \begin_layout Plain Layout
15134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15137 \begin_layout Plain Layout
15138 \begin_inset Formula $\prod$
15148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15151 \begin_layout Plain Layout
15159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15162 \begin_layout Plain Layout
15163 \begin_inset Formula $\coprod$
15173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15176 \begin_layout Plain Layout
15184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15187 \begin_layout Plain Layout
15188 \begin_inset Formula $\bigodot$
15198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15201 \begin_layout Plain Layout
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15212 \begin_layout Plain Layout
15213 \begin_inset Formula $\bigotimes$
15223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15226 \begin_layout Plain Layout
15234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15237 \begin_layout Plain Layout
15238 \begin_inset Formula $\bigoplus$
15248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15251 \begin_layout Plain Layout
15259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15262 \begin_layout Plain Layout
15263 \begin_inset Formula $\bigwedge$
15273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15276 \begin_layout Plain Layout
15284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15287 \begin_layout Plain Layout
15288 \begin_inset Formula $\bigvee$
15298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15301 \begin_layout Plain Layout
15309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15312 \begin_layout Plain Layout
15313 \begin_inset Formula $\bigsqcup$
15323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15326 \begin_layout Plain Layout
15334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15337 \begin_layout Plain Layout
15338 \begin_inset Formula $\biguplus$
15352 \begin_inset space \hfill{}
15358 \begin_layout Standard
15359 All big operators can also be inserted via the math toolbar button
15360 \begin_inset Graphics
15361 filename ../images/math/intop.png
15369 \begin_layout Standard
15370 The operators are called big because they are bigger than the sometimes
15371 equal looking binary operators.
15372 All big operators can have limits as described in the next subsection.
15375 \begin_layout Standard
15401 \begin_inset space ~
15404 in the style the operator limits are displayed, see
15405 \begin_inset CommandInset ref
15407 reference "sub:Operator-Limits"
15415 \begin_layout Subsubsection*
15416 Advices for Integrals
15419 \begin_layout Standard
15424 in an integral is an operator, that therefore has to be set upright.
15425 This is done by highlighting the
15429 and using the keyboard shortcut
15432 \begin_inset space ~
15441 \begin_layout Plain Layout
15447 \begin_inset CommandInset ref
15449 reference "sub:Font-Styles"
15459 Finally the smallest space is inserted before the
15463 , as this is usual for operators.
15467 \begin_layout Standard
15469 \begin_inset Formula $\int A(x)dx$
15473 \begin_inset Newline newline
15480 \begin_layout Plain Layout
15490 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15496 \begin_layout Standard
15497 For multiple integrals there are the following commands:
15498 \begin_inset VSpace medskip
15504 \begin_layout Standard
15505 \begin_inset space \hfill{}
15509 \begin_inset Tabular
15510 <lyxtabular version="3" rows="4" columns="2">
15512 <column alignment="center" valignment="top" width="0">
15513 <column alignment="center" valignment="top" width="0">
15515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15518 \begin_layout Plain Layout
15524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15527 \begin_layout Plain Layout
15529 \begin_inset Note Note
15532 \begin_layout Plain Layout
15539 is only used as spacer.
15551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15554 \begin_layout Plain Layout
15562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15565 \begin_layout Plain Layout
15566 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15579 \begin_layout Plain Layout
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15590 \begin_layout Plain Layout
15591 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15604 \begin_layout Plain Layout
15612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15615 \begin_layout Plain Layout
15616 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15630 \begin_inset space \hfill{}
15634 \begin_inset Tabular
15635 <lyxtabular version="3" rows="4" columns="2">
15637 <column alignment="center" valignment="top" width="0">
15638 <column alignment="center" valignment="top" width="0">
15640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15643 \begin_layout Plain Layout
15649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15652 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15663 \begin_layout Plain Layout
15671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15674 \begin_layout Plain Layout
15675 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15688 \begin_layout Plain Layout
15696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15699 \begin_layout Plain Layout
15700 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15713 \begin_layout Plain Layout
15721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15724 \begin_layout Plain Layout
15725 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15739 \begin_inset space \hfill{}
15745 \begin_layout Subsection
15747 \begin_inset CommandInset label
15749 name "sub:Operator-Limits"
15757 \begin_layout Plain Layout
15766 \begin_layout Standard
15767 Limits are created by super- and subscripts:
15770 \begin_layout Standard
15772 \begin_inset Tabular
15773 <lyxtabular version="3" rows="2" columns="2">
15775 <column alignment="center" valignment="top" width="0pt">
15776 <column alignment="center" valignment="top" width="0pt">
15778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15781 \begin_layout Plain Layout
15787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15790 \begin_layout Plain Layout
15792 \begin_inset Note Note
15795 \begin_layout Plain Layout
15802 is only used as spacer.
15814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15817 \begin_layout Plain Layout
15826 \begin_layout Plain Layout
15836 \begin_inset Formula $\to$
15840 \begin_inset Formula $\to$
15848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15851 \begin_layout Plain Layout
15852 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15868 \begin_layout Standard
15869 Limits of inline formulas are set right beside the operator.
15870 Limits in displayed formulas are set above or below the operator, except
15871 of integral limits.
15874 \begin_layout Standard
15875 To force that the limits are set beside the operator, the cursor is set
15876 directly behind the operator and the limits type is changed with the menu
15879 Edit\SpecialChar \menuseparator
15880 Math\SpecialChar \menuseparator
15892 \begin_inset space ~
15901 \begin_layout Standard
15902 The default limits type is this:
15903 \begin_inset Formula \[
15904 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15908 This is how it looks when the limits type was changed to
15915 \begin_inset Formula \[
15916 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15920 For integrals, except of
15932 , the limits are by default set beside the operator.
15933 But for multiple integrals the limits are often set below the operator.
15934 In the following example the limits type was therefore set to
15938 and so set below the integrals:
15939 \begin_inset Formula \begin{equation}
15940 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15947 \begin_layout Standard
15948 \begin_inset VSpace medskip
15951 To specify conditions for limits, the commands
15961 \begin_layout Plain Layout
15979 \begin_layout Plain Layout
15988 To create for example this expression
15989 \begin_inset Formula \begin{equation}
15990 \sum_{\begin{subarray}{c}
15992 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15999 \begin_layout Standard
16000 the following has to be done:
16001 \begin_inset Newline newline
16016 \begin_layout Plain Layout
16028 One is now in a blue box under the summation operator and insert there
16037 \begin_layout Plain Layout
16049 The blue box is now within a purple box and now several lines can be written
16051 A new line is created by inserting a line break (
16057 \begin_inset Newline newline
16062 0<k<1000 Ctrl-Return
16063 \begin_inset Newline newline
16068 is typed in, a new box appears below for the new line.
16071 \begin_layout Standard
16072 The alignment of the lines can be changed to left aligned with the
16082 Edit\SpecialChar \menuseparator
16086 To get right alignment,
16094 \begin_layout Plain Layout
16105 is inserted at the beginning of the line.
16108 \begin_layout Standard
16121 with the difference that the lines are always centered.
16124 \begin_layout Standard
16125 \begin_inset VSpace bigskip
16129 \begin_inset CommandInset ref
16131 reference "eq:substack"
16135 there can be too much space beside an operator, because the characters
16136 following the operator are set beside the limits.
16139 \begin_layout Standard
16140 To avoid this, the following macro can be used in the LaTeX-preamble:
16143 \begin_layout Standard
16157 \begin_inset Newline newline
16169 \begin_inset Newline newline
16176 mathclapinternal #1#2{
16180 mathsurround =0pt #1{#2}$}}
16183 \begin_layout Standard
16184 This defines the command
16194 \begin_layout Plain Layout
16202 that sets the width of the limit to 0
16203 \begin_inset space \thinspace{}
16207 The command scheme is
16210 \begin_layout Standard
16218 \begin_layout Standard
16219 where the limit can consist of several conditions.
16222 \begin_layout Standard
16224 \begin_inset CommandInset ref
16226 reference "eq:substack"
16230 , one uses the command
16233 \begin_layout Standard
16246 \begin_layout Plain Layout
16255 0<k<1000 Ctrl-Enter
16258 \begin_layout Standard
16259 to create the lower limit.
16260 The summand is now directly behind the summation operator:
16261 \begin_inset Formula \[
16262 \sum_{\mathclap{\substack{0<k<1000\\
16263 \\k\,\in\,\mathbb{N}}
16271 \begin_layout Standard
16272 \begin_inset VSpace bigskip
16275 How to use one limit for several operators is described in
16276 \begin_inset CommandInset ref
16278 reference "sub:Self-defined-Operators"
16285 \begin_layout Standard
16286 \begin_inset Newpage newpage
16292 \begin_layout Subsection
16294 \begin_inset CommandInset label
16296 name "sub:Binary-Operators"
16304 \begin_layout Plain Layout
16313 \begin_layout Standard
16314 Binary operators are surrounded by space when there is a character before
16316 \begin_inset VSpace medskip
16322 \begin_layout Standard
16323 \begin_inset space \hfill{}
16327 \begin_inset Tabular
16328 <lyxtabular version="3" rows="13" columns="2">
16330 <column alignment="center" valignment="top" width="0pt">
16331 <column alignment="center" valignment="top" width="0pt">
16333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16336 \begin_layout Plain Layout
16338 \begin_inset Note Note
16341 \begin_layout Plain Layout
16348 is only used as spacer.
16358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16361 \begin_layout Plain Layout
16369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16372 \begin_layout Plain Layout
16378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16381 \begin_layout Plain Layout
16382 \begin_inset Formula $+$
16392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16395 \begin_layout Plain Layout
16401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16404 \begin_layout Plain Layout
16405 \begin_inset Formula $-$
16415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16418 \begin_layout Plain Layout
16426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16429 \begin_layout Plain Layout
16430 \begin_inset Formula $\pm$
16440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16443 \begin_layout Plain Layout
16451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16454 \begin_layout Plain Layout
16455 \begin_inset Formula $\mp$
16465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16468 \begin_layout Plain Layout
16476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16479 \begin_layout Plain Layout
16480 \begin_inset Formula $\cdot$
16490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16493 \begin_layout Plain Layout
16501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16504 \begin_layout Plain Layout
16505 \begin_inset Formula $\times$
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16518 \begin_layout Plain Layout
16526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16529 \begin_layout Plain Layout
16530 \begin_inset Formula $\div$
16540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16543 \begin_layout Plain Layout
16547 \begin_layout Plain Layout
16560 \begin_layout Plain Layout
16572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16575 \begin_layout Plain Layout
16576 \begin_inset Formula $*$
16586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16589 \begin_layout Plain Layout
16597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16600 \begin_layout Plain Layout
16601 \begin_inset Formula $\star$
16611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16614 \begin_layout Plain Layout
16622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16625 \begin_layout Plain Layout
16626 \begin_inset Formula $\circ$
16636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16639 \begin_layout Plain Layout
16647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16650 \begin_layout Plain Layout
16651 \begin_inset Formula $\diamond$
16661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16664 \begin_layout Plain Layout
16672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16675 \begin_layout Plain Layout
16676 \begin_inset Formula $\bullet$
16690 \begin_inset space \hfill{}
16694 \begin_inset Tabular
16695 <lyxtabular version="3" rows="13" columns="2">
16697 <column alignment="center" valignment="top" width="0pt">
16698 <column alignment="center" valignment="top" width="0pt">
16700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16703 \begin_layout Plain Layout
16709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16712 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16723 \begin_layout Plain Layout
16731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16734 \begin_layout Plain Layout
16735 \begin_inset Formula $\nabla$
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16748 \begin_layout Plain Layout
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16759 \begin_layout Plain Layout
16760 \begin_inset Formula $\bigtriangledown$
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16773 \begin_layout Plain Layout
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16784 \begin_layout Plain Layout
16785 \begin_inset Formula $\bigtriangleup$
16795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16798 \begin_layout Plain Layout
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16809 \begin_layout Plain Layout
16810 \begin_inset Formula $\Box$
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16823 \begin_layout Plain Layout
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16834 \begin_layout Plain Layout
16835 \begin_inset Formula $\cap$
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16848 \begin_layout Plain Layout
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16859 \begin_layout Plain Layout
16860 \begin_inset Formula $\cup$
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16873 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $\dagger$
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $\ddagger$
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\wr$
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16959 \begin_layout Plain Layout
16960 \begin_inset Formula $\bigcirc$
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16973 \begin_layout Plain Layout
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16984 \begin_layout Plain Layout
16985 \begin_inset Formula $\wedge$
16995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16998 \begin_layout Plain Layout
17006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\vee$
17024 \begin_inset space \hfill{}
17028 \begin_inset Tabular
17029 <lyxtabular version="3" rows="13" columns="2">
17031 <column alignment="center" valignment="top" width="0pt">
17032 <column alignment="center" valignment="top" width="0pt">
17034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17037 \begin_layout Plain Layout
17043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17057 \begin_layout Plain Layout
17065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17068 \begin_layout Plain Layout
17069 \begin_inset Formula $\oplus$
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17082 \begin_layout Plain Layout
17090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17093 \begin_layout Plain Layout
17094 \begin_inset Formula $\ominus$
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17107 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17119 \begin_inset Formula $\otimes$
17129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17132 \begin_layout Plain Layout
17140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17143 \begin_layout Plain Layout
17144 \begin_inset Formula $\oslash$
17154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17157 \begin_layout Plain Layout
17165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17168 \begin_layout Plain Layout
17169 \begin_inset Formula $\odot$
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17182 \begin_layout Plain Layout
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\amalg$
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\uplus$
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17243 \begin_layout Plain Layout
17244 \begin_inset Formula $\setminus$
17254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17257 \begin_layout Plain Layout
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17268 \begin_layout Plain Layout
17269 \begin_inset Formula $\sqcap$
17279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17294 \begin_inset Formula $\sqcup$
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17318 \begin_layout Plain Layout
17319 \begin_inset Formula $\triangleleft$
17329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17332 \begin_layout Plain Layout
17340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17343 \begin_layout Plain Layout
17344 \begin_inset Formula $\triangleright$
17358 \begin_inset space \hfill{}
17364 \begin_layout Standard
17365 All binary operators can also be inserted via the math toolbar button
17366 \begin_inset Graphics
17367 filename ../images/math/pm.png
17375 \begin_layout Standard
17376 To typeset the Laplace operator also
17393 \begin_inset Formula $\nabla^{2}$
17396 ) can be used instead of
17405 \begin_layout Standard
17412 Insert\SpecialChar \menuseparator
17424 \begin_layout Subsection
17425 Self-defined Operators
17426 \begin_inset CommandInset label
17428 name "sub:Self-defined-Operators"
17436 \begin_layout Plain Layout
17437 Operators ! self-defined
17445 \begin_layout Standard
17446 With the help of the command
17450 DeclareMathOperator
17456 \begin_layout Plain Layout
17461 DeclareMathOperator
17466 custom operators can be defined in the LaTeX-preamble.
17467 Its command scheme is:
17470 \begin_layout Standard
17475 DeclareMathOperator{new command}{display}
17478 \begin_layout Standard
17479 Display can be characters or symbols that define how the operator looks
17481 To define a big operator a * is set behind the command.
17482 All self-defined big operators can have limits as described in
17483 \begin_inset CommandInset ref
17485 reference "sub:Operator-Limits"
17492 \begin_layout Standard
17493 For example the LaTeX-preamble line
17496 \begin_layout Standard
17501 DeclareMathOperator*{
17508 \begin_layout Standard
17509 defines the command
17515 , that inserts a big operator consisting of the lozenge symbol from
17516 \begin_inset CommandInset ref
17518 reference "sub:Miscellaneous-Symbols"
17523 \begin_inset Formula \[
17524 \Lozenge_{n=1}^{\infty}\]
17528 The command for this formula is:
17539 \begin_inset Formula $\to$
17545 \begin_layout Standard
17546 \begin_inset VSpace bigskip
17549 When self-defined operators are not used several times in the document,
17550 they can also be defined with the commands
17560 \begin_layout Plain Layout
17578 \begin_layout Plain Layout
17586 , which have the following scheme:
17589 \begin_layout Standard
17603 \begin_layout Standard
17610 defines big operators,
17619 \begin_layout Standard
17627 \begin_inset space \thinspace{}
17631 \begin_inset space ~
17634 be used to use one limit for several operators:
17637 \begin_layout Standard
17638 \begin_inset Formula \[
17639 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17646 \begin_layout Standard
17647 The command for the formula above is:
17648 \begin_inset Newline newline
17667 \begin_layout Plain Layout
17679 \begin_inset Formula $\to$
17688 \begin_layout Plain Layout
17702 \begin_layout Section
17707 \begin_layout Plain Layout
17716 \begin_layout Subsection
17718 \begin_inset CommandInset label
17720 name "sub:Font-Styles"
17728 \begin_layout Plain Layout
17737 \begin_layout Standard
17738 Latin letters in formulas can be set in one of the following font styles:
17739 \begin_inset VSpace -2mm
17745 \begin_layout Standard
17747 \begin_inset Tabular
17748 <lyxtabular version="3" rows="6" columns="3">
17750 <column alignment="center" valignment="top" width="0">
17751 <column alignment="center" valignment="top" width="0">
17752 <column alignment="center" valignment="top" width="0">
17754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17757 \begin_layout Plain Layout
17763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17766 \begin_layout Plain Layout
17772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17775 \begin_layout Plain Layout
17783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17786 \begin_layout Plain Layout
17795 \begin_layout Plain Layout
17811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17814 \begin_layout Plain Layout
17815 \begin_inset Formula $\mathbb{ABC}$
17823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17826 \begin_layout Plain Layout
17834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17837 \begin_layout Plain Layout
17846 \begin_layout Plain Layout
17862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17865 \begin_layout Plain Layout
17866 \begin_inset Formula $\mathbf{AbC}$
17874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17877 \begin_layout Plain Layout
17885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17888 \begin_layout Plain Layout
17897 \begin_layout Plain Layout
17913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17916 \begin_layout Plain Layout
17917 \begin_inset Formula $\boldsymbol{AbC}$
17925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17928 \begin_layout Plain Layout
17936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17939 \begin_layout Plain Layout
17948 \begin_layout Plain Layout
17964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17967 \begin_layout Plain Layout
17968 \begin_inset Formula $\mathcal{ABC}$
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17979 \begin_layout Plain Layout
17987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17990 \begin_layout Plain Layout
17999 \begin_layout Plain Layout
18015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18018 \begin_layout Plain Layout
18019 \begin_inset Formula $\mathfrak{AbC}$
18027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18030 \begin_layout Plain Layout
18044 \begin_layout Standard
18046 \begin_inset Tabular
18047 <lyxtabular version="3" rows="5" columns="3">
18049 <column alignment="center" valignment="top" width="0">
18050 <column alignment="center" valignment="top" width="0">
18051 <column alignment="center" valignment="top" width="0">
18053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18056 \begin_layout Plain Layout
18062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18065 \begin_layout Plain Layout
18071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18074 \begin_layout Plain Layout
18082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18085 \begin_layout Plain Layout
18094 \begin_layout Plain Layout
18110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18113 \begin_layout Plain Layout
18114 \begin_inset Formula $\mathit{AbC}$
18122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18125 \begin_layout Plain Layout
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18136 \begin_layout Plain Layout
18145 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18164 \begin_layout Plain Layout
18165 \begin_inset Formula $\mathrm{AbC}$
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18176 \begin_layout Plain Layout
18184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18187 \begin_layout Plain Layout
18196 \begin_layout Plain Layout
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18215 \begin_layout Plain Layout
18216 \begin_inset Formula $\mathsf{AbC}$
18224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18227 \begin_layout Plain Layout
18235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18238 \begin_layout Plain Layout
18247 \begin_layout Plain Layout
18263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18267 \begin_inset Formula $\mathtt{AbC}$
18275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18278 \begin_layout Plain Layout
18292 \begin_layout Standard
18293 \begin_inset Note Greyedout
18296 \begin_layout Plain Layout
18313 can only be used for big letters.
18321 \begin_layout Standard
18322 Predefined is the style
18331 \begin_layout Standard
18332 The style commands work also for letters in mathematical constructs:
18333 \begin_inset Formula \[
18334 \mathfrak{A=\frac{b}{C}}\]
18341 \begin_layout Standard
18342 Characters in mathematical text don't appear in a math font style but in
18343 the text font style
18350 That their style can't be set correctly via the text style dialog is a
18355 \begin_layout Plain Layout
18356 \begin_inset CommandInset href
18358 name "LyX-bug #4091"
18359 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18371 \begin_layout Standard
18372 Instead of the style commands the dialog
18374 Edit\SpecialChar \menuseparator
18375 Math\SpecialChar \menuseparator
18378 or the toolbar button
18379 \begin_inset Graphics
18380 filename ../images/math/font.png
18388 \begin_layout Subsection
18390 \begin_inset CommandInset label
18392 name "sub:Bold-Formulas"
18400 \begin_layout Plain Layout
18409 \begin_layout Standard
18410 To make a complete formula bold, the command
18416 from the previous subsection cannot be used, because it doesn't work for
18417 small Greek letters.
18418 Furthermore it prints Latin letters always upright, like in the following
18422 \begin_layout Standard
18423 \begin_inset Formula \[
18424 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18431 \begin_layout Standard
18432 To display the formula correctly, the command
18439 \begin_inset Formula \[
18440 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18444 It is also possible to set the formula in a
18446 boldmath environment
18449 This environment is created by inserting the command
18457 \begin_layout Plain Layout
18468 To end the environment, the command
18476 \begin_layout Plain Layout
18486 is inserted in TeX-mode.
18490 \begin_layout Plain Layout
18500 \begin_inset Formula \[
18501 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18509 \begin_layout Plain Layout
18521 \begin_layout Subsection
18523 \begin_inset CommandInset label
18525 name "sub:Font-Sizes"
18533 \begin_layout Plain Layout
18542 \begin_layout Standard
18543 For characters in formulas there are, analog to characters in text, the
18544 following size commands:
18547 \begin_layout Standard
18591 \begin_inset Newline newline
18613 \begin_layout Standard
18614 The size produced by the commands depends on the document font size, that
18615 corresponds with the command
18622 The other commands produce smaller or larger sizes than
18629 The font size can however not exceed a certain value.
18630 Is for example the document font size 12
18631 \begin_inset space \thinspace{}
18640 switches to the same size as
18650 \begin_layout Standard
18651 A size command is inserted in TeX-mode before the formula and sets the size
18652 for all following formula and text characters.
18653 To switch back to the initial size, the command
18659 is inserted behind the formula in TeX-mode.
18662 \begin_layout Standard
18663 Within a formula the size can only be changed for symbols or letters in
18665 To do this, the size command is inserted in mathematical text.
18666 All following characters until the end of the mathematical text or until
18667 another size command will have the selected size.
18669 \begin_inset VSpace -2mm
18675 \begin_layout Standard
18679 \begin_layout Plain Layout
18689 \begin_inset Formula \[
18690 A=\frac{B}{c}\cdot\maltese\]
18695 \begin_inset Formula \[
18696 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18704 \begin_layout Plain Layout
18716 \begin_layout Standard
18717 \begin_inset VSpace medskip
18720 Before both formulas the command
18727 The command for the second formula is:
18728 \begin_inset Newline newline
18739 \begin_layout Plain Layout
18754 \begin_layout Plain Layout
18769 \begin_layout Plain Layout
18784 \begin_layout Plain Layout
18794 \begin_inset Formula $\to$
18798 \begin_inset Formula $\to$
18802 \begin_inset Newline newline
18806 \begin_inset space \hspace*{}
18820 \begin_layout Plain Layout
18835 \begin_layout Plain Layout
18850 \begin_layout Plain Layout
18862 \begin_layout Standard
18863 If a symbol cannot be displayed in different sizes, it will always be displayed
18864 in the default size.
18867 \begin_layout Section
18872 \begin_layout Plain Layout
18881 \begin_layout Standard
18882 All Greek letters can also be inserted via the toolbar button
18883 \begin_inset Graphics
18884 filename ../images/math/alpha.png
18892 \begin_layout Subsection
18894 \begin_inset CommandInset label
18896 name "sub:Small-Letters"
18904 \begin_layout Plain Layout
18905 Greek letters ! small
18913 \begin_layout Standard
18914 \begin_inset space \hfill{}
18918 \begin_inset Tabular
18919 <lyxtabular version="3" rows="11" columns="2">
18921 <column alignment="center" valignment="top" width="0pt">
18922 <column alignment="center" valignment="top" width="0pt">
18924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18927 \begin_layout Plain Layout
18933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18936 \begin_layout Plain Layout
18944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18947 \begin_layout Plain Layout
18955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18958 \begin_layout Plain Layout
18959 \begin_inset Formula $\alpha$
18969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18972 \begin_layout Plain Layout
18980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18983 \begin_layout Plain Layout
18984 \begin_inset Formula $\beta$
18994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18997 \begin_layout Plain Layout
19005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19008 \begin_layout Plain Layout
19009 \begin_inset Formula $\gamma$
19019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19022 \begin_layout Plain Layout
19030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19033 \begin_layout Plain Layout
19034 \begin_inset Formula $\delta$
19044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19047 \begin_layout Plain Layout
19055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19058 \begin_layout Plain Layout
19059 \begin_inset Formula $\epsilon$
19069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19072 \begin_layout Plain Layout
19080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19083 \begin_layout Plain Layout
19084 \begin_inset Formula $\varepsilon$
19094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19097 \begin_layout Plain Layout
19105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19108 \begin_layout Plain Layout
19109 \begin_inset Formula $\zeta$
19119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19122 \begin_layout Plain Layout
19130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19133 \begin_layout Plain Layout
19134 \begin_inset Formula $\eta$
19144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19147 \begin_layout Plain Layout
19155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19158 \begin_layout Plain Layout
19159 \begin_inset Formula $\theta$
19169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19172 \begin_layout Plain Layout
19180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19183 \begin_layout Plain Layout
19184 \begin_inset Formula $\vartheta$
19198 \begin_inset space \hfill{}
19202 \begin_inset Tabular
19203 <lyxtabular version="3" rows="12" columns="2">
19205 <column alignment="center" valignment="top" width="0pt">
19206 <column alignment="center" valignment="top" width="0pt">
19208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19211 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19231 \begin_layout Plain Layout
19239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19242 \begin_layout Plain Layout
19243 \begin_inset Formula $\iota$
19253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19256 \begin_layout Plain Layout
19264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19267 \begin_layout Plain Layout
19268 \begin_inset Formula $\kappa$
19278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19281 \begin_layout Plain Layout
19289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19292 \begin_layout Plain Layout
19293 \begin_inset Formula $\varkappa$
19303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19306 \begin_layout Plain Layout
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19317 \begin_layout Plain Layout
19318 \begin_inset Formula $\lambda$
19328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19331 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19343 \begin_inset Formula $\mu$
19353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19356 \begin_layout Plain Layout
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19367 \begin_layout Plain Layout
19368 \begin_inset Formula $\nu$
19378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19381 \begin_layout Plain Layout
19389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19392 \begin_layout Plain Layout
19393 \begin_inset Formula $\xi$
19403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19406 \begin_layout Plain Layout
19412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19415 \begin_layout Plain Layout
19416 \begin_inset Formula $o$
19426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19429 \begin_layout Plain Layout
19437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19440 \begin_layout Plain Layout
19441 \begin_inset Formula $\pi$
19451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19454 \begin_layout Plain Layout
19462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19465 \begin_layout Plain Layout
19466 \begin_inset Formula $\varpi$
19476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19479 \begin_layout Plain Layout
19487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19490 \begin_layout Plain Layout
19491 \begin_inset Formula $\rho$
19505 \begin_inset space \hfill{}
19509 \begin_inset Tabular
19510 <lyxtabular version="3" rows="11" columns="2">
19512 <column alignment="center" valignment="top" width="0pt">
19513 <column alignment="center" valignment="top" width="0pt">
19515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19518 \begin_layout Plain Layout
19524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19527 \begin_layout Plain Layout
19535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19538 \begin_layout Plain Layout
19546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19549 \begin_layout Plain Layout
19550 \begin_inset Formula $\varrho$
19560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19574 \begin_layout Plain Layout
19575 \begin_inset Formula $\sigma$
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\varsigma$
19610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\tau$
19635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19638 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19650 \begin_inset Formula $\upsilon$
19660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19663 \begin_layout Plain Layout
19671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19674 \begin_layout Plain Layout
19675 \begin_inset Formula $\phi$
19685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19688 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $\varphi$
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\chi$
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\psi$
19760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\omega$
19789 \begin_inset space \hfill{}
19795 \begin_layout Standard
19796 \begin_inset VSpace medskip
19802 \begin_layout Standard
19803 How to create upright Greek letters is explained in
19804 \begin_inset CommandInset ref
19806 reference "sub:Upright-small-Greek"
19813 \begin_layout Subsection
19818 \begin_layout Plain Layout
19819 Greek letters ! big
19827 \begin_layout Standard
19828 \begin_inset space \hfill{}
19832 \begin_inset Tabular
19833 <lyxtabular version="3" rows="7" columns="2">
19835 <column alignment="center" valignment="top" width="0pt">
19836 <column alignment="center" valignment="top" width="0pt">
19838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19841 \begin_layout Plain Layout
19847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\Gamma$
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\Delta$
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\Theta$
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\Lambda$
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\Xi$
19983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19997 \begin_layout Plain Layout
19998 \begin_inset Formula $\Pi$
20012 \begin_inset space \hfill{}
20016 \begin_inset Tabular
20017 <lyxtabular version="3" rows="6" columns="2">
20019 <column alignment="center" valignment="top" width="0pt">
20020 <column alignment="center" valignment="top" width="0pt">
20022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20025 \begin_layout Plain Layout
20031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $\Sigma$
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\Upsilon$
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\Phi$
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20120 \begin_layout Plain Layout
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Plain Layout
20132 \begin_inset Formula $\Psi$
20142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Plain Layout
20157 \begin_inset Formula $\Omega$
20171 \begin_inset space \hfill{}
20177 \begin_layout Standard
20178 \begin_inset VSpace medskip
20181 That the big Greek letters appear upright is caused by a design bug when
20183 To get correct italic big letters, begin every command with
20188 For example the command
20195 \begin_inset Formula $\varGamma$
20201 \begin_layout Subsection
20206 \begin_layout Plain Layout
20207 Greek letters ! bold
20215 \begin_layout Standard
20216 Greek letters cannot be set with different font styles like Latin letters.
20217 They can only be made bold with the command
20227 \begin_layout Plain Layout
20238 \begin_layout Standard
20240 \begin_inset Tabular
20241 <lyxtabular version="3" rows="3" columns="2">
20243 <column alignment="center" valignment="top" width="0">
20244 <column alignment="center" valignment="top" width="0">
20246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20258 \begin_layout Plain Layout
20266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20269 \begin_layout Plain Layout
20281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20284 \begin_layout Plain Layout
20285 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20298 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\theta\boldsymbol{\theta}$
20330 \begin_layout Section
20335 \begin_layout Plain Layout
20348 \begin_layout Plain Layout
20349 A list with all symbols of most of the LaTeX-packages can be found in
20350 \begin_inset CommandInset citation
20365 \begin_layout Plain Layout
20373 \begin_inset Note Note
20376 \begin_layout Plain Layout
20379 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20382 \begin_layout Plain Layout
20385 texorpdfstring is in section
20386 \begin_inset CommandInset ref
20388 reference "sub:Formulas-in-Section"
20401 \begin_layout Plain Layout
20410 \begin_layout Standard
20411 Many of the symbols listed in this section can also be inserted via the
20413 \begin_inset Graphics
20414 filename ../images/math/nabla.png
20420 \begin_inset Graphics
20421 filename ../images/math/digamma.png
20429 \begin_layout Subsection
20430 Mathematical Symbols
20431 \begin_inset CommandInset label
20433 name "sub:Mathematical-Symbols"
20441 \begin_layout Plain Layout
20442 Symbols ! mathematical
20450 \begin_layout Standard
20451 \begin_inset space \hfill{}
20455 \begin_inset Tabular
20456 <lyxtabular version="3" rows="10" columns="2">
20458 <column alignment="center" valignment="top" width="0pt">
20459 <column alignment="center" valignment="top" width="0pt">
20461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20464 \begin_layout Plain Layout
20470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20473 \begin_layout Plain Layout
20481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20484 \begin_layout Plain Layout
20492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20495 \begin_layout Plain Layout
20496 \begin_inset Formula $\neg$
20506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20520 \begin_layout Plain Layout
20521 \begin_inset Formula $\Im$
20531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20534 \begin_layout Plain Layout
20542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20545 \begin_layout Plain Layout
20546 \begin_inset Formula $\Re$
20556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\aleph$
20581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\partial$
20606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20609 \begin_layout Plain Layout
20617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20620 \begin_layout Plain Layout
20621 \begin_inset Formula $\infty$
20631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20646 \begin_inset Formula $\wp$
20656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20670 \begin_layout Plain Layout
20671 \begin_inset Formula $\imath$
20681 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20684 \begin_layout Plain Layout
20692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20695 \begin_layout Plain Layout
20696 \begin_inset Formula $\jmath$
20710 \begin_inset space \hfill{}
20714 \begin_inset Tabular
20715 <lyxtabular version="3" rows="10" columns="2">
20717 <column alignment="center" valignment="top" width="0pt">
20718 <column alignment="center" valignment="top" width="0pt">
20720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20723 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20734 \begin_inset Note Note
20737 \begin_layout Plain Layout
20744 is only used as spacer.
20756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20770 \begin_layout Plain Layout
20771 \begin_inset Formula $\forall$
20781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20784 \begin_layout Plain Layout
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20795 \begin_layout Plain Layout
20796 \begin_inset Formula $\exists$
20806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20809 \begin_layout Plain Layout
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20820 \begin_layout Plain Layout
20821 \begin_inset Formula $\nexists$
20831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20834 \begin_layout Plain Layout
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20845 \begin_layout Plain Layout
20846 \begin_inset Formula $\emptyset$
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20859 \begin_layout Plain Layout
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20870 \begin_layout Plain Layout
20871 \begin_inset Formula $\varnothing$
20881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20884 \begin_layout Plain Layout
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20895 \begin_layout Plain Layout
20896 \begin_inset Formula $\dag$
20906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20909 \begin_layout Plain Layout
20917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20920 \begin_layout Plain Layout
20921 \begin_inset Formula $\ddag$
20931 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20934 \begin_layout Plain Layout
20942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20945 \begin_layout Plain Layout
20949 \begin_layout Plain Layout
20959 \begin_inset Formula $\complement$
20966 \begin_layout Plain Layout
20980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20983 \begin_layout Plain Layout
20991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20994 \begin_layout Plain Layout
20995 \begin_inset Formula $\Bbbk$
21009 \begin_inset space \hfill{}
21013 \begin_inset Tabular
21014 <lyxtabular version="3" rows="10" columns="2">
21016 <column alignment="center" valignment="top" width="0pt">
21017 <column alignment="center" valignment="top" width="0pt">
21019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21022 \begin_layout Plain Layout
21028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21031 \begin_layout Plain Layout
21039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21042 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21053 \begin_layout Plain Layout
21054 \begin_inset Formula $\prime$
21064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21067 \begin_layout Plain Layout
21075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21078 \begin_layout Plain Layout
21079 \begin_inset Formula $\backprime$
21089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21092 \begin_layout Plain Layout
21100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21103 \begin_layout Plain Layout
21104 \begin_inset Formula $\mho$
21114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21117 \begin_layout Plain Layout
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21128 \begin_layout Plain Layout
21129 \begin_inset Formula $\triangle$
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21142 \begin_layout Plain Layout
21150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21153 \begin_layout Plain Layout
21154 \begin_inset Formula $\angle$
21164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21167 \begin_layout Plain Layout
21175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21178 \begin_layout Plain Layout
21179 \begin_inset Formula $\measuredangle$
21189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21192 \begin_layout Plain Layout
21200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21203 \begin_layout Plain Layout
21204 \begin_inset Formula $\sphericalangle$
21214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21217 \begin_layout Plain Layout
21225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21228 \begin_layout Plain Layout
21229 \begin_inset Formula $\top$
21239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21242 \begin_layout Plain Layout
21250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21253 \begin_layout Plain Layout
21254 \begin_inset Formula $\bot$
21268 \begin_inset space \hfill{}
21274 \begin_layout Standard
21275 \begin_inset Newpage newpage
21281 \begin_layout Subsection
21282 Miscellaneous Symbols
21283 \begin_inset CommandInset label
21285 name "sub:Miscellaneous-Symbols"
21293 \begin_layout Plain Layout
21294 Symbols ! miscellaneous
21302 \begin_layout Standard
21305 \begin_inset Tabular
21306 <lyxtabular version="3" rows="10" columns="2">
21308 <column alignment="center" valignment="top" width="0pt">
21309 <column alignment="center" valignment="top" width="0pt">
21311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21314 \begin_layout Plain Layout
21320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21334 \begin_layout Plain Layout
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21345 \begin_layout Plain Layout
21346 \begin_inset Formula $\flat$
21356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21359 \begin_layout Plain Layout
21367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21370 \begin_layout Plain Layout
21371 \begin_inset Formula $\natural$
21381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21384 \begin_layout Plain Layout
21392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21395 \begin_layout Plain Layout
21396 \begin_inset Formula $\sharp$
21406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21409 \begin_layout Plain Layout
21417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21420 \begin_layout Plain Layout
21421 \begin_inset Formula $\surd$
21431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21434 \begin_layout Plain Layout
21442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21445 \begin_layout Plain Layout
21446 \begin_inset Formula $\checkmark$
21456 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21459 \begin_layout Plain Layout
21467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21470 \begin_layout Plain Layout
21471 \begin_inset Formula $\yen$
21481 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21484 \begin_layout Plain Layout
21492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21495 \begin_layout Plain Layout
21496 \begin_inset Formula $\pounds$
21506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21509 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21519 \begin_inset Formula $\$$
21529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21541 \begin_layout Plain Layout
21542 \begin_inset Formula $§$
21556 \begin_inset Tabular
21557 <lyxtabular version="3" rows="10" columns="2">
21559 <column alignment="center" valignment="top" width="0">
21560 <column alignment="center" valignment="top" width="0">
21562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21565 \begin_layout Plain Layout
21571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21574 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21585 \begin_layout Plain Layout
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21596 \begin_layout Plain Layout
21597 \begin_inset Formula $\hbar$
21607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21610 \begin_layout Plain Layout
21618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21621 \begin_layout Plain Layout
21622 \begin_inset Formula $\hslash$
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21635 \begin_layout Plain Layout
21643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21646 \begin_layout Plain Layout
21647 \begin_inset Formula $\clubsuit$
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21660 \begin_layout Plain Layout
21668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21671 \begin_layout Plain Layout
21672 \begin_inset Formula $\spadesuit$
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21685 \begin_layout Plain Layout
21693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21696 \begin_layout Plain Layout
21697 \begin_inset Formula $\bigstar$
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21710 \begin_layout Plain Layout
21718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21721 \begin_layout Plain Layout
21722 \begin_inset Formula $\blacklozenge$
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21746 \begin_layout Plain Layout
21747 \begin_inset Formula $\blacktriangle$
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21771 \begin_layout Plain Layout
21772 \begin_inset Formula $\blacktriangledown$
21782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21785 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\bullet$
21811 \begin_inset Tabular
21812 <lyxtabular version="3" rows="10" columns="2">
21814 <column alignment="center" valignment="top" width="0pt">
21815 <column alignment="center" valignment="top" width="0pt">
21817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21820 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21829 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Plain Layout
21852 \begin_inset Formula $\diamondsuit$
21862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21865 \begin_layout Plain Layout
21873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21876 \begin_layout Plain Layout
21877 \begin_inset Formula $\Diamond$
21887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21890 \begin_layout Plain Layout
21898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21901 \begin_layout Plain Layout
21902 \begin_inset Formula $\heartsuit$
21912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21915 \begin_layout Plain Layout
21923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21926 \begin_layout Plain Layout
21927 \begin_inset Formula $\P$
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21940 \begin_layout Plain Layout
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21951 \begin_layout Plain Layout
21952 \begin_inset Formula $\copyright$
21962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21965 \begin_layout Plain Layout
21973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21976 \begin_layout Plain Layout
21977 \begin_inset Formula $\circledR$
21987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21990 \begin_layout Plain Layout
21998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22001 \begin_layout Plain Layout
22002 \begin_inset Formula $\maltese$
22012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22015 \begin_layout Plain Layout
22023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22026 \begin_layout Plain Layout
22027 \begin_inset Formula $\diagup$
22037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22040 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22051 \begin_layout Plain Layout
22052 \begin_inset Formula $\diagdown$
22068 \begin_layout Standard
22069 \begin_inset VSpace medskip
22072 More symbols are listed in
22073 \begin_inset CommandInset ref
22075 reference "sub:Miscellaneous-Special-Characters"
22082 \begin_layout Standard
22083 Some symbols can be displayed in different sizes, see
22084 \begin_inset CommandInset ref
22086 reference "sub:Font-Sizes"
22093 \begin_layout Subsection
22098 \begin_layout Plain Layout
22099 Symbols ! Euro-symbol
22108 \begin_layout Plain Layout
22112 \begin_layout Plain Layout
22129 \begin_layout Standard
22130 To use the Euro symbol in formulas, the LaTeX-package
22138 \begin_layout Plain Layout
22144 must be installed and loaded with the LaTeX-preamble line
22147 \begin_layout Standard
22152 usepackage[gennarrow]{eurosym}
22155 \begin_layout Standard
22156 The Euro symbol can now be inserted with the command
22166 \begin_layout Plain Layout
22177 \begin_layout Standard
22178 The Euro symbol can directly be inserted with the € key in mathematical
22179 text, without having
22194 can also be inserted in TeX-mode.
22195 The official currency symbol can then be inserted with the command
22205 \begin_layout Plain Layout
22213 , that is only available in TeX-mode.
22216 \begin_layout Standard
22220 \begin_layout Plain Layout
22230 \begin_inset Note Note
22233 \begin_layout Plain Layout
22234 The following table will only be displayed when the LaTeX-package
22246 \begin_layout Standard
22247 An overview about the different Euro symbols:
22250 \begin_layout Standard
22252 \begin_inset Tabular
22253 <lyxtabular version="3" rows="4" columns="3">
22255 <column alignment="center" valignment="top" width="0pt">
22256 <column alignment="center" valignment="top" width="0pt">
22257 <column alignment="center" valignment="top" width="0pt">
22259 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22262 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22291 \begin_layout Plain Layout
22297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22300 \begin_layout Plain Layout
22308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22311 \begin_layout Plain Layout
22312 \begin_inset Formula $\euro$
22322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22325 \begin_layout Plain Layout
22331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22344 \begin_inset Formula $\mbox{€}$
22354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22357 \begin_layout Plain Layout
22363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22366 \begin_layout Plain Layout
22374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22377 \begin_layout Plain Layout
22381 \begin_layout Plain Layout
22403 \begin_layout Standard
22407 \begin_layout Plain Layout
22417 \begin_inset Note Note
22420 \begin_layout Plain Layout
22421 The following will be displayed when the LaTeX-package
22433 \begin_layout Standard
22434 You need to install the LaTeX-package
22438 to see the rest of this subsection in the output.
22441 \begin_layout Standard
22445 \begin_layout Plain Layout
22457 \begin_layout Section
22459 \begin_inset CommandInset label
22461 name "sec:Relations"
22469 \begin_layout Plain Layout
22479 \begin_layout Plain Layout
22484 \begin_layout Plain Layout
22495 \begin_layout Plain Layout
22510 \begin_layout Standard
22511 All relations can also be inserted via the toolbar button
22512 \begin_inset Graphics
22513 filename ../images/math/leq.png
22521 \begin_layout Standard
22522 \begin_inset space \hfill{}
22526 \begin_inset Tabular
22527 <lyxtabular version="3" rows="17" columns="2">
22529 <column alignment="center" valignment="top" width="0pt">
22530 <column alignment="center" valignment="top" width="0pt">
22532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22544 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22555 \begin_layout Plain Layout
22561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22564 \begin_layout Plain Layout
22565 \begin_inset Formula $<$
22575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22578 \begin_layout Plain Layout
22586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22589 \begin_layout Plain Layout
22590 \begin_inset Formula $\le$
22600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22603 \begin_layout Plain Layout
22611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22614 \begin_layout Plain Layout
22615 \begin_inset Formula $\ll$
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22628 \begin_layout Plain Layout
22636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22639 \begin_layout Plain Layout
22640 \begin_inset Formula $\prec$
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22653 \begin_layout Plain Layout
22661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22664 \begin_layout Plain Layout
22665 \begin_inset Formula $\preceq$
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22678 \begin_layout Plain Layout
22686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22689 \begin_layout Plain Layout
22690 \begin_inset Formula $\subset$
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22703 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22715 \begin_inset Formula $\subseteq$
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22728 \begin_layout Plain Layout
22736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22739 \begin_layout Plain Layout
22740 \begin_inset Formula $\sqsubseteq$
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22753 \begin_layout Plain Layout
22761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22764 \begin_layout Plain Layout
22765 \begin_inset Formula $\in$
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22778 \begin_layout Plain Layout
22786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22789 \begin_layout Plain Layout
22790 \begin_inset Formula $\vdash$
22800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22803 \begin_layout Plain Layout
22811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22814 \begin_layout Plain Layout
22815 \begin_inset Formula $\smile$
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22828 \begin_layout Plain Layout
22836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22839 \begin_layout Plain Layout
22840 \begin_inset Formula $\lhd$
22850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22853 \begin_layout Plain Layout
22861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22864 \begin_layout Plain Layout
22865 \begin_inset Formula $\unlhd$
22875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22878 \begin_layout Plain Layout
22886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22889 \begin_layout Plain Layout
22890 \begin_inset Formula $\gtrless$
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22903 \begin_layout Plain Layout
22911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22914 \begin_layout Plain Layout
22915 \begin_inset Formula $\mid$
22925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22928 \begin_layout Plain Layout
22936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22939 \begin_layout Plain Layout
22940 \begin_inset Formula $\nmid$
22954 \begin_inset space \hfill{}
22958 \begin_inset Tabular
22959 <lyxtabular version="3" rows="17" columns="2">
22961 <column alignment="center" valignment="top" width="0pt">
22962 <column alignment="center" valignment="top" width="0pt">
22964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22967 \begin_layout Plain Layout
22973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22976 \begin_layout Plain Layout
22984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22987 \begin_layout Plain Layout
22993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22996 \begin_layout Plain Layout
22997 \begin_inset Formula $=$
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23010 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23021 \begin_layout Plain Layout
23022 \begin_inset Formula $\not=$
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\equiv$
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23072 \begin_inset Formula $\sim$
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23096 \begin_layout Plain Layout
23097 \begin_inset Formula $\simeq$
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23110 \begin_layout Plain Layout
23118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23121 \begin_layout Plain Layout
23122 \begin_inset Formula $\approx$
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23135 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23147 \begin_inset Formula $\cong$
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23172 \begin_inset Formula $\bowtie$
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23185 \begin_layout Plain Layout
23193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23196 \begin_layout Plain Layout
23197 \begin_inset Formula $\notin$
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23210 \begin_layout Plain Layout
23218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23221 \begin_layout Plain Layout
23222 \begin_inset Formula $\perp$
23232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23235 \begin_layout Plain Layout
23243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23246 \begin_layout Plain Layout
23247 \begin_inset Formula $\propto$
23257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23260 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23271 \begin_layout Plain Layout
23272 \begin_inset Formula $\asymp$
23282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23285 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23297 \begin_inset Formula $\doteq$
23307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23310 \begin_layout Plain Layout
23318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23321 \begin_layout Plain Layout
23322 \begin_inset Formula $\circeq$
23332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23335 \begin_layout Plain Layout
23343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23346 \begin_layout Plain Layout
23347 \begin_inset Formula $\models$
23357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23360 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23371 \begin_layout Plain Layout
23372 \begin_inset Formula $\widehat{=}$
23386 \begin_inset space \hfill{}
23390 \begin_inset Tabular
23391 <lyxtabular version="3" rows="17" columns="2">
23393 <column alignment="center" valignment="top" width="0pt">
23394 <column alignment="center" valignment="top" width="0pt">
23396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23399 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23419 \begin_layout Plain Layout
23425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23428 \begin_layout Plain Layout
23429 \begin_inset Formula $>$
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23442 \begin_layout Plain Layout
23450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23453 \begin_layout Plain Layout
23454 \begin_inset Formula $\ge$
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23467 \begin_layout Plain Layout
23475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23478 \begin_layout Plain Layout
23479 \begin_inset Formula $\gg$
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23492 \begin_layout Plain Layout
23500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23503 \begin_layout Plain Layout
23504 \begin_inset Formula $\succ$
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23517 \begin_layout Plain Layout
23525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23528 \begin_layout Plain Layout
23529 \begin_inset Formula $\succeq$
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23542 \begin_layout Plain Layout
23550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23553 \begin_layout Plain Layout
23554 \begin_inset Formula $\supset$
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23567 \begin_layout Plain Layout
23575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23578 \begin_layout Plain Layout
23579 \begin_inset Formula $\supseteq$
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23592 \begin_layout Plain Layout
23600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23603 \begin_layout Plain Layout
23604 \begin_inset Formula $\sqsupseteq$
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23617 \begin_layout Plain Layout
23625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23628 \begin_layout Plain Layout
23629 \begin_inset Formula $\ni$
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23642 \begin_layout Plain Layout
23650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23653 \begin_layout Plain Layout
23654 \begin_inset Formula $\dashv$
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23667 \begin_layout Plain Layout
23675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23678 \begin_layout Plain Layout
23679 \begin_inset Formula $\frown$
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23692 \begin_layout Plain Layout
23700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23703 \begin_layout Plain Layout
23704 \begin_inset Formula $\rhd$
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23717 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23729 \begin_inset Formula $\unrhd$
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23753 \begin_layout Plain Layout
23754 \begin_inset Formula $\lessgtr$
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23767 \begin_layout Plain Layout
23775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23778 \begin_layout Plain Layout
23779 \begin_inset Formula $\parallel$
23789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23792 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23803 \begin_layout Plain Layout
23804 \begin_inset Formula $\nparallel$
23818 \begin_inset space \hfill{}
23824 \begin_layout Standard
23825 \begin_inset VSpace medskip
23840 are bigger than the equal looking operators
23855 \begin_layout Standard
23856 Relations are, in contrary to symbols, always surrounded by space.
23859 \begin_layout Standard
23860 Relations with labels can be created with the command
23870 \begin_layout Plain Layout
23881 \begin_layout Standard
23883 \begin_inset Tabular
23884 <lyxtabular version="3" rows="2" columns="2">
23886 <column alignment="center" valignment="top" width="0">
23887 <column alignment="center" valignment="top" width="0">
23889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23901 \begin_layout Plain Layout
23903 \begin_inset Note Note
23906 \begin_layout Plain Layout
23913 is only used as spacer.
23925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23928 \begin_layout Plain Layout
23935 \begin_layout Plain Layout
23952 \begin_layout Plain Layout
23962 \begin_inset Formula $\downarrow$
23971 \begin_layout Plain Layout
23984 \begin_layout Plain Layout
23998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24001 \begin_layout Plain Layout
24002 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24018 \begin_layout Section
24022 \begin_layout Subsection
24023 Predefined Functions
24024 \begin_inset CommandInset label
24026 name "sub:Predefined-Functions"
24034 \begin_layout Plain Layout
24035 Functions ! predefined
24043 \begin_layout Standard
24044 In general, variables are set
24048 in mathematical expressions, but not function names, because
24049 \begin_inset Formula $sin$
24052 could be misunderstood as
24053 \begin_inset Formula $s\cdot i\cdot n$
24057 Therefore there are predefined functions, that are additionally a bit separated
24059 They are inserted as commands starting with a backslash before their name.
24062 \begin_layout Standard
24064 \begin_inset Tabular
24065 <lyxtabular version="3" rows="2" columns="4">
24067 <column alignment="center" valignment="top" width="0pt">
24068 <column alignment="center" valignment="top" width="0pt">
24069 <column alignment="center" valignment="top" width="0pt">
24070 <column alignment="center" valignment="top" width="0pt">
24072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24102 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24122 \begin_layout Plain Layout
24123 \begin_inset Formula $Asin(x)+B$
24131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24134 \begin_layout Plain Layout
24142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24145 \begin_layout Plain Layout
24146 \begin_inset Formula $A\sin(x)+B$
24160 \begin_inset Newpage pagebreak
24166 \begin_layout Standard
24167 The following functions are predefined:
24170 \begin_layout Standard
24171 \begin_inset VSpace -2mm
24177 \begin_layout Standard
24179 \begin_inset Tabular
24180 <lyxtabular version="3" rows="9" columns="4">
24182 <column alignment="center" valignment="top" width="0pt">
24183 <column alignment="center" valignment="top" width="0pt">
24184 <column alignment="center" valignment="top" width="0pt">
24185 <column alignment="center" valignment="top" width="0pt">
24187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24190 \begin_layout Plain Layout
24196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24199 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24228 \begin_layout Plain Layout
24236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24239 \begin_layout Plain Layout
24247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24250 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24261 \begin_layout Plain Layout
24271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24274 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24285 \begin_layout Plain Layout
24293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24296 \begin_layout Plain Layout
24304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24307 \begin_layout Plain Layout
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24320 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24331 \begin_layout Plain Layout
24339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24342 \begin_layout Plain Layout
24350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24353 \begin_layout Plain Layout
24363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24366 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24388 \begin_layout Plain Layout
24396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24399 \begin_layout Plain Layout
24409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24412 \begin_layout Plain Layout
24420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24434 \begin_layout Plain Layout
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24445 \begin_layout Plain Layout
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24480 \begin_layout Plain Layout
24488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24491 \begin_layout Plain Layout
24501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24515 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24537 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24583 \begin_layout Plain Layout
24599 \begin_layout Standard
24600 They can also be inserted with the math toolbar button
24601 \begin_inset Graphics
24602 filename ../images/math/functions.png
24610 \begin_layout Subsection
24611 Self-defined Functions
24615 \begin_layout Plain Layout
24616 Functions ! self-defined
24624 \begin_layout Standard
24625 To use a function that is not predefined, like for example the sign function
24626 sgn(x), there are two possibilities:
24629 \begin_layout Itemize
24630 Define the function by inserting the following line to the LaTeX-preamble
24634 \begin_layout Plain Layout
24639 DeclareMathOperator
24642 \begin_inset CommandInset ref
24644 reference "sub:Self-defined-Operators"
24654 \begin_inset Newline newline
24658 \begin_inset VSpace -3mm
24662 \begin_inset Newline newline
24669 DeclareMathOperator{
24677 \begin_layout Plain Layout
24682 DeclareMathOperator
24688 \begin_inset Newline newline
24692 \begin_inset VSpace -2mm
24696 \begin_inset Newline newline
24699 Now the new defined function can be called with the command
24708 \begin_layout Itemize
24709 Write the the formula as usual, mark the formula name, in our example the
24714 , and change it to mathematical text.
24715 At last a space is inserted between prefactor and function.
24718 \begin_layout Standard
24719 The result is the same with both methods as with a predefined function
24723 \begin_layout Plain Layout
24724 In LyX self-defined functions are displayed red, predefined ones black.
24732 \begin_layout Standard
24734 \begin_inset Tabular
24735 <lyxtabular version="3" rows="3" columns="2">
24737 <column alignment="center" valignment="top" width="0pt">
24738 <column alignment="center" valignment="top" width="0pt">
24740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24743 \begin_layout Plain Layout
24749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24752 \begin_layout Plain Layout
24760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24763 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24774 \begin_layout Plain Layout
24775 \begin_inset Formula $A\sgn(x)+B$
24785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24788 \begin_layout Plain Layout
24792 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24803 \begin_layout Plain Layout
24804 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24820 \begin_layout Standard
24821 The first method is more suitable when the self-defined function should
24822 be used several times.
24825 \begin_layout Subsection
24830 \begin_layout Plain Layout
24839 \begin_layout Standard
24840 For limits there are defined besides
24850 \begin_layout Plain Layout
24870 furthermore the following functions:
24873 \begin_layout Standard
24875 \begin_inset Tabular
24876 <lyxtabular version="3" rows="5" columns="2">
24878 <column alignment="center" valignment="top" width="0">
24879 <column alignment="center" valignment="top" width="0">
24881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24884 \begin_layout Plain Layout
24890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24893 \begin_layout Plain Layout
24895 \begin_inset Note Note
24898 \begin_layout Plain Layout
24905 is only used as spacer.
24917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24920 \begin_layout Plain Layout
24928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24931 \begin_layout Plain Layout
24932 \begin_inset Formula $\varliminf$
24942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24956 \begin_layout Plain Layout
24957 \begin_inset Formula $\varlimsup$
24967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24970 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24981 \begin_layout Plain Layout
24982 \begin_inset Formula $\varprojlim$
24992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25006 \begin_layout Plain Layout
25007 \begin_inset Formula $\varinjlim$
25011 \begin_inset Formula $\raisebox{-2.5mm}{}$
25027 \begin_layout Standard
25028 \begin_inset VSpace medskip
25031 The limit is created by inserting a subscript.
25032 It is set right beside the function in an inline formula:
25035 \begin_layout Standard
25037 \begin_inset Tabular
25038 <lyxtabular version="3" rows="2" columns="2">
25040 <column alignment="center" valignment="top" width="0pt">
25041 <column alignment="center" valignment="top" width="0pt">
25043 <cell alignment="center" valignment="top" usebox="none">
25046 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" usebox="none">
25055 \begin_layout Plain Layout
25056 \begin_inset space \hspace{}
25061 \begin_inset Note Note
25064 \begin_layout Plain Layout
25077 are used here as spacer.
25089 <cell alignment="center" valignment="top" usebox="none">
25092 \begin_layout Plain Layout
25101 \begin_layout Plain Layout
25114 \begin_layout Plain Layout
25128 <cell alignment="center" valignment="top" usebox="none">
25131 \begin_layout Plain Layout
25132 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25148 \begin_layout Standard
25149 In a displayed formula the limit is set below the formula, as usual:
25150 \begin_inset Formula \[
25158 \begin_layout Subsection
25163 \begin_layout Plain Layout
25164 Functions ! modulo-
25172 \begin_layout Standard
25173 The modulo-function is special, because it exists in four variants.
25176 \begin_layout Standard
25177 The variants in a displayed formula:
25178 \begin_inset Formula \begin{align*}
25179 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25180 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25181 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25182 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25183 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25190 \begin_layout Standard
25191 In an inline formula less space is set before the function names for all
25195 \begin_layout Section
25200 \begin_layout Plain Layout
25209 \begin_layout Subsection
25210 Special Characters in Mathematical Text
25213 \begin_layout Standard
25214 The following commands can only be used in mathematical text or in TeX-mode:
25217 \begin_layout Standard
25218 \begin_inset space \hfill{}
25222 \begin_inset Tabular
25223 <lyxtabular version="3" rows="8" columns="2">
25225 <column alignment="block" valignment="top" width="0">
25226 <column alignment="block" valignment="top" width="0">
25228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25231 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25251 \begin_layout Plain Layout
25259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25262 \begin_layout Plain Layout
25263 \begin_inset Formula $\textrm{œ}$
25273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25276 \begin_layout Plain Layout
25284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25287 \begin_layout Plain Layout
25288 \begin_inset Formula $\textrm{Œ}$
25298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25301 \begin_layout Plain Layout
25309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25312 \begin_layout Plain Layout
25313 \begin_inset Formula $\textrm{æ}$
25323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25326 \begin_layout Plain Layout
25334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25337 \begin_layout Plain Layout
25338 \begin_inset Formula $\textrm{Æ}$
25348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25351 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25362 \begin_layout Plain Layout
25363 \begin_inset Formula $\textrm{\aa}$
25373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25376 \begin_layout Plain Layout
25383 \begin_layout Plain Layout
25387 \begin_layout Plain Layout
25410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25413 \begin_layout Plain Layout
25414 \begin_inset Formula $\textrm{Å}$
25424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25427 \begin_layout Plain Layout
25435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25438 \begin_layout Plain Layout
25439 \begin_inset Formula $\textrm{ı}$
25453 \begin_inset space \hfill{}
25457 \begin_inset Tabular
25458 <lyxtabular version="3" rows="8" columns="2">
25460 <column alignment="block" valignment="top" width="0">
25461 <column alignment="center" valignment="top" width="0">
25463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25466 \begin_layout Plain Layout
25468 \begin_inset Note Note
25471 \begin_layout Plain Layout
25478 is used for separation, because otherwise the output will be ¡ and ¿ respective
25489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25492 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25503 \begin_layout Plain Layout
25511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25514 \begin_layout Plain Layout
25515 \begin_inset Formula $\textrm{ø}$
25525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25528 \begin_layout Plain Layout
25536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25539 \begin_layout Plain Layout
25540 \begin_inset Formula $\textrm{Ø}$
25550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25553 \begin_layout Plain Layout
25561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25564 \begin_layout Plain Layout
25565 \begin_inset Formula $\textrm{ł}$
25575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25578 \begin_layout Plain Layout
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25589 \begin_layout Plain Layout
25590 \begin_inset Formula $\textrm{Ł}$
25600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25603 \begin_layout Plain Layout
25605 \begin_inset space \hspace{}
25613 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25630 \begin_layout Plain Layout
25631 \begin_inset Formula $\textrm{!`}$
25641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25644 \begin_layout Plain Layout
25646 \begin_inset space \hspace{}
25654 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25671 \begin_layout Plain Layout
25672 \begin_inset Formula $\textrm{?`}$
25682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25685 \begin_layout Plain Layout
25693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25696 \begin_layout Plain Layout
25697 \begin_inset Formula $\textrm{ȷ}$
25711 \begin_inset space \hfill{}
25717 \begin_layout Standard
25719 \begin_inset Formula $\textrm{\textrm{Å}}$
25723 \begin_inset Formula $\textrm{\textrm{Ø}}$
25726 can also be inserted via the math toolbar button
25727 \begin_inset Graphics
25728 filename ../images/math/digamma.png
25736 \begin_layout Standard
25737 An exception are the commands
25740 \begin_inset space \hspace{}
25749 \begin_inset space \hspace{}
25755 , because they can be inserted in LyX directly to text.
25758 \begin_layout Subsection
25760 \begin_inset CommandInset label
25762 name "sub:Accents-in-Text"
25770 \begin_layout Plain Layout
25779 \begin_layout Standard
25780 With the following commands all letters can be accented.
25781 The commands must be inserted in TeX-mode.
25784 \begin_layout Standard
25785 \begin_inset space \hfill{}
25789 \begin_inset Tabular
25790 <lyxtabular version="3" rows="8" columns="2">
25792 <column alignment="block" valignment="top" width="0">
25793 <column alignment="block" valignment="top" width="0">
25795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25818 \begin_layout Plain Layout
25822 \begin_inset Quotes grd
25830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25833 \begin_layout Plain Layout
25837 \begin_layout Plain Layout
25853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25856 \begin_layout Plain Layout
25864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25867 \begin_layout Plain Layout
25871 \begin_layout Plain Layout
25887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25890 \begin_layout Plain Layout
25897 \begin_layout Plain Layout
25911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25914 \begin_layout Plain Layout
25918 \begin_layout Plain Layout
25934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25937 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25952 \begin_layout Plain Layout
25968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25971 \begin_layout Plain Layout
25978 \begin_layout Plain Layout
25992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25995 \begin_layout Plain Layout
25999 \begin_layout Plain Layout
26015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26018 \begin_layout Plain Layout
26025 \begin_layout Plain Layout
26039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26042 \begin_layout Plain Layout
26046 \begin_layout Plain Layout
26062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26065 \begin_layout Plain Layout
26072 \begin_layout Plain Layout
26086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26089 \begin_layout Plain Layout
26093 \begin_layout Plain Layout
26113 \begin_inset space \hfill{}
26117 \begin_inset Tabular
26118 <lyxtabular version="3" rows="8" columns="2">
26120 <column alignment="block" valignment="top" width="0">
26121 <column alignment="center" valignment="top" width="0">
26123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26135 \begin_layout Plain Layout
26143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26146 \begin_layout Plain Layout
26153 \begin_layout Plain Layout
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26170 \begin_layout Plain Layout
26174 \begin_layout Plain Layout
26190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26193 \begin_layout Plain Layout
26201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26204 \begin_layout Plain Layout
26208 \begin_layout Plain Layout
26224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26227 \begin_layout Plain Layout
26234 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26248 \begin_layout Plain Layout
26252 \begin_layout Plain Layout
26268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26271 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26282 \begin_layout Plain Layout
26286 \begin_layout Plain Layout
26302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26305 \begin_layout Plain Layout
26312 \begin_layout Plain Layout
26326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26329 \begin_layout Plain Layout
26333 \begin_layout Plain Layout
26349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26359 \begin_layout Plain Layout
26373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26376 \begin_layout Plain Layout
26380 \begin_layout Plain Layout
26396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26399 \begin_layout Plain Layout
26406 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26423 \begin_layout Plain Layout
26427 \begin_layout Plain Layout
26447 \begin_inset space \hfill{}
26453 \begin_layout Standard
26454 \begin_inset VSpace medskip
26463 also two different characters can be accented.
26472 \begin_layout Plain Layout
26487 \begin_layout Plain Layout
26499 \begin_layout Standard
26512 can in combination with vowels directly be inserted with the keyboard without
26514 The same applies for the tilde
26518 \begin_layout Plain Layout
26519 This only applies for keyboards where the tilde is defined as accent.
26528 in combination with
26543 \begin_layout Standard
26586 , and accents inserted directly with the keyboard are also available in
26588 For the other accents there are special math commands to be used in formulas,
26590 \begin_inset CommandInset ref
26592 reference "sub:Accents-for-one"
26599 \begin_layout Standard
26600 \begin_inset VSpace bigskip
26603 Furthermore, with the command
26613 \begin_layout Plain Layout
26621 all numbers and letters can be set into a circle, quasi accented with a
26622 circle, similar to the the copyright symbol.
26625 \begin_layout Standard
26627 \begin_inset Tabular
26628 <lyxtabular version="3" rows="3" columns="2">
26630 <column alignment="center" valignment="top" width="0">
26631 <column alignment="center" valignment="top" width="0">
26633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26636 \begin_layout Plain Layout
26642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26645 \begin_layout Plain Layout
26647 \begin_inset Note Note
26650 \begin_layout Plain Layout
26657 is only used as spacer.
26669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26672 \begin_layout Plain Layout
26680 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26683 \begin_layout Plain Layout
26687 \begin_layout Plain Layout
26703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26706 \begin_layout Plain Layout
26717 raisebox{-1.5pt}{W}}
26722 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26725 \begin_layout Plain Layout
26726 \begin_inset Formula $\raisebox{4.5mm}{}$
26733 \begin_layout Plain Layout
26751 \begin_inset Formula $\raisebox{-2mm}{}$
26767 \begin_layout Standard
26768 One has to take care that the character fits in the circle.
26779 \begin_layout Plain Layout
26781 \begin_inset CommandInset ref
26783 reference "sub:Font-Sizes"
26792 specifies thereby the size of the circle.
26803 \begin_layout Plain Layout
26805 \begin_inset CommandInset ref
26807 reference "sub:Boxes-without-Frame"
26816 the character can be centered.
26819 \begin_layout Subsection
26824 \begin_layout Plain Layout
26833 \begin_layout Standard
26834 Minuscule numbers are created with the command
26844 \begin_layout Plain Layout
26853 The command can be used in formulas and in TeX-mode.
26854 The command scheme is:
26857 \begin_layout Standard
26862 oldstylenums{number}
26865 \begin_layout Standard
26870 oldstylenums{0123456789
26873 \begin_inset Formula $\oldstylenums{0123456789}$
26879 \begin_layout Subsection
26880 Miscellaneous Special Characters
26881 \begin_inset CommandInset label
26883 name "sub:Miscellaneous-Special-Characters"
26891 \begin_layout Plain Layout
26892 Special characters ! miscellaneous
26900 \begin_layout Standard
26901 The following characters can only be inserted to formulas by using commands:
26904 \begin_layout Standard
26906 \begin_inset Tabular
26907 <lyxtabular version="3" rows="4" columns="2">
26909 <column alignment="center" valignment="top" width="0">
26910 <column alignment="center" valignment="top" width="0">
26912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26915 \begin_layout Plain Layout
26921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26924 \begin_layout Plain Layout
26932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26935 \begin_layout Plain Layout
26942 \begin_layout Plain Layout
26956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26959 \begin_layout Plain Layout
26960 \begin_inset Formula $\mathcircumflex$
26970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26973 \begin_layout Plain Layout
26981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26984 \begin_layout Plain Layout
26985 \begin_inset Formula $\_$
26995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26998 \begin_layout Plain Layout
27003 \begin_layout Plain Layout
27018 \begin_layout Plain Layout
27029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27032 \begin_layout Plain Layout
27033 \begin_inset Formula $^{\circ}$
27049 \begin_layout Standard
27050 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27051 contains the following line
27055 \begin_layout Plain Layout
27056 More about this is described in
27057 \begin_inset CommandInset ref
27059 reference "sub:Text-Characters-in"
27071 \begin_layout Standard
27076 DeclareInputtext{176}{
27089 \begin_layout Section
27091 \begin_inset CommandInset label
27093 name "sec:Formula-Styles"
27101 \begin_layout Plain Layout
27110 \begin_layout Itemize
27111 There are two different alignment styles:
27115 \begin_layout Description
27116 Centered is the predefined standard
27119 \begin_layout Description
27120 Indented for this the option
27124 must be inserted in the menu
27126 Document\SpecialChar \menuseparator
27132 \begin_inset space ~
27138 \begin_layout Standard
27143 is used, the indentation can be adjusted with the length
27153 \begin_layout Plain Layout
27162 Should the distance be 15
27163 \begin_inset space \thinspace{}
27166 mm, the following command line is inserted in the LaTeX-preamble
27169 \begin_layout Standard
27179 \begin_layout Standard
27180 When no length is specified, the predefined value of 30
27181 \begin_inset space \thinspace{}
27188 \begin_layout Itemize
27189 And two different numbering styles:
27193 \begin_layout Description
27194 Right is the predefined standard
27197 \begin_layout Description
27198 Left for this the option
27202 must be inserted in the menu
27204 Document\SpecialChar \menuseparator
27210 \begin_inset space ~
27217 \begin_layout Standard
27226 can also be used together.
27227 In this case both options are inserted, separated by a comma.
27230 \begin_layout Standard
27231 The chosen styles are used for all displayed formulas of the document.
27232 When both, centered and indented formulas should be created in a document,
27238 The indented formulas are then set in a flalign environment, see
27239 \begin_inset CommandInset ref
27241 reference "sub:Flalign-Environment"
27248 \begin_layout Section
27250 \begin_inset CommandInset label
27252 name "sec:Multiline-Formulas"
27260 \begin_layout Plain Layout
27261 Formula ! multiline
27269 \begin_layout Subsection
27273 \begin_layout Standard
27274 In LyX multiline formulas are created by pressing
27281 This creates either an
27283 eqnarray environment
27285 that is described in
27286 \begin_inset CommandInset ref
27288 reference "sub:Eqnarray-Environment"
27292 or, when the option
27294 Use AMS math package
27296 in the document settings is selected, an
27300 that is described in
27301 \begin_inset CommandInset ref
27303 reference "sub:Standard-align-Environment"
27310 \begin_layout Standard
27311 There are other multiline formula environments that can be created via the
27314 Insert\SpecialChar \menuseparator
27318 These environments are described in the following sections.
27321 \begin_layout Standard
27322 In all multiline formula environments a new line is created by pressing
27328 To add or delete lines, the math toolbar buttons
27329 \begin_inset Graphics
27330 filename ../images/tabular-feature_append-row.png
27336 \begin_inset Graphics
27337 filename ../images/tabular-feature_delete-row.png
27342 , respectively, or the menu
27344 Edit\SpecialChar \menuseparator
27350 \begin_layout Subsubsection
27352 \begin_inset CommandInset label
27354 name "sub:Line-Separation"
27362 \begin_layout Plain Layout
27363 Formula ! multiline ! Line separation
27371 \begin_layout Standard
27372 There is sometimes not enough space in multiline formulas between the lines:
27373 \begin_inset Formula \begin{eqnarray*}
27374 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}\\
27375 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*}
27382 \begin_layout Standard
27383 In LaTeX additional line space is specified as optional argument of the
27385 This is not yet possible in LyX
27389 \begin_layout Plain Layout
27391 \begin_inset CommandInset href
27393 name "LyX-bug #1505"
27394 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27403 , therefore the whole formula must be inserted in TeX-mode.
27404 To add in our example space, the command
27412 is inserted at the end of the first line.
27417 \begin_layout Plain Layout
27424 \begin_layout Plain Layout
27426 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27429 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27436 \begin_layout Plain Layout
27440 left(B^{2}+x_{0}^{2}
27448 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27453 \begin_layout Plain Layout
27465 \begin_layout Standard
27466 \begin_inset VSpace bigskip
27469 To set the the line separation for all lines in a formula, the length
27479 \begin_layout Plain Layout
27489 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27500 \begin_inset space \thinspace{}
27505 \begin_inset space \thinspace{}
27508 mm additional line separation as in the previous example, the command
27511 \begin_layout Standard
27521 \begin_layout Standard
27522 is inserted in TeX-mode before the formula.
27523 This requires that the LaTeX-package
27531 \begin_layout Plain Layout
27536 is part of every LaTeX standard installation.
27545 \begin_layout Plain Layout
27551 was loaded in LaTeX-preamble with the line
27554 \begin_layout Standard
27562 \begin_layout Standard
27567 \begin_layout Plain Layout
27579 \begin_inset Formula \begin{eqnarray*}
27580 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}\\
27581 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*}
27588 \begin_layout Standard
27592 \begin_layout Plain Layout
27603 To get back to the predefined distance,
27609 is set to the value 3
27610 \begin_inset space \thinspace{}
27616 \begin_layout Subsubsection
27618 \begin_inset CommandInset label
27620 name "sub:Column-Separation"
27628 \begin_layout Plain Layout
27629 Formula ! multiline ! Column separation
27637 \begin_layout Standard
27638 Multiline formulas form a matrix.
27639 A formula in the eqnarray environment is for example a matrix with three
27641 By changing the column separation in this environment, the space beside
27642 the relation sign can be changed.
27645 \begin_layout Standard
27646 The column separation is specified with the length
27656 \begin_layout Plain Layout
27665 \begin_inset Newline newline
27668 column separation = 2
27669 \begin_inset space \thinspace{}
27679 \begin_inset Newline newline
27685 \begin_layout Standard
27695 \begin_layout Standard
27696 inserted in TeX-mode, sets for all following formulas a column separation
27698 \begin_inset space \thinspace{}
27702 To get back to the predefined distance,
27709 \begin_inset space \thinspace{}
27715 \begin_layout Standard
27717 \begin_inset space \thinspace{}
27720 cm column separation:
27724 \begin_layout Plain Layout
27736 \begin_inset Formula \begin{eqnarray*}
27738 C & \ne & A\end{eqnarray*}
27742 A formula with the predefined column separation for matrices of 10
27743 \begin_inset space \thinspace{}
27750 \begin_layout Plain Layout
27762 \begin_inset Formula \begin{eqnarray*}
27764 C & \ne & A\end{eqnarray*}
27771 \begin_layout Subsubsection
27776 \begin_layout Plain Layout
27785 \begin_layout Standard
27786 Long formulas can be typeset using these methods:
27789 \begin_layout Itemize
27790 When one side of the equation is much shorther than the line width, this
27791 one is chosen for the left side and the right side is typeset over two
27796 \begin_layout Plain Layout
27806 \begin_inset Formula \begin{eqnarray}
27807 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 \\
27808 & & -\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}
27816 \begin_layout Plain Layout
27826 \begin_inset Newline newline
27829 The minus sign at the beginning of the second line does normally not appear
27830 as operator because it is the first character of the line.
27831 Thus it would not be surrounded by space and could not be distinguished
27832 from the fraction bar.
27833 To avoid this, space was inserted behind the minus sign with the command
27844 \begin_layout Plain Layout
27852 \begin_inset CommandInset ref
27854 reference "sub:Variable-Space"
27867 \begin_layout Plain Layout
27878 \begin_layout Itemize
27879 When both sides of the equation are too long, the command
27889 \begin_layout Plain Layout
27898 It is inserted to the first column of the first line and effects that all
27899 further insertions overwrite the following columns:
27903 \begin_layout Plain Layout
27913 \begin_inset Formula \begin{eqnarray}
27914 \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 \\
27915 & & -\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 \\
27916 & & =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}
27924 \begin_layout Plain Layout
27934 \begin_inset Newline newline
27937 After the insertion of
27943 , the cursor is in a purple box that is a bit shifted to the left from the
27945 In this the formula is inserted.
27949 \begin_layout Plain Layout
27959 \begin_inset Newline newline
27962 The content of the further lines is inserted to the second or another formula
27964 The greater the column number where it was inserted, the larger the indentation.
27968 \begin_layout Plain Layout
27978 \begin_inset Newline newline
27982 \begin_inset Note Greyedout
27985 \begin_layout Plain Layout
27986 Note the following when using
27995 \begin_layout Itemize
27996 The formula doesn't use the full page width.
27998 \begin_inset space \thinspace{}
28002 \begin_inset space ~
28006 \begin_inset Formula $-B^{2}$
28009 is added to the first line in the above example, it would have been outside
28011 To better use the width, negative space can be inserted at the beginning
28015 \begin_layout Itemize
28016 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28021 \begin_layout Plain Layout
28022 \begin_inset CommandInset href
28024 name "LyX-bug #1429"
28025 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28034 One can only set the cursor at the beginning of the line and move it with
28043 \begin_layout Itemize
28044 Other methods to set long formulas are offered by the environments described
28046 \begin_inset CommandInset ref
28048 reference "sub:Multline-Environment"
28053 \begin_inset CommandInset ref
28055 reference "sub:Multiline-Formula-Parts"
28062 \begin_layout Subsubsection
28064 \begin_inset CommandInset label
28066 name "sub:Multiline-Brackets"
28074 \begin_layout Plain Layout
28075 Brackets ! for multiline expressions
28083 \begin_layout Standard
28084 For brackets spanning multiple lines the following problem occurs:
28085 \begin_inset Formula \begin{eqnarray*}
28086 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28087 & & \left.\cdots+B-D\right]\end{eqnarray*}
28094 \begin_layout Standard
28095 The closing bracket is smaller than the opening bracket because brackets
28096 with variable size may not span multiple lines.
28099 \begin_layout Standard
28100 To set the bracket size for the second line correctly, the first line is
28111 \begin_layout Plain Layout
28119 and the second line with
28127 \begin_layout Plain Layout
28141 \begin_inset CommandInset ref
28143 reference "sub:Automatic-Bracket-Size"
28158 \begin_layout Plain Layout
28184 \begin_layout Plain Layout
28203 \begin_layout Plain Layout
28222 \begin_layout Plain Layout
28234 \begin_inset Formula $\downarrow$
28243 \begin_layout Plain Layout
28251 is inserted, because the multiplication operator with its limits is the
28252 largest symbol in the first line and this should be the size for the bracket
28253 in the second line.
28256 \begin_layout Standard
28257 The result is this:
28258 \begin_inset Formula \begin{eqnarray*}
28259 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28260 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28267 \begin_layout Subsection
28271 \begin_layout Standard
28272 Align environments can be used for every kind of multiline formulas.
28273 They are specially useful to set several formulas side by side.
28276 \begin_layout Standard
28277 Align environments consist of columns.
28278 The odd columns are right aligned, the even ones left aligned.
28279 Every line in an Align environment can be numbered.
28282 \begin_layout Standard
28283 Align environments are created via the menu
28285 Insert\SpecialChar \menuseparator
28291 Edit\SpecialChar \menuseparator
28292 Math\SpecialChar \menuseparator
28293 Change Formula Type
28295 already existing formulas can be converted to Align environments.
28298 \begin_layout Standard
28299 To add or delete columns, the math toolbar buttons
28300 \begin_inset Graphics
28301 filename ../images/tabular-feature_append-column.png
28307 \begin_inset Graphics
28308 filename ../images/tabular-feature_delete-column.png
28313 , respectively, or the menu
28315 Edit\SpecialChar \menuseparator
28321 \begin_layout Subsubsection
28322 Standard align Environment
28323 \begin_inset CommandInset label
28325 name "sub:Standard-align-Environment"
28333 \begin_layout Plain Layout
28334 Formula ! multiline ! align environment
28342 \begin_layout Standard
28343 This Align environment is created by presssing
28347 in a formula or by the menu
28349 Insert\SpecialChar \menuseparator
28350 Math\SpecialChar \menuseparator
28351 AMS align Environment
28356 \begin_layout Standard
28357 An example for two formulas set side by side, that are created with a four
28358 column align environment:
28359 \begin_inset Formula \begin{align*}
28360 A & =\sin(B) & C & =D\\
28361 C & \ne A & B & \ne D\end{align*}
28365 As it can be seen, the formulas in this environment are placed so as if
28374 \begin_layout Plain Layout
28382 \begin_inset CommandInset ref
28384 reference "sub:Variable-Space"
28395 before the first and after every even column.
28396 When the formula style
28402 \begin_layout Plain Layout
28404 \begin_inset CommandInset ref
28406 reference "sec:Formula-Styles"
28417 is used, the formula is set without the
28423 before the first column.
28426 \begin_layout Subsubsection
28427 Alignat Environment
28431 \begin_layout Plain Layout
28432 Formula ! multiline ! alignat environment
28440 \begin_layout Standard
28441 The alignat environment has no predefined column separation.
28442 It can be inserted manually with the spaces that are described
28443 \begin_inset CommandInset ref
28445 reference "sub:Space"
28452 \begin_layout Standard
28453 The above example in the alignat environment where 1
28454 \begin_inset space \thinspace{}
28457 cm space was inserted at the beginning of the second formula:
28458 \begin_inset Formula \begin{alignat*}{2}
28459 A & =\sin(B) & \hspace{1cm}C & =D\\
28460 C & \ne A & B & \ne D\end{alignat*}
28464 Because the column separation can be set separately for every column, this
28465 environment is especially suitable to set three and more formulas side
28469 \begin_layout Subsubsection
28470 Flalign Environment
28471 \begin_inset CommandInset label
28473 name "sub:Flalign-Environment"
28481 \begin_layout Plain Layout
28482 Formula ! multiline ! flalign environment
28490 \begin_layout Standard
28491 In this environment the first two columns are always set as much as possible
28492 to the left and the last two ones to the right.
28494 \begin_inset Formula \begin{flalign*}
28495 A & =1 & B & =2 & C & =3\\
28496 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28503 \begin_layout Standard
28504 By creating a flalign environment with an odd number of columns where an
28505 empty TeX-brace is inserted to the last column, several formulas in a document
28506 can be set to the left, although the formula style
28511 As example the indented formula
28512 \begin_inset CommandInset ref
28514 reference "eq:VolInt"
28519 \begin_inset Formula \begin{flalign}
28520 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28524 The first two columns contain the formula.
28525 To indent it as with the formula style
28530 \begin_inset space \thinspace{}
28533 pt space was inserted at the beginning of the first column.
28536 \begin_layout Subsection
28537 Eqnarray Environment
28538 \begin_inset CommandInset label
28540 name "sub:Eqnarray-Environment"
28548 \begin_layout Plain Layout
28549 Formula ! multiline ! eqnarray environment
28557 \begin_layout Standard
28558 When this environment has been created, three blue boxes appear.
28559 The content of the first box is right aligned, the content of the last
28561 The content of the middle box appears centered and a bit smaller, because
28562 it is designed to insert there only relation characters.
28563 \begin_inset Formula \begin{eqnarray*}
28564 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28566 A & = & A\end{eqnarray*}
28573 \begin_layout Subsection
28578 \begin_layout Plain Layout
28579 Formula ! multiline ! gather environment
28587 \begin_layout Standard
28588 This environment consists of only one centered column.
28589 Every line can be numbered.
28590 \begin_inset Formula \begin{gather}
28592 X=\textrm{-}1\end{gather}
28599 \begin_layout Subsection
28600 Multline Environment
28601 \begin_inset CommandInset label
28603 name "sub:Multline-Environment"
28611 \begin_layout Plain Layout
28612 Formula ! multiline ! multline environment
28620 \begin_layout Standard
28621 The multline environment consists, like the gather environment, of only
28623 But the first line is left aligned, the last one right aligned.
28624 All other lines are centered.
28625 Therefore this environment is suitable for long formulas.
28627 \begin_inset CommandInset ref
28629 reference "eq:lefteqn"
28633 in the multline environment:
28634 \begin_inset Formula \begin{multline}
28635 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}\\
28636 -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}\\
28637 =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}
28644 \begin_layout Standard
28645 In the output only the last (first) line of a multline environment appears
28646 numbered when the document numbering is right (left).
28650 \begin_layout Plain Layout
28651 numbering styles see
28652 \begin_inset CommandInset ref
28654 reference "sec:Formula-Styles"
28666 \begin_layout Standard
28675 \begin_layout Plain Layout
28693 \begin_layout Plain Layout
28703 a centered line can be right or left aligned, respectively.
28704 The commands are used as follows:
28707 \begin_layout Standard
28712 shoveright{line content}
28718 shoveleft{line content}
28721 \begin_layout Standard
28722 \begin_inset VSpace medskip
28733 \begin_layout Plain Layout
28743 specifies the distance of the first line from the left page margin.
28744 Predefined is the length 0
28745 \begin_inset space \thinspace{}
28751 \begin_layout Standard
28752 As example the above formula where the command
28755 \begin_layout Standard
28765 \begin_layout Standard
28766 was inserted in TeX-mode before:
28770 \begin_layout Plain Layout
28782 \begin_inset Formula \begin{multline}
28783 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}\\
28784 \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}}\\
28785 =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}
28793 \begin_layout Plain Layout
28804 The second line was left aligned using
28813 \begin_layout Subsection
28814 Multiline Formula Parts
28815 \begin_inset CommandInset label
28817 name "sub:Multiline-Formula-Parts"
28825 \begin_layout Plain Layout
28826 Formula ! multiline ! formula parts
28834 \begin_layout Standard
28835 To display only parts of a formula with multiple lines, one of the following
28836 environments are used:
28853 They can be inserted via the menu
28855 Insert\SpecialChar \menuseparator
28858 or by using the commands described in this section.
28861 \begin_layout Standard
28862 The first three have the same properties as the corresponding multiline
28863 formula environments, but it is possible to set further formula parts beside
28866 \begin_inset Formula \[
28867 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28868 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28869 \right\} \textrm{Uncertainty relations}\]
28876 \begin_layout Standard
28877 To get this formula, a displayed formula is created where the command
28885 \begin_layout Plain Layout
28896 A purple box appears around the blue formula box where now columns and
28897 lines can be added.
28898 Outside the multiline environment other formula parts can be set, like
28902 \begin_layout Standard
28903 The aligned environment is also suitable for long formulas whose lines are
28904 horizontally aligned.
28905 Using aligned in a displayed formula has the advantage that the formula
28906 number is vertically centered behind the lines.
28908 \begin_inset CommandInset ref
28910 reference "eq:kurzlang"
28914 in the aligned environment:
28915 \begin_inset Formula \begin{equation}
28916 \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}|}\\
28917 & -\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}
28925 \begin_layout Standard
28926 To use the environments
28948 \begin_layout Plain Layout
28966 \begin_layout Plain Layout
28984 \begin_layout Plain Layout
28992 are inserted, respectively.
28993 The split environment has the same properties as the aligned environment
28994 but it can only have two columns.
28997 \begin_layout Subsection
28998 Text in multiline Formulas
28999 \begin_inset CommandInset label
29001 name "sub:Text-in-multiline"
29009 \begin_layout Plain Layout
29019 \begin_layout Plain Layout
29020 Formula ! multiline ! text
29028 \begin_layout Standard
29029 In the Align environments, and the multline and gather environment, text
29030 can be inserted that will appear in a separate line and doesn't affect
29031 the column alignment.
29032 To do this, the command
29040 \begin_layout Plain Layout
29050 is used in the following scheme:
29053 \begin_layout Standard
29061 \begin_layout Standard
29062 The text should not be longer than a line because it cannot be hyphenated.
29063 As LyX doesn't yet support
29069 directly, the text is written as mathematical text.
29076 must hereby be at the beginning of a line and appears in the output above
29078 An example where the text was inserted at the beginning of the second line:
29079 \begin_inset Formula \begin{align}
29080 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29081 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29088 \begin_layout Section
29093 \begin_layout Plain Layout
29103 \begin_layout Plain Layout
29104 Formula ! numbering|see
29108 \begin_layout Plain Layout
29119 \begin_layout Plain Layout
29134 \begin_layout Subsection
29138 \begin_layout Standard
29139 Numbered formulas can be created with the menu
29141 Insert\SpecialChar \menuseparator
29142 Math\SpecialChar \menuseparator
29144 \begin_inset space ~
29152 \begin_inset space ~
29158 Existing formulas can be numbered with the menu
29160 Edit\SpecialChar \menuseparator
29161 Math\SpecialChar \menuseparator
29163 \begin_inset space ~
29171 \begin_inset space ~
29177 The formula number is displayed in LyX behind the formula as number sign
29179 The number sign is replaced in the output by the formula number.
29182 \begin_layout Standard
29183 When numbering is turned on in multiline formulas, all lines will be numbered.
29184 But the numbering can be controlled with the menu
29186 Edit\SpecialChar \menuseparator
29187 Math\SpecialChar \menuseparator
29189 \begin_inset space ~
29193 \begin_inset space ~
29197 \begin_inset space ~
29205 \begin_inset space ~
29213 \begin_layout Standard
29214 Except of inline formulas, all formulas can be numbered with two different
29216 \begin_inset CommandInset ref
29218 reference "sec:Formula-Styles"
29225 \begin_layout Subsection
29227 \begin_inset CommandInset label
29229 name "sub:Cross-References"
29237 \begin_layout Plain Layout
29238 Cross-references ! to formulas
29246 \begin_layout Standard
29247 All labeled formulas can be cross-referenced.
29248 A label is added by the menu
29250 Insert\SpecialChar \menuseparator
29253 or the toolbar button
29254 \begin_inset Graphics
29255 filename ../images/label-insert.png
29261 The cursor must hereby be inside a displayed formula.
29262 A dialog pops up displaying the prefix
29267 The label is inserted there behind the prefix.
29268 The predefined prefix means
29269 \begin_inset Quotes eld
29273 \begin_inset Quotes erd
29276 and makes it easier to find labels in large documents because it marks
29277 it as formula label to divide it from e.
29278 \begin_inset space \thinspace{}
29282 \begin_inset space ~
29286 To change a label, the menu
29288 Insert\SpecialChar \menuseparator
29294 \begin_layout Standard
29295 The name of the label is displayed in LyX within two parentheses behind
29297 A formula with a label is always numbered.
29300 \begin_layout Standard
29301 Cross-references are inserted via the menu
29303 Insert\SpecialChar \menuseparator
29306 or with the toolbar button
29307 \begin_inset Graphics
29308 filename ../images/dialog-show-new-inset_ref.png
29314 A formula cross-reference appears in the output as formula number.
29315 When in the cross-reference dialog window the format
29319 is chosen, the cross-reference appears in the output as formula number
29321 \begin_inset Newline newline
29324 By right-clicking on a cross-reference in LyX, one jumps to the formula
29325 that is referenced.
29328 \begin_layout Standard
29329 Here are as examples cross-references to formulas of the following subsections:
29330 \begin_inset Note Note
29333 \begin_layout Plain Layout
29334 Note the different cross-reference types.
29342 \begin_layout Standard
29344 \begin_inset CommandInset ref
29351 \begin_inset CommandInset ref
29359 \begin_inset CommandInset ref
29365 ) big Latin letters are used for the numbering in contrary to (
29366 \begin_inset CommandInset ref
29375 \begin_layout Standard
29376 \begin_inset VSpace medskip
29379 When the argument of
29387 \begin_layout Plain Layout
29395 \begin_inset CommandInset ref
29397 reference "sub:User-defined-Numbering"
29408 contains a box like in
29409 \begin_inset CommandInset ref
29411 reference "sub:Paragraph-Boxes"
29415 , the formula cannot be referenced.
29418 \begin_layout Subsection
29423 \begin_layout Plain Layout
29424 Formula numbering ! subnumbering
29432 \begin_layout Standard
29433 With the help of the commands
29437 begin{subequations}
29445 formulas can be subnumbered.
29446 Both commands are inserted in TeX-mode.
29449 \begin_layout Standard
29451 \begin_inset Formula \begin{equation}
29452 A=C-B\label{eq:a}\end{equation}
29460 \begin_layout Plain Layout
29464 addtocounter{equation}{-1}
29473 \begin_layout Plain Layout
29477 begin{subequations}
29483 \begin_inset VSpace -5mm
29487 \begin_inset Formula \begin{equation}
29488 B=C-A\label{eq:b}\end{equation}
29493 \begin_inset Formula \begin{equation}
29494 C=A+B\label{eq:c}\end{equation}
29501 \begin_layout Standard
29505 \begin_layout Plain Layout
29517 \begin_layout Standard
29518 To create the example, the following is done:
29521 \begin_layout Enumerate
29522 first formula is inserted
29525 \begin_layout Enumerate
29530 addtocounter{equation}{-1}
29532 begin{subequations}
29536 \begin_layout Plain Layout
29545 \begin_inset Newline newline
29550 is inserted after the first formula
29553 \begin_layout Enumerate
29554 second formula is inserted
29557 \begin_layout Enumerate
29558 third formula is inserted
29561 \begin_layout Enumerate
29568 is inserted after the third formula
29571 \begin_layout Standard
29572 Every formula between the commands
29584 is subnumbered as a, b,
29585 \begin_inset Newline linebreak
29588 c, \SpecialChar \ldots{}
29589 For multiline formulas every line will be subnumbered.
29590 All subnumbered formulas are treated as
29595 But as every numbered formula increases the counter
29599 by one, the command
29605 is needed to decrease it.
29606 Otherwise the formulas
29607 \begin_inset CommandInset ref
29614 \begin_inset CommandInset ref
29621 \begin_inset CommandInset ref
29627 would be numbered as
29628 \begin_inset CommandInset ref
29635 \begin_inset CommandInset ref
29642 \begin_inset CommandInset ref
29651 \begin_layout Standard
29652 By inserting the commands in TeX-mode, a space is created between the first
29655 \begin_inset space \thinspace{}
29658 mm vertical space is inserted after the command
29662 begin{subequations}
29665 When the formula style
29671 \begin_layout Plain Layout
29673 \begin_inset CommandInset ref
29675 reference "sec:Formula-Styles"
29687 \begin_inset space \thinspace{}
29690 mm space is inserted instead.
29693 \begin_layout Standard
29694 Here is an example for a multiline formula where the numbering was turned
29695 off for the second line:
29699 \begin_layout Plain Layout
29703 begin{subequations}
29709 \begin_inset Formula \begin{eqnarray}
29710 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29711 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29712 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29720 \begin_layout Plain Layout
29732 \begin_layout Subsection
29733 User-defined Numbering
29734 \begin_inset CommandInset label
29736 name "sub:User-defined-Numbering"
29744 \begin_layout Plain Layout
29745 Formula numbering ! user-defined
29753 \begin_layout Standard
29757 \begin_layout Plain Layout
29758 Formula numbering ! self-defined delimiters
29763 With the standard numbering parentheses are set around the formula number.
29764 To replace the parentheses for example by vertical bars, the following
29765 line is added to the LaTeX-preamble:
29768 \begin_layout Standard
29780 \begin_inset Note Note
29783 \begin_layout Plain Layout
29784 This macro is already declared in the LaTeX-preamble for testing.
29785 To activate it, remove the percent sign at the beginning.
29793 \begin_layout Standard
29794 To use other characters, the vertical bars besides the
29798 are replaced by one ore more characters.
29799 To get only the formula number the vertical bars are omitted.
29802 \begin_layout Standard
29803 \begin_inset VSpace bigskip
29806 When there should be an expression of your choice instead of the consecutive
29807 formula number in parentheses behind the formula, the command
29817 \begin_layout Plain Layout
29826 \begin_inset Formula \begin{equation}
29827 A+B=C\tag{something}\label{eq:tag}\end{equation}
29831 In this example the command
29839 \begin_layout Plain Layout
29850 was inserted to the formula.
29853 \begin_layout Standard
29862 \begin_layout Plain Layout
29873 is inserted instead, the star prevents the parentheses around the expression:
29874 \begin_inset Formula \[
29875 A+B=C\tag*{something}\]
29882 \begin_layout Standard
29883 \begin_inset VSpace bigskip
29886 To restart the formula numbering with new document parts or sections, the
29887 following command is used:
29890 \begin_layout Standard
29895 @addtoreset{equation}{part}
29901 \begin_layout Plain Layout
29906 \begin_layout Plain Layout
29917 \begin_layout Plain Layout
29930 \begin_layout Plain Layout
29941 \begin_layout Plain Layout
29954 \begin_inset Newline newline
29958 \begin_inset Newline newline
29965 @addtoreset{equation}{section}
29968 \begin_layout Standard
29969 To be able to use these commands in TeX-mode, the
29970 \begin_inset Quotes eld
29974 \begin_inset Quotes erd
29977 character has to be made
29978 \begin_inset Quotes eld
29982 \begin_inset Quotes erd
29985 for LaTeX using the command
29999 So the command sequence in TeX-mode is:
30002 \begin_layout Standard
30008 \begin_inset Newline newline
30013 @addtoreset{equation}{section}
30014 \begin_inset Newline newline
30022 \begin_layout Standard
30023 In the LaTeX-preamble
30035 can be omitted as they are automatically internally inserted by LyX.
30038 \begin_layout Standard
30053 \begin_layout Plain Layout
30058 is part of the LaTeX-package
30066 \begin_layout Plain Layout
30067 Packages ! carlisle
30072 that is part of every LaTeX standard installation.
30081 \begin_layout Plain Layout
30082 Packages ! remreset
30087 has to be loaded in the LaTeX-preamble with the line
30090 \begin_layout Standard
30095 usepackage{remreset}
30098 \begin_layout Standard
30109 \begin_layout Plain Layout
30114 \begin_layout Plain Layout
30125 \begin_layout Plain Layout
30138 \begin_layout Plain Layout
30149 \begin_layout Plain Layout
30161 can be used with the same scheme as
30170 \begin_layout Standard
30171 \begin_inset VSpace bigskip
30174 Sometimes formulas should be numbered in the following form:
30177 \begin_layout Standard
30180 (section number.formula number)
30183 \begin_layout Standard
30184 The formula number should start with every section with
30185 \begin_inset Quotes eld
30189 \begin_inset Quotes erd
30195 \begin_layout Standard
30196 For this case there is the command
30206 \begin_layout Plain Layout
30214 , which is used with the following scheme:
30217 \begin_layout Standard
30222 numberwithin{counter}{sectioning}
30225 \begin_layout Standard
30226 Counter denotes what kind of numbering is affected, sectioning denotes what
30227 number is before the dot.
30230 \begin_layout Standard
30231 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30234 \begin_layout Standard
30239 numberwithin{equation}{section}
30242 \begin_layout Standard
30243 This is the result:
30247 \begin_layout Plain Layout
30251 numberwithin{equation}{section}
30257 \begin_inset Formula \begin{equation}
30258 A+B=C\end{equation}
30265 \begin_layout Standard
30267 \begin_inset space \thinspace{}
30271 \begin_inset space ~
30274 tables so that the number of the part is the sectioning,
30275 \begin_inset Newline newline
30282 numberwithin{table}{part}
30287 \begin_layout Standard
30288 To go back to the standard numbering or to prevent this kind of numbering
30289 when it is defined by the document class, the following command is inserted
30290 as TeX-Code or to the LaTeX-preamble:
30293 \begin_layout Standard
30306 \begin_layout Plain Layout
30320 \begin_layout Plain Layout
30336 \begin_inset Newline newline
30344 \begin_inset Newline newline
30356 \begin_layout Standard
30363 uses internally the command
30369 , described above, that also needs to be reverted.
30373 \begin_layout Plain Layout
30380 \begin_layout Plain Layout
30384 @removefromreset{equation}{section}
30387 \begin_layout Plain Layout
30399 \begin_layout Subsection
30400 Numbering with Roman Numbers and Letters
30401 \begin_inset CommandInset label
30403 name "sub:Numbering-with-Roman"
30411 \begin_layout Plain Layout
30412 Formula numbering ! with letters
30421 \begin_layout Plain Layout
30422 Formula numbering ! with Roman numbers
30430 \begin_layout Standard
30431 Formulas can also be numbered with Roman numbers and Latin letters.
30432 To number for example with small Roman numbers, the command
30435 \begin_layout Standard
30447 \begin_layout Standard
30448 is inserted before the formula in TeX-mode.
30459 \begin_layout Plain Layout
30467 redefines the predefined command
30483 \begin_layout Plain Layout
30490 has the same scheme like the command
30496 that is described in
30497 \begin_inset CommandInset ref
30499 reference "sec:User-defined-commands"
30513 is the formula counter.
30520 is used as prefix for a counter, the value of the counter is output as
30522 When a formula is numbered, LaTeX sets internally the command
30528 behind the formula.
30537 \begin_layout Plain Layout
30547 outputs the counter as small Roman number.
30550 \begin_layout Standard
30551 All formulas behind the command
30561 are now numbered Roman.
30562 To switch to numbering with big Roman numbers, the command is inserted
30579 \begin_layout Plain Layout
30591 \begin_inset Quotes eld
30595 \begin_inset Quotes erd
30598 with small Latin letters there is the command
30608 \begin_layout Plain Layout
30616 , for big ones there is the command
30626 \begin_layout Plain Layout
30639 \begin_layout Standard
30640 \begin_inset Note Greyedout
30643 \begin_layout Plain Layout
30648 Only maximal 26 formulas can be numbered with Latin letters in one document.
30656 \begin_layout Standard
30660 \begin_layout Plain Layout
30676 \begin_layout Standard
30677 \begin_inset Formula \begin{equation}
30678 A=\textrm{small roman}\label{eq:rom}\end{equation}
30686 \begin_layout Plain Layout
30700 \begin_inset Formula \begin{equation}
30701 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30709 \begin_layout Plain Layout
30723 \begin_inset Formula \begin{equation}
30724 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30732 \begin_layout Plain Layout
30746 \begin_inset Formula \begin{equation}
30747 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30754 \begin_layout Standard
30755 To switch back to the default numbering, insert the command:
30758 \begin_layout Standard
30771 \begin_layout Plain Layout
30782 \begin_layout Standard
30786 \begin_layout Plain Layout
30800 \begin_inset Formula \begin{equation}
30801 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30808 \begin_layout Standard
30809 \begin_inset VSpace medskip
30812 As you see, formulas are numbered serially independent from the numbering
30814 When then numbering should start with
30815 \begin_inset Quotes eld
30819 \begin_inset Quotes erd
30822 when the style is changed, new equation counters have to be defined.
30823 A description about this can be found in the file
30824 \begin_inset CommandInset href
30826 target "Formula-numbering.lyx"
30833 \begin_layout Section
30834 User-defined commands
30835 \begin_inset CommandInset label
30837 name "sec:User-defined-commands"
30845 \begin_layout Plain Layout
30846 User-defined commands
30854 \begin_layout Standard
30855 Many LaTeX-commands are too long to be used frequently.
30856 But it is possible to define with the command
30866 \begin_layout Plain Layout
30874 new shorter commands.
30877 \begin_layout Standard
30878 The command scheme of
30887 \begin_layout Standard
30892 newcommand{new command name}[number of arguments][optional
30897 \begin_inset Newline newline
30904 \begin_layout Plain Layout
30919 \begin_layout Plain Layout
30926 {command definition}
30929 \begin_layout Standard
30930 \begin_inset Note Greyedout
30933 \begin_layout Plain Layout
30938 Assure that the name of the new command is not already used in your document
30939 or by LaTeX-packages that you use.
30940 When you for example define the command
30952 , you get an error message because
30958 is already defined as command for
30959 \begin_inset Quotes eld
30963 \begin_inset Formula $\le$
30967 \begin_inset Quotes erd
30978 \begin_layout Standard
30979 \begin_inset Note Greyedout
30982 \begin_layout Plain Layout
30987 The names of user-defined commands may only consist of Latin letters.
30995 \begin_layout Standard
30996 The number of arguments is an integer in the range 0
30997 \begin_inset space \thinspace{}
31001 \begin_inset space \thinspace{}
31004 9 and specifies how many arguments the new command should have.
31005 With the optional value a value for an optional argument can be predefined.
31006 When this is done, the
31014 rgument of the new command is automatically an optional one.
31017 \begin_layout Standard
31018 Here are some examples:
31021 \begin_layout Itemize
31022 To define the command
31034 , the LaTeX-preamble line is:
31038 \begin_layout Plain Layout
31050 \begin_inset Newline newline
31062 \begin_layout Itemize
31063 To define the command
31075 , the argument (that should be underlined) must be taken into account.
31076 For this the preamble line is:
31080 \begin_layout Plain Layout
31092 \begin_inset Newline newline
31107 \begin_layout Plain Layout
31119 \begin_inset Newline newline
31128 acts as argument placeholder, the
31132 behind it denotes that it is the placeholder for the first argument.
31135 \begin_layout Itemize
31143 \begin_inset space \thinspace{}
31147 \begin_inset space ~
31160 \begin_layout Plain Layout
31172 \begin_inset Newline newline
31181 framebox#1#2{$#3$}}
31187 \begin_layout Plain Layout
31199 \begin_inset Newline newline
31204 The two Dollar signs creates the extra formula needed for
31211 \begin_inset CommandInset ref
31213 reference "sub:Boxes-with-Frame"
31220 \begin_layout Itemize
31221 To create a new command for
31227 where the color for the box needn't to be specified, the argument for the
31228 color is defined optional:
31232 \begin_layout Plain Layout
31244 \begin_inset Newline newline
31253 fcolorbox{#2}{#1}{$#3$}}
31259 \begin_layout Plain Layout
31269 \begin_inset Newline newline
31272 When the color is not specified when using
31278 , the predefined color
31285 \begin_layout Standard
31286 A test of the new defined commands:
31289 \begin_layout Standard
31291 \begin_inset Tabular
31292 <lyxtabular version="3" rows="6" columns="2">
31294 <column alignment="center" valignment="top" width="0">
31295 <column alignment="center" valignment="top" width="0">
31297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31300 \begin_layout Plain Layout
31306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31309 \begin_layout Plain Layout
31311 \begin_inset Note Note
31314 \begin_layout Plain Layout
31321 is only used as spacer.
31333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31336 \begin_layout Plain Layout
31343 \begin_layout Plain Layout
31357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31360 \begin_layout Plain Layout
31361 \begin_inset Formula $A\gr B$
31371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31374 \begin_layout Plain Layout
31382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31385 \begin_layout Plain Layout
31386 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31399 \begin_layout Plain Layout
31403 \begin_inset Formula $\to$
31409 \begin_inset Formula $\to$
31420 \begin_layout Plain Layout
31434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31437 \begin_layout Plain Layout
31438 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31451 \begin_layout Plain Layout
31455 \begin_inset Formula $\to$
31466 \begin_layout Plain Layout
31480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31483 \begin_layout Plain Layout
31484 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31497 \begin_layout Plain Layout
31503 \begin_inset Formula $\to$
31514 \begin_layout Plain Layout
31528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31531 \begin_layout Plain Layout
31532 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31548 \begin_layout Section
31552 \begin_layout Standard
31553 LyX supports two types of commutative diagrams:
31561 that are explained in the following.
31564 \begin_layout Subsection
31569 \begin_layout Plain Layout
31578 \begin_layout Standard
31579 Diagrams of this type visualize relations by vertical and horizontal lines
31581 \begin_inset Formula \[
31582 \begin{CD}A@>>>B@>>>C\\
31584 F@<<<E@<<<D\end{CD}\]
31591 \begin_layout Standard
31592 To get them, the command
31600 \begin_layout Plain Layout
31610 is inserted to a formula.
31611 A blue box appears with two dashed lines where further commands can be
31617 a new line is created.
31618 Horizontal relations are inserted in odd, vertical in even formula lines.
31621 \begin_layout Standard
31622 To create the relations there are the following commands:
31625 \begin_layout Itemize
31630 creates a left arrow,
31641 \begin_layout Itemize
31646 creates an up arrow,
31654 a vertical equal sign
31657 \begin_layout Itemize
31663 is a placeholder for non-existent relations
31666 \begin_layout Standard
31667 All arrows can be labeled as follows:
31670 \begin_layout Itemize
31671 Is text inserted between the first and second < or >, resp., it is placed
31673 When it is inserted between the second and third one, it appears under
31677 \begin_layout Itemize
31678 When text for vertical arrows is inserted between the first and second A
31679 or V, resp., it is placed left beside the arrow.
31680 When it is inserted between the second and third one, it appears right
31682 If the text contains an A or V, these letters must be set into a TeX-brace.
31685 \begin_layout Standard
31686 As example a diagram with all possible relations:
31689 \begin_layout Standard
31690 \begin_inset Formula \[
31691 \begin{CD}A@>j>>B@>>k>C@=F\\
31693 D@<<j<E@>k>>F@=C\end{CD}\]
31700 \begin_layout Standard
31701 The command for this is:
31702 \begin_inset Newline newline
31713 \begin_layout Plain Layout
31722 A@>j>>B@>>k>C@=F Ctrl-Enter
31723 \begin_inset Newline newline
31730 \begin_layout Plain Layout
31745 \begin_layout Plain Layout
31758 \begin_layout Plain Layout
31770 \begin_inset Formula $\to$
31776 \begin_inset Newline newline
31783 \begin_layout Plain Layout
31798 \begin_layout Plain Layout
31811 \begin_layout Plain Layout
31821 \begin_layout Subsection
31826 \begin_layout Plain Layout
31827 Diagrams ! xymatrix
31835 \begin_layout Standard
31836 To be able to use xymatrices, the LaTeX-package
31841 A xymatrix is created by inserting the command
31848 Then you are able to add new matrix columns and rows like for normal matrices,
31850 \begin_inset CommandInset ref
31852 reference "sec:Matrices"
31859 \begin_layout Standard
31860 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31862 All possibilities to create commutative diagrams and decorations are explained
31863 in detail in this manual:
31864 \begin_inset CommandInset href
31866 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31873 \begin_layout Standard
31874 \begin_inset Newpage newpage
31880 \begin_layout Section
31885 \begin_layout Plain Layout
31898 \begin_layout Plain Layout
31899 Other useful math tips can be found in
31900 \begin_inset CommandInset citation
31915 \begin_layout Plain Layout
31923 \begin_inset Note Note
31926 \begin_layout Plain Layout
31929 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31932 \begin_layout Plain Layout
31935 texorpdfstring is in section
31936 \begin_inset CommandInset ref
31938 reference "sub:Formulas-in-Section"
31951 \begin_layout Plain Layout
31961 \begin_layout Plain Layout
31966 \begin_layout Plain Layout
31973 Chemical characters
31977 \begin_layout Plain Layout
31992 \begin_layout Subsection
31993 Chemical Symbols and Equations
31994 \begin_inset CommandInset label
31996 name "sub:Chemical-Symbols-and"
32004 \begin_layout Plain Layout
32005 Chemical characters ! Symbols
32014 \begin_layout Plain Layout
32024 \begin_layout Plain Layout
32033 \begin_layout Standard
32034 An example text from chemistry:
32037 \begin_layout Quote
32039 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32042 -ion reacts with two
32043 \begin_inset Formula $\mathrm{Na^{+}}$
32046 -ions to sodium sulfate
32047 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32051 The chemical equation for this is:
32052 \begin_inset Formula \[
32053 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32060 \begin_layout Standard
32061 This chemical equation can directly be created as formula.
32062 To avoid that the symbols appear italic, everything is highlighted and
32063 changed by the shortcut
32066 \begin_inset space ~
32071 to the upright font style.
32075 \begin_layout Plain Layout
32081 \begin_inset CommandInset ref
32083 reference "sub:Font-Styles"
32095 \begin_layout Subsection
32100 \begin_layout Plain Layout
32109 \begin_layout Standard
32110 Negative numbers often look ugly in formulas because the minus sign before
32111 the number is set with the same length as the minus operator sign.
32112 When writing the negative number in normal text, the minus sign appears
32116 \begin_layout Standard
32117 Thus, the problem disappears when converting the minus sign to mathematical
32121 \begin_layout Standard
32122 An example to visualize the problem:
32125 \begin_layout Standard
32127 \begin_inset Tabular
32128 <lyxtabular version="3" rows="3" columns="2">
32130 <column alignment="right" valignment="top" width="0">
32131 <column alignment="left" valignment="top" width="0">
32133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32136 \begin_layout Plain Layout
32142 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32145 \begin_layout Plain Layout
32153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32156 \begin_layout Plain Layout
32162 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32165 \begin_layout Plain Layout
32166 \begin_inset Formula $x=-2$
32176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32179 \begin_layout Plain Layout
32185 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32188 \begin_layout Plain Layout
32189 \begin_inset Formula $x=\textrm{-}2$
32205 \begin_layout Subsection
32206 Comma as Decimal Separator
32210 \begin_layout Plain Layout
32219 \begin_layout Standard
32220 In LaTeX a comma inside a formula is used, according to the English convention,
32221 as number group separator.
32222 So there will be space added behind all commas in formulas.
32225 \begin_layout Standard
32226 To avoid this, the comma is highlighted and changed to mathematical text
32230 \begin_inset space ~
32238 \begin_layout Standard
32239 To use all formula commas in the document as decimal separator, the file
32248 \begin_layout Plain Layout
32253 is part of the LaTeX-package
32261 \begin_layout Plain Layout
32266 \begin_layout Plain Layout
32289 \begin_layout Plain Layout
32295 is loaded with the LaTeX-preamble line
32298 \begin_layout Standard
32306 \begin_layout Subsection
32308 \begin_inset CommandInset label
32310 name "sub:Physical-Vectors"
32318 \begin_layout Plain Layout
32327 \begin_layout Standard
32328 Predefined vectors are offered by the LaTeX-package
32336 \begin_layout Plain Layout
32341 should be part of every LaTeX standard installation.
32350 \begin_layout Plain Layout
32356 that is loaded with the LaTeX-preamble line
32359 \begin_layout Standard
32367 \begin_layout Standard
32371 \begin_layout Plain Layout
32381 \begin_inset Note Note
32384 \begin_layout Plain Layout
32385 The following table will only be displayed when the LaTeX-package
32394 The following commands are defined:
32397 \begin_layout Standard
32399 \begin_inset Tabular
32400 <lyxtabular version="3" rows="4" columns="2">
32402 <column alignment="center" valignment="top" width="0">
32403 <column alignment="center" valignment="top" width="0">
32405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32408 \begin_layout Plain Layout
32414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32417 \begin_layout Plain Layout
32425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32428 \begin_layout Plain Layout
32438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32441 \begin_layout Plain Layout
32442 \begin_inset Formula $\Bra{\psi}$
32452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32455 \begin_layout Plain Layout
32465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32468 \begin_layout Plain Layout
32469 \begin_inset Formula $\Ket{\psi}$
32479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32482 \begin_layout Plain Layout
32494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32497 \begin_layout Plain Layout
32498 \begin_inset Formula $\Braket{\psi|\phi}$
32514 \begin_layout Standard
32521 assures that all vertical bars are set in the size of the surrounding brackets:
32522 \begin_inset Formula \[
32523 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32531 \begin_layout Plain Layout
32541 \begin_inset Note Note
32544 \begin_layout Plain Layout
32545 The following will be displayed when the LaTeX-package
32557 \begin_layout Standard
32558 You need to install the LaTeX-package
32562 to see the rest of this subsection in the output.
32565 \begin_layout Standard
32569 \begin_layout Plain Layout
32581 \begin_layout Standard
32588 can also be achieved using the command
32594 , that is described in
32595 \begin_inset CommandInset ref
32597 reference "sub:Automatic-Bracket-Size"
32604 \begin_layout Subsection
32605 Self-defined Fractions
32606 \begin_inset CommandInset label
32608 name "sub:Self-defined-Fractions"
32616 \begin_layout Plain Layout
32617 Fractions ! self-defined
32625 \begin_layout Standard
32626 To define custom commands for fractions, the command
32636 \begin_layout Plain Layout
32644 is used in the following scheme:
32647 \begin_layout Standard
32660 bracket}{fraction bar thickness}{style}
32661 \begin_inset Newline newline
32668 \begin_layout Plain Layout
32683 \begin_layout Plain Layout
32690 {numerator}{denominator}
32693 \begin_layout Standard
32694 The style is a number in the range of 0
32695 \begin_inset space \thinspace{}
32699 \begin_inset space \thinspace{}
32705 \begin_layout Standard
32707 \begin_inset Tabular
32708 <lyxtabular version="3" rows="5" columns="2">
32710 <column alignment="center" valignment="top" width="0">
32711 <column alignment="center" valignment="top" width="0">
32713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32716 \begin_layout Plain Layout
32722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32725 \begin_layout Plain Layout
32733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32736 \begin_layout Plain Layout
32742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32745 \begin_layout Plain Layout
32746 display style formula
32753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32756 \begin_layout Plain Layout
32762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32765 \begin_layout Plain Layout
32773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32776 \begin_layout Plain Layout
32782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32785 \begin_layout Plain Layout
32793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32796 \begin_layout Plain Layout
32802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32805 \begin_layout Plain Layout
32819 \begin_layout Standard
32820 When no style is given, the size is adjusted to the surrounding environment
32821 like for the command
32830 \begin_layout Standard
32831 When no fraction bar thickness is given, the predefined value of 0.4
32832 \begin_inset space \thinspace{}
32838 \begin_layout Standard
32839 \begin_inset VSpace medskip
32842 For example, the commands
32855 \begin_inset CommandInset ref
32857 reference "sub:Fractions"
32861 are defined with the commands
32864 \begin_layout Standard
32873 genfrac{}{}{}{0}{#1}{#2}}
32876 \begin_layout Standard
32880 \begin_layout Standard
32889 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32892 \begin_layout Standard
32893 \begin_inset VSpace medskip
32896 To define a fraction where the fraction bar thickness can be given as optional
32897 argument, the following line is inserted to the LaTeX-preamble:
32900 \begin_layout Standard
32909 genfrac{}{}{#1}{}{#2}{#3}}
32912 \begin_layout Standard
32914 \begin_inset Formula \begin{align*}
32915 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32916 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32920 As one can see, the distance of the numerator and the denominator to the
32921 fraction bar is round about three times the bar thickness.
32924 \begin_layout Subsection
32926 \begin_inset CommandInset label
32928 name "sub:Canceled-Formulas"
32936 \begin_layout Plain Layout
32945 \begin_layout Standard
32946 To cancel formulas or formula parts, the LaTeX-package
32954 \begin_layout Plain Layout
32959 is part of every LaTeX standard installation.
32968 \begin_layout Plain Layout
32974 has to be loaded with the LaTeX-preamble line
32977 \begin_layout Standard
32982 usepackage[samesize]{cancel}
32985 \begin_layout Standard
32986 There are four ways to cancel formulas:
32989 \begin_layout Standard
32991 \begin_inset Tabular
32992 <lyxtabular version="3" rows="5" columns="2">
32994 <column alignment="center" valignment="top" width="0">
32995 <column alignment="center" valignment="top" width="0">
32997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33000 \begin_layout Plain Layout
33006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33009 \begin_layout Plain Layout
33011 \begin_inset Note Note
33014 \begin_layout Plain Layout
33027 are used here as spacer.
33039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33042 \begin_layout Plain Layout
33051 \begin_layout Plain Layout
33065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33068 \begin_layout Plain Layout
33069 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33082 \begin_layout Plain Layout
33091 \begin_layout Plain Layout
33105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33108 \begin_layout Plain Layout
33109 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33122 \begin_layout Plain Layout
33131 \begin_layout Plain Layout
33145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33148 \begin_layout Plain Layout
33149 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33162 \begin_layout Plain Layout
33166 \begin_inset Formula $\to$
33177 \begin_layout Plain Layout
33191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33194 \begin_layout Plain Layout
33195 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33211 \begin_layout Standard
33218 is especially suitable to visualize the reduction of fractions within formulas:
33219 \begin_inset Formula \[
33220 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33227 \begin_layout Subsection
33228 Formulas in Section Headings
33229 \begin_inset CommandInset label
33231 name "sub:Formulas-in-Section"
33239 \begin_layout Plain Layout
33240 Formula ! in section headings
33248 \begin_layout Standard
33249 When formulas are used in section headings, the following has to be taken
33253 \begin_layout Standard
33254 \begin_inset Note Greyedout
33257 \begin_layout Plain Layout
33266 \begin_layout Plain Layout
33267 Packages ! hyperref
33272 support is enabled in the document settings dialog under
33275 \begin_inset space ~
33280 , PDF-bookmarks are created for every section heading in the table of contents.
33281 If a section heading contains formulas, they are incorrectly displayed
33282 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33291 \begin_layout Standard
33292 Both problems can be solved by inserting at the end of the section heading
33293 a short title with the menu
33295 Insert\SpecialChar \menuseparator
33297 \begin_inset space ~
33303 Short titles are used as alternative for multiline section headings to
33304 keep the table of contents clearly arranged.
33305 Only the short title appears in the table of contents and therefore also
33306 in the PDF-bookmark.
33309 \begin_layout Standard
33310 When formulas should be used in the table of contents but
33314 is used, one can use the following command in TeX-mode:
33317 \begin_layout Standard
33322 texorpdfstring{part}{alternative}
33326 \begin_layout Plain Layout
33337 \begin_layout Standard
33338 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33339 This can be characters, formulas, footnotes, but also cross-references.
33340 The alternative is used instead of the part for the bookmark.
33343 \begin_layout Standard
33344 Here are two example headings:
33345 \begin_inset VSpace -3mm
33352 \begin_layout Plain Layout
33364 \begin_layout Subsubsection
33365 Heading without formula in table of contents
33366 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33370 \begin_inset OptArg
33373 \begin_layout Plain Layout
33374 Heading without formula in table of contents
33382 \begin_layout Subsubsection
33383 Heading with formula in table of contents
33387 \begin_layout Plain Layout
33397 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33404 \begin_layout Plain Layout
33414 \begin_layout Standard
33418 \begin_layout Plain Layout
33427 In the first heading a short title was used, in the second one
33436 \begin_layout Standard
33437 To get the same formatting as for the other headings, the complete heading
33446 \begin_layout Plain Layout
33448 \begin_inset CommandInset ref
33450 reference "sub:Bold-Formulas"
33462 \begin_layout Subsection
33463 Formulas in multi-column Text
33467 \begin_layout Plain Layout
33468 Formula ! in multi-column text
33476 \begin_layout Standard
33477 Formulas in multi-column text are often too wide to fit into a column and
33478 thus need to be set over the whole page width.
33479 This is done by using the LaTeX-package
33487 \begin_layout Plain Layout
33492 is part of every LaTeX standard installation.
33501 \begin_layout Plain Layout
33502 Packages ! multicol
33507 , that is loaded with the LaTeX-preamble line
33510 \begin_layout Standard
33515 usepackage{multicol}
33518 \begin_layout Standard
33519 \begin_inset Note Greyedout
33522 \begin_layout Plain Layout
33523 Note herby that the setting
33526 \begin_inset space ~
33533 Document\SpecialChar \menuseparator
33539 \begin_inset space ~
33559 \begin_layout Standard
33560 Before the multi-column text the command
33563 \begin_layout Standard
33568 begin{multicols}{column number}
33571 \begin_layout Standard
33572 is written in TeX-mode.
33573 The column number is a number in the range of 2
33574 \begin_inset space \thinspace{}
33578 \begin_inset space \thinspace{}
33582 Before the formula the multi-column text is ended by inserting the command
33585 \begin_layout Standard
33593 \begin_layout Standard
33597 \begin_layout Standard
33598 Due to the command some space is automatically added before the formula.
33600 \begin_inset space \thinspace{}
33603 mm vertical space is inserted before the formula.
33604 When the formula style
33610 \begin_layout Plain Layout
33612 \begin_inset CommandInset ref
33614 reference "sec:Formula-Styles"
33626 \begin_inset space \thinspace{}
33629 mm space is inserted instead.
33632 \begin_layout Standard
33633 As example a multi-column text with a displayed formula:
33636 \begin_layout Standard
33640 \begin_layout Plain Layout
33644 begin{multicols}{2}
33649 Das Spektrum wird fouriertransformiert.
33650 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33651 , Lösungsmittel) zu trennen.
33652 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33653 nun das Aussehen des Ausgangssignals.
33654 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33655 über alle Phasen integrieren muss.
33657 \begin_inset Formula $S$
33660 unser normiertes Ausgangssignal and
33661 \begin_inset Formula $P$
33664 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33668 \begin_layout Plain Layout
33678 \begin_inset VSpace -6mm
33682 \begin_inset Formula \begin{equation}
33683 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33691 \begin_layout Plain Layout
33695 begin{multicols}{2}
33701 \begin_inset Formula $S_{0}$
33704 das Signal ohne Gradient ist and the Normierungsbedingung
33705 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33709 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33711 \begin_inset Formula $\nicefrac{\pi}{2}$
33715 \begin_inset space \thinspace{}
33718 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33719 das Signal zusätzlich abschwächt.
33720 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33722 \begin_inset Formula $T_{2}$
33728 \begin_layout Standard
33732 \begin_layout Plain Layout
33744 \begin_layout Subsection
33745 Formulas with Description of Variables
33749 \begin_layout Plain Layout
33750 Formula ! with description of variables
33758 \begin_layout Standard
33759 To describe variables within a formula, like in formula
33760 \begin_inset CommandInset ref
33762 reference "eq:within"
33771 \begin_inset Formula $n$
33775 \begin_inset space ~
33778 matrix is used with left aligned columns for the
33779 \begin_inset Formula $n$
33786 \begin_layout Plain Layout
33788 \begin_inset CommandInset ref
33790 reference "sec:Matrices"
33799 To set the description in a smaller size, before the matrix e.
33800 \begin_inset space \thinspace{}
33804 \begin_inset space ~
33817 \begin_layout Plain Layout
33819 \begin_inset CommandInset ref
33821 reference "sub:Font-Sizes"
33833 \begin_layout Standard
33834 When the formula style
33840 \begin_layout Plain Layout
33842 \begin_inset CommandInset ref
33844 reference "sec:Formula-Styles"
33865 \begin_layout Plain Layout
33872 only works in formulas with the style
33877 \begin_inset CommandInset ref
33879 reference "sub:Variable-Space"
33888 is inserted before and after the matrix to have the same separation of
33889 the matrix from the equation and the side margin.
33892 \begin_layout Standard
33893 When the formula style
33897 is used, the method described in
33898 \begin_inset CommandInset ref
33900 reference "sub:Flalign-Environment"
33904 is used to indent formulas.
33906 \begin_inset CommandInset ref
33908 reference "eq:within"
33912 consists of five columns whereas in the first two columns contain the equation,
33913 the third the matrix, and the last one an empty TeX-brace.
33914 \begin_inset Formula \begin{flalign}
33915 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33916 \rho & \textrm{density}\\
33917 V & \textrm{volume}\\
33918 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33925 \begin_layout Subsection
33926 Upright small Greek Letters
33927 \begin_inset CommandInset label
33929 name "sub:Upright-small-Greek"
33937 \begin_layout Plain Layout
33938 Greek letters ! upright
33946 \begin_layout Standard
33947 Most of the math fonts only provide italic small Greek letters.
33948 But for symbols of elementary particles like pions and neutrinos, upright
33949 Greek letters are needed.
33958 \begin_layout Plain Layout
33963 is part of the LaTeX-package
33971 \begin_layout Plain Layout
33976 \begin_layout Plain Layout
33999 \begin_layout Plain Layout
34005 that is loaded with the LaTeX-preamble line
34008 \begin_layout Standard
34013 usepackage{upgreek}
34016 \begin_layout Standard
34022 \begin_layout Plain Layout
34032 \begin_inset Note Note
34035 \begin_layout Plain Layout
34036 The following table will only be displayed when the LaTeX-package
34045 They are created when the command for a small Greek letters is started
34051 For example the command
34058 \begin_inset Formula $\uptau$
34064 \begin_layout Standard
34065 With these commands reactions of elementary particles can be typeset:
34066 \begin_inset Formula \[
34067 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34074 \begin_layout Standard
34075 The upright letters are more bold and wider than the italic ones.
34076 They should therefore not be used for units like
34077 \begin_inset Quotes eld
34081 \begin_inset Quotes erd
34087 \begin_layout Standard
34091 \begin_layout Plain Layout
34101 \begin_inset Note Note
34104 \begin_layout Plain Layout
34105 The following will be displayed when the LaTeX-package
34117 \begin_layout Standard
34118 You need to install the LaTeX-package
34122 to see the rest of this subsection in the output.
34125 \begin_layout Standard
34129 \begin_layout Plain Layout
34141 \begin_layout Subsection
34142 Text Characters in Formulas
34143 \begin_inset CommandInset label
34145 name "sub:Text-Characters-in"
34153 \begin_layout Plain Layout
34162 \begin_layout Standard
34163 In some cases you might want to insert text characters directly into formulas.
34164 When for example the centered dot · is often used in formulas like
34165 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34168 , one would have to insert the command
34178 \begin_layout Plain Layout
34180 \begin_inset CommandInset ref
34182 reference "sub:Binary-Operators"
34191 all the time, because this character is defined in all encodings as text
34193 But the encoding can be changed by this LaTeX-preamble line:
34196 \begin_layout Standard
34201 Declare Inputtext{183}{
34211 f\SpecialChar \textcompwordmark{}
34215 \begin_layout Standard
34216 The character encoding (menu
34218 Document\SpecialChar \menuseparator
34219 Settings\SpecialChar \menuseparator
34222 ) specifies what character appears when a keyboard key is pressed.
34223 When the key for the character '·' is pressed, internally the command
34230 But this command is not available in a formula so that you would get LaTeX-erro
34232 With the changed encoding the right command is chosen automatically, depending
34233 on if the character was inserted into a formula or not.
34236 \begin_layout Standard
34237 The encoding of several characters is saved in definition files.
34238 Fore example the encoding
34242 is defined in the file
34246 that is in the installation folder of LaTeX.
34247 Encodings should only be changed via the LaTeX-preamble and not in the
34249 Otherwise own documents could not be edited by other LyX users working
34250 on other computers.
34253 \begin_layout Standard
34254 \begin_inset VSpace medskip
34257 Besides the centered dot, in this document the degree sign ° is defined
34258 with the following LaTeX-preamble line so that it can directly be inserted
34262 \begin_layout Standard
34267 DeclareInputtext{176}{
34277 f\SpecialChar \textcompwordmark{}
34281 \begin_layout Standard
34282 \begin_inset Newpage newpage
34288 \begin_layout Section
34290 Typographic Advises
34294 \begin_layout Plain Layout
34295 Typographic Advises
34303 \begin_layout Standard
34304 This section is a summary of the most important typographic rules, listed
34309 \begin_layout Plain Layout
34310 This collection was partly taken from the German semi-official dictionary
34312 \begin_inset Quotes eld
34316 \begin_inset Quotes erd
34320 \begin_inset CommandInset citation
34326 that lists some of the ISO rules.
34334 \begin_layout Itemize
34343 \begin_layout Plain Layout
34344 done with font styles, see
34345 \begin_inset CommandInset ref
34347 reference "sub:Font-Styles"
34357 \begin_inset space \thinspace{}
34361 \begin_inset Newline newline
34364 Between the value and the unit is the smallest space, see
34365 \begin_inset CommandInset ref
34367 reference "sub:Predefined-Space"
34372 \begin_inset Newline newline
34375 This convention is automatically fulfilled when the command
34382 When it is entered to a formula, two boxes appear.
34383 In the first one the value is inserted, in the second one the unit, and
34385 \begin_inset Formula $\unit[30]{km/h}$
34389 \begin_inset space \thinspace{}
34399 is not a real LaTeX command but the command
34405 , therefore you cannot use it in TeX code.
34408 \begin_layout Itemize
34409 Percent and perthousand signs are set like physical units:
34410 \begin_inset Newline newline
34414 \begin_inset space \thinspace{}
34420 \begin_layout Itemize
34421 The degree sign follows directly on the value: 15°, but not when it is used
34423 \begin_inset space \thinspace{}
34429 \begin_layout Itemize
34430 In numbers with more than four digits the smallest space is inserted before
34431 every third digit to group them:
34441 \begin_inset space \thinspace{}
34445 \begin_inset space \thinspace{}
34451 \begin_layout Itemize
34452 For dimensions like 120×90×40
34453 \begin_inset space \thinspace{}
34456 cm the multiplication sign
34457 \begin_inset Quotes eld
34461 \begin_inset Quotes erd
34465 It is available with the LaTeX-command
34471 , but can also directly be inserted with some keyboard definitions.
34474 \begin_layout Itemize
34475 Functions with names consisting of several letters are set upright to avoid
34477 \begin_inset CommandInset ref
34479 reference "sub:Predefined-Functions"
34486 \begin_layout Itemize
34487 Indices consisting of several letters, are set upright:
34488 \begin_inset Formula $E_{\mathrm{kin}}$
34492 \begin_inset Newline newline
34495 Components of matrices are set italic:
34496 \begin_inset Formula $\hat{H}_{kl}$
34502 \begin_layout Itemize
34503 The differentiation/integration operator 'd', the Euler's number 'e', and
34504 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34508 \begin_layout Standard
34509 \begin_inset Newpage newpage
34515 \begin_layout Section
34520 \begin_layout Plain Layout
34529 \begin_layout Standard
34530 Some characters and symbols can be created with several commands.
34531 Here is a list of the synonym commands:
34534 \begin_layout Standard
34535 \begin_inset VSpace bigskip
34539 \begin_inset space \hfill{}
34543 \begin_inset Tabular
34544 <lyxtabular version="3" rows="12" columns="2">
34546 <column alignment="center" valignment="top" width="0pt">
34547 <column alignment="center" valignment="top" width="0pt">
34549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34552 \begin_layout Plain Layout
34558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34561 \begin_layout Plain Layout
34563 \begin_inset Note Note
34566 \begin_layout Plain Layout
34573 is only used as spacer.
34585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34588 \begin_layout Plain Layout
34596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34599 \begin_layout Plain Layout
34603 \begin_layout Plain Layout
34616 \begin_layout Plain Layout
34630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34633 \begin_layout Plain Layout
34641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34644 \begin_layout Plain Layout
34654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34657 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34668 \begin_layout Plain Layout
34678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34681 \begin_layout Plain Layout
34689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34692 \begin_layout Plain Layout
34700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34703 \begin_layout Plain Layout
34711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34714 \begin_layout Plain Layout
34722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34725 \begin_layout Plain Layout
34733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34736 \begin_layout Plain Layout
34746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34749 \begin_layout Plain Layout
34757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34760 \begin_layout Plain Layout
34770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34773 \begin_layout Plain Layout
34781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34784 \begin_layout Plain Layout
34794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34797 \begin_layout Plain Layout
34805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34808 \begin_layout Plain Layout
34818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34821 \begin_layout Plain Layout
34829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34832 \begin_layout Plain Layout
34840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34843 \begin_layout Plain Layout
34851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34854 \begin_layout Plain Layout
34866 \begin_inset space \hfill{}
34870 \begin_inset Tabular
34871 <lyxtabular version="3" rows="12" columns="2">
34873 <column alignment="center" valignment="top" width="0pt">
34874 <column alignment="center" valignment="top" width="0pt">
34876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34879 \begin_layout Plain Layout
34885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34888 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34910 \begin_layout Plain Layout
34922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34925 \begin_layout Plain Layout
34933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34936 \begin_layout Plain Layout
34946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34949 \begin_layout Plain Layout
34957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34960 \begin_layout Plain Layout
34970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34973 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34984 \begin_layout Plain Layout
34992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34995 \begin_layout Plain Layout
35003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35006 \begin_layout Plain Layout
35014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35017 \begin_layout Plain Layout
35025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35028 \begin_layout Plain Layout
35038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35041 \begin_layout Plain Layout
35049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35052 \begin_layout Plain Layout
35062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35065 \begin_layout Plain Layout
35073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35076 \begin_layout Plain Layout
35086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35089 \begin_layout Plain Layout
35097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35100 \begin_layout Plain Layout
35110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35113 \begin_layout Plain Layout
35121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35124 \begin_layout Plain Layout
35134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35137 \begin_layout Plain Layout
35145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35148 \begin_layout Plain Layout
35162 \begin_inset space \hfill{}
35168 \begin_layout Standard
35169 \begin_inset Newpage newpage
35175 \begin_layout Bibliography
35176 \begin_inset CommandInset bibitem
35177 LatexCommand bibitem
35189 The LaTeX Companion
35192 Addison Wesley, 2004
35195 \begin_layout Bibliography
35196 \begin_inset CommandInset bibitem
35197 LatexCommand bibitem
35203 \begin_inset CommandInset href
35206 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35210 of LaTeX's math abilities
35213 \begin_layout Bibliography
35214 \begin_inset CommandInset bibitem
35215 LatexCommand bibitem
35220 LaTeX tips and tricks-
35221 \begin_inset CommandInset href
35224 target "http://tug.org/TeXnik/"
35231 \begin_layout Bibliography
35232 \begin_inset CommandInset bibitem
35233 LatexCommand bibitem
35239 \begin_inset CommandInset href
35242 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35250 \begin_layout Plain Layout
35262 \begin_layout Bibliography
35263 \begin_inset CommandInset bibitem
35264 LatexCommand bibitem
35270 \begin_inset CommandInset href
35273 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35277 of all symbols available with LaTeX-packages
35280 \begin_layout Bibliography
35281 \begin_inset CommandInset bibitem
35282 LatexCommand bibitem
35288 \begin_inset CommandInset href
35290 name "Documentation"
35291 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35295 of the LaTeX-package
35303 \begin_layout Plain Layout
35304 Packages ! hyperref
35312 \begin_layout Bibliography
35313 \begin_inset CommandInset bibitem
35314 LatexCommand bibitem
35320 \begin_inset CommandInset href
35323 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35334 \begin_inset CommandInset ref
35336 reference "sub:Operator-Limits"
35344 \begin_layout Plain Layout
35355 \begin_layout Bibliography
35356 \begin_inset CommandInset bibitem
35357 LatexCommand bibitem
35368 Auflage, Duden 2001
35371 \begin_layout Subsubsection*
35372 \begin_inset CommandInset index_print
35373 LatexCommand printindex