1 #LyX 1.6.3svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % center multirows (e.g. in sec. 13.3)
86 \renewcommand{\multirowsetup}{\centering}
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % redefine the greyed out note
113 \renewenvironment{lyxgreyedout}
114 {\textcolor{blue}\bgroup}{\egroup}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % needed in sec. 22.4
129 % check for package braket
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % needed in sec. 22.10
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
145 \use_default_options false
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pdfusetitle false
174 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
181 \paperorientation portrait
184 \paragraph_separation skip
186 \quotes_language english
189 \paperpagestyle plain
193 \tracking_changes false
194 \output_changes false
202 LyX's detailed Math manual
210 \begin_layout Plain Layout
212 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_inset CommandInset href
218 name "lyx-docs@lists.lyx.org"
219 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
230 \begin_inset Note Note
233 \begin_layout Plain Layout
240 \begin_inset Newline newline
244 \begin_inset Newline newline
252 \begin_layout Standard
253 \begin_inset CommandInset toc
254 LatexCommand tableofcontents
261 \begin_layout Standard
262 \begin_inset Note Note
265 \begin_layout Plain Layout
266 To export this document to PDF, PS, or DVI the LaTeX-packages
279 If they are not installed you can export the document anyway but the sections
280 where the packages are required won't appear in the output.
283 \begin_layout Plain Layout
284 The latest PDF-version of this document can be found here:
285 \begin_inset Newline newline
290 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
298 \begin_layout Standard
299 \begin_inset Newpage newpage
305 \begin_layout Section
309 \begin_layout Standard
310 This document explains LyX's math features and is furthermore a collection
311 of LaTeX-commands used for mathematical characters and constructs.
312 The explanations are designed for the usage of commands.
313 It is therefore required that you have read the section
324 \begin_layout Standard
325 Most of the characters and many constructs explained in this manual are
326 also accessible via the menu
330 \SpecialChar \menuseparator
346 But everybody who has to write lots of formulas will notice that it is
347 much faster to use commands instead of the math toolbar.
348 Therefore this manual is focused on commands but also mentions the correspondin
349 g toolbar buttons when available.
352 \begin_layout Standard
353 If not specially mentioned the commands are only available within formulas.
354 To be able to use all commands explained in this document, the option
358 must be used in the document settings (menu
360 Document\SpecialChar \menuseparator
361 Settings\SpecialChar \menuseparator
372 \begin_layout Plain Layout
375 Use AMS math package automatically
381 \begin_layout Plain Layout
390 -math when math constructs are found that are supported by LyX.
398 \begin_layout Standard
399 This document doesn't list all
403 \begin_layout Plain Layout
416 \begin_layout Plain Layout
421 \begin_layout Plain Layout
430 -math commands is in the file
433 \begin_inset CommandInset href
436 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
442 , which is part of every LaTeX standard installation.
447 for lucidity reasons.
450 \begin_layout Section
454 \begin_layout Standard
455 To create an inline formula
459 \begin_layout Plain Layout
465 that is embedded into a text line, use one of the shortcuts
471 or the toolbar button
472 \begin_inset Graphics
473 filename ../images/math-mode.png
479 \begin_inset Newline newline
482 To create a display style formula
486 \begin_layout Plain Layout
487 Formula ! display style
492 that will appear bigger and in an own paragraph, use one of these shortcuts:
502 \begin_layout Standard
503 To change a display style formula to an inline formula, set the cursor into
504 the formula and use one of the shortcuts
512 Edit\SpecialChar \menuseparator
513 Math\SpecialChar \menuseparator
517 The same way is used to change an inline formula to a display style formula.
520 \begin_layout Standard
521 To display parts of an inline formula in the size of a display style formula,
530 \begin_layout Plain Layout
541 Then a new blue box appears in which the desired formula part is inserted.
544 \begin_layout Standard
545 Only inline formulas are allowed inside tables.
548 \begin_layout Standard
553 can be turned on in the menu
555 View\SpecialChar \menuseparator
559 When you click there on
560 \begin_inset Quotes eld
564 \begin_inset Quotes erd
567 the toolbar will be shown permanently at the bottom; this state is visualized
572 menu with a checkmark.
573 When you click in this state again on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
589 is only shown when the cursor is within a formula; this state is visualized
590 by the renaming of the menu entry from
591 \begin_inset Quotes eld
595 \begin_inset Quotes erd
599 \begin_inset Quotes eld
607 \begin_inset Quotes erd
613 \begin_layout Standard
618 \begin_layout Plain Layout
624 is invoked by pressing the toolbar button
625 \begin_inset Graphics
626 filename ../images/ert-insert.png
633 Insert\SpecialChar \menuseparator
638 \begin_layout Plain Layout
654 \begin_inset Note Note
657 \begin_layout Plain Layout
658 In LyX there are three
659 \begin_inset Quotes eld
663 \begin_inset Quotes erd
666 that appear in the output with sub- and superscript letters: TeX, LaTeX,
670 \begin_layout Plain Layout
671 To avoid that these names are recognized as proper names, a TeX-brace pair
680 \begin_layout Standard
681 To change the LaTeX-preamble
685 \begin_layout Plain Layout
693 Document\SpecialChar \menuseparator
694 Settings\SpecialChar \menuseparator
699 \begin_layout Plain Layout
715 \begin_layout Standard
716 To edit matrices, case differentiations, and multiline formulas subsequently,
719 Edit\SpecialChar \menuseparator
724 Edit\SpecialChar \menuseparator
726 \begin_inset space \thinspace{}
730 \begin_inset space \thinspace{}
740 When lines and columns are swapped via the menu, the column or line where
741 the cursor is in is exchanged with the column to the right or the line
743 Is the cursor in the last column or row, the exchange is done with the
744 column to the left or the line above.
747 \begin_layout Standard
748 To write text in formulas
752 \begin_layout Plain Layout
753 For multiline formulas the command
760 \begin_inset CommandInset ref
762 reference "sub:Text-in-multiline"
779 \begin_layout Plain Layout
789 \begin_layout Plain Layout
796 This mode is invoked with the the shortcut
802 or by the insertion of the command
810 \begin_layout Plain Layout
821 The text appears black in LyX and can therefore be distinguished from the
822 other formula parts that appear blue.
823 In the output mathematical text is set upright, in contrary to other formula
827 \begin_layout Subsection*
831 \begin_layout Standard
832 Most of the LaTeX-commands for math constructs have the following scheme:
835 \begin_layout Standard
851 \begin_layout Standard
852 A command starts always with a backslash
853 \begin_inset Quotes gld
863 \begin_inset Quotes grd
867 To omit optional arguments, also omit the associated brackets.
868 The braces around the required arguments are named in this document as
873 \begin_layout Plain Layout
880 If you add in a formula a left brace to a command name, LyX creates automatical
882 In all other cases TeX-braces are created in formulas with the command
890 TeX-braces appear red in LyX, in contrary to normal braces that appear
892 In TeX-mode no command is needed to get TeX-braces.
893 TeX-braces don't appear in the output.
896 \begin_layout Standard
897 When commands without arguments, like commands for symbols are entered in
898 TeX-mode, a space character must
902 be behind the command to end it.
903 This space doesn't appear in the output.
904 When the space should appear in the output, the space must be followed
905 by a protected space in normal text.
908 \begin_layout Standard
909 A protected space is inserted with
912 arg "space-insert protected"
918 \begin_layout Subsection*
919 \begin_inset Newpage newpage
925 \begin_layout Itemize
930 \begin_layout Plain Layout
931 This visible space character can be created with the command
941 \begin_layout Plain Layout
949 , inserted in TeX-mode.
958 \begin_layout Plain Layout
971 denotes a space character to be input.
974 \begin_layout Itemize
976 \begin_inset Formula $\to$
979 denotes the usage of the corresponding arrow key on the keyboard.
982 \begin_layout Subsection*
986 \begin_layout Standard
988 \begin_inset Float table
994 \begin_layout Plain Layout
998 \begin_layout Plain Layout
999 \begin_inset CommandInset label
1001 name "tab:Available-units"
1013 \begin_layout Plain Layout
1015 \begin_inset Tabular
1016 <lyxtabular version="3" rows="13" columns="2">
1018 <column alignment="center" valignment="top" width="0">
1019 <column alignment="center" valignment="top" width="0">
1021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1084 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1093 \begin_layout Plain Layout
1095 \begin_inset space \thinspace{}
1099 \begin_inset space \thinspace{}
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset Formula $\approx$
1243 \begin_inset space \thinspace{}
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1256 \begin_layout Plain Layout
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1265 \begin_layout Plain Layout
1267 \begin_inset space \thinspace{}
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1297 \begin_inset Quotes eld
1303 \begin_inset Quotes erd
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1316 \begin_layout Plain Layout
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1325 \begin_layout Plain Layout
1327 \begin_inset Quotes eld
1335 \begin_inset Quotes erd
1345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1348 \begin_layout Plain Layout
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1357 \begin_layout Plain Layout
1359 \begin_inset space \thinspace{}
1363 \begin_inset Formula $\nicefrac{1}{18}$
1367 \begin_inset space \thinspace{}
1388 \begin_layout Standard
1389 \begin_inset Newpage newpage
1395 \begin_layout Section
1399 \begin_layout Subsection
1404 \begin_layout Plain Layout
1414 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1487 \begin_layout Standard
1488 Indices are created with an underscore
1489 \begin_inset Quotes eld
1493 \begin_inset Quotes erd
1496 or via the math toolbar button
1497 \begin_inset Graphics
1498 filename ../images/math-subscript.png
1503 , exponents with a caret
1504 \begin_inset Quotes eld
1508 \begin_inset Quotes erd
1511 or via the math toolbar button
1512 \begin_inset Graphics
1513 filename ../images/math-superscript.png
1521 \begin_layout Standard
1523 \begin_inset Tabular
1524 <lyxtabular version="3" rows="4" columns="2">
1526 <column alignment="center" valignment="top" width="0pt">
1527 <column alignment="center" valignment="top" width="0pt">
1529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1541 \begin_layout Plain Layout
1543 \begin_inset Note Note
1546 \begin_layout Plain Layout
1553 is only used as spacer.
1565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1568 \begin_layout Plain Layout
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1577 \begin_layout Plain Layout
1578 \begin_inset Formula $B_{V}$
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1591 \begin_layout Plain Layout
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1619 \begin_layout Plain Layout
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1636 \begin_layout Plain Layout
1637 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1653 \begin_layout Standard
1654 As the caret is in some languages an accent, vowels will be accentuated
1655 in this case and not set as exponents
1659 \begin_layout Plain Layout
1660 Depending on the used keyboard settings this can also happen for other character
1667 To get in this case exponents, press
1671 after the caret as in the last example.
1674 \begin_layout Subsection
1676 \begin_inset CommandInset label
1678 name "sub:Fractions"
1686 \begin_layout Plain Layout
1695 \begin_layout Standard
1696 Fractions are generated with the command
1706 \begin_layout Plain Layout
1714 or via the math toolbar button
1715 \begin_inset Graphics
1716 filename ../images/math/frac.png
1722 The font size is adjusted automatically, depending on whether the fraction
1723 is in an inline or display style formula.
1724 With the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac-square.png
1731 you can select different fraction types.
1734 \begin_layout Standard
1743 \begin_layout Plain Layout
1753 a fraction can be created that has in any case the size of a display style
1763 \begin_layout Plain Layout
1773 the fraction appears always with the size of an inline formula.
1777 \begin_layout Standard
1778 A line with the fraction
1779 \begin_inset Formula $\frac{1}{2}$
1782 that was created with the command
1791 \begin_layout Standard
1792 A line with the fraction
1793 \begin_inset Formula $\dfrac{1}{2}$
1796 that was created with the command
1805 \begin_layout Standard
1807 \begin_inset Tabular
1808 <lyxtabular version="3" rows="4" columns="2">
1810 <column alignment="center" valignment="top" width="0pt">
1811 <column alignment="center" valignment="top" width="0pt">
1813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1816 \begin_layout Plain Layout
1822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1825 \begin_layout Plain Layout
1827 \begin_inset Note Note
1830 \begin_layout Plain Layout
1837 is only used as spacer.
1849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1852 \begin_layout Plain Layout
1859 \begin_layout Plain Layout
1869 \begin_inset Formula $\downarrow$
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1894 \begin_layout Plain Layout
1901 \begin_layout Plain Layout
1911 \begin_inset Formula $\downarrow$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1922 \begin_layout Plain Layout
1923 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1936 \begin_layout Plain Layout
1943 \begin_layout Plain Layout
1956 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow\downarrow$
1993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1996 \begin_layout Plain Layout
1997 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2013 \begin_layout Standard
2014 \begin_inset VSpace bigskip
2018 \begin_inset Newpage newpage
2021 For nested fractions the command
2031 \begin_layout Plain Layout
2041 \begin_inset VSpace -3mm
2047 \begin_layout Standard
2048 \begin_inset Formula \begin{align*}
2049 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2050 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2057 \begin_layout Standard
2058 The command for the example above is:
2061 \begin_layout Standard
2070 \begin_layout Plain Layout
2080 \begin_inset Formula $\downarrow$
2089 \begin_layout Plain Layout
2104 \begin_layout Plain Layout
2114 \begin_inset Formula $\downarrow$
2118 \begin_inset Formula $\downarrow$
2124 \begin_layout Standard
2125 \begin_inset VSpace medskip
2131 \begin_layout Standard
2138 sets the fraction always in the size of a displayed formula, also when
2139 it is part of another fraction.
2142 \begin_layout Standard
2143 It is possible to specify the alignment of the numerator.
2150 is used to left align it, the command
2163 centers the numerator.
2164 These fractions demonstrate the different alignments:
2167 \begin_layout Standard
2168 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2172 \begin_inset Formula $\cfrac{A}{B+C}$
2176 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2182 \begin_layout Standard
2183 \begin_inset Note Greyedout
2186 \begin_layout Plain Layout
2203 are no real LaTeX commands but represent the command
2207 cfrac[alignment]{numerator}{denominator}
2210 Therefore you cannot use them in TeX code.
2218 \begin_layout Standard
2219 \begin_inset VSpace medskip
2222 It is often advantageous to combine
2235 \begin_inset Formula \[
2236 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2243 \begin_layout Standard
2244 For inline fractions with a sloped fraction stroke you can use the command
2255 \begin_layout Plain Layout
2264 \begin_inset Formula $\nicefrac{5}{31}$
2277 \begin_layout Plain Layout
2286 \begin_inset Formula $\unitfrac{5}{31}$
2289 There is furthermore the command
2295 that offers to write a fraction in combination with a number:
2296 \begin_inset Formula $\unitfrac[2]{1}{3}$
2302 \begin_layout Standard
2303 \begin_inset Note Greyedout
2306 \begin_layout Plain Layout
2317 is not a real LaTeX command but the command
2318 \begin_inset Newline newline
2325 unitfrac[number]{numerator}{denominator}
2328 Therefore you cannot use it in TeX code.
2336 \begin_layout Standard
2337 How to define own fractions where the fraction stroke can be changed, is
2339 \begin_inset CommandInset ref
2341 reference "sub:Self-defined-Fractions"
2348 \begin_layout Subsection
2353 \begin_layout Plain Layout
2362 \begin_layout Standard
2363 Square roots are created with
2373 \begin_layout Plain Layout
2381 or the math toolbar button
2382 \begin_inset Graphics
2383 filename ../images/math/sqrt.png
2388 , all other roots with the command
2398 \begin_layout Plain Layout
2406 or with the math toolbar button
2407 \begin_inset Graphics
2408 filename ../images/math/root.png
2416 \begin_layout Standard
2418 \begin_inset Tabular
2419 <lyxtabular version="3" rows="3" columns="2">
2421 <column alignment="center" valignment="top" width="0pt">
2422 <column alignment="center" valignment="top" width="0pt">
2424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2427 \begin_layout Plain Layout
2433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2438 \begin_inset Note Note
2441 \begin_layout Plain Layout
2448 is only used as spacer.
2460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2463 \begin_layout Plain Layout
2470 \begin_layout Plain Layout
2484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2487 \begin_layout Plain Layout
2488 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2501 \begin_layout Plain Layout
2508 \begin_layout Plain Layout
2518 \begin_inset Formula $\downarrow$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2529 \begin_layout Plain Layout
2530 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2546 \begin_layout Standard
2547 A square root can also be created with
2553 when the root index field is left empty.
2556 \begin_layout Standard
2557 With certain indices the distance to the root is too small, like in this
2559 \begin_inset Formula $\sqrt[\beta]{B}$
2563 \begin_inset Newline newline
2567 \begin_inset Formula $\beta$
2571 To avoid this, the commands
2581 \begin_layout Plain Layout
2599 \begin_layout Plain Layout
2607 are used with the following scheme:
2610 \begin_layout Standard
2624 \begin_layout Standard
2625 Distance is the number of Big Points (unit bp;
2626 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2629 ), that the index should be moved to the left or top, resp..
2630 The commands are written to the index.
2631 This way the command
2632 \begin_inset Newline newline
2642 \begin_inset Formula $\to$
2648 \begin_inset Formula $\to$
2657 \begin_layout Plain Layout
2667 \begin_inset Formula $\to$
2671 \begin_inset Newline newline
2676 produces a correct typeset formula:
2677 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2683 \begin_layout Subsection
2684 Binomial Coefficients
2688 \begin_layout Plain Layout
2689 Binomial coefficients
2697 \begin_layout Standard
2698 Binomial coefficients are inserted with the command
2708 \begin_layout Plain Layout
2716 or with the submenu of the math toolbar button
2717 \begin_inset Graphics
2718 filename ../images/math/frac-square.png
2724 Analog to fractions (
2744 \begin_layout Plain Layout
2764 \begin_layout Plain Layout
2773 For other brackets around binomial coeficients there are the commands
2783 \begin_layout Plain Layout
2801 \begin_layout Plain Layout
2812 \begin_layout Standard
2814 \begin_inset Tabular
2815 <lyxtabular version="3" rows="6" columns="2">
2817 <column alignment="center" valignment="top" width="0pt">
2818 <column alignment="center" valignment="top" width="0pt">
2820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2823 \begin_layout Plain Layout
2829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2832 \begin_layout Plain Layout
2834 \begin_inset Note Note
2837 \begin_layout Plain Layout
2844 is only used as spacer.
2856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2859 \begin_layout Plain Layout
2866 \begin_layout Plain Layout
2876 \begin_inset Formula $\downarrow$
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2887 \begin_layout Plain Layout
2888 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2901 \begin_layout Plain Layout
2908 \begin_layout Plain Layout
2918 \begin_inset Formula $\downarrow$
2926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2929 \begin_layout Plain Layout
2930 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2943 \begin_layout Plain Layout
2950 \begin_layout Plain Layout
2960 \begin_inset Formula $\downarrow$
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2971 \begin_layout Plain Layout
2972 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2985 \begin_layout Plain Layout
2992 \begin_layout Plain Layout
3002 \begin_inset Formula $\downarrow$
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3013 \begin_layout Plain Layout
3014 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3027 \begin_layout Plain Layout
3034 \begin_layout Plain Layout
3044 \begin_inset Formula $\downarrow$
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3055 \begin_layout Plain Layout
3056 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3072 \begin_layout Subsection
3073 Case Differentiations
3077 \begin_layout Plain Layout
3078 Case differentiations
3086 \begin_layout Standard
3088 \begin_inset Tabular
3089 <lyxtabular version="3" rows="3" columns="2">
3091 <column alignment="center" valignment="top" width="0pt">
3092 <column alignment="center" valignment="top" width="0pt">
3094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3097 \begin_layout Plain Layout
3103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3106 \begin_layout Plain Layout
3114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3117 \begin_layout Plain Layout
3124 \begin_layout Plain Layout
3134 \begin_inset Formula $\to$
3141 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3157 \begin_layout Plain Layout
3158 \begin_inset Formula $\begin{cases}
3169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3172 \begin_layout Plain Layout
3179 \begin_layout Plain Layout
3191 arg "newline-insert newline"
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3202 \begin_layout Plain Layout
3203 \begin_inset Formula $\begin{cases}
3204 A & \textrm{for }x>0\\
3205 B & \textrm{for }x=0\end{cases}$
3221 \begin_layout Standard
3228 or the usage of the math toolbar button
3229 \begin_inset Graphics
3230 filename ../images/math/cases.png
3235 you can create new lines with the shortcut
3238 arg "newline-insert newline"
3241 or the table toolbar button
3242 \begin_inset Graphics
3243 filename ../images/tabular-feature_append-row.png
3251 \begin_layout Standard
3258 is also available via the menu
3260 Insert\SpecialChar \menuseparator
3261 Math\SpecialChar \menuseparator
3267 \begin_layout Subsection
3272 \begin_layout Plain Layout
3281 \begin_layout Standard
3292 \begin_layout Plain Layout
3300 every character can be displayed canceled.
3301 The characters are quasi accentuated by a slash.
3304 \begin_layout Standard
3306 \begin_inset Tabular
3307 <lyxtabular version="3" rows="4" columns="2">
3309 <column alignment="center" valignment="top" width="0pt">
3310 <column alignment="center" valignment="top" width="0pt">
3312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3315 \begin_layout Plain Layout
3321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3324 \begin_layout Plain Layout
3332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3335 \begin_layout Plain Layout
3343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3346 \begin_layout Plain Layout
3347 \begin_inset Formula $\not=$
3357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3360 \begin_layout Plain Layout
3370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3373 \begin_layout Plain Layout
3374 \begin_inset Formula $\not\le$
3384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3387 \begin_layout Plain Layout
3397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3400 \begin_layout Plain Layout
3401 \begin_inset Formula $\not\parallel$
3417 \begin_layout Standard
3418 The last example shows, that not all negations look good.
3419 Therefore there are for some negations special commands (see
3420 \begin_inset CommandInset ref
3422 reference "sub:Mathematical-Symbols"
3427 \begin_inset CommandInset ref
3429 reference "sec:Relations"
3436 \begin_layout Subsection
3438 \begin_inset CommandInset label
3440 name "sub:Placeholders"
3448 \begin_layout Plain Layout
3458 \begin_layout Plain Layout
3459 Chemical characters ! Isotopes
3468 \begin_layout Plain Layout
3473 \begin_layout Plain Layout
3484 \begin_layout Plain Layout
3499 \begin_layout Standard
3501 \begin_inset space \thinspace{}
3505 \begin_inset space \space{}
3512 \begin_layout Plain Layout
3513 More about chemical symbols is written in
3514 \begin_inset CommandInset ref
3516 reference "sub:Chemical-Symbols-and"
3525 the following problem occurs:
3528 \begin_layout Standard
3530 \begin_inset Tabular
3531 <lyxtabular version="3" rows="2" columns="2">
3533 <column alignment="center" valignment="top" width="0pt">
3534 <column alignment="center" valignment="top" width="0pt">
3536 <cell alignment="center" valignment="top" usebox="none">
3539 \begin_layout Plain Layout
3540 Indices created with sub- and superscripts:
3545 <cell alignment="center" valignment="top" usebox="none">
3548 \begin_layout Plain Layout
3549 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3559 <cell alignment="center" valignment="top" usebox="none">
3562 \begin_layout Plain Layout
3568 <cell alignment="center" valignment="top" usebox="none">
3571 \begin_layout Plain Layout
3572 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3586 \begin_inset Note Note
3589 \begin_layout Plain Layout
3596 is only used as spacer.
3604 \begin_layout Standard
3605 The shorter index is by default placed below or above the first character
3606 of the longer index.
3607 To avoid this there is the command
3617 \begin_layout Plain Layout
3625 or the math toolbar button
3626 \begin_inset space \thinspace{}
3633 \begin_layout Plain Layout
3634 can be found in the submenu of the toolbar button
3635 \begin_inset Graphics
3636 filename ../images/math/space.png
3647 \begin_inset Graphics
3648 filename ../images/math/phantom.png
3653 that creates one or more phantom characters.
3660 a small blue box appears that is superposed with two red arrows.
3661 The arrows indicate that the complete width and height of the box content
3662 will be created as placeholder.
3663 Phantom characters are accordingly placeholders with the size of the characters.
3666 \begin_layout Standard
3668 \begin_inset Tabular
3669 <lyxtabular version="3" rows="4" columns="2">
3671 <column alignment="center" valignment="top" width="0">
3672 <column alignment="center" valignment="top" width="0">
3674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3677 \begin_layout Plain Layout
3683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3686 \begin_layout Plain Layout
3688 \begin_inset Note Note
3691 \begin_layout Plain Layout
3698 is only used as spacer.
3710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3713 \begin_layout Plain Layout
3718 \begin_layout Plain Layout
3733 \begin_layout Plain Layout
3743 \begin_inset Formula $\to$
3750 \begin_layout Plain Layout
3764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3767 \begin_layout Plain Layout
3768 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3781 \begin_layout Plain Layout
3786 \begin_layout Plain Layout
3801 \begin_layout Plain Layout
3811 \begin_inset Formula $\to$
3818 \begin_layout Plain Layout
3832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3835 \begin_layout Plain Layout
3836 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3849 \begin_layout Plain Layout
3856 \begin_layout Plain Layout
3871 \begin_layout Plain Layout
3881 \begin_inset Formula $\to$
3888 \begin_layout Plain Layout
3902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3905 \begin_layout Plain Layout
3906 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3922 \begin_layout Standard
3923 Furthermore there are the commands
3933 \begin_layout Plain Layout
3942 \begin_inset space ~
3946 \begin_inset Graphics
3947 filename ../images/math/vphantom.png
3962 \begin_layout Plain Layout
3971 \begin_inset space ~
3975 \begin_inset Graphics
3976 filename ../images/math/hphantom.png
3988 creates only space for the maximal height of the characters in the box
3989 but not for its width.
3996 creates only space for the width of the box content.
3997 Therefore the boxes of both commands have only one red arrow.
4000 \begin_layout Standard
4011 \begin_layout Plain Layout
4026 space for the height of the integral sign,
4030 \begin_layout Plain Layout
4037 creates an integral sign, see
4038 \begin_inset CommandInset ref
4040 reference "sub:Big-Operators"
4049 because this is the larger character.
4050 An example application is in
4051 \begin_inset CommandInset ref
4053 reference "sub:Multiline-Brackets"
4060 \begin_layout Subsection
4065 \begin_layout Plain Layout
4075 \begin_layout Plain Layout
4076 Formula ! underlined
4084 \begin_layout Standard
4086 \begin_inset Tabular
4087 <lyxtabular version="3" rows="4" columns="2">
4089 <column alignment="center" valignment="top" width="0pt">
4090 <column alignment="center" valignment="top" width="0pt">
4092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4095 \begin_layout Plain Layout
4101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4104 \begin_layout Plain Layout
4106 \begin_inset Note Note
4109 \begin_layout Plain Layout
4116 is only used as spacer.
4128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4131 \begin_layout Plain Layout
4138 \begin_layout Plain Layout
4151 \begin_layout Plain Layout
4164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4167 \begin_layout Plain Layout
4168 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4178 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4181 \begin_layout Plain Layout
4188 \begin_layout Plain Layout
4201 \begin_layout Plain Layout
4214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4217 \begin_layout Plain Layout
4218 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4231 \begin_layout Plain Layout
4238 \begin_layout Plain Layout
4253 \begin_layout Plain Layout
4267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4270 \begin_layout Plain Layout
4271 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4287 \begin_layout Standard
4288 In the last example it doesn't matter if first
4303 \begin_layout Standard
4304 To double underline e.
4305 \begin_inset space \thinspace{}
4309 \begin_inset space \space{}
4321 \begin_layout Standard
4322 It is possible to place up to 6 lines above or below characters.
4325 \begin_layout Standard
4326 \begin_inset VSpace bigskip
4329 Custom lines can be created using the command
4339 \begin_layout Plain Layout
4347 which has the following scheme:
4350 \begin_layout Standard
4355 rule[vertical offset]{length}{thickness}
4358 \begin_layout Standard
4359 The optional vertical offset shifts the line upwards (or downwards, when
4360 the value is negative).
4362 \begin_inset CommandInset ref
4364 reference "tab:Available-units"
4368 can be used for the values.
4369 Here are two example lines created with the commands
4370 \begin_inset Newline newline
4377 rule[-2ex]{3cm}{2pt}
4388 \begin_layout Standard
4390 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4396 \begin_layout Standard
4403 can also be used for text when it is inserted in TeX-mode.
4406 \begin_layout Subsection
4408 \begin_inset CommandInset label
4418 \begin_layout Plain Layout
4427 \begin_layout Standard
4428 There are different types of ellipses available.
4432 \begin_layout Plain Layout
4433 In the math toolbar in the submenu of the button
4434 \begin_inset Graphics
4435 filename ../images/math/ldots.png
4445 For listings dots at the baseline are used (
4455 \begin_layout Plain Layout
4463 ), while for operations dots are needed that are on the same height as the
4474 \begin_layout Plain Layout
4483 When using the command
4493 \begin_layout Plain Layout
4501 , LaTeX decides on the basis of the next character what type is used.
4504 \begin_layout Standard
4506 \begin_inset Tabular
4507 <lyxtabular version="3" rows="8" columns="2">
4509 <column alignment="center" valignment="top" width="0pt">
4510 <column alignment="center" valignment="top" width="0pt">
4512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4515 \begin_layout Plain Layout
4521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4524 \begin_layout Plain Layout
4532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4535 \begin_layout Plain Layout
4540 \begin_layout Plain Layout
4555 \begin_layout Plain Layout
4569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4572 \begin_layout Plain Layout
4573 \begin_inset Formula $A_{1},\dots,A_{n}$
4583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4586 \begin_layout Plain Layout
4591 \begin_layout Plain Layout
4606 \begin_layout Plain Layout
4620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4623 \begin_layout Plain Layout
4624 \begin_inset Formula $A_{1}+\dots+A_{n}$
4634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4637 \begin_layout Plain Layout
4642 \begin_layout Plain Layout
4657 \begin_layout Plain Layout
4671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4674 \begin_layout Plain Layout
4675 \begin_inset Formula $A_{1},\ldots,A_{n}$
4685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4688 \begin_layout Plain Layout
4693 \begin_layout Plain Layout
4708 \begin_layout Plain Layout
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 $A_{1}+\cdots+A_{n}$
4736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4739 \begin_layout Plain Layout
4747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4750 \begin_layout Plain Layout
4751 \begin_inset Formula $\vdots$
4761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4764 \begin_layout Plain Layout
4772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4775 \begin_layout Plain Layout
4776 \begin_inset Formula $\ddots$
4786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4789 \begin_layout Plain Layout
4791 \begin_inset space \thinspace{}
4794 matrix with the different dots
4799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4802 \begin_layout Plain Layout
4803 \begin_inset Formula $\begin{array}{ccc}
4804 A_{11} & \cdots & A_{1m}\\
4805 \vdots & \ddots & \vdots\\
4806 A_{n1} & \cdots & A_{nm}\end{array}$
4822 \begin_layout Standard
4823 The ellipses available in menu
4825 Insert\SpecialChar \menuseparator
4827 \begin_inset space ~
4841 \begin_layout Standard
4842 \begin_inset VSpace medskip
4845 Specially for matrices there are ellipses that span over several columns.
4846 They are created with the command
4856 \begin_layout Plain Layout
4864 , that has the following scheme:
4867 \begin_layout Standard
4872 hdotsfor[distance]{number of columns}
4875 \begin_layout Standard
4876 The number of columns specifies how many columns should be spanned.
4877 Distance is a factor for the distance between the dots.
4880 \begin_layout Standard
4881 In the following matrix the command
4887 was inserted in the first box of the second line, to get an ellipsis with
4888 a dot distance twice as long as with the command
4895 \begin_inset Formula \[
4896 \left(\begin{array}{cccc}
4899 q & w & e & r\end{array}\right)\]
4903 Note that the matrix fields that should be spanned must be empty, otherwise
4904 you get LaTeX-errors.
4907 \begin_layout Standard
4908 \begin_inset VSpace bigskip
4911 Furthermore you can fill with the command
4921 \begin_layout Plain Layout
4929 the rest of a line with dots.
4930 The effect of these commands is the same like with
4937 \begin_inset CommandInset ref
4939 reference "sub:Variable-Space"
4946 \begin_layout Standard
4947 For example the command
4955 \begin_layout Plain Layout
4969 \begin_layout Standard
4970 \begin_inset Formula $A\dotfill B$
4976 \begin_layout Standard
4983 there is for a line the command
4993 \begin_layout Plain Layout
5004 \begin_layout Standard
5005 \begin_inset Formula $A\hrulefill B$
5011 \begin_layout Standard
5012 To use the commands for text, they have to be inserted in TeX-mode.
5015 \begin_layout Section
5017 \begin_inset CommandInset label
5027 \begin_layout Plain Layout
5036 \begin_layout Standard
5037 Matrices can be inserted via the math toolbar button
5038 \begin_inset Graphics
5039 filename ../images/dialog-show_mathmatrix.png
5046 Insert\SpecialChar \menuseparator
5047 Math\SpecialChar \menuseparator
5051 You will be asked for the number of matrix columns and rows, and the alignment.
5052 The vertical alignment is hereby only of importance for matrices in inline
5056 \begin_layout Standard
5057 The first matrix is top
5058 \begin_inset Formula $\begin{array}[t]{cccc}
5061 C & F & I & L\end{array}$
5065 \begin_inset Formula $\begin{array}{cccc}
5068 C & F & I & L\end{array}$
5071 , and the third bottom
5072 \begin_inset Formula $\begin{array}[b]{cccc}
5075 C & F & I & L\end{array}$
5081 \begin_layout Standard
5082 The horizontal alignment specifies how the column entries should be aligned.
5083 It is set by entering a letter for every column.
5088 denotes left aligned,
5097 To create for example a 4
5102 \begin_inset space ~
5105 matrix where the first column is left aligned, the second and third are
5106 centered, and the last one is right aligned, one enters for the horizontal
5112 Normally are in a matrix all columns centered, therefore the default is
5113 for every column is a
5120 \begin_layout Standard
5121 Horizontal alignment:
5124 \begin_layout Standard
5130 \begin_inset Formula $\begin{array}{lll}
5133 C & F & 10000\end{array}$
5141 \begin_inset Formula $\begin{array}{ccc}
5144 C & F & 10000\end{array}$
5152 \begin_inset Formula $\begin{array}{rrr}
5155 C & F & 10000\end{array}$
5161 \begin_layout Standard
5162 To add or delete rows and columns subsequently, the math toolbar buttons
5164 \begin_inset Graphics
5165 filename ../images/tabular-feature_append-row.png
5171 \begin_inset Graphics
5172 filename ../images/tabular-feature_delete-row.png
5178 \begin_inset space \thinspace{}
5183 Edit\SpecialChar \menuseparator
5187 New rows can also be created with
5190 arg "newline-insert newline"
5196 \begin_layout Standard
5197 \begin_inset VSpace bigskip
5200 Parentheses around a matrix can can either be created with the commands
5211 \begin_layout Plain Layout
5229 \begin_layout Plain Layout
5240 \begin_inset space ~
5246 \begin_inset CommandInset ref
5248 reference "sub:Automatic-Bracket-Size"
5252 , or by using the following commands:
5253 \begin_inset VSpace medskip
5259 \begin_layout Standard
5260 \begin_inset space \hfill{}
5264 \begin_inset Tabular
5265 <lyxtabular version="3" rows="4" columns="2">
5267 <column alignment="center" valignment="top" width="0">
5268 <column alignment="center" valignment="top" width="0">
5270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5273 \begin_layout Plain Layout
5279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5282 \begin_layout Plain Layout
5284 \begin_inset Note Note
5287 \begin_layout Plain Layout
5294 is only used as spacer.
5306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5309 \begin_layout Plain Layout
5316 \begin_layout Plain Layout
5330 \begin_inset space \thinspace{}
5338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5341 \begin_layout Plain Layout
5342 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5343 0 & \textrm{-}\mathrm{i}\\
5344 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5357 \begin_layout Plain Layout
5364 \begin_layout Plain Layout
5378 \begin_inset space \thinspace{}
5386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5389 \begin_layout Plain Layout
5390 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5391 0 & \textrm{-}\mathrm{i}\\
5392 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5405 \begin_layout Plain Layout
5412 \begin_layout Plain Layout
5426 \begin_inset space \thinspace{}
5434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5437 \begin_layout Plain Layout
5438 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5439 0 & \textrm{-}\mathrm{i}\\
5440 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5454 \begin_inset space \hfill{}
5458 \begin_inset Tabular
5459 <lyxtabular version="3" rows="4" columns="2">
5461 <column alignment="center" valignment="top" width="0">
5462 <column alignment="center" valignment="top" width="0">
5464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5467 \begin_layout Plain Layout
5473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5476 \begin_layout Plain Layout
5484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5487 \begin_layout Plain Layout
5494 \begin_layout Plain Layout
5508 \begin_inset space \thinspace{}
5516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5519 \begin_layout Plain Layout
5520 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5521 0 & \textrm{-}\mathrm{i}\\
5522 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5535 \begin_layout Plain Layout
5542 \begin_layout Plain Layout
5556 \begin_inset space \thinspace{}
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5567 \begin_layout Plain Layout
5568 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5569 0 & \textrm{-}\mathrm{i}\\
5570 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5583 \begin_layout Plain Layout
5590 \begin_layout Plain Layout
5604 \begin_inset space \thinspace{}
5612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5615 \begin_layout Plain Layout
5616 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5617 0 & \textrm{-}\mathrm{i}\\
5618 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5632 \begin_inset space \hfill{}
5638 \begin_layout Standard
5639 \begin_inset VSpace medskip
5643 \begin_inset space \thinspace{}
5647 \begin_inset space \space{}
5656 is inserted, a blue box appears between two vertical lines where the matrix
5660 \begin_layout Standard
5661 \begin_inset VSpace bigskip
5664 As all multiline formulas are matrices, the length
5674 \begin_layout Plain Layout
5682 that is described in
5683 \begin_inset CommandInset ref
5685 reference "sub:Column-Separation"
5689 can also be used to change the column separation of matrices.
5692 \begin_layout Standard
5693 To change the row separation, the command
5703 \begin_layout Plain Layout
5712 It is used as follows:
5715 \begin_layout Standard
5722 arraystretch}{stretch factor}
5726 \begin_layout Plain Layout
5737 \begin_layout Standard
5744 assigns the stretch factor to the predefined command
5752 \begin_inset space \thinspace{}
5756 \begin_inset space \space{}
5759 the row separation, use the factor 2.
5760 This is then used for all following matrices.
5761 To go back to the original separation, assign the factor 1 to
5770 \begin_layout Standard
5771 To set matrices into a text line, the command
5781 \begin_layout Plain Layout
5790 When it is inserted a blue box with two dashed lines appears.
5791 In this box the matrix is inserted.
5794 \begin_layout Standard
5796 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5797 C & D\end{smallmatrix}\right)$
5803 \begin_layout Section
5804 Brackets and Delimiters
5808 \begin_layout Plain Layout
5818 \begin_layout Plain Layout
5827 \begin_layout Subsection
5828 Vertical Brackets and Delimiters
5832 \begin_layout Plain Layout
5841 \begin_layout Standard
5842 \begin_inset space \hfill{}
5846 \begin_inset Tabular
5847 <lyxtabular version="3" rows="9" columns="2">
5849 <column alignment="center" valignment="top" width="0pt">
5850 <column alignment="center" valignment="top" width="0pt">
5852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5855 \begin_layout Plain Layout
5861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5864 \begin_layout Plain Layout
5872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5875 \begin_layout Plain Layout
5881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5884 \begin_layout Plain Layout
5885 \begin_inset Formula $($
5895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5898 \begin_layout Plain Layout
5904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5907 \begin_layout Plain Layout
5908 \begin_inset Formula $\{$
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5921 \begin_layout Plain Layout
5927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5930 \begin_layout Plain Layout
5931 \begin_inset Formula $[$
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5944 \begin_layout Plain Layout
5952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5955 \begin_layout Plain Layout
5956 \begin_inset Formula $\langle$
5966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5969 \begin_layout Plain Layout
5977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5980 \begin_layout Plain Layout
5981 \begin_inset Formula $\lceil$
5991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5994 \begin_layout Plain Layout
6002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6005 \begin_layout Plain Layout
6006 \begin_inset Formula $\lfloor$
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6029 \begin_inset Formula $/$
6039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6042 \begin_layout Plain Layout
6048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6051 \begin_layout Plain Layout
6052 \begin_inset Formula $|$
6066 \begin_inset space \hfill{}
6070 \begin_inset Tabular
6071 <lyxtabular version="3" rows="9" columns="2">
6073 <column alignment="center" valignment="top" width="0pt">
6074 <column alignment="center" valignment="top" width="0pt">
6076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6079 \begin_layout Plain Layout
6085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6088 \begin_layout Plain Layout
6096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6099 \begin_layout Plain Layout
6105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6108 \begin_layout Plain Layout
6109 \begin_inset Formula $)$
6119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6122 \begin_layout Plain Layout
6128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6131 \begin_layout Plain Layout
6132 \begin_inset Formula $\}$
6142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6145 \begin_layout Plain Layout
6151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6154 \begin_layout Plain Layout
6155 \begin_inset Formula $]$
6165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6168 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\rangle$
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6193 \begin_layout Plain Layout
6201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6204 \begin_layout Plain Layout
6205 \begin_inset Formula $\rceil$
6215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6218 \begin_layout Plain Layout
6226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6229 \begin_layout Plain Layout
6230 \begin_inset Formula $\rfloor$
6240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6243 \begin_layout Plain Layout
6253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6256 \begin_layout Plain Layout
6257 \begin_inset Formula $\backslash$
6267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6270 \begin_layout Plain Layout
6278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6281 \begin_layout Plain Layout
6282 \begin_inset Formula $\|$
6296 \begin_inset space \hfill{}
6302 \begin_layout Standard
6305 \begin_inset Note Greyedout
6308 \begin_layout Plain Layout
6313 In TeX-mode the command
6323 \begin_layout Plain Layout
6331 must be used for the backslash, because the command
6339 produces there a line break.
6347 \begin_layout Standard
6348 For all characters listed above the size can be adjusted with the commands
6349 described in the following two subsections.
6350 When using these commands, the characters < and > can directly be used
6351 instead of the commands
6366 \begin_layout Subsubsection
6368 \begin_inset CommandInset label
6370 name "sub:Manual-Bracket-Size"
6378 \begin_layout Plain Layout
6379 Bracket size ! manual
6387 \begin_layout Standard
6388 The bracket size can be specified manually by the LaTeX-commands
6398 \begin_layout Plain Layout
6431 denotes the smallest and
6437 the largest bracket size.
6440 \begin_layout Standard
6441 These commands are used to emphasize levels of brackets:
6444 \begin_layout Standard
6446 \begin_inset Tabular
6447 <lyxtabular version="3" rows="2" columns="2">
6449 <column alignment="center" valignment="top" width="0pt">
6450 <column alignment="center" valignment="top" width="0pt">
6452 <cell alignment="center" valignment="top" usebox="none">
6455 \begin_layout Plain Layout
6456 all brackets in the same size:
6461 <cell alignment="center" valignment="top" usebox="none">
6464 \begin_layout Plain Layout
6465 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6475 <cell alignment="center" valignment="top" usebox="none">
6478 \begin_layout Plain Layout
6484 <cell alignment="center" valignment="top" usebox="none">
6487 \begin_layout Plain Layout
6488 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6502 \begin_inset Note Note
6505 \begin_layout Plain Layout
6512 is only used as spacer.
6520 \begin_layout Standard
6521 For the second formula the command
6531 \begin_layout Plain Layout
6545 \begin_layout Standard
6546 Here is an overview about all bracket sizes:
6549 \begin_layout Standard
6569 \begin_layout Plain Layout
6586 \begin_layout Plain Layout
6599 \begin_layout Plain Layout
6615 \begin_layout Standard
6617 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6623 \begin_layout Standard
6630 -commands there is the variant
6640 \begin_layout Plain Layout
6648 that adds a bit more space between the bracket and its content, and the
6665 \begin_layout Plain Layout
6675 , that don't add additional space.
6680 at the end of the command
6686 is for a left bracket; for a right bracket this will be replaced by an
6692 A left or right bracket can each be an opening or closing bracket.
6695 \begin_layout Standard
6696 In the following table is a comparison of the variants:
6699 \begin_layout Standard
6701 \begin_inset Tabular
6702 <lyxtabular version="3" rows="5" columns="2">
6704 <column alignment="center" valignment="middle" width="0">
6705 <column alignment="center" valignment="middle" width="0">
6707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6710 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6719 \begin_layout Plain Layout
6721 \begin_inset Note Note
6724 \begin_layout Plain Layout
6731 is only used as spacer.
6743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6746 \begin_layout Plain Layout
6761 \begin_layout Plain Layout
6779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6782 \begin_layout Plain Layout
6783 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6796 \begin_layout Plain Layout
6811 \begin_layout Plain Layout
6829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6832 \begin_layout Plain Layout
6833 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6846 \begin_layout Plain Layout
6861 \begin_layout Plain Layout
6879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6882 \begin_layout Plain Layout
6883 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6896 \begin_layout Plain Layout
6908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6911 \begin_layout Plain Layout
6912 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6928 \begin_layout Subsubsection
6929 Automatic Bracket Size
6930 \begin_inset CommandInset label
6932 name "sub:Automatic-Bracket-Size"
6940 \begin_layout Plain Layout
6941 Bracket size ! automatic
6949 \begin_layout Standard
6950 Brackets with variable size can be inserted with the commands
6960 \begin_layout Plain Layout
6978 \begin_layout Plain Layout
6986 or via the math toolbar button
6987 \begin_inset Graphics
6988 filename ../images/dialog-show_mathdelimiter.png
7006 the wanted bracket must be inserted.
7007 The bracket size will then automatically be calculated for the output.
7010 \begin_layout Standard
7012 normal bracket: The command
7022 \begin_layout Plain Layout
7032 \begin_inset Formula $\downarrow$
7039 \begin_layout Plain Layout
7051 \begin_inset Formula \[
7059 \begin_layout Standard
7061 multiline bracket: The command
7073 \begin_layout Plain Layout
7083 \begin_inset Formula $\downarrow$
7090 \begin_layout Plain Layout
7104 \begin_inset Formula \[
7105 \ln\left(\frac{A}{C}\right)\]
7112 \begin_layout Standard
7128 \begin_inset space ~
7134 This has the advantage that you can see in LyX immediately the real bracket
7135 size and that the matching right bracket will be created too.
7136 \begin_inset Newline newline
7139 The command for the last example would then be:
7153 \begin_layout Plain Layout
7163 \begin_inset Formula $\downarrow$
7169 \begin_layout Standard
7170 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7171 For example the command
7181 \begin_layout Plain Layout
7191 \begin_inset Formula $\downarrow$
7198 \begin_layout Plain Layout
7214 \begin_inset Formula \[
7215 \left.\frac{A}{B}\right\} \]
7233 will be converted by LyX to brackets in the right size when the document
7234 is reloaded and an omitted bracket will appear as dashed line.
7237 \begin_layout Standard
7238 \begin_inset VSpace bigskip
7241 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7252 \begin_layout Plain Layout
7260 is additionally available for all brackets and limits.
7261 With this command the height of the following character is adapted to the
7262 one of the surrounding brackets, what is e.
7263 \begin_inset space \thinspace{}
7267 \begin_inset space \space{}
7270 needed for physical vectors:
7271 \begin_inset Formula \[
7272 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7276 For physical vectors there is a special LaTeX-package, described in
7277 \begin_inset CommandInset ref
7279 reference "sub:Physical-Vectors"
7286 \begin_layout Subsection
7291 \begin_layout Plain Layout
7292 Brackets ! horizontal
7300 \begin_layout Standard
7302 \begin_inset Tabular
7303 <lyxtabular version="3" rows="4" columns="2">
7305 <column alignment="center" valignment="top" width="0pt">
7306 <column alignment="center" valignment="top" width="0pt">
7308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7311 \begin_layout Plain Layout
7313 \begin_inset Note Note
7316 \begin_layout Plain Layout
7323 is only used as spacer.
7333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7336 \begin_layout Plain Layout
7344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7347 \begin_layout Plain Layout
7351 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7379 \begin_layout Plain Layout
7392 \begin_layout Plain Layout
7405 \begin_layout Plain Layout
7416 \begin_layout Plain Layout
7429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7432 \begin_layout Plain Layout
7433 \begin_inset Formula $\overbrace{A+B}^{3}$
7443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7446 \begin_layout Plain Layout
7450 \begin_layout Plain Layout
7465 \begin_layout Plain Layout
7478 \begin_layout Plain Layout
7491 \begin_layout Plain Layout
7502 \begin_layout Plain Layout
7515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7518 \begin_layout Plain Layout
7519 \begin_inset Formula $\underbrace{A+B}_{5}$
7529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7532 \begin_layout Plain Layout
7539 \begin_layout Plain Layout
7554 \begin_layout Plain Layout
7567 \begin_layout Plain Layout
7580 \begin_layout Plain Layout
7593 \begin_layout Plain Layout
7606 \begin_layout Plain Layout
7619 \begin_layout Plain Layout
7633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7636 \begin_layout Plain Layout
7637 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7653 \begin_layout Standard
7654 In the last example it doesn't matter if
7666 is inserted at first.
7669 \begin_layout Standard
7670 \begin_inset VSpace bigskip
7673 When brackets are needed that overlap each other, multiline formulas, as
7675 \begin_inset CommandInset ref
7677 reference "sec:Multiline-Formulas"
7682 \begin_inset Formula \begin{eqnarray*}
7683 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7684 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7688 In the first row the formula is inserted together with the first brace.
7689 It is hereby important that the space command
7693 \begin_layout Plain Layout
7694 Space commands are explained in
7695 \begin_inset CommandInset ref
7697 reference "sub:Predefined-Space"
7712 is inserted before the first
7713 \begin_inset Formula $d$
7716 , because the brace that ends behind the
7717 \begin_inset Formula $q$
7720 prevents that the following
7721 \begin_inset Quotes eld
7725 \begin_inset Quotes erd
7728 is surrounded by space.
7732 \begin_layout Plain Layout
7733 because a bracket is not handled as character, see
7734 \begin_inset CommandInset ref
7736 reference "sub:Binary-Operators"
7745 In the second row the second brace is inserted.
7746 As it should begin before the
7747 \begin_inset Formula $b$
7762 \begin_layout Plain Layout
7770 \begin_inset CommandInset ref
7772 reference "sub:Placeholders"
7781 This space is needed because the
7782 \begin_inset Quotes eld
7786 \begin_inset Quotes erd
7789 is also surrounded by space in the formula.
7790 The brace is placed under the command
7799 \begin_layout Standard
7800 It gets more complicated when brackets overlap each other, like in the following
7805 \begin_layout Plain Layout
7817 \begin_inset Formula \begin{eqnarray*}
7818 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7819 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7827 \begin_layout Plain Layout
7838 The first formula row is the same as the second row of the previous example,
7839 with the difference that the brace is above.
7840 The second row contains the formula together with the second brace.
7841 To avoid that there is space between the upper brace in the first row and
7842 the formula, the row spacing need to be reduced.
7843 This is not easily possible due to a bug in LyX
7847 \begin_layout Plain Layout
7848 \begin_inset CommandInset href
7850 name "LyX-bug #1505"
7851 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7861 As solution for the problem, the global formula row separation
7871 \begin_layout Plain Layout
7879 must be changed to -6
7880 \begin_inset space \thinspace{}
7883 pt before the formula with the command
7898 is set back after the formula to the standard value of 3
7899 \begin_inset space \thinspace{}
7902 pt using the same command.
7903 More about the row separation in formulas is explained in
7904 \begin_inset CommandInset ref
7906 reference "sub:Line-Separation"
7913 \begin_layout Section
7918 \begin_layout Plain Layout
7927 \begin_layout Standard
7928 Arrows can be inserted via the math toolbar button
7929 \begin_inset Graphics
7930 filename ../images/math/leftarrow.png
7935 or the commands listed in the following subsections.
7938 \begin_layout Standard
7939 \begin_inset Newpage newpage
7945 \begin_layout Subsection
7950 \begin_layout Plain Layout
7959 \begin_layout Standard
7960 \begin_inset space \hfill{}
7964 \begin_inset Tabular
7965 <lyxtabular version="3" rows="8" columns="2">
7967 <column alignment="center" valignment="top" width="0pt">
7968 <column alignment="center" valignment="top" width="0pt">
7970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7982 \begin_layout Plain Layout
7990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7993 \begin_layout Plain Layout
8001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8004 \begin_layout Plain Layout
8005 \begin_inset Formula $\gets$
8015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8018 \begin_layout Plain Layout
8026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8029 \begin_layout Plain Layout
8030 \begin_inset Formula $\Leftarrow$
8040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8043 \begin_layout Plain Layout
8051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8054 \begin_layout Plain Layout
8055 \begin_inset Formula $\longleftarrow$
8065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8068 \begin_layout Plain Layout
8076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8079 \begin_layout Plain Layout
8080 \begin_inset Formula $\Longleftarrow$
8090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8093 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8104 \begin_layout Plain Layout
8105 \begin_inset Formula $\leftharpoonup$
8115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\leftharpoondown$
8140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\hookleftarrow$
8169 \begin_inset space \hfill{}
8173 \begin_inset Tabular
8174 <lyxtabular version="3" rows="8" columns="2">
8176 <column alignment="center" valignment="top" width="0pt">
8177 <column alignment="center" valignment="top" width="0pt">
8179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8182 \begin_layout Plain Layout
8188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8191 \begin_layout Plain Layout
8199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\to$
8224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8227 \begin_layout Plain Layout
8235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8238 \begin_layout Plain Layout
8239 \begin_inset Formula $\Rightarrow$
8249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8252 \begin_layout Plain Layout
8260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8263 \begin_layout Plain Layout
8264 \begin_inset Formula $\longrightarrow$
8274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8277 \begin_layout Plain Layout
8285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8288 \begin_layout Plain Layout
8289 \begin_inset Formula $\Longrightarrow$
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\rightharpoonup$
8324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\rightharpoondown$
8349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8364 \begin_inset Formula $\hookrightarrow$
8378 \begin_inset space \hfill{}
8384 \begin_layout Standard
8385 \begin_inset space \hfill{}
8389 \begin_inset Tabular
8390 <lyxtabular version="3" rows="6" columns="2">
8392 <column alignment="center" valignment="top" width="0pt">
8393 <column alignment="center" valignment="top" width="0pt">
8395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8398 \begin_layout Plain Layout
8404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8407 \begin_layout Plain Layout
8415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8418 \begin_layout Plain Layout
8426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8429 \begin_layout Plain Layout
8430 \begin_inset Formula $\leftrightarrow$
8440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8443 \begin_layout Plain Layout
8451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8454 \begin_layout Plain Layout
8455 \begin_inset Formula $\Leftrightarrow$
8465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8468 \begin_layout Plain Layout
8476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8479 \begin_layout Plain Layout
8480 \begin_inset Formula $\longleftrightarrow$
8490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8493 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8504 \begin_layout Plain Layout
8505 \begin_inset Formula $\Longleftrightarrow$
8515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8518 \begin_layout Plain Layout
8526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Plain Layout
8530 \begin_inset Formula $\rightleftharpoons$
8544 \begin_inset space \hspace{}
8549 \begin_inset space \hfill{}
8553 \begin_inset Tabular
8554 <lyxtabular version="3" rows="5" columns="2">
8556 <column alignment="center" valignment="top" width="0pt">
8557 <column alignment="center" valignment="top" width="0pt">
8559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8571 \begin_layout Plain Layout
8579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8582 \begin_layout Plain Layout
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8593 \begin_layout Plain Layout
8594 \begin_inset Formula $\mapsto$
8604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8607 \begin_layout Plain Layout
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8618 \begin_layout Plain Layout
8619 \begin_inset Formula $\longmapsto$
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8632 \begin_layout Plain Layout
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8643 \begin_layout Plain Layout
8644 \begin_inset Formula $\leadsto$
8654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8657 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\dasharrow$
8683 \begin_inset space \hfill{}
8689 \begin_layout Standard
8690 \begin_inset VSpace medskip
8693 Arrows used as accent like e.
8694 \begin_inset space \thinspace{}
8698 \begin_inset space \space{}
8701 vector arrows are listed in
8702 \begin_inset CommandInset ref
8704 reference "sec:Accents"
8711 \begin_layout Standard
8712 \begin_inset VSpace bigskip
8715 Furthermore there are the labeled arrows
8719 \begin_layout Plain Layout
8735 \begin_layout Plain Layout
8753 \begin_layout Plain Layout
8760 \begin_layout Plain Layout
8775 When inserting one of these commands in a formula, an arrow with two blue
8776 boxes appear where the label can be inserted.
8777 The length of the arrow adapts to the label width.
8780 \begin_layout Standard
8782 \begin_inset Tabular
8783 <lyxtabular version="3" rows="3" columns="2">
8785 <column alignment="center" valignment="top" width="0pt">
8786 <column alignment="center" valignment="top" width="0pt">
8788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8791 \begin_layout Plain Layout
8797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8800 \begin_layout Plain Layout
8802 \begin_inset Note Note
8805 \begin_layout Plain Layout
8812 is only used as spacer.
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8827 \begin_layout Plain Layout
8834 \begin_layout Plain Layout
8844 \begin_inset Formula $\downarrow$
8848 \begin_inset Formula $\to$
8856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8859 \begin_layout Plain Layout
8860 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8873 \begin_layout Plain Layout
8880 \begin_layout Plain Layout
8890 \begin_inset Formula $\downarrow$
8894 \begin_inset Formula $\to$
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8905 \begin_layout Plain Layout
8906 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8922 \begin_layout Subsection
8923 Vertical and diagonal Arrows
8927 \begin_layout Plain Layout
8937 \begin_layout Plain Layout
8946 \begin_layout Standard
8947 \begin_inset space \hfill{}
8951 \begin_inset Tabular
8952 <lyxtabular version="3" rows="7" columns="2">
8954 <column alignment="center" valignment="top" width="0pt">
8955 <column alignment="center" valignment="top" width="0pt">
8957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8960 \begin_layout Plain Layout
8966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8969 \begin_layout Plain Layout
8977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8980 \begin_layout Plain Layout
8988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8991 \begin_layout Plain Layout
8992 \begin_inset Formula $\uparrow$
9002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9005 \begin_layout Plain Layout
9013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9016 \begin_layout Plain Layout
9017 \begin_inset Formula $\Uparrow$
9027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9030 \begin_layout Plain Layout
9038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9041 \begin_layout Plain Layout
9042 \begin_inset Formula $\updownarrow$
9052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9055 \begin_layout Plain Layout
9063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9066 \begin_layout Plain Layout
9067 \begin_inset Formula $\Updownarrow$
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\Downarrow$
9102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9116 \begin_layout Plain Layout
9117 \begin_inset Formula $\downarrow$
9131 \begin_inset space \hfill{}
9135 \begin_inset Tabular
9136 <lyxtabular version="3" rows="5" columns="2">
9138 <column alignment="center" valignment="top" width="0pt">
9139 <column alignment="center" valignment="top" width="0pt">
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9153 \begin_layout Plain Layout
9161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9164 \begin_layout Plain Layout
9172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9175 \begin_layout Plain Layout
9176 \begin_inset Formula $\nearrow$
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9189 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $\searrow$
9211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9214 \begin_layout Plain Layout
9222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9225 \begin_layout Plain Layout
9226 \begin_inset Formula $\swarrow$
9236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9239 \begin_layout Plain Layout
9247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9250 \begin_layout Plain Layout
9251 \begin_inset Formula $\nwarrow$
9265 \begin_inset space \hfill{}
9271 \begin_layout Standard
9272 \begin_inset VSpace medskip
9275 Vertical arrows can be used also as delimiter together with the commands
9277 \begin_inset CommandInset ref
9279 reference "sub:Manual-Bracket-Size"
9284 \begin_inset CommandInset ref
9286 reference "sub:Automatic-Bracket-Size"
9293 \begin_layout Standard
9294 \begin_inset Newpage newpage
9300 \begin_layout Section
9302 \begin_inset CommandInset label
9312 \begin_layout Plain Layout
9321 \begin_layout Standard
9322 Accents can be inserted via the math toolbar button
9323 \begin_inset Graphics
9324 filename ../images/math/hat.png
9329 or the commands listed in the following subsections.
9332 \begin_layout Subsection
9333 Accents for one Character
9337 \begin_layout Plain Layout
9350 \begin_layout Plain Layout
9352 \begin_inset CommandInset ref
9354 reference "sub:Accents-in-Text"
9367 \begin_layout Plain Layout
9375 \begin_inset Note Note
9378 \begin_layout Plain Layout
9381 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9384 \begin_layout Plain Layout
9387 texorpdfstring is in section
9388 \begin_inset CommandInset ref
9390 reference "sub:Formulas-in-Section"
9400 \begin_inset CommandInset label
9402 name "sub:Accents-for-one"
9410 \begin_layout Plain Layout
9411 Accents ! for one character
9419 \begin_layout Standard
9420 \begin_inset space \hfill{}
9424 \begin_inset Tabular
9425 <lyxtabular version="3" rows="8" columns="2">
9427 <column alignment="center" valignment="top" width="0pt">
9428 <column alignment="center" valignment="top" width="0pt">
9430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9433 \begin_layout Plain Layout
9439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9442 \begin_layout Plain Layout
9444 \begin_inset Note Note
9447 \begin_layout Plain Layout
9454 is only used as spacer.
9466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9469 \begin_layout Plain Layout
9476 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9507 \begin_layout Plain Layout
9514 \begin_layout Plain Layout
9528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9531 \begin_layout Plain Layout
9532 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9545 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9569 \begin_layout Plain Layout
9570 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9583 \begin_layout Plain Layout
9591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9594 \begin_layout Plain Layout
9595 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9608 \begin_layout Plain Layout
9615 \begin_layout Plain Layout
9628 \begin_layout Plain Layout
9639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9642 \begin_layout Plain Layout
9643 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9656 \begin_layout Plain Layout
9663 \begin_layout Plain Layout
9677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9680 \begin_layout Plain Layout
9681 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9694 \begin_layout Plain Layout
9701 \begin_layout Plain Layout
9715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9718 \begin_layout Plain Layout
9719 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9733 \begin_inset space \hfill{}
9737 \begin_inset Tabular
9738 <lyxtabular version="3" rows="7" columns="2">
9740 <column alignment="center" valignment="top" width="0pt">
9741 <column alignment="center" valignment="top" width="0pt">
9743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9746 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9766 \begin_layout Plain Layout
9773 \begin_layout Plain Layout
9787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9790 \begin_layout Plain Layout
9791 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9804 \begin_layout Plain Layout
9811 \begin_layout Plain Layout
9825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9828 \begin_layout Plain Layout
9829 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9842 \begin_layout Plain Layout
9849 \begin_layout Plain Layout
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9880 \begin_layout Plain Layout
9887 \begin_layout Plain Layout
9901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9904 \begin_layout Plain Layout
9905 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9918 \begin_layout Plain Layout
9925 \begin_layout Plain Layout
9939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9942 \begin_layout Plain Layout
9943 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9956 \begin_layout Plain Layout
9963 \begin_layout Plain Layout
9977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9980 \begin_layout Plain Layout
9981 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9995 \begin_inset space \hfill{}
10001 \begin_layout Standard
10002 \begin_inset VSpace bigskip
10008 \begin_layout Standard
10009 You can directly insert accents like é to formulas.
10010 LyX will transform them to the corresponding accent command.
10015 \begin_layout Plain Layout
10021 it is better to insert a quotation mark before the vowel.
10022 These two characters are then treated by LaTeX as
10026 character when the formula part with the umlaut is marked as German.
10034 \begin_inset Quotes eld
10038 \begin_inset Quotes erd
10041 umlauts are created as demonstrated in the following example:
10044 \begin_layout Standard
10045 \begin_inset VSpace -2mm
10051 \begin_layout Standard
10053 \begin_inset Tabular
10054 <lyxtabular version="3" rows="3" columns="2">
10056 <column alignment="center" valignment="top" width="0">
10057 <column alignment="center" valignment="top" width="0">
10059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10062 \begin_layout Plain Layout
10068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10071 \begin_layout Plain Layout
10073 \begin_inset Note Note
10076 \begin_layout Plain Layout
10084 \begin_inset space \thinspace{}
10087 pt space are only used as spacer.
10099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10102 \begin_layout Plain Layout
10105 \begin_inset Quotes grd
10113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10116 \begin_layout Plain Layout
10117 \begin_inset space \hspace{}
10124 \begin_inset Formula $"i$
10134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10137 \begin_layout Plain Layout
10144 \begin_layout Plain Layout
10158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10161 \begin_layout Plain Layout
10162 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10178 \begin_layout Standard
10179 Another advantage to
10185 is that umlauts can directly be converted to mathematical text because
10186 the accent commands above are
10192 in mathematical text
10195 To convert an accented character to mathematical text, only the character
10196 under the accent may be converted.
10197 This applies also for all other conversions, e.
10198 \begin_inset space \thinspace{}
10202 \begin_inset space \space{}
10208 \begin_layout Standard
10209 In mathematical text, umlauts and other accented characters can directly
10213 \begin_layout Subsection
10214 Accents for Operators
10218 \begin_layout Plain Layout
10219 Accents ! for operators
10227 \begin_layout Standard
10238 \begin_layout Plain Layout
10256 \begin_layout Plain Layout
10264 characters can be placed above or below an operator, respectively, to accent
10276 \begin_layout Plain Layout
10284 characters can be set before and behind an operator.
10285 The command scheme is:
10288 \begin_layout Standard
10304 \begin_layout Standard
10311 must always be before the operator that should be accented.
10312 You can accent with several characters and even with other operators and
10320 for example only characters behind an operator, write nothing between the
10321 first braces but don't omit the braces.
10324 \begin_layout Standard
10325 For example the command
10330 \begin_inset Formula $\to$
10340 \begin_inset Formula $\to$
10349 \begin_layout Plain Layout
10365 \begin_inset Formula \[
10366 \sideset{}{'}\sum_{k=1}^{n}\]
10373 \begin_layout Standard
10382 \begin_layout Plain Layout
10397 \begin_layout Plain Layout
10409 \begin_inset Formula $\uparrow$
10417 \begin_inset Formula \[
10418 \overset{a}{\maltese}\]
10422 As seen in the last example, with
10434 also symbols and characters can be accented; with
10440 this is not possible.
10443 \begin_layout Subsection
10444 Accents for several Characters
10448 \begin_layout Plain Layout
10449 Accents ! for several characters
10457 \begin_layout Standard
10458 \begin_inset space \hfill{}
10462 \begin_inset Tabular
10463 <lyxtabular version="3" rows="5" columns="2">
10465 <column alignment="center" valignment="top" width="0pt">
10466 <column alignment="center" valignment="top" width="0pt">
10468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10471 \begin_layout Plain Layout
10477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10480 \begin_layout Plain Layout
10482 \begin_inset Note Note
10485 \begin_layout Plain Layout
10492 is only used as spacer.
10504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10507 \begin_layout Plain Layout
10514 \begin_layout Plain Layout
10528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10531 \begin_layout Plain Layout
10532 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10545 \begin_layout Plain Layout
10552 \begin_layout Plain Layout
10566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10569 \begin_layout Plain Layout
10570 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10590 \begin_layout Plain Layout
10604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Plain Layout
10608 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10621 \begin_layout Plain Layout
10624 underleftrightarrow
10628 \begin_layout Plain Layout
10642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10646 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10660 \begin_inset space \hfill{}
10664 \begin_inset Tabular
10665 <lyxtabular version="3" rows="5" columns="2">
10667 <column alignment="center" valignment="top" width="0pt">
10668 <column alignment="center" valignment="top" width="0pt">
10670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10673 \begin_layout Plain Layout
10679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10693 \begin_layout Plain Layout
10700 \begin_layout Plain Layout
10714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10717 \begin_layout Plain Layout
10718 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10731 \begin_layout Plain Layout
10738 \begin_layout Plain Layout
10752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10755 \begin_layout Plain Layout
10756 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10769 \begin_layout Plain Layout
10776 \begin_layout Plain Layout
10790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10793 \begin_layout Plain Layout
10794 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10807 \begin_layout Plain Layout
10814 \begin_layout Plain Layout
10828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10831 \begin_layout Plain Layout
10832 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10846 \begin_inset space \hfill{}
10852 \begin_layout Standard
10853 \begin_inset VSpace medskip
10856 With these commands as many characters as you like can be accented.
10869 will only be set in the output with a length of three characters, as shown
10870 in the following example:
10871 \begin_inset Formula \[
10872 \widetilde{A+B=C-D}\]
10879 \begin_layout Standard
10890 \begin_layout Plain Layout
10908 \begin_layout Plain Layout
10916 described in the previous subsection it is also possible to accent several
10926 \begin_layout Plain Layout
10936 \begin_inset Formula $\downarrow$
10942 \begin_inset Formula \[
10943 \underset{***}{A=B}\]
10950 \begin_layout Section
10952 \begin_inset CommandInset label
10962 \begin_layout Plain Layout
10971 \begin_layout Subsection
10973 \begin_inset CommandInset label
10975 name "sub:Predefined-Space"
10983 \begin_layout Plain Layout
10984 Space ! horizontal ! predefined
10992 \begin_layout Standard
10993 Sometimes it is necessary to insert horizontal space to a formula.
10994 This is done by inserting a protected space (shortcut
10997 arg "space-insert protected"
11002 \begin_inset Quotes eld
11011 \begin_layout Plain Layout
11023 \begin_inset Quotes erd
11026 appears and by pressing
11030 several times one can select one of eight different space sizes.
11031 The spaces can also be inserted using the math toolbar button
11032 \begin_inset Graphics
11033 filename ../images/math/space.png
11038 or special commands.
11039 Independent from the inserted command, one can select the size again by
11047 \begin_layout Standard
11050 \begin_inset VSpace -5mm
11054 \begin_inset Tabular
11055 <lyxtabular version="3" rows="3" columns="7">
11057 <column alignment="center" valignment="middle" width="6.8cm">
11058 <column alignment="center" valignment="top" width="0">
11059 <column alignment="center" valignment="top" width="0">
11060 <column alignment="center" valignment="top" width="0">
11061 <column alignment="center" valignment="top" width="0">
11062 <column alignment="center" valignment="top" width="0">
11063 <column alignment="center" valignment="top" width="0">
11065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11068 \begin_layout Plain Layout
11074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11077 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11088 \begin_layout Plain Layout
11096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11099 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11121 \begin_layout Plain Layout
11129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11132 \begin_layout Plain Layout
11142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11150 keystrokes after inserting the protected space
11155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11158 \begin_layout Plain Layout
11164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11167 \begin_layout Plain Layout
11173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11176 \begin_layout Plain Layout
11182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11185 \begin_layout Plain Layout
11191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11194 \begin_layout Plain Layout
11200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11203 \begin_layout Plain Layout
11211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11214 \begin_layout Plain Layout
11220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11223 \begin_layout Plain Layout
11224 \begin_inset Formula $A\, B$
11232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11236 \begin_inset Formula $A\: B$
11244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11247 \begin_layout Plain Layout
11248 \begin_inset Formula $A\; B$
11256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11259 \begin_layout Plain Layout
11260 \begin_inset Formula $A\quad B$
11268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11272 \begin_inset Formula $A\qquad B$
11280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11283 \begin_layout Plain Layout
11284 \begin_inset Formula $A\! B$
11300 \begin_layout Standard
11301 The last size seem to produce no space.
11302 It is displayed red in LyX contrary to the other sizes, because it is a
11304 There are two more negative spaces:
11307 \begin_layout Standard
11309 \begin_inset Tabular
11310 <lyxtabular version="3" rows="3" columns="3">
11312 <column alignment="center" valignment="middle" width="6.8cm">
11313 <column alignment="center" valignment="top" width="0pt">
11314 <column alignment="center" valignment="top" width="0pt">
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11328 \begin_layout Plain Layout
11336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11339 \begin_layout Plain Layout
11349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11352 \begin_layout Plain Layout
11357 keystrokes after inserting the protected space
11362 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11365 \begin_layout Plain Layout
11371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11374 \begin_layout Plain Layout
11382 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11395 \begin_inset Formula $A\negmedspace B$
11403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11406 \begin_layout Plain Layout
11407 \begin_inset Formula $A\negthickspace B$
11423 \begin_layout Standard
11424 Negative spaces can lead to characters overlapping each other.
11425 Thus they can be used to enforce ligatures, what is e.
11426 \begin_inset space \thinspace{}
11430 \begin_inset space \space{}
11433 useful for summation operators:
11436 \begin_layout Standard
11438 \begin_inset Tabular
11439 <lyxtabular version="3" rows="3" columns="2">
11441 <column alignment="center" valignment="top" width="0">
11442 <column alignment="center" valignment="top" width="0">
11444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11447 \begin_layout Plain Layout
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11456 \begin_layout Plain Layout
11458 \begin_inset Note Note
11461 \begin_layout Plain Layout
11468 is only used as spacer.
11480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11492 \begin_layout Plain Layout
11506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11509 \begin_layout Plain Layout
11510 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11523 \begin_layout Plain Layout
11534 \begin_layout Plain Layout
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11551 \begin_layout Plain Layout
11552 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11568 \begin_layout Standard
11569 Relations like for example equal signs, are always surrounded by space.
11570 To suppress this, the equal sign is placed into a TeX-brace.
11571 The following example demonstrates this:
11574 \begin_layout Standard
11576 \begin_inset Tabular
11577 <lyxtabular version="3" rows="2" columns="2">
11579 <column alignment="center" valignment="top" width="0pt">
11580 <column alignment="center" valignment="top" width="0pt">
11582 <cell alignment="center" valignment="top" usebox="none">
11585 \begin_layout Plain Layout
11591 <cell alignment="center" valignment="top" usebox="none">
11594 \begin_layout Plain Layout
11595 \begin_inset Formula $A=B$
11605 <cell alignment="center" valignment="top" usebox="none">
11608 \begin_layout Plain Layout
11609 \begin_inset Note Note
11612 \begin_layout Plain Layout
11619 is only used as spacer.
11625 \begin_inset Formula $\raisebox{5mm}{}$
11628 equation without space
11633 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11636 \begin_layout Plain Layout
11637 \begin_inset Formula $A{=}B$
11653 \begin_layout Standard
11655 The command for the last formula is:
11660 \begin_inset Formula $\to$
11666 \begin_layout Standard
11667 \begin_inset VSpace bigskip
11670 Spaces are needed for physical units, because the space between the value
11671 and the unit is the smallest one and not a normal space.
11672 For units in text, the smallest space is inserted via the menu
11674 Insert\SpecialChar \menuseparator
11675 Formatting\SpecialChar \menuseparator
11677 \begin_inset space ~
11685 arg "space-insert thin"
11691 \begin_layout Standard
11692 An example to visualize the difference:
11695 \begin_layout Standard
11696 \begin_inset Tabular
11697 <lyxtabular version="3" rows="2" columns="2">
11699 <column alignment="left" valignment="top" width="0">
11700 <column alignment="left" valignment="top" width="0">
11702 <cell alignment="center" valignment="top" usebox="none">
11705 \begin_layout Plain Layout
11707 \begin_inset Formula $\cdot$
11715 <cell alignment="center" valignment="top" usebox="none">
11718 \begin_layout Plain Layout
11719 space between value and unit
11726 <cell alignment="center" valignment="top" usebox="none">
11729 \begin_layout Plain Layout
11731 \begin_inset space \thinspace{}
11735 \begin_inset Formula $\cdot$
11743 <cell alignment="center" valignment="top" usebox="none">
11746 \begin_layout Plain Layout
11747 smallest space between value and unit
11760 \begin_layout Subsection
11765 \begin_layout Plain Layout
11778 \begin_layout Plain Layout
11779 for vertical space in formulas see
11780 \begin_inset CommandInset ref
11782 reference "sub:Line-Separation"
11795 \begin_layout Plain Layout
11803 \begin_inset Note Note
11806 \begin_layout Plain Layout
11809 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11812 \begin_layout Plain Layout
11815 texorpdfstring is in section
11816 \begin_inset CommandInset ref
11818 reference "sub:Formulas-in-Section"
11828 \begin_inset CommandInset label
11830 name "sub:Variable-Space"
11838 \begin_layout Plain Layout
11839 Space ! horizontal ! variable
11847 \begin_layout Standard
11848 Space with a defined length can be inserted with the command
11858 \begin_layout Plain Layout
11868 \begin_inset Quotes eld
11877 \begin_layout Plain Layout
11889 \begin_inset Quotes erd
11893 The length can be specified by left-clicking on the
11894 \begin_inset Quotes eld
11903 \begin_layout Plain Layout
11915 \begin_inset Quotes erd
11919 The length may also be negative.
11920 To insert so many space that the formula uses all available space, the
11931 \begin_layout Plain Layout
11942 \begin_layout Standard
11943 \begin_inset VSpace -1mm
11949 \begin_layout Standard
11951 \begin_inset Tabular
11952 <lyxtabular version="3" rows="4" columns="2">
11954 <column alignment="center" valignment="top" width="0">
11955 <column alignment="center" valignment="top" width="0">
11957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11960 \begin_layout Plain Layout
11968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11971 \begin_layout Plain Layout
11979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11982 \begin_layout Plain Layout
11989 \begin_layout Plain Layout
11999 \begin_inset Formula $\to$
12005 \begin_inset space \thinspace{}
12013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12016 \begin_layout Plain Layout
12017 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12030 \begin_layout Plain Layout
12037 \begin_layout Plain Layout
12047 \begin_inset Formula $\to$
12053 \begin_inset space \thinspace{}
12061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12064 \begin_layout Plain Layout
12065 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12078 \begin_layout Plain Layout
12085 \begin_layout Plain Layout
12099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12102 \begin_layout Plain Layout
12103 \begin_inset Formula $A=A\hfill B=B$
12119 \begin_layout Standard
12120 In the last example the available space is given by the longest column entry
12122 In an inline formula the space depends on the length of the line in which
12130 Thus, when the line uses the full width, no space will be created.
12137 only has an effect on displayed formulas when the formula style
12142 (Formula styles are explained in
12143 \begin_inset CommandInset ref
12145 reference "sec:Formula-Styles"
12152 \begin_layout Standard
12159 , there are the commands
12171 that fill the space with a pattern, see
12172 \begin_inset CommandInset ref
12174 reference "sub:Ellipses"
12181 \begin_layout Standard
12182 For text, variable space can be inserted via the menu
12184 Insert\SpecialChar \menuseparator
12185 Formatting\SpecialChar \menuseparator
12187 \begin_inset space ~
12195 \begin_layout Standard
12196 This is a line with
12197 \begin_inset space \hspace{}
12202 \begin_inset space \thinspace{}
12208 \begin_layout Standard
12209 This is a line with
12210 \begin_inset space \hfill{}
12216 \begin_layout Subsection
12217 Space besides inline Formulas
12221 \begin_layout Plain Layout
12222 Space ! besides inline formulas
12230 \begin_layout Standard
12231 The space that surrounds inline formulas can be adjusted with the length
12240 \begin_layout Plain Layout
12251 The value of a length is set with the command
12259 \begin_layout Plain Layout
12269 that has the following scheme:
12272 \begin_layout Standard
12277 setlength{length name}{value}
12280 \begin_layout Standard
12288 \begin_inset space \thinspace{}
12294 \begin_layout Standard
12304 \begin_layout Standard
12305 is inserted in TeX-mode.
12307 \begin_inset space \thinspace{}
12310 mm space will now be set around all inline formulas:
12314 \begin_layout Plain Layout
12328 \begin_layout Standard
12329 This is a line with an inline formula
12330 \begin_inset Formula $A=B$
12334 \begin_inset space \thinspace{}
12337 mm surrounding space.
12341 \begin_layout Plain Layout
12355 \begin_layout Standard
12356 To return to the predefined value,
12362 is set to the value 0
12363 \begin_inset space \thinspace{}
12369 \begin_layout Section
12374 \begin_layout Plain Layout
12384 \begin_layout Plain Layout
12389 \begin_layout Plain Layout
12400 \begin_layout Plain Layout
12415 \begin_layout Standard
12416 Boxes for text are described in chapter
12423 \begin_inset space ~
12431 \begin_layout Subsection
12433 \begin_inset CommandInset label
12435 name "sub:Boxes-with-Frame"
12443 \begin_layout Plain Layout
12452 \begin_layout Standard
12453 It is possible to frame formulas or parts of it with the commands
12463 \begin_layout Plain Layout
12481 \begin_layout Plain Layout
12492 \begin_layout Standard
12493 When one of these commands is inserted to a formula, a blue box appears
12494 within a frame to enter formula parts.
12501 an additional formula has to be created by
12509 \begin_layout Plain Layout
12510 Due to a bug in LyX it is not possible to create a new formula with
12515 \begin_inset CommandInset href
12517 name "LyX-bug #1435"
12518 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12527 , because the box content will otherwise be treated as mathematical text.
12534 is used, a new formula is automatically created inside the frame.
12537 \begin_layout Standard
12544 is not suitable to frame displayed formulas, because the formula will always
12545 be set in the size of the text.
12552 is in contrary not suitable to frame inline formulas, because the formula
12553 will always be set in the size of a displayed formula.
12556 \begin_layout Standard
12563 there is the command
12573 \begin_layout Plain Layout
12581 where additionally the frame width and the alignment can be specified.
12588 is used in the following scheme:
12591 \begin_layout Standard
12596 framebox[frame width][position]{box content}
12599 \begin_layout Standard
12600 The position can either be
12617 right aligns the formula in the box.
12618 When no position is given, the formula will be centered.
12619 \begin_inset Newline newline
12622 Is no width given, also no position can be given.
12623 In this case the frame width is adjusted to the box content like for
12632 \begin_layout Standard
12639 is inserted, a box appears containing three blue boxes.
12640 The first two boxes are surrounded by brackets and denote the two optional
12642 The third box is for formula parts like for
12651 \begin_layout Standard
12653 \begin_inset Note Note
12656 \begin_layout Plain Layout
12657 The table has been set into a minipage to make the footnote appearing.
12658 Otherwise the footnote text would not be displayed.
12664 \begin_inset Box Frameless
12673 height_special "totalheight"
12676 \begin_layout Plain Layout
12678 \begin_inset Tabular
12679 <lyxtabular version="3" rows="5" columns="2">
12681 <column alignment="center" valignment="top" width="0">
12682 <column alignment="center" valignment="top" width="0">
12684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12687 \begin_layout Plain Layout
12692 \begin_layout Plain Layout
12693 Due to a bug in LyX it is not possible to create a new formula with
12698 \begin_inset CommandInset href
12700 name "LyX-bug #1435"
12701 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12718 \begin_layout Plain Layout
12720 \begin_inset Note Note
12723 \begin_layout Plain Layout
12730 is only used as spacer.
12742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12745 \begin_layout Plain Layout
12752 \begin_layout Plain Layout
12771 \begin_layout Plain Layout
12785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12788 \begin_layout Plain Layout
12789 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12802 \begin_layout Plain Layout
12809 \begin_layout Plain Layout
12824 \begin_layout Plain Layout
12838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12841 \begin_layout Plain Layout
12842 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12855 \begin_layout Plain Layout
12862 \begin_layout Plain Layout
12876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12879 \begin_layout Plain Layout
12880 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12893 \begin_layout Plain Layout
12900 \begin_layout Plain Layout
12910 \begin_inset Formula $\to$
12914 \begin_inset Formula $\to$
12927 \begin_layout Plain Layout
12937 \begin_inset Formula $\downarrow$
12945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12948 \begin_layout Plain Layout
12949 \begin_inset Formula $\raisebox{6mm}{}$
12953 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12957 \begin_inset Formula $\raisebox{-4mm}{}$
12978 \begin_layout Standard
12979 The frame thickness can also be adjusted.
12980 To do this the following commands have to be inserted in TeX-mode before
12984 \begin_layout Standard
12994 \begin_inset Quotes eld
12998 \begin_inset Quotes erd
13012 \begin_inset Quotes eld
13016 \begin_inset Quotes erd
13022 \begin_layout Standard
13023 \begin_inset Quotes eld
13027 \begin_inset Quotes erd
13030 specifies the minimal distance between the frame and the first character
13032 An example for this is the following framed formula:
13036 \begin_layout Plain Layout
13048 \begin_inset Formula \[
13053 Before this formula the commands
13056 \begin_layout Standard
13078 \begin_layout Standard
13079 were inserted in TeX-mode.
13080 The given values are used for all following boxes.
13083 \begin_layout Standard
13084 To return to the standard frame size, the command
13087 \begin_layout Standard
13112 \begin_layout Plain Layout
13126 \begin_layout Standard
13127 is inserted in TeX-mode before the next formula.
13130 \begin_layout Subsection
13131 Boxes without Frame
13132 \begin_inset CommandInset label
13134 name "sub:Boxes-without-Frame"
13142 \begin_layout Plain Layout
13143 Boxes ! without frame
13151 \begin_layout Standard
13152 For boxes without a frame there are the following box commands:
13162 \begin_layout Plain Layout
13180 \begin_layout Plain Layout
13198 \begin_layout Plain Layout
13209 \begin_layout Standard
13216 a box can be super- or subscripted.
13217 But in contrary to normal super- and subscripting, the characters in the
13218 box keep their font size.
13225 is used in the following scheme:
13228 \begin_layout Standard
13233 raisebox{height}{box content}
13236 \begin_layout Standard
13237 When the box should contain a formula, an extra formula is needed like for
13247 \begin_layout Standard
13249 \begin_inset Tabular
13250 <lyxtabular version="3" rows="4" columns="2">
13252 <column alignment="center" valignment="top" width="0">
13253 <column alignment="center" valignment="top" width="0">
13255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13258 \begin_layout Plain Layout
13264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13267 \begin_layout Plain Layout
13275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13278 \begin_layout Plain Layout
13282 \begin_inset Formula $\to$
13288 \begin_inset Formula $\to$
13296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13299 \begin_layout Plain Layout
13300 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13313 \begin_layout Plain Layout
13317 \begin_inset Formula $\to$
13323 \begin_inset Formula $\to$
13331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13334 \begin_layout Plain Layout
13335 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13348 \begin_layout Plain Layout
13352 \begin_inset Formula $\to$
13367 \begin_layout Plain Layout
13381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13384 \begin_layout Plain Layout
13388 \begin_layout Plain Layout
13412 \begin_layout Standard
13413 The last formula can currently only be created using TeX-mode because LyX
13414 inserts a box instead of the needed extra formula.
13418 \begin_layout Plain Layout
13420 \begin_inset CommandInset href
13422 name "LyX-bug #1435"
13423 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13435 \begin_layout Standard
13460 , with the difference that there is no frame.
13463 \begin_layout Subsection
13465 \begin_inset CommandInset label
13467 name "sub:Colored-Boxes"
13475 \begin_layout Plain Layout
13484 \begin_layout Standard
13485 To be able to use all commands explained in this section, the LaTeX-package
13494 \begin_layout Plain Layout
13499 is part of every LaTeX standard installation.
13508 \begin_layout Plain Layout
13514 has to be loaded in the LaTeX-preamble with the line
13518 \begin_layout Plain Layout
13519 When text is colored somewhere in the document with a predefined color,
13520 LyX loads the LaTeX-package
13525 Thus it is possible that the package is loaded twice, but this doesn't
13532 \begin_inset Note Note
13535 \begin_layout Plain Layout
13536 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13545 \begin_layout Standard
13553 \begin_layout Standard
13554 \begin_inset VSpace medskip
13557 To color boxes, the command
13567 \begin_layout Plain Layout
13575 is used in the following scheme:
13578 \begin_layout Standard
13583 colorbox{color}{box content}
13586 \begin_layout Standard
13587 The box content can also be a box and a
13593 can also be part of another box (see the 2nd and 3rd example).
13594 When the box should contain a formula, an extra formula has to be created,
13605 \begin_layout Plain Layout
13606 This also applies for the command
13614 \begin_inset CommandInset href
13616 name "LyX-bug #1435"
13617 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13629 \begin_layout Standard
13630 One of the following predefined colors can be chosen:
13633 \begin_layout Standard
13667 \begin_layout Standard
13669 \begin_inset Tabular
13670 <lyxtabular version="3" rows="4" columns="2">
13672 <column alignment="center" valignment="top" width="0">
13673 <column alignment="center" valignment="top" width="0">
13675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13678 \begin_layout Plain Layout
13684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13687 \begin_layout Plain Layout
13689 \begin_inset Note Note
13692 \begin_layout Plain Layout
13699 is only used as spacer.
13711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13714 \begin_layout Plain Layout
13718 \begin_inset Formula $\to$
13728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13731 \begin_layout Plain Layout
13732 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13745 \begin_layout Plain Layout
13749 \begin_inset Formula $\to$
13760 \begin_layout Plain Layout
13774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13777 \begin_layout Plain Layout
13778 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13791 \begin_layout Plain Layout
13798 \begin_layout Plain Layout
13810 \begin_inset Formula $\to$
13820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13823 \begin_layout Plain Layout
13824 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13840 \begin_layout Standard
13847 only colors the box but not the characters in the box.
13848 To color all characters, the whole formula is highlighted and the wanted
13849 color is chosen in the
13852 \begin_inset space ~
13858 The dialog can be called with the toolbar button
13859 \begin_inset Graphics
13860 filename ../images/dialog-show_character.png
13867 Edit\SpecialChar \menuseparator
13869 \begin_inset space ~
13872 Style\SpecialChar \menuseparator
13876 The formula number has then the same color as the formula.
13877 When the formula number should get another color than the formula characters,
13878 the color must be changed within the formula.
13881 \begin_layout Standard
13885 \begin_layout Standard
13888 \begin_inset Formula \begin{equation}
13889 \int A=B\label{eq:red}\end{equation}
13896 \begin_inset Formula \begin{equation}
13897 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13904 \begin_layout Standard
13906 \begin_inset CommandInset ref
13912 is completely colored red.
13913 \begin_inset Newline newline
13917 \begin_inset CommandInset ref
13919 reference "eq:redgreen"
13923 was first completely colored green to set the color for the formula number.
13924 Subsequently the formula characters were colored red.
13927 \begin_layout Standard
13928 \begin_inset VSpace bigskip
13931 To color the frame different than the rest of the box, the command
13941 \begin_layout Plain Layout
13949 is used in the following scheme:
13952 \begin_layout Standard
13957 fcolorbox{frame color}{color}{box content}
13960 \begin_layout Standard
13967 is an extension of the command
13974 The frame width is set, like for
13997 \begin_layout Plain Layout
14009 \begin_inset Formula \[
14010 \fcolorbox{cyan}{magenta}{A=B}\]
14018 \begin_layout Plain Layout
14032 \begin_layout Standard
14033 This formula was created with the command
14034 \begin_inset Newline newline
14042 \begin_inset Formula $\to$
14048 \begin_inset Formula $\to$
14058 \begin_layout Standard
14059 \begin_inset VSpace bigskip
14062 To use other colors than the predefined ones, they have to be defined first.
14065 \begin_layout Standard
14066 One can for example define the color
14067 \begin_inset Quotes eld
14075 \begin_inset Quotes erd
14078 with the LaTeX-preamble line:
14081 \begin_layout Standard
14086 definecolor{darkgreen}{cmyk}{0.5,
14104 \begin_layout Plain Layout
14115 \begin_layout Standard
14120 is the color space that denotes the colors
14137 The four comma separated numbers are the portion factor for the corresponding
14138 colors of the color space.
14139 The factors can be in the range of 0
14140 \begin_inset space \thinspace{}
14144 \begin_inset space \thinspace{}
14152 also the color space
14156 can be used for definitions.
14173 , so that there are in this case three portion factors for the corresponding
14175 Furthermore there is the color space
14179 with one portion factor for the gray value.
14182 \begin_layout Standard
14183 As example a framed box with the new defined color
14187 where the characters have been colored
14192 \begin_inset Formula \begin{equation}
14193 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14200 \begin_layout Standard
14201 Self-defined colors can also be used for text with the help of the command
14212 \begin_layout Plain Layout
14221 \begin_layout Standard
14225 \begin_layout Plain Layout
14229 textcolor{darkgreen}{
14235 \begin_inset Quotes eld
14239 \begin_inset Quotes erd
14246 \begin_layout Plain Layout
14256 \begin_layout Standard
14267 \begin_layout Plain Layout
14275 is used in the scheme
14279 textcolor{color}{characters to color}
14284 \begin_layout Subsection
14286 \begin_inset CommandInset label
14288 name "sub:Paragraph-Boxes"
14296 \begin_layout Plain Layout
14297 Boxes ! as paragraph
14305 \begin_layout Standard
14306 A box that can contain several lines and paragraphs, a so called paragraph
14307 box (parbox), can be created with the menu
14309 Insert\SpecialChar \menuseparator
14312 or the toolbar button
14313 \begin_inset Graphics
14314 filename ../images/box-insert.png
14322 \begin_layout Standard
14323 The following example shows a framed parbox in a line:
14326 \begin_layout Standard
14327 \begin_inset VSpace medskip
14331 \begin_inset Box Boxed
14340 height_special "totalheight"
14343 \begin_layout Plain Layout
14344 This is a paragraph box.
14346 \begin_inset space \thinspace{}
14349 cm long and can also contain formulas:
14350 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14361 \begin_layout Standard
14362 \begin_inset VSpace medskip
14368 \begin_layout Standard
14369 Such a box is created by right-clicking on the gray box inset.
14370 A dialog pops up showing the box properties.
14384 \begin_inset space \thinspace{}
14389 Vertical Box Alignment
14394 \begin_layout Standard
14395 \begin_inset VSpace medskip
14398 In LaTeX a parbox is created with the command
14408 \begin_layout Plain Layout
14416 that has the following scheme:
14419 \begin_layout Standard
14424 parbox[position]{width}{box content}
14427 \begin_layout Standard
14441 for bottom means that the box is aligned within the surrounding text with
14447 for top this is done with the first line.
14448 When no position is given, the box will be vertically centered, see section
14456 \begin_inset space ~
14461 manual for examples.
14464 \begin_layout Standard
14465 \begin_inset VSpace bigskip
14468 To frame formulas completely, including the formula number, the formula
14469 must be set into a parbox.
14470 To do this, the command
14484 is inserted in TeX-mode before the formula.
14493 \begin_layout Plain Layout
14503 is hereby the line width set for the document.
14504 Because the frame is outside the parbox, 2
14505 \begin_inset space \thinspace{}
14508 times the frame separation and the frame thickness must be subtracted from
14510 As this is not automatically done by LyX due to a bug
14514 \begin_layout Plain Layout
14515 \begin_inset CommandInset href
14517 name "LyX-bug #4483"
14518 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14527 , TeX-mode has to be used.
14528 To be able to multiply and subtract in arguments, the LaTeX-package
14536 \begin_layout Plain Layout
14541 is part of every LaTeX standard installation.
14550 \begin_layout Plain Layout
14556 must be loaded in the LaTeX-preamble with the line
14559 \begin_layout Standard
14567 \begin_layout Standard
14568 Behind the formula both boxes are closed by entering
14573 Here is an example:
14577 \begin_layout Plain Layout
14591 \begin_layout Standard
14595 \begin_layout Plain Layout
14613 \begin_inset Formula \begin{equation}
14614 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14622 \begin_layout Plain Layout
14633 \begin_layout Plain Layout
14647 \begin_layout Standard
14648 \begin_inset VSpace medskip
14651 As a parbox is used as argument of
14657 , there is in this case no difference between
14672 \begin_layout Standard
14673 \begin_inset VSpace bigskip
14676 Paragraph boxes are very useful to comment formulas directly.
14683 is used in combination with the command
14697 \begin_inset CommandInset ref
14699 reference "sub:User-defined-Numbering"
14706 \begin_layout Standard
14707 An example of a formula commented with
14716 \begin_layout Standard
14720 \begin_layout Plain Layout
14733 This is a description.
14734 It is distinctly separated from the formula and multiline.
14738 \begin_layout Plain Layout
14750 \begin_layout Standard
14751 Such a formula must be inserted completely in TeX-mode because LyX does
14752 not yet support the command
14759 The formula is created with the following command sequence:
14762 \begin_layout Standard
14775 is inserted in TeX-mode.
14779 \begin_layout Plain Layout
14780 When the formula style
14792 can also be replaced by
14799 (formula styles see
14800 \begin_inset CommandInset ref
14802 reference "sec:Formula-Styles"
14811 Then the description follows as normal text, and finally
14817 is inserted in TeX-mode.
14830 hereby create a displayed formula.
14833 \begin_layout Standard
14840 can be seen in this example that was
14841 \begin_inset Quotes eld
14845 \begin_inset Quotes erd
14848 using the mathematical textmode:
14849 \begin_inset Formula \[
14850 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14857 \begin_layout Section
14862 \begin_layout Plain Layout
14871 \begin_layout Subsection
14873 \begin_inset CommandInset label
14875 name "sub:Big-Operators"
14883 \begin_layout Plain Layout
14893 \begin_layout Plain Layout
14903 \begin_layout Plain Layout
14912 \begin_layout Standard
14913 To be able to use all integral operators listed here, the option
14915 Use esint package automatically
14917 must be set in the document settings under
14920 \begin_inset space ~
14928 \begin_layout Standard
14929 \begin_inset space \hfill{}
14933 \begin_inset Tabular
14934 <lyxtabular version="3" rows="11" columns="2">
14936 <column alignment="center" valignment="top" width="0pt">
14937 <column alignment="center" valignment="top" width="0pt">
14939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14942 \begin_layout Plain Layout
14948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14951 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14962 \begin_layout Plain Layout
14969 \begin_layout Plain Layout
14982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14985 \begin_layout Plain Layout
14986 \begin_inset Formula $\int$
14996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14999 \begin_layout Plain Layout
15007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15010 \begin_layout Plain Layout
15011 \begin_inset Formula $\oint$
15021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15024 \begin_layout Plain Layout
15032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15035 \begin_layout Plain Layout
15036 \begin_inset Formula $\ointctrclockwise$
15046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15049 \begin_layout Plain Layout
15057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15060 \begin_layout Plain Layout
15061 \begin_inset Formula $\ointclockwise$
15071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15074 \begin_layout Plain Layout
15082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15085 \begin_layout Plain Layout
15086 \begin_inset Formula $\sqint$
15096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15099 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15112 \begin_inset Formula $\fint$
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15125 \begin_layout Plain Layout
15133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15136 \begin_layout Plain Layout
15138 \begin_inset Formula $\landupint$
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
15164 \begin_inset Formula $\landdownint$
15174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15177 \begin_layout Plain Layout
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15188 \begin_layout Plain Layout
15189 \begin_inset Formula $\bigcap$
15199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15202 \begin_layout Plain Layout
15210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15213 \begin_layout Plain Layout
15214 \begin_inset Formula $\bigcup$
15228 \begin_inset space \hfill{}
15232 \begin_inset Tabular
15233 <lyxtabular version="3" rows="11" columns="2">
15235 <column alignment="center" valignment="top" width="0pt">
15236 <column alignment="center" valignment="top" width="0pt">
15238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15241 \begin_layout Plain Layout
15247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15250 \begin_layout Plain Layout
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15261 \begin_layout Plain Layout
15268 \begin_layout Plain Layout
15281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15285 \begin_inset Formula $\sum$
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15298 \begin_layout Plain Layout
15305 \begin_layout Plain Layout
15318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15321 \begin_layout Plain Layout
15322 \begin_inset Formula $\prod$
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15335 \begin_layout Plain Layout
15343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15346 \begin_layout Plain Layout
15347 \begin_inset Formula $\coprod$
15357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15360 \begin_layout Plain Layout
15368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15371 \begin_layout Plain Layout
15372 \begin_inset Formula $\bigodot$
15382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15385 \begin_layout Plain Layout
15393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15396 \begin_layout Plain Layout
15397 \begin_inset Formula $\bigotimes$
15407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15410 \begin_layout Plain Layout
15418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15421 \begin_layout Plain Layout
15422 \begin_inset Formula $\bigoplus$
15432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15435 \begin_layout Plain Layout
15443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15446 \begin_layout Plain Layout
15447 \begin_inset Formula $\bigwedge$
15457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15460 \begin_layout Plain Layout
15468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15471 \begin_layout Plain Layout
15472 \begin_inset Formula $\bigvee$
15482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15485 \begin_layout Plain Layout
15493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15496 \begin_layout Plain Layout
15497 \begin_inset Formula $\bigsqcup$
15507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15510 \begin_layout Plain Layout
15518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15521 \begin_layout Plain Layout
15522 \begin_inset Formula $\biguplus$
15536 \begin_inset space \hfill{}
15542 \begin_layout Standard
15543 All big operators can also be inserted via the math toolbar button
15544 \begin_inset Graphics
15545 filename ../images/math/intop.png
15553 \begin_layout Standard
15554 The operators are called big because they are bigger than the sometimes
15555 equal looking binary operators.
15556 All big operators can have limits as described in the next subsection.
15559 \begin_layout Standard
15560 For all integral operators there is a second version available, ending on
15578 These operators are different from
15585 \begin_inset space \space{}
15588 in the style the operator limits are displayed, see
15589 \begin_inset CommandInset ref
15591 reference "sub:Operator-Limits"
15599 \begin_layout Subsubsection*
15600 Advices for Integrals
15603 \begin_layout Standard
15608 in an integral is an operator, that therefore has to be set upright.
15609 This is done by highlighting the
15613 and using the keyboard shortcut
15623 \begin_layout Plain Layout
15629 \begin_inset CommandInset ref
15631 reference "sub:Font-Styles"
15641 Finally the smallest space is inserted before the
15645 , as this is usual for operators.
15649 \begin_layout Standard
15651 \begin_inset Formula $\int A(x)dx$
15655 \begin_inset Newline newline
15662 \begin_layout Plain Layout
15672 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15678 \begin_layout Standard
15679 For multiple integrals there are the following commands:
15680 \begin_inset VSpace medskip
15686 \begin_layout Standard
15687 \begin_inset space \hfill{}
15691 \begin_inset Tabular
15692 <lyxtabular version="3" rows="4" columns="2">
15694 <column alignment="center" valignment="top" width="0">
15695 <column alignment="center" valignment="top" width="0">
15697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15700 \begin_layout Plain Layout
15706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15709 \begin_layout Plain Layout
15711 \begin_inset Note Note
15714 \begin_layout Plain Layout
15721 is only used as spacer.
15733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15736 \begin_layout Plain Layout
15744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15747 \begin_layout Plain Layout
15748 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15761 \begin_layout Plain Layout
15769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15773 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15786 \begin_layout Plain Layout
15794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15797 \begin_layout Plain Layout
15798 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15812 \begin_inset space \hfill{}
15816 \begin_inset Tabular
15817 <lyxtabular version="3" rows="4" columns="2">
15819 <column alignment="center" valignment="top" width="0">
15820 <column alignment="center" valignment="top" width="0">
15822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15825 \begin_layout Plain Layout
15831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15834 \begin_layout Plain Layout
15842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15845 \begin_layout Plain Layout
15853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15856 \begin_layout Plain Layout
15857 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15870 \begin_layout Plain Layout
15878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15881 \begin_layout Plain Layout
15882 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15895 \begin_layout Plain Layout
15903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15906 \begin_layout Plain Layout
15907 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15921 \begin_inset space \hfill{}
15927 \begin_layout Subsection
15929 \begin_inset CommandInset label
15931 name "sub:Operator-Limits"
15939 \begin_layout Plain Layout
15948 \begin_layout Standard
15949 Limits are created by super- and subscripts:
15952 \begin_layout Standard
15954 \begin_inset Tabular
15955 <lyxtabular version="3" rows="2" columns="2">
15957 <column alignment="center" valignment="top" width="0pt">
15958 <column alignment="center" valignment="top" width="0pt">
15960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15963 \begin_layout Plain Layout
15969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15972 \begin_layout Plain Layout
15974 \begin_inset Note Note
15977 \begin_layout Plain Layout
15984 is only used as spacer.
15996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15999 \begin_layout Plain Layout
16008 \begin_layout Plain Layout
16018 \begin_inset Formula $\to$
16022 \begin_inset Formula $\to$
16030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16033 \begin_layout Plain Layout
16034 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16050 \begin_layout Standard
16051 Limits of inline formulas are set right beside the operator.
16052 Limits in displayed formulas are set above or below the operator, except
16053 for integral limits.
16056 \begin_layout Standard
16057 To force that the limits are set beside the operator, the cursor is set
16058 directly behind the operator and the limits type is changed with the menu
16061 Edit\SpecialChar \menuseparator
16062 Math\SpecialChar \menuseparator
16081 \begin_layout Standard
16082 The default limits type is this:
16083 \begin_inset Formula \[
16084 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16088 This is how it looks when the limits type was changed to
16095 \begin_inset Formula \[
16096 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16100 For integrals, except those ending with
16116 etc., the limits are by default set beside the operator.
16117 But for multiple integrals the limits are often set below the operator.
16118 In the following example the limits type was therefore set to
16122 and so set below the integrals:
16123 \begin_inset Formula \begin{equation}
16124 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16131 \begin_layout Standard
16132 \begin_inset VSpace medskip
16135 To specify conditions for limits, the commands
16145 \begin_layout Plain Layout
16163 \begin_layout Plain Layout
16172 To create for example this expression
16173 \begin_inset Formula \begin{equation}
16174 \sum_{\begin{subarray}{c}
16176 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16183 \begin_layout Standard
16184 the following has to be done:
16185 \begin_inset Newline newline
16200 \begin_layout Plain Layout
16212 One is now in a blue box under the summation operator and insert there
16221 \begin_layout Plain Layout
16233 The blue box is now within a purple box and now several lines can be written
16235 A new line is created by inserting a line break (
16238 arg "newline-insert newline"
16243 \begin_inset Newline newline
16248 0<k<1000 Ctrl+Return
16249 \begin_inset Newline newline
16254 is typed in, a new box appears below for the new line.
16257 \begin_layout Standard
16258 The alignment of the lines can be changed to left aligned with the
16268 Edit\SpecialChar \menuseparator
16272 To get right alignment,
16280 \begin_layout Plain Layout
16291 is inserted at the beginning of the line.
16294 \begin_layout Standard
16307 with the difference that the lines are always centered.
16310 \begin_layout Standard
16311 \begin_inset VSpace bigskip
16315 \begin_inset CommandInset ref
16317 reference "eq:substack"
16321 there can be too much space beside an operator, because the characters
16322 following the operator are set beside the limits.
16325 \begin_layout Standard
16326 To avoid this, the following macro can be used in the LaTeX-preamble:
16329 \begin_layout Standard
16343 \begin_inset Newline newline
16355 \begin_inset Newline newline
16362 mathclapinternal #1#2{
16366 mathsurround =0pt #1{#2}$}}
16369 \begin_layout Standard
16370 This defines the command
16380 \begin_layout Plain Layout
16388 that sets the width of the limit to 0
16389 \begin_inset space \thinspace{}
16393 The command scheme is
16396 \begin_layout Standard
16404 \begin_layout Standard
16405 where the limit can consist of several conditions.
16408 \begin_layout Standard
16410 \begin_inset CommandInset ref
16412 reference "eq:substack"
16416 , one uses the command
16419 \begin_layout Standard
16432 \begin_layout Plain Layout
16441 0<k<1000 Ctrl+Return
16444 \begin_layout Standard
16445 to create the lower limit.
16446 The summand is now directly behind the summation operator:
16447 \begin_inset Formula \[
16448 \sum_{\mathclap{\substack{0<k<1000\\
16449 \\k\,\in\,\mathbb{N}}
16457 \begin_layout Standard
16458 \begin_inset VSpace bigskip
16461 How to use one limit for several operators is described in
16462 \begin_inset CommandInset ref
16464 reference "sub:Self-defined-Operators"
16471 \begin_layout Standard
16472 \begin_inset Newpage newpage
16478 \begin_layout Subsection
16480 \begin_inset CommandInset label
16482 name "sub:Binary-Operators"
16490 \begin_layout Plain Layout
16499 \begin_layout Standard
16500 Binary operators are surrounded by space when there is a character before
16502 \begin_inset VSpace medskip
16508 \begin_layout Standard
16509 \begin_inset space \hfill{}
16513 \begin_inset Tabular
16514 <lyxtabular version="3" rows="13" columns="2">
16516 <column alignment="center" valignment="top" width="0pt">
16517 <column alignment="center" valignment="top" width="0pt">
16519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16522 \begin_layout Plain Layout
16524 \begin_inset Note Note
16527 \begin_layout Plain Layout
16534 is only used as spacer.
16544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16547 \begin_layout Plain Layout
16555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16558 \begin_layout Plain Layout
16564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16567 \begin_layout Plain Layout
16568 \begin_inset Formula $+$
16578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16581 \begin_layout Plain Layout
16587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16590 \begin_layout Plain Layout
16591 \begin_inset Formula $-$
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16604 \begin_layout Plain Layout
16612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16615 \begin_layout Plain Layout
16616 \begin_inset Formula $\pm$
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16629 \begin_layout Plain Layout
16637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16640 \begin_layout Plain Layout
16641 \begin_inset Formula $\mp$
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16654 \begin_layout Plain Layout
16662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16665 \begin_layout Plain Layout
16666 \begin_inset Formula $\cdot$
16676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16679 \begin_layout Plain Layout
16687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16690 \begin_layout Plain Layout
16691 \begin_inset Formula $\times$
16701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16704 \begin_layout Plain Layout
16712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16715 \begin_layout Plain Layout
16716 \begin_inset Formula $\div$
16726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16729 \begin_layout Plain Layout
16733 \begin_layout Plain Layout
16746 \begin_layout Plain Layout
16758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16761 \begin_layout Plain Layout
16762 \begin_inset Formula $*$
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16775 \begin_layout Plain Layout
16783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16787 \begin_inset Formula $\star$
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16800 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $\circ$
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\diamond$
16847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\bullet$
16876 \begin_inset space \hfill{}
16880 \begin_inset Tabular
16881 <lyxtabular version="3" rows="13" columns="2">
16883 <column alignment="center" valignment="top" width="0pt">
16884 <column alignment="center" valignment="top" width="0pt">
16886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16889 \begin_layout Plain Layout
16895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16909 \begin_layout Plain Layout
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16920 \begin_layout Plain Layout
16921 \begin_inset Formula $\nabla$
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16934 \begin_layout Plain Layout
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16945 \begin_layout Plain Layout
16946 \begin_inset Formula $\bigtriangledown$
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16959 \begin_layout Plain Layout
16967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16970 \begin_layout Plain Layout
16971 \begin_inset Formula $\bigtriangleup$
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16984 \begin_layout Plain Layout
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16995 \begin_layout Plain Layout
16996 \begin_inset Formula $\Box$
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17009 \begin_layout Plain Layout
17017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17020 \begin_layout Plain Layout
17021 \begin_inset Formula $\cap$
17031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17034 \begin_layout Plain Layout
17042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17045 \begin_layout Plain Layout
17046 \begin_inset Formula $\cup$
17056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17059 \begin_layout Plain Layout
17067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17070 \begin_layout Plain Layout
17071 \begin_inset Formula $\dagger$
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17084 \begin_layout Plain Layout
17092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17095 \begin_layout Plain Layout
17096 \begin_inset Formula $\ddagger$
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17120 \begin_layout Plain Layout
17121 \begin_inset Formula $\wr$
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\bigcirc$
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\wedge$
17181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\vee$
17210 \begin_inset space \hfill{}
17214 \begin_inset Tabular
17215 <lyxtabular version="3" rows="13" columns="2">
17217 <column alignment="center" valignment="top" width="0pt">
17218 <column alignment="center" valignment="top" width="0pt">
17220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17223 \begin_layout Plain Layout
17229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17243 \begin_layout Plain Layout
17251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17254 \begin_layout Plain Layout
17255 \begin_inset Formula $\oplus$
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17268 \begin_layout Plain Layout
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17279 \begin_layout Plain Layout
17280 \begin_inset Formula $\ominus$
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17293 \begin_layout Plain Layout
17301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17304 \begin_layout Plain Layout
17305 \begin_inset Formula $\otimes$
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17318 \begin_layout Plain Layout
17326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17329 \begin_layout Plain Layout
17330 \begin_inset Formula $\oslash$
17340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17343 \begin_layout Plain Layout
17351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17354 \begin_layout Plain Layout
17355 \begin_inset Formula $\odot$
17365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17368 \begin_layout Plain Layout
17376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17379 \begin_layout Plain Layout
17380 \begin_inset Formula $\amalg$
17390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17393 \begin_layout Plain Layout
17401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17404 \begin_layout Plain Layout
17405 \begin_inset Formula $\uplus$
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17418 \begin_layout Plain Layout
17426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17429 \begin_layout Plain Layout
17430 \begin_inset Formula $\setminus$
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17454 \begin_layout Plain Layout
17455 \begin_inset Formula $\sqcap$
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\sqcup$
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\triangleleft$
17515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17529 \begin_layout Plain Layout
17530 \begin_inset Formula $\triangleright$
17544 \begin_inset space \hfill{}
17550 \begin_layout Standard
17551 All binary operators can also be inserted via the math toolbar button
17552 \begin_inset Graphics
17553 filename ../images/math/pm.png
17561 \begin_layout Standard
17562 To typeset the Laplace operator also
17579 \begin_inset Formula $\nabla^{2}$
17582 ) can be used instead of
17591 \begin_layout Standard
17598 Insert\SpecialChar \menuseparator
17610 \begin_layout Subsection
17611 Self-defined Operators
17612 \begin_inset CommandInset label
17614 name "sub:Self-defined-Operators"
17622 \begin_layout Plain Layout
17623 Operators ! self-defined
17631 \begin_layout Standard
17632 With the help of the command
17636 DeclareMathOperator
17642 \begin_layout Plain Layout
17647 DeclareMathOperator
17652 custom operators can be defined in the LaTeX-preamble.
17653 Its command scheme is:
17656 \begin_layout Standard
17661 DeclareMathOperator{new command}{display}
17664 \begin_layout Standard
17665 Display can be characters or symbols that define how the operator looks
17667 To define a big operator a * is set behind the command.
17668 All self-defined big operators can have limits as described in
17669 \begin_inset CommandInset ref
17671 reference "sub:Operator-Limits"
17678 \begin_layout Standard
17679 For example the LaTeX-preamble line
17682 \begin_layout Standard
17687 DeclareMathOperator*{
17694 \begin_layout Standard
17695 defines the command
17701 , that inserts a big operator consisting of the lozenge symbol from
17702 \begin_inset CommandInset ref
17704 reference "sub:Miscellaneous-Symbols"
17709 \begin_inset Formula \[
17710 \Lozenge_{n=1}^{\infty}\]
17714 The command for this formula is:
17725 \begin_inset Formula $\to$
17731 \begin_layout Standard
17732 \begin_inset VSpace bigskip
17735 When self-defined operators are not used several times in the document,
17736 they can also be defined with the commands
17746 \begin_layout Plain Layout
17764 \begin_layout Plain Layout
17772 , which have the following scheme:
17775 \begin_layout Standard
17789 \begin_layout Standard
17796 defines big operators,
17805 \begin_layout Standard
17813 \begin_inset space \thinspace{}
17817 \begin_inset space \space{}
17820 be used to use one limit for several operators:
17823 \begin_layout Standard
17824 \begin_inset Formula \[
17825 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17832 \begin_layout Standard
17833 The command for the formula above is:
17834 \begin_inset Newline newline
17853 \begin_layout Plain Layout
17865 \begin_inset Formula $\to$
17874 \begin_layout Plain Layout
17888 \begin_layout Section
17893 \begin_layout Plain Layout
17902 \begin_layout Subsection
17904 \begin_inset CommandInset label
17906 name "sub:Font-Styles"
17914 \begin_layout Plain Layout
17923 \begin_layout Standard
17924 Latin letters in formulas can be set in one of the following font styles:
17925 \begin_inset VSpace -2mm
17931 \begin_layout Standard
17933 \begin_inset Tabular
17934 <lyxtabular version="3" rows="6" columns="3">
17936 <column alignment="center" valignment="top" width="0">
17937 <column alignment="center" valignment="top" width="0">
17938 <column alignment="center" valignment="top" width="0">
17940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17943 \begin_layout Plain Layout
17949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17952 \begin_layout Plain Layout
17958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17961 \begin_layout Plain Layout
17969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17972 \begin_layout Plain Layout
17981 \begin_layout Plain Layout
17997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18000 \begin_layout Plain Layout
18001 \begin_inset Formula $\mathbb{ABC}$
18009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18012 \begin_layout Plain Layout
18025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18028 \begin_layout Plain Layout
18037 \begin_layout Plain Layout
18053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18056 \begin_layout Plain Layout
18057 \begin_inset Formula $\mathbf{AbC}$
18065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18068 \begin_layout Plain Layout
18081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18084 \begin_layout Plain Layout
18093 \begin_layout Plain Layout
18109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18112 \begin_layout Plain Layout
18113 \begin_inset Formula $\boldsymbol{AbC}$
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18124 \begin_layout Plain Layout
18127 arg "font-boldsymbol"
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18140 \begin_layout Plain Layout
18149 \begin_layout Plain Layout
18165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18168 \begin_layout Plain Layout
18169 \begin_inset Formula $\mathcal{ABC}$
18177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18180 \begin_layout Plain Layout
18193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18196 \begin_layout Plain Layout
18205 \begin_layout Plain Layout
18221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18224 \begin_layout Plain Layout
18225 \begin_inset Formula $\mathfrak{AbC}$
18233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18250 \begin_layout Standard
18252 \begin_inset Tabular
18253 <lyxtabular version="3" rows="5" columns="3">
18255 <column alignment="center" valignment="top" width="0">
18256 <column alignment="center" valignment="top" width="0">
18257 <column alignment="center" valignment="top" width="0">
18259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18271 \begin_layout Plain Layout
18277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18291 \begin_layout Plain Layout
18300 \begin_layout Plain Layout
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18319 \begin_layout Plain Layout
18320 \begin_inset Formula $\mathit{AbC}$
18328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Plain Layout
18339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18342 \begin_layout Plain Layout
18351 \begin_layout Plain Layout
18367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18370 \begin_layout Plain Layout
18371 \begin_inset Formula $\mathrm{AbC}$
18379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18382 \begin_layout Plain Layout
18395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18398 \begin_layout Plain Layout
18407 \begin_layout Plain Layout
18423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18426 \begin_layout Plain Layout
18427 \begin_inset Formula $\mathsf{AbC}$
18435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18438 \begin_layout Plain Layout
18451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18454 \begin_layout Plain Layout
18463 \begin_layout Plain Layout
18479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18482 \begin_layout Plain Layout
18483 \begin_inset Formula $\mathtt{AbC}$
18491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18494 \begin_layout Plain Layout
18497 arg "font-typewriter"
18513 \begin_layout Standard
18514 \begin_inset Note Greyedout
18517 \begin_layout Plain Layout
18534 can only be used for big letters.
18542 \begin_layout Standard
18543 Predefined is the style
18552 \begin_layout Standard
18553 The style commands work also for letters in mathematical constructs:
18554 \begin_inset Formula \[
18555 \mathfrak{A=\frac{b}{C}}\]
18562 \begin_layout Standard
18563 Characters in mathematical text don't appear in a math font style but in
18564 the text font style
18571 That their style can't be set correctly via the text style dialog is a
18576 \begin_layout Plain Layout
18577 \begin_inset CommandInset href
18579 name "LyX-bug #4091"
18580 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18592 \begin_layout Standard
18593 Instead of the style commands the dialog
18595 Edit\SpecialChar \menuseparator
18596 Math\SpecialChar \menuseparator
18599 or the toolbar button
18600 \begin_inset Graphics
18601 filename ../images/math/font.png
18609 \begin_layout Subsection
18611 \begin_inset CommandInset label
18613 name "sub:Bold-Formulas"
18621 \begin_layout Plain Layout
18630 \begin_layout Standard
18631 To make a complete formula bold, the command
18637 from the previous subsection cannot be used, because it doesn't work for
18638 small Greek letters.
18639 Furthermore it prints Latin letters always upright, like in the following
18643 \begin_layout Standard
18644 \begin_inset Formula \[
18645 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18652 \begin_layout Standard
18653 To display the formula correctly, the command
18660 \begin_inset Formula \[
18661 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18665 It is also possible to set the formula in a
18667 boldmath environment
18670 This environment is created by inserting the command
18678 \begin_layout Plain Layout
18689 To end the environment, the command
18697 \begin_layout Plain Layout
18707 is inserted in TeX-mode.
18711 \begin_layout Plain Layout
18721 \begin_inset Formula \[
18722 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18730 \begin_layout Plain Layout
18742 \begin_layout Subsection
18747 \begin_layout Plain Layout
18756 \begin_layout Standard
18757 Formulas can be colored like normal text: Highlight a formula or a formula
18763 Here is a formula in magenta:
18764 \begin_inset Formula \[
18765 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18772 \begin_layout Standard
18773 You can also define your own colors as described in
18774 \begin_inset CommandInset ref
18776 reference "sub:Colored-Boxes"
18781 They can be used with the TeX code command
18791 \begin_layout Plain Layout
18802 \begin_layout Standard
18807 textcolor{color}{characters or formula}
18810 \begin_layout Standard
18811 The following example was colored completely dark green and partly red:
18814 \begin_layout Standard
18818 \begin_layout Plain Layout
18822 textcolor{darkgreen}{
18828 \begin_inset Formula \[
18829 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18837 \begin_layout Plain Layout
18847 \begin_layout Standard
18848 Due to a bug in LyX only complete formulas can be colored with self-defined
18853 \begin_layout Plain Layout
18854 \begin_inset CommandInset href
18856 name "LyX-bug #5269"
18857 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18869 \begin_layout Subsection
18871 \begin_inset CommandInset label
18873 name "sub:Font-Sizes"
18881 \begin_layout Plain Layout
18890 \begin_layout Standard
18891 For characters in formulas there are, analog to characters in text, the
18892 following size commands:
18895 \begin_layout Standard
18939 \begin_inset Newline newline
18961 \begin_layout Standard
18962 The size produced by the commands depends on the document font size, that
18963 corresponds with the command
18970 The other commands produce smaller or larger sizes than
18977 The font size can however not exceed a certain value.
18978 Is for example the document font size 12
18979 \begin_inset space \thinspace{}
18988 switches to the same size as
18998 \begin_layout Standard
18999 A size command is inserted in TeX-mode before the formula and sets the size
19000 for all following formula and text characters.
19001 To switch back to the initial size, the command
19007 is inserted behind the formula in TeX-mode.
19010 \begin_layout Standard
19011 Within a formula the size can only be changed for symbols or letters in
19013 To do this, the size command is inserted in mathematical text.
19014 All following characters until the end of the mathematical text or until
19015 another size command will have the selected size.
19017 \begin_inset VSpace -2mm
19023 \begin_layout Standard
19027 \begin_layout Plain Layout
19037 \begin_inset Formula \[
19038 A=\frac{B}{c}\cdot\maltese\]
19043 \begin_inset Formula \[
19044 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19052 \begin_layout Plain Layout
19064 \begin_layout Standard
19065 \begin_inset VSpace medskip
19068 Before both formulas the command
19075 The command for the second formula is:
19076 \begin_inset Newline newline
19087 \begin_layout Plain Layout
19102 \begin_layout Plain Layout
19117 \begin_layout Plain Layout
19132 \begin_layout Plain Layout
19142 \begin_inset Formula $\to$
19146 \begin_inset Formula $\to$
19150 \begin_inset Newline newline
19154 \begin_inset space \hspace*{}
19168 \begin_layout Plain Layout
19183 \begin_layout Plain Layout
19198 \begin_layout Plain Layout
19210 \begin_layout Standard
19211 If a symbol cannot be displayed in different sizes, it will always be displayed
19212 in the default size.
19215 \begin_layout Section
19220 \begin_layout Plain Layout
19229 \begin_layout Standard
19230 All Greek letters can also be inserted via the toolbar button
19231 \begin_inset Graphics
19232 filename ../images/math/alpha.png
19240 \begin_layout Subsection
19245 \begin_layout Plain Layout
19246 Greek letters ! small
19254 \begin_layout Standard
19255 \begin_inset space \hfill{}
19259 \begin_inset Tabular
19260 <lyxtabular version="3" rows="11" columns="2">
19262 <column alignment="center" valignment="top" width="0pt">
19263 <column alignment="center" valignment="top" width="0pt">
19265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19268 \begin_layout Plain Layout
19274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19277 \begin_layout Plain Layout
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\alpha$
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $\beta$
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19338 \begin_layout Plain Layout
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19349 \begin_layout Plain Layout
19350 \begin_inset Formula $\gamma$
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19363 \begin_layout Plain Layout
19371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19374 \begin_layout Plain Layout
19375 \begin_inset Formula $\delta$
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19399 \begin_layout Plain Layout
19400 \begin_inset Formula $\epsilon$
19410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19413 \begin_layout Plain Layout
19421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19424 \begin_layout Plain Layout
19425 \begin_inset Formula $\varepsilon$
19435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19438 \begin_layout Plain Layout
19446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19449 \begin_layout Plain Layout
19450 \begin_inset Formula $\zeta$
19460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19463 \begin_layout Plain Layout
19471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19474 \begin_layout Plain Layout
19475 \begin_inset Formula $\eta$
19485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19488 \begin_layout Plain Layout
19496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19499 \begin_layout Plain Layout
19500 \begin_inset Formula $\theta$
19510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19513 \begin_layout Plain Layout
19521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19524 \begin_layout Plain Layout
19525 \begin_inset Formula $\vartheta$
19539 \begin_inset space \hfill{}
19543 \begin_inset Tabular
19544 <lyxtabular version="3" rows="12" columns="2">
19546 <column alignment="center" valignment="top" width="0pt">
19547 <column alignment="center" valignment="top" width="0pt">
19549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19552 \begin_layout Plain Layout
19558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19572 \begin_layout Plain Layout
19580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19583 \begin_layout Plain Layout
19584 \begin_inset Formula $\iota$
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19597 \begin_layout Plain Layout
19605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19608 \begin_layout Plain Layout
19609 \begin_inset Formula $\kappa$
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19622 \begin_layout Plain Layout
19630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19633 \begin_layout Plain Layout
19634 \begin_inset Formula $\varkappa$
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19647 \begin_layout Plain Layout
19655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19658 \begin_layout Plain Layout
19659 \begin_inset Formula $\lambda$
19669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19672 \begin_layout Plain Layout
19680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19683 \begin_layout Plain Layout
19684 \begin_inset Formula $\mu$
19694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19697 \begin_layout Plain Layout
19705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19708 \begin_layout Plain Layout
19709 \begin_inset Formula $\nu$
19719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19722 \begin_layout Plain Layout
19730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19733 \begin_layout Plain Layout
19734 \begin_inset Formula $\xi$
19744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19747 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $o$
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\pi$
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19795 \begin_layout Plain Layout
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19806 \begin_layout Plain Layout
19807 \begin_inset Formula $\varpi$
19817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19820 \begin_layout Plain Layout
19828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19831 \begin_layout Plain Layout
19832 \begin_inset Formula $\rho$
19846 \begin_inset space \hfill{}
19850 \begin_inset Tabular
19851 <lyxtabular version="3" rows="11" columns="2">
19853 <column alignment="center" valignment="top" width="0pt">
19854 <column alignment="center" valignment="top" width="0pt">
19856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19859 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\varrho$
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19904 \begin_layout Plain Layout
19912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19915 \begin_layout Plain Layout
19916 \begin_inset Formula $\sigma$
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19929 \begin_layout Plain Layout
19937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19940 \begin_layout Plain Layout
19941 \begin_inset Formula $\varsigma$
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19965 \begin_layout Plain Layout
19966 \begin_inset Formula $\tau$
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19979 \begin_layout Plain Layout
19987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19990 \begin_layout Plain Layout
19991 \begin_inset Formula $\upsilon$
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20004 \begin_layout Plain Layout
20012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20015 \begin_layout Plain Layout
20016 \begin_inset Formula $\phi$
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20029 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20040 \begin_layout Plain Layout
20041 \begin_inset Formula $\varphi$
20051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20054 \begin_layout Plain Layout
20062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20065 \begin_layout Plain Layout
20066 \begin_inset Formula $\chi$
20076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20079 \begin_layout Plain Layout
20087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20090 \begin_layout Plain Layout
20091 \begin_inset Formula $\psi$
20101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20104 \begin_layout Plain Layout
20112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20115 \begin_layout Plain Layout
20116 \begin_inset Formula $\omega$
20130 \begin_inset space \hfill{}
20136 \begin_layout Standard
20137 \begin_inset VSpace medskip
20143 \begin_layout Standard
20144 How to create upright Greek letters is explained in
20145 \begin_inset CommandInset ref
20147 reference "sub:Upright-small-Greek"
20154 \begin_layout Subsection
20159 \begin_layout Plain Layout
20160 Greek letters ! big
20168 \begin_layout Standard
20169 \begin_inset space \hfill{}
20173 \begin_inset Tabular
20174 <lyxtabular version="3" rows="7" columns="2">
20176 <column alignment="center" valignment="top" width="0pt">
20177 <column alignment="center" valignment="top" width="0pt">
20179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20182 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20202 \begin_layout Plain Layout
20210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20213 \begin_layout Plain Layout
20214 \begin_inset Formula $\Gamma$
20224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20227 \begin_layout Plain Layout
20235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20238 \begin_layout Plain Layout
20239 \begin_inset Formula $\Delta$
20249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20252 \begin_layout Plain Layout
20260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20263 \begin_layout Plain Layout
20264 \begin_inset Formula $\Theta$
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Plain Layout
20289 \begin_inset Formula $\Lambda$
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\Xi$
20324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20338 \begin_layout Plain Layout
20339 \begin_inset Formula $\Pi$
20353 \begin_inset space \hfill{}
20357 \begin_inset Tabular
20358 <lyxtabular version="3" rows="6" columns="2">
20360 <column alignment="center" valignment="top" width="0pt">
20361 <column alignment="center" valignment="top" width="0pt">
20363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20366 \begin_layout Plain Layout
20372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20375 \begin_layout Plain Layout
20383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20386 \begin_layout Plain Layout
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20397 \begin_layout Plain Layout
20398 \begin_inset Formula $\Sigma$
20408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20411 \begin_layout Plain Layout
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20422 \begin_layout Plain Layout
20423 \begin_inset Formula $\Upsilon$
20433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20436 \begin_layout Plain Layout
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20447 \begin_layout Plain Layout
20448 \begin_inset Formula $\Phi$
20458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20461 \begin_layout Plain Layout
20469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20472 \begin_layout Plain Layout
20473 \begin_inset Formula $\Psi$
20483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20486 \begin_layout Plain Layout
20494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20497 \begin_layout Plain Layout
20498 \begin_inset Formula $\Omega$
20512 \begin_inset space \hfill{}
20518 \begin_layout Standard
20519 \begin_inset VSpace medskip
20522 That the big Greek letters appear upright is caused by a design bug when
20524 To get correct italic big letters, begin every command with
20529 For example the command
20536 \begin_inset Formula $\varGamma$
20542 \begin_layout Subsection
20547 \begin_layout Plain Layout
20548 Greek letters ! bold
20556 \begin_layout Standard
20557 Greek letters cannot be set with different font styles like Latin letters.
20558 They can only be made bold with the command
20568 \begin_layout Plain Layout
20579 \begin_layout Standard
20581 \begin_inset Tabular
20582 <lyxtabular version="3" rows="3" columns="2">
20584 <column alignment="center" valignment="top" width="0">
20585 <column alignment="center" valignment="top" width="0">
20587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20590 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20610 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20625 \begin_layout Plain Layout
20626 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20639 \begin_layout Plain Layout
20651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20654 \begin_layout Plain Layout
20655 \begin_inset Formula $\theta\boldsymbol{\theta}$
20671 \begin_layout Section
20676 \begin_layout Plain Layout
20689 \begin_layout Plain Layout
20690 A list with all symbols of most of the LaTeX-packages can be found in
20691 \begin_inset CommandInset citation
20706 \begin_layout Plain Layout
20714 \begin_inset Note Note
20717 \begin_layout Plain Layout
20720 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20723 \begin_layout Plain Layout
20726 texorpdfstring is in section
20727 \begin_inset CommandInset ref
20729 reference "sub:Formulas-in-Section"
20742 \begin_layout Plain Layout
20751 \begin_layout Standard
20752 Many of the symbols listed in this section can also be inserted via the
20754 \begin_inset Graphics
20755 filename ../images/math/nabla.png
20761 \begin_inset Graphics
20762 filename ../images/math/digamma.png
20770 \begin_layout Subsection
20771 Mathematical Symbols
20772 \begin_inset CommandInset label
20774 name "sub:Mathematical-Symbols"
20782 \begin_layout Plain Layout
20783 Symbols ! mathematical
20791 \begin_layout Standard
20792 \begin_inset space \hfill{}
20796 \begin_inset Tabular
20797 <lyxtabular version="3" rows="10" columns="2">
20799 <column alignment="center" valignment="top" width="0pt">
20800 <column alignment="center" valignment="top" width="0pt">
20802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20805 \begin_layout Plain Layout
20811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20825 \begin_layout Plain Layout
20833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20836 \begin_layout Plain Layout
20837 \begin_inset Formula $\neg$
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20850 \begin_layout Plain Layout
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20861 \begin_layout Plain Layout
20862 \begin_inset Formula $\Im$
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20875 \begin_layout Plain Layout
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20886 \begin_layout Plain Layout
20887 \begin_inset Formula $\Re$
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\aleph$
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\partial$
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20962 \begin_inset Formula $\infty$
20972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20975 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\wp$
20997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21000 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21012 \begin_inset Formula $\imath$
21022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21025 \begin_layout Plain Layout
21033 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21036 \begin_layout Plain Layout
21037 \begin_inset Formula $\jmath$
21051 \begin_inset space \hfill{}
21055 \begin_inset Tabular
21056 <lyxtabular version="3" rows="10" columns="2">
21058 <column alignment="center" valignment="top" width="0pt">
21059 <column alignment="center" valignment="top" width="0pt">
21061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21064 \begin_layout Plain Layout
21070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21073 \begin_layout Plain Layout
21075 \begin_inset Note Note
21078 \begin_layout Plain Layout
21085 is only used as spacer.
21097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21100 \begin_layout Plain Layout
21108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21111 \begin_layout Plain Layout
21112 \begin_inset Formula $\forall$
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21125 \begin_layout Plain Layout
21133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21136 \begin_layout Plain Layout
21137 \begin_inset Formula $\exists$
21147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21150 \begin_layout Plain Layout
21158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21161 \begin_layout Plain Layout
21162 \begin_inset Formula $\nexists$
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21186 \begin_layout Plain Layout
21187 \begin_inset Formula $\emptyset$
21197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21200 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21212 \begin_inset Formula $\varnothing$
21222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21225 \begin_layout Plain Layout
21233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21236 \begin_layout Plain Layout
21237 \begin_inset Formula $\dag$
21247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21250 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21261 \begin_layout Plain Layout
21262 \begin_inset Formula $\ddag$
21272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21275 \begin_layout Plain Layout
21283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21286 \begin_layout Plain Layout
21290 \begin_layout Plain Layout
21300 \begin_inset Formula $\complement$
21307 \begin_layout Plain Layout
21321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21324 \begin_layout Plain Layout
21332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21335 \begin_layout Plain Layout
21336 \begin_inset Formula $\Bbbk$
21350 \begin_inset space \hfill{}
21354 \begin_inset Tabular
21355 <lyxtabular version="3" rows="10" columns="2">
21357 <column alignment="center" valignment="top" width="0pt">
21358 <column alignment="center" valignment="top" width="0pt">
21360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21363 \begin_layout Plain Layout
21369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21372 \begin_layout Plain Layout
21380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21383 \begin_layout Plain Layout
21391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21394 \begin_layout Plain Layout
21395 \begin_inset Formula $\prime$
21405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21408 \begin_layout Plain Layout
21416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21419 \begin_layout Plain Layout
21420 \begin_inset Formula $\backprime$
21430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21433 \begin_layout Plain Layout
21441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21444 \begin_layout Plain Layout
21445 \begin_inset Formula $\mho$
21455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21458 \begin_layout Plain Layout
21466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21469 \begin_layout Plain Layout
21470 \begin_inset Formula $\triangle$
21480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21483 \begin_layout Plain Layout
21491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21494 \begin_layout Plain Layout
21495 \begin_inset Formula $\angle$
21505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21508 \begin_layout Plain Layout
21516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21519 \begin_layout Plain Layout
21520 \begin_inset Formula $\measuredangle$
21530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21533 \begin_layout Plain Layout
21541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21544 \begin_layout Plain Layout
21545 \begin_inset Formula $\sphericalangle$
21555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21558 \begin_layout Plain Layout
21566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21569 \begin_layout Plain Layout
21570 \begin_inset Formula $\top$
21580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21583 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21595 \begin_inset Formula $\bot$
21609 \begin_inset space \hfill{}
21615 \begin_layout Subsection
21616 Miscellaneous Symbols
21617 \begin_inset CommandInset label
21619 name "sub:Miscellaneous-Symbols"
21627 \begin_layout Plain Layout
21628 Symbols ! miscellaneous
21636 \begin_layout Standard
21639 \begin_inset Tabular
21640 <lyxtabular version="3" rows="10" columns="2">
21642 <column alignment="center" valignment="top" width="0pt">
21643 <column alignment="center" valignment="top" width="0pt">
21645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21648 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21668 \begin_layout Plain Layout
21676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21679 \begin_layout Plain Layout
21680 \begin_inset Formula $\flat$
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21693 \begin_layout Plain Layout
21701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21704 \begin_layout Plain Layout
21705 \begin_inset Formula $\natural$
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21718 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21730 \begin_inset Formula $\sharp$
21740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21754 \begin_layout Plain Layout
21755 \begin_inset Formula $\surd$
21765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21768 \begin_layout Plain Layout
21776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21779 \begin_layout Plain Layout
21780 \begin_inset Formula $\checkmark$
21790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21793 \begin_layout Plain Layout
21801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21804 \begin_layout Plain Layout
21805 \begin_inset Formula $\yen$
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21818 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21829 \begin_layout Plain Layout
21830 \begin_inset Formula $\pounds$
21840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21843 \begin_layout Plain Layout
21849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21852 \begin_layout Plain Layout
21853 \begin_inset Formula $\$$
21863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21866 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $§$
21890 \begin_inset Tabular
21891 <lyxtabular version="3" rows="10" columns="2">
21893 <column alignment="center" valignment="top" width="0">
21894 <column alignment="center" valignment="top" width="0">
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21919 \begin_layout Plain Layout
21927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21930 \begin_layout Plain Layout
21931 \begin_inset Formula $\hbar$
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21944 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21955 \begin_layout Plain Layout
21956 \begin_inset Formula $\hslash$
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21969 \begin_layout Plain Layout
21977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21980 \begin_layout Plain Layout
21981 \begin_inset Formula $\clubsuit$
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21994 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22005 \begin_layout Plain Layout
22006 \begin_inset Formula $\spadesuit$
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22019 \begin_layout Plain Layout
22027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22030 \begin_layout Plain Layout
22031 \begin_inset Formula $\bigstar$
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22044 \begin_layout Plain Layout
22052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22055 \begin_layout Plain Layout
22056 \begin_inset Formula $\blacklozenge$
22066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22069 \begin_layout Plain Layout
22077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22080 \begin_layout Plain Layout
22081 \begin_inset Formula $\blacktriangle$
22091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22094 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22106 \begin_inset Formula $\blacktriangledown$
22116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22119 \begin_layout Plain Layout
22127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22131 \begin_inset Formula $\bullet$
22145 \begin_inset Tabular
22146 <lyxtabular version="3" rows="10" columns="2">
22148 <column alignment="center" valignment="top" width="0pt">
22149 <column alignment="center" valignment="top" width="0pt">
22151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22154 \begin_layout Plain Layout
22160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22163 \begin_layout Plain Layout
22171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22174 \begin_layout Plain Layout
22182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22185 \begin_layout Plain Layout
22186 \begin_inset Formula $\diamondsuit$
22196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22199 \begin_layout Plain Layout
22207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22210 \begin_layout Plain Layout
22211 \begin_inset Formula $\Diamond$
22221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22224 \begin_layout Plain Layout
22232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22235 \begin_layout Plain Layout
22236 \begin_inset Formula $\heartsuit$
22246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22249 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22261 \begin_inset Formula $\P$
22271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22274 \begin_layout Plain Layout
22282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22285 \begin_layout Plain Layout
22286 \begin_inset Formula $\copyright$
22296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22299 \begin_layout Plain Layout
22307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22310 \begin_layout Plain Layout
22311 \begin_inset Formula $\circledR$
22321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22324 \begin_layout Plain Layout
22332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22335 \begin_layout Plain Layout
22336 \begin_inset Formula $\maltese$
22346 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22349 \begin_layout Plain Layout
22357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22360 \begin_layout Plain Layout
22361 \begin_inset Formula $\diagup$
22371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22374 \begin_layout Plain Layout
22382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22385 \begin_layout Plain Layout
22386 \begin_inset Formula $\diagdown$
22402 \begin_layout Standard
22403 \begin_inset VSpace medskip
22406 More symbols are listed in
22407 \begin_inset CommandInset ref
22409 reference "sub:Miscellaneous-special-Characters"
22416 \begin_layout Standard
22417 Some symbols can be displayed in different sizes, see
22418 \begin_inset CommandInset ref
22420 reference "sub:Font-Sizes"
22427 \begin_layout Subsection
22432 \begin_layout Plain Layout
22433 Symbols ! Euro-symbol
22442 \begin_layout Plain Layout
22449 \begin_layout Plain Layout
22466 \begin_layout Standard
22467 To use the Euro symbol in formulas, the LaTeX-package
22475 \begin_layout Plain Layout
22481 must be installed and loaded with the LaTeX-preamble line
22484 \begin_layout Standard
22489 usepackage[gennarrow]{eurosym}
22492 \begin_layout Standard
22493 The Euro symbol can now be inserted with the command
22503 \begin_layout Plain Layout
22514 \begin_layout Standard
22515 The Euro symbol can directly be inserted with the € key in mathematical
22516 text, without having
22531 can also be inserted in TeX-mode.
22532 The official currency symbol can then be inserted with the command
22542 \begin_layout Plain Layout
22550 , that is only available in TeX-mode.
22553 \begin_layout Standard
22557 \begin_layout Plain Layout
22567 \begin_inset Note Note
22570 \begin_layout Plain Layout
22571 The following table will only be displayed when the LaTeX-package
22583 \begin_layout Standard
22584 An overview about the different Euro symbols:
22587 \begin_layout Standard
22589 \begin_inset Tabular
22590 <lyxtabular version="3" rows="4" columns="3">
22592 <column alignment="center" valignment="top" width="0pt">
22593 <column alignment="center" valignment="top" width="0pt">
22594 <column alignment="center" valignment="top" width="0pt">
22596 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22628 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22648 \begin_layout Plain Layout
22649 \begin_inset Formula $\euro$
22659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22662 \begin_layout Plain Layout
22668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22671 \begin_layout Plain Layout
22677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22680 \begin_layout Plain Layout
22681 \begin_inset Formula $\mbox{€}$
22691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22694 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22703 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22718 \begin_layout Plain Layout
22740 \begin_layout Standard
22744 \begin_layout Plain Layout
22754 \begin_inset Note Note
22757 \begin_layout Plain Layout
22758 The following will be displayed when the LaTeX-package
22770 \begin_layout Standard
22771 You need to install the LaTeX-package
22775 to see the rest of this subsection in the output.
22778 \begin_layout Standard
22782 \begin_layout Plain Layout
22794 \begin_layout Section
22796 \begin_inset CommandInset label
22798 name "sec:Relations"
22806 \begin_layout Plain Layout
22816 \begin_layout Plain Layout
22821 \begin_layout Plain Layout
22832 \begin_layout Plain Layout
22847 \begin_layout Standard
22848 All relations can also be inserted via the toolbar button
22849 \begin_inset Graphics
22850 filename ../images/math/leq.png
22858 \begin_layout Standard
22859 \begin_inset space \hfill{}
22863 \begin_inset Tabular
22864 <lyxtabular version="3" rows="17" columns="2">
22866 <column alignment="center" valignment="top" width="0pt">
22867 <column alignment="center" valignment="top" width="0pt">
22869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22872 \begin_layout Plain Layout
22878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22881 \begin_layout Plain Layout
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22901 \begin_layout Plain Layout
22902 \begin_inset Formula $<$
22912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22926 \begin_layout Plain Layout
22927 \begin_inset Formula $\le$
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22940 \begin_layout Plain Layout
22948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22951 \begin_layout Plain Layout
22952 \begin_inset Formula $\ll$
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22965 \begin_layout Plain Layout
22973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22976 \begin_layout Plain Layout
22977 \begin_inset Formula $\prec$
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22990 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23001 \begin_layout Plain Layout
23002 \begin_inset Formula $\preceq$
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23015 \begin_layout Plain Layout
23023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23026 \begin_layout Plain Layout
23027 \begin_inset Formula $\subset$
23037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23040 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\subseteq$
23062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23076 \begin_layout Plain Layout
23077 \begin_inset Formula $\sqsubseteq$
23087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23090 \begin_layout Plain Layout
23098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23101 \begin_layout Plain Layout
23102 \begin_inset Formula $\in$
23112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23115 \begin_layout Plain Layout
23123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23126 \begin_layout Plain Layout
23127 \begin_inset Formula $\vdash$
23137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23140 \begin_layout Plain Layout
23148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23151 \begin_layout Plain Layout
23152 \begin_inset Formula $\smile$
23162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23165 \begin_layout Plain Layout
23173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23176 \begin_layout Plain Layout
23177 \begin_inset Formula $\lhd$
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Plain Layout
23198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23201 \begin_layout Plain Layout
23202 \begin_inset Formula $\unlhd$
23212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23215 \begin_layout Plain Layout
23223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23226 \begin_layout Plain Layout
23227 \begin_inset Formula $\gtrless$
23237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23240 \begin_layout Plain Layout
23248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23251 \begin_layout Plain Layout
23252 \begin_inset Formula $\mid$
23262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23265 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23277 \begin_inset Formula $\nmid$
23291 \begin_inset space \hfill{}
23295 \begin_inset Tabular
23296 <lyxtabular version="3" rows="17" columns="2">
23298 <column alignment="center" valignment="top" width="0pt">
23299 <column alignment="center" valignment="top" width="0pt">
23301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23304 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23324 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $=$
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\not=$
23369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\equiv$
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\sim$
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\simeq$
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\approx$
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\cong$
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\bowtie$
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\notin$
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\perp$
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\propto$
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\asymp$
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\doteq$
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\circeq$
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23684 \begin_inset Formula $\models$
23694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23697 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23709 \begin_inset Formula $\widehat{=}$
23723 \begin_inset space \hfill{}
23727 \begin_inset Tabular
23728 <lyxtabular version="3" rows="17" columns="2">
23730 <column alignment="center" valignment="top" width="0pt">
23731 <column alignment="center" valignment="top" width="0pt">
23733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23736 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23756 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $>$
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\ge$
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\gg$
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\succ$
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\succeq$
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\supset$
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\supseteq$
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\sqsupseteq$
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\ni$
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\dashv$
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\frown$
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\rhd$
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\unrhd$
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\lessgtr$
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24115 \begin_layout Plain Layout
24116 \begin_inset Formula $\parallel$
24126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24129 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24141 \begin_inset Formula $\nparallel$
24155 \begin_inset space \hfill{}
24161 \begin_layout Standard
24162 \begin_inset VSpace medskip
24177 are bigger than the equal looking operators
24192 \begin_layout Standard
24193 Relations are, in contrary to symbols, always surrounded by space.
24196 \begin_layout Standard
24197 Relations with labels can be created with the command
24207 \begin_layout Plain Layout
24218 \begin_layout Standard
24220 \begin_inset Tabular
24221 <lyxtabular version="3" rows="2" columns="2">
24223 <column alignment="center" valignment="top" width="0">
24224 <column alignment="center" valignment="top" width="0">
24226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24229 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24238 \begin_layout Plain Layout
24240 \begin_inset Note Note
24243 \begin_layout Plain Layout
24250 is only used as spacer.
24262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24272 \begin_layout Plain Layout
24289 \begin_layout Plain Layout
24299 \begin_inset Formula $\downarrow$
24308 \begin_layout Plain Layout
24321 \begin_layout Plain Layout
24335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24338 \begin_layout Plain Layout
24339 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24355 \begin_layout Section
24359 \begin_layout Subsection
24360 Predefined Functions
24361 \begin_inset CommandInset label
24363 name "sub:Predefined-Functions"
24371 \begin_layout Plain Layout
24372 Functions ! predefined
24380 \begin_layout Standard
24381 In general, variables are set
24385 in mathematical expressions, but not function names, because
24386 \begin_inset Formula $sin$
24389 could be misunderstood as
24390 \begin_inset Formula $s\cdot i\cdot n$
24394 Therefore there are predefined functions, that are additionally a bit separated
24396 They are inserted as commands starting with a backslash before their name.
24399 \begin_layout Standard
24401 \begin_inset Tabular
24402 <lyxtabular version="3" rows="2" columns="4">
24404 <column alignment="center" valignment="top" width="0pt">
24405 <column alignment="center" valignment="top" width="0pt">
24406 <column alignment="center" valignment="top" width="0pt">
24407 <column alignment="center" valignment="top" width="0pt">
24409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24412 \begin_layout Plain Layout
24418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24421 \begin_layout Plain Layout
24427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24430 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24459 \begin_layout Plain Layout
24460 \begin_inset Formula $Asin(x)+B$
24468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24471 \begin_layout Plain Layout
24479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24482 \begin_layout Plain Layout
24483 \begin_inset Formula $A\sin(x)+B$
24499 \begin_layout Standard
24500 The following functions are predefined:
24503 \begin_layout Standard
24504 \begin_inset VSpace -2mm
24510 \begin_layout Standard
24512 \begin_inset Tabular
24513 <lyxtabular version="3" rows="9" columns="4">
24515 <column alignment="center" valignment="top" width="0pt">
24516 <column alignment="center" valignment="top" width="0pt">
24517 <column alignment="center" valignment="top" width="0pt">
24518 <column alignment="center" valignment="top" width="0pt">
24520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24523 \begin_layout Plain Layout
24529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24532 \begin_layout Plain Layout
24538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24541 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Plain Layout
24604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24618 \begin_layout Plain Layout
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24629 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24640 \begin_layout Plain Layout
24650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24675 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24686 \begin_layout Plain Layout
24696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24699 \begin_layout Plain Layout
24707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24710 \begin_layout Plain Layout
24718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24721 \begin_layout Plain Layout
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24732 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24745 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24756 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24767 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24778 \begin_layout Plain Layout
24788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24791 \begin_layout Plain Layout
24799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24802 \begin_layout Plain Layout
24810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24813 \begin_layout Plain Layout
24821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24824 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24905 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24916 \begin_layout Plain Layout
24932 \begin_layout Standard
24933 They can also be inserted with the math toolbar button
24934 \begin_inset Graphics
24935 filename ../images/math/functions.png
24943 \begin_layout Subsection
24944 Self-defined Functions
24948 \begin_layout Plain Layout
24949 Functions ! self-defined
24957 \begin_layout Standard
24958 To use a function that is not predefined, like for example the sign function
24959 sgn(x), there are two possibilities:
24962 \begin_layout Itemize
24963 Define the function by inserting the following line to the LaTeX-preamble
24967 \begin_layout Plain Layout
24972 DeclareMathOperator
24975 \begin_inset CommandInset ref
24977 reference "sub:Self-defined-Operators"
24987 \begin_inset Newline newline
24991 \begin_inset VSpace -3mm
24995 \begin_inset Newline newline
25002 DeclareMathOperator{
25010 \begin_layout Plain Layout
25015 DeclareMathOperator
25021 \begin_inset Newline newline
25025 \begin_inset VSpace -2mm
25029 \begin_inset Newline newline
25032 Now the new defined function can be called with the command
25041 \begin_layout Itemize
25042 Write the the formula as usual, mark the formula name, in our example the
25047 , and change it to mathematical text.
25048 At last a space is inserted between prefactor and function.
25051 \begin_layout Standard
25052 The result is the same with both methods as with a predefined function
25056 \begin_layout Plain Layout
25057 In LyX self-defined functions are displayed red, predefined ones black.
25065 \begin_layout Standard
25067 \begin_inset Tabular
25068 <lyxtabular version="3" rows="3" columns="2">
25070 <column alignment="center" valignment="top" width="0pt">
25071 <column alignment="center" valignment="top" width="0pt">
25073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25076 \begin_layout Plain Layout
25082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25085 \begin_layout Plain Layout
25093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25096 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25107 \begin_layout Plain Layout
25108 \begin_inset Formula $A\sgn(x)+B$
25118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25121 \begin_layout Plain Layout
25125 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25136 \begin_layout Plain Layout
25137 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25153 \begin_layout Standard
25154 The first method is more suitable when the self-defined function should
25155 be used several times.
25158 \begin_layout Subsection
25163 \begin_layout Plain Layout
25172 \begin_layout Standard
25173 For limits there are defined besides
25183 \begin_layout Plain Layout
25203 furthermore the following functions:
25206 \begin_layout Standard
25208 \begin_inset Tabular
25209 <lyxtabular version="3" rows="5" columns="2">
25211 <column alignment="center" valignment="top" width="0">
25212 <column alignment="center" valignment="top" width="0">
25214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25217 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25226 \begin_layout Plain Layout
25228 \begin_inset Note Note
25231 \begin_layout Plain Layout
25238 is only used as spacer.
25250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25253 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25264 \begin_layout Plain Layout
25265 \begin_inset Formula $\varliminf$
25275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25278 \begin_layout Plain Layout
25286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25289 \begin_layout Plain Layout
25290 \begin_inset Formula $\varlimsup$
25300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25303 \begin_layout Plain Layout
25311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25314 \begin_layout Plain Layout
25315 \begin_inset Formula $\varprojlim$
25325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25328 \begin_layout Plain Layout
25336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25339 \begin_layout Plain Layout
25340 \begin_inset Formula $\varinjlim$
25344 \begin_inset Formula $\raisebox{-2.5mm}{}$
25360 \begin_layout Standard
25361 \begin_inset VSpace medskip
25364 The limit is created by inserting a subscript.
25365 It is set right beside the function in an inline formula:
25368 \begin_layout Standard
25370 \begin_inset Tabular
25371 <lyxtabular version="3" rows="2" columns="2">
25373 <column alignment="center" valignment="top" width="0pt">
25374 <column alignment="center" valignment="top" width="0pt">
25376 <cell alignment="center" valignment="top" usebox="none">
25379 \begin_layout Plain Layout
25385 <cell alignment="center" valignment="top" usebox="none">
25388 \begin_layout Plain Layout
25389 \begin_inset space \hspace{}
25394 \begin_inset Note Note
25397 \begin_layout Plain Layout
25404 are used here as spacer.
25416 <cell alignment="center" valignment="top" usebox="none">
25419 \begin_layout Plain Layout
25428 \begin_layout Plain Layout
25441 \begin_layout Plain Layout
25455 <cell alignment="center" valignment="top" usebox="none">
25458 \begin_layout Plain Layout
25459 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25475 \begin_layout Standard
25476 In a displayed formula the limit is set below the formula, as usual:
25477 \begin_inset Formula \[
25485 \begin_layout Subsection
25490 \begin_layout Plain Layout
25491 Functions ! modulo-
25499 \begin_layout Standard
25500 The modulo-function is special, because it exists in four variants.
25503 \begin_layout Standard
25504 The variants in a displayed formula:
25505 \begin_inset Formula \begin{align*}
25506 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25507 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25508 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25509 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25510 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25517 \begin_layout Standard
25518 In an inline formula less space is set before the function names for all
25522 \begin_layout Section
25527 \begin_layout Plain Layout
25536 \begin_layout Subsection
25537 Special Characters in Mathematical Text
25540 \begin_layout Standard
25541 The following commands can only be used in mathematical text or in TeX-mode:
25544 \begin_layout Standard
25545 \begin_inset space \hfill{}
25549 \begin_inset Tabular
25550 <lyxtabular version="3" rows="8" columns="2">
25552 <column alignment="block" valignment="top" width="0">
25553 <column alignment="block" valignment="top" width="0">
25555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25558 \begin_layout Plain Layout
25564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25567 \begin_layout Plain Layout
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 $\textrm{œ}$
25600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25603 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25614 \begin_layout Plain Layout
25615 \begin_inset Formula $\textrm{Œ}$
25625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25639 \begin_layout Plain Layout
25640 \begin_inset Formula $\textrm{æ}$
25650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25653 \begin_layout Plain Layout
25661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25664 \begin_layout Plain Layout
25665 \begin_inset Formula $\textrm{Æ}$
25675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25678 \begin_layout Plain Layout
25686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25689 \begin_layout Plain Layout
25690 \begin_inset Formula $\textrm{\aa}$
25700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25703 \begin_layout Plain Layout
25710 \begin_layout Plain Layout
25717 \begin_layout Plain Layout
25738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25741 \begin_layout Plain Layout
25742 \begin_inset Formula $\textrm{Å}$
25752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25755 \begin_layout Plain Layout
25763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25766 \begin_layout Plain Layout
25767 \begin_inset Formula $\textrm{ı}$
25781 \begin_inset space \hfill{}
25785 \begin_inset Tabular
25786 <lyxtabular version="3" rows="8" columns="2">
25788 <column alignment="block" valignment="top" width="0">
25789 <column alignment="center" valignment="top" width="0">
25791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25794 \begin_layout Plain Layout
25796 \begin_inset Note Note
25799 \begin_layout Plain Layout
25801 \begin_inset space \thinspace{}
25804 mm is used for separation, because otherwise the output will be ¡ and ¿
25815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25818 \begin_layout Plain Layout
25826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25829 \begin_layout Plain Layout
25837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25840 \begin_layout Plain Layout
25841 \begin_inset Formula $\textrm{ø}$
25851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25854 \begin_layout Plain Layout
25862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25865 \begin_layout Plain Layout
25866 \begin_inset Formula $\textrm{Ø}$
25876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25879 \begin_layout Plain Layout
25887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25890 \begin_layout Plain Layout
25891 \begin_inset Formula $\textrm{ł}$
25901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25904 \begin_layout Plain Layout
25912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25915 \begin_layout Plain Layout
25916 \begin_inset Formula $\textrm{Ł}$
25926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25929 \begin_layout Plain Layout
25931 \begin_inset space \hspace{}
25939 \begin_layout Plain Layout
25953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25956 \begin_layout Plain Layout
25957 \begin_inset Formula $\textrm{!`}$
25967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25970 \begin_layout Plain Layout
25972 \begin_inset space \hspace{}
25980 \begin_layout Plain Layout
25994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25997 \begin_layout Plain Layout
25998 \begin_inset Formula $\textrm{?`}$
26008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26011 \begin_layout Plain Layout
26019 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26022 \begin_layout Plain Layout
26023 \begin_inset Formula $\textrm{ȷ}$
26037 \begin_inset space \hfill{}
26043 \begin_layout Standard
26045 \begin_inset Formula $\textrm{\textrm{Å}}$
26049 \begin_inset Formula $\textrm{\textrm{Ø}}$
26052 can also be inserted via the math toolbar button
26053 \begin_inset Graphics
26054 filename ../images/math/digamma.png
26062 \begin_layout Standard
26063 An exception are the commands
26066 \begin_inset space \hspace{}
26075 \begin_inset space \hspace{}
26081 , because they can be inserted in LyX directly to text.
26084 \begin_layout Subsection
26086 \begin_inset CommandInset label
26088 name "sub:Accents-in-Text"
26096 \begin_layout Plain Layout
26105 \begin_layout Standard
26106 With the following commands all letters can be accented.
26107 The commands must be inserted in TeX-mode.
26110 \begin_layout Standard
26111 \begin_inset space \hfill{}
26115 \begin_inset Tabular
26116 <lyxtabular version="3" rows="8" columns="2">
26118 <column alignment="block" valignment="top" width="0">
26119 <column alignment="block" valignment="top" width="0">
26121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26124 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26133 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26144 \begin_layout Plain Layout
26148 \begin_inset Quotes grd
26156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26159 \begin_layout Plain Layout
26163 \begin_layout Plain Layout
26179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26182 \begin_layout Plain Layout
26190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26193 \begin_layout Plain Layout
26197 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26216 \begin_layout Plain Layout
26223 \begin_layout Plain Layout
26237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26240 \begin_layout Plain Layout
26244 \begin_layout Plain Layout
26260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26263 \begin_layout Plain Layout
26271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26274 \begin_layout Plain Layout
26278 \begin_layout Plain Layout
26294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26297 \begin_layout Plain Layout
26304 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26321 \begin_layout Plain Layout
26325 \begin_layout Plain Layout
26341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26344 \begin_layout Plain Layout
26351 \begin_layout Plain Layout
26365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26368 \begin_layout Plain Layout
26372 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26391 \begin_layout Plain Layout
26398 \begin_layout Plain Layout
26412 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26415 \begin_layout Plain Layout
26419 \begin_layout Plain Layout
26439 \begin_inset space \hfill{}
26443 \begin_inset Tabular
26444 <lyxtabular version="3" rows="8" columns="2">
26446 <column alignment="block" valignment="top" width="0">
26447 <column alignment="center" valignment="top" width="0">
26449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26452 \begin_layout Plain Layout
26458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26461 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26479 \begin_layout Plain Layout
26493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26496 \begin_layout Plain Layout
26500 \begin_layout Plain Layout
26516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26519 \begin_layout Plain Layout
26527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26530 \begin_layout Plain Layout
26534 \begin_layout Plain Layout
26550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26553 \begin_layout Plain Layout
26560 \begin_layout Plain Layout
26571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26574 \begin_layout Plain Layout
26578 \begin_layout Plain Layout
26594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26597 \begin_layout Plain Layout
26605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26608 \begin_layout Plain Layout
26612 \begin_layout Plain Layout
26628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26631 \begin_layout Plain Layout
26638 \begin_layout Plain Layout
26652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26655 \begin_layout Plain Layout
26659 \begin_layout Plain Layout
26675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26678 \begin_layout Plain Layout
26685 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26706 \begin_layout Plain Layout
26722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26725 \begin_layout Plain Layout
26732 \begin_layout Plain Layout
26746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26749 \begin_layout Plain Layout
26753 \begin_layout Plain Layout
26773 \begin_inset space \hfill{}
26779 \begin_layout Standard
26780 \begin_inset VSpace medskip
26789 also two different characters can be accented.
26798 \begin_layout Plain Layout
26813 \begin_layout Plain Layout
26825 \begin_layout Standard
26838 can in combination with vowels directly be inserted with the keyboard without
26840 The same applies for the tilde
26844 \begin_layout Plain Layout
26845 This only applies for keyboards where the tilde is defined as accent.
26854 in combination with
26869 \begin_layout Standard
26912 , and accents inserted directly with the keyboard are also available in
26914 For the other accents there are special math commands to be used in formulas,
26916 \begin_inset CommandInset ref
26918 reference "sub:Accents-for-one"
26925 \begin_layout Standard
26926 \begin_inset VSpace bigskip
26929 Furthermore, with the command
26939 \begin_layout Plain Layout
26947 all numbers and letters can be set into a circle, quasi accented with a
26948 circle, similar to the the copyright symbol.
26951 \begin_layout Standard
26953 \begin_inset Tabular
26954 <lyxtabular version="3" rows="3" columns="2">
26956 <column alignment="center" valignment="top" width="0">
26957 <column alignment="center" valignment="top" width="0">
26959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26962 \begin_layout Plain Layout
26968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26971 \begin_layout Plain Layout
26973 \begin_inset Note Note
26976 \begin_layout Plain Layout
26983 is only used as spacer.
26995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26998 \begin_layout Plain Layout
27006 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27009 \begin_layout Plain Layout
27013 \begin_layout Plain Layout
27029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27032 \begin_layout Plain Layout
27043 raisebox{-1.5pt}{W}}
27048 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27051 \begin_layout Plain Layout
27052 \begin_inset Formula $\raisebox{4.5mm}{}$
27059 \begin_layout Plain Layout
27077 \begin_inset Formula $\raisebox{-2mm}{}$
27093 \begin_layout Standard
27094 One has to take care that the character fits in the circle.
27105 \begin_layout Plain Layout
27107 \begin_inset CommandInset ref
27109 reference "sub:Font-Sizes"
27118 specifies thereby the size of the circle.
27129 \begin_layout Plain Layout
27131 \begin_inset CommandInset ref
27133 reference "sub:Boxes-without-Frame"
27142 the character can be centered.
27145 \begin_layout Subsection
27150 \begin_layout Plain Layout
27159 \begin_layout Standard
27160 Minuscule numbers are created with the command
27170 \begin_layout Plain Layout
27179 The command can be used in formulas and in TeX-mode.
27180 The command scheme is:
27183 \begin_layout Standard
27188 oldstylenums{number}
27191 \begin_layout Standard
27196 oldstylenums{0123456789
27199 \begin_inset Formula $\oldstylenums{0123456789}$
27205 \begin_layout Subsection
27206 Miscellaneous special Characters
27207 \begin_inset CommandInset label
27209 name "sub:Miscellaneous-special-Characters"
27217 \begin_layout Plain Layout
27218 Special characters ! miscellaneous
27226 \begin_layout Standard
27227 The following characters can only be inserted to formulas by using commands:
27230 \begin_layout Standard
27232 \begin_inset Tabular
27233 <lyxtabular version="3" rows="4" columns="2">
27235 <column alignment="center" valignment="top" width="0">
27236 <column alignment="center" valignment="top" width="0">
27238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27241 \begin_layout Plain Layout
27247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27250 \begin_layout Plain Layout
27258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27261 \begin_layout Plain Layout
27268 \begin_layout Plain Layout
27282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27285 \begin_layout Plain Layout
27286 \begin_inset Formula $\mathcircumflex$
27296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27299 \begin_layout Plain Layout
27307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27310 \begin_layout Plain Layout
27311 \begin_inset Formula $\_$
27321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27324 \begin_layout Plain Layout
27329 \begin_layout Plain Layout
27344 \begin_layout Plain Layout
27357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27360 \begin_layout Plain Layout
27361 \begin_inset Formula $^{\circ}$
27377 \begin_layout Standard
27378 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27379 contains the following line
27383 \begin_layout Plain Layout
27384 More about this is described in
27385 \begin_inset CommandInset ref
27387 reference "sub:Text-Characters-in"
27399 \begin_layout Standard
27404 DeclareInputtext{176}{
27417 \begin_layout Section
27419 \begin_inset CommandInset label
27421 name "sec:Formula-Styles"
27429 \begin_layout Plain Layout
27438 \begin_layout Itemize
27439 There are two different alignment styles:
27443 \begin_layout Description
27444 Centered is the predefined standard
27447 \begin_layout Description
27448 Indented for this the option
27452 must be inserted in the menu
27454 Document\SpecialChar \menuseparator
27460 \begin_inset space ~
27466 \begin_layout Standard
27471 is used, the indentation can be adjusted with the length
27481 \begin_layout Plain Layout
27490 Should the distance be 15
27491 \begin_inset space \thinspace{}
27494 mm, the following command line is inserted in the LaTeX-preamble
27497 \begin_layout Standard
27507 \begin_layout Standard
27508 When no length is specified, the predefined value of 30
27509 \begin_inset space \thinspace{}
27516 \begin_layout Itemize
27517 And two different numbering styles:
27521 \begin_layout Description
27522 Right is the predefined standard
27525 \begin_layout Description
27526 Left for this the option
27530 must be inserted in the menu
27532 Document\SpecialChar \menuseparator
27538 \begin_inset space ~
27545 \begin_layout Standard
27554 can also be used together.
27555 In this case both options are inserted, separated by a comma.
27558 \begin_layout Standard
27559 The chosen styles are used for all displayed formulas of the document.
27560 When both, centered and indented formulas should be created in a document,
27566 The indented formulas are then set in a flalign environment, see
27567 \begin_inset CommandInset ref
27569 reference "sub:Flalign-Environment"
27576 \begin_layout Section
27578 \begin_inset CommandInset label
27580 name "sec:Multiline-Formulas"
27588 \begin_layout Plain Layout
27589 Formula ! multiline
27597 \begin_layout Subsection
27601 \begin_layout Standard
27602 In LyX multiline formulas are created by pressing
27607 arg "newline-insert newline"
27613 This creates either an
27615 eqnarray environment
27617 that is described in
27618 \begin_inset CommandInset ref
27620 reference "sub:Eqnarray-Environment"
27624 or, when the option
27626 Use AMS math package
27628 in the document settings is selected, an
27632 that is described in
27633 \begin_inset CommandInset ref
27635 reference "sub:Standard-align-Environment"
27642 \begin_layout Standard
27643 There are other multiline formula environments that can be created via the
27646 Insert\SpecialChar \menuseparator
27650 These environments are described in the following sections.
27653 \begin_layout Standard
27654 In all multiline formula environments a new line is created by pressing
27658 arg "newline-insert newline"
27662 To add or delete lines, the math toolbar buttons
27663 \begin_inset Graphics
27664 filename ../images/tabular-feature_append-row.png
27670 \begin_inset Graphics
27671 filename ../images/tabular-feature_delete-row.png
27676 , respectively, or the menu
27678 Edit\SpecialChar \menuseparator
27684 \begin_layout Subsubsection
27686 \begin_inset CommandInset label
27688 name "sub:Line-Separation"
27696 \begin_layout Plain Layout
27697 Formula ! multiline ! Line separation
27705 \begin_layout Standard
27706 There is sometimes not enough space in multiline formulas between the lines:
27707 \begin_inset Formula \begin{eqnarray*}
27708 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}\\
27709 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*}
27716 \begin_layout Standard
27717 In LaTeX additional line space is specified as optional argument of the
27719 This is not yet possible in LyX
27723 \begin_layout Plain Layout
27725 \begin_inset CommandInset href
27727 name "LyX-bug #1505"
27728 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27737 , therefore the whole formula must be inserted in TeX-mode.
27738 To add in our example space, the command
27746 is inserted at the end of the first line.
27751 \begin_layout Plain Layout
27758 \begin_layout Plain Layout
27760 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27763 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27770 \begin_layout Plain Layout
27774 left(B^{2}+x_{0}^{2}
27782 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27787 \begin_layout Plain Layout
27799 \begin_layout Standard
27800 \begin_inset VSpace bigskip
27803 To set the the line separation for all lines in a formula, the length
27813 \begin_layout Plain Layout
27823 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27834 \begin_inset space \thinspace{}
27839 \begin_inset space \thinspace{}
27842 mm additional line separation as in the previous example, the command
27845 \begin_layout Standard
27855 \begin_layout Standard
27856 is inserted in TeX-mode before the formula.
27857 This requires that the LaTeX-package
27865 \begin_layout Plain Layout
27870 is part of every LaTeX standard installation.
27879 \begin_layout Plain Layout
27885 was loaded in LaTeX-preamble with the line
27888 \begin_layout Standard
27896 \begin_layout Standard
27901 \begin_layout Plain Layout
27913 \begin_inset Formula \begin{eqnarray*}
27914 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}\\
27915 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*}
27922 \begin_layout Standard
27926 \begin_layout Plain Layout
27937 To get back to the predefined distance,
27943 is set to the value 3
27944 \begin_inset space \thinspace{}
27950 \begin_layout Subsubsection
27952 \begin_inset CommandInset label
27954 name "sub:Column-Separation"
27962 \begin_layout Plain Layout
27963 Formula ! multiline ! Column separation
27971 \begin_layout Standard
27972 Multiline formulas form a matrix.
27973 A formula in the eqnarray environment is for example a matrix with three
27975 By changing the column separation in this environment, the space beside
27976 the relation sign can be changed.
27979 \begin_layout Standard
27980 The column separation is specified with the length
27990 \begin_layout Plain Layout
27999 \begin_inset Newline newline
28002 column separation = 2
28003 \begin_inset space \thinspace{}
28013 \begin_inset Newline newline
28019 \begin_layout Standard
28029 \begin_layout Standard
28030 inserted in TeX-mode, sets for all following formulas a column separation
28032 \begin_inset space \thinspace{}
28036 To get back to the predefined distance,
28043 \begin_inset space \thinspace{}
28049 \begin_layout Standard
28051 \begin_inset space \thinspace{}
28054 cm column separation:
28058 \begin_layout Plain Layout
28070 \begin_inset Formula \begin{eqnarray*}
28072 C & \ne & A\end{eqnarray*}
28076 A formula with the predefined column separation for matrices of 10
28077 \begin_inset space \thinspace{}
28084 \begin_layout Plain Layout
28096 \begin_inset Formula \begin{eqnarray*}
28098 C & \ne & A\end{eqnarray*}
28105 \begin_layout Subsubsection
28110 \begin_layout Plain Layout
28119 \begin_layout Standard
28120 Long formulas can be typeset using these methods:
28123 \begin_layout Itemize
28124 When one side of the equation is much shorther than the line width, this
28125 one is chosen for the left side and the right side is typeset over two
28127 \begin_inset Formula \begin{eqnarray}
28128 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 \\
28129 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}\end{eqnarray}
28133 The minus sign at the beginning of the second line does normally not appear
28134 as operator because it is the first character of the line.
28135 Thus it would not be surrounded by space and could not be distinguished
28136 from the fraction bar.
28138 \begin_inset space \thinspace{}
28141 pt space was inserted behind the minus sign with the command
28151 \begin_layout Plain Layout
28159 \begin_inset CommandInset ref
28161 reference "sub:Variable-Space"
28174 \begin_layout Plain Layout
28185 \begin_layout Itemize
28186 When both sides of the equation are too long, the command
28196 \begin_layout Plain Layout
28205 It is inserted to the first column of the first line and effects that all
28206 further insertions overwrite the following columns:
28207 \begin_inset Formula \begin{eqnarray}
28208 \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 \\
28209 & & -\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 \\
28210 & & =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}
28214 After the insertion of
28220 , the cursor is in a purple box that is a bit shifted to the left from the
28222 In this the formula is inserted.
28223 \begin_inset Newline newline
28226 The content of the further lines is inserted to the second or another formula
28228 The greater the column number where it was inserted, the larger the indentation.
28229 \begin_inset VSpace medskip
28233 \begin_inset Newline newline
28237 \begin_inset Note Greyedout
28240 \begin_layout Plain Layout
28241 Note the following when using
28250 \begin_layout Itemize
28251 The formula doesn't use the full page width.
28253 \begin_inset space \thinspace{}
28257 \begin_inset space \space{}
28261 \begin_inset Formula $-B^{2}$
28264 is added to the first line in the above example, it would have been outside
28266 To better use the width, negative space can be inserted at the beginning
28270 \begin_layout Itemize
28271 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28276 \begin_layout Plain Layout
28277 \begin_inset CommandInset href
28279 name "LyX-bug #1429"
28280 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28289 One can only set the cursor at the beginning of the line and move it with
28298 \begin_layout Itemize
28299 Other methods to set long formulas are offered by the environments described
28301 \begin_inset CommandInset ref
28303 reference "sub:Multline-Environment"
28308 \begin_inset CommandInset ref
28310 reference "sub:Multiline-Formula-Parts"
28317 \begin_layout Subsubsection
28319 \begin_inset CommandInset label
28321 name "sub:Multiline-Brackets"
28329 \begin_layout Plain Layout
28330 Brackets ! for multiline expressions
28338 \begin_layout Standard
28339 For brackets spanning multiple lines the following problem occurs:
28340 \begin_inset Formula \begin{eqnarray*}
28341 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28342 & & \left.\cdots+B-D\right]\end{eqnarray*}
28349 \begin_layout Standard
28350 The closing bracket is smaller than the opening bracket because brackets
28351 with variable size may not span multiple lines.
28354 \begin_layout Standard
28355 To set the bracket size for the second line correctly, the first line is
28366 \begin_layout Plain Layout
28374 and the second line with
28382 \begin_layout Plain Layout
28396 \begin_inset CommandInset ref
28398 reference "sub:Automatic-Bracket-Size"
28413 \begin_layout Plain Layout
28439 \begin_layout Plain Layout
28458 \begin_layout Plain Layout
28477 \begin_layout Plain Layout
28489 \begin_inset Formula $\downarrow$
28498 \begin_layout Plain Layout
28506 is inserted, because the multiplication operator with its limits is the
28507 largest symbol in the first line and this should be the size for the bracket
28508 in the second line.
28511 \begin_layout Standard
28512 The result is this:
28513 \begin_inset Formula \begin{eqnarray*}
28514 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28515 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28522 \begin_layout Subsection
28526 \begin_layout Standard
28527 Align environments can be used for every kind of multiline formulas.
28528 They are specially useful to set several formulas side by side.
28531 \begin_layout Standard
28532 Align environments consist of columns.
28533 The odd columns are right aligned, the even ones left aligned.
28534 Every line in an Align environment can be numbered.
28537 \begin_layout Standard
28538 Align environments are created via the menu
28540 Insert\SpecialChar \menuseparator
28546 Edit\SpecialChar \menuseparator
28547 Math\SpecialChar \menuseparator
28548 Change Formula Type
28550 already existing formulas can be converted to Align environments.
28553 \begin_layout Standard
28554 To add or delete columns, the math toolbar buttons
28555 \begin_inset Graphics
28556 filename ../images/tabular-feature_append-column.png
28562 \begin_inset Graphics
28563 filename ../images/tabular-feature_delete-column.png
28568 , respectively, or the menu
28570 Edit\SpecialChar \menuseparator
28576 \begin_layout Subsubsection
28577 Standard align Environment
28578 \begin_inset CommandInset label
28580 name "sub:Standard-align-Environment"
28588 \begin_layout Plain Layout
28589 Formula ! multiline ! align environment
28597 \begin_layout Standard
28598 This Align environment is created by presssing
28601 arg "newline-insert newline"
28604 in a formula or by the menu
28606 Insert\SpecialChar \menuseparator
28607 Math\SpecialChar \menuseparator
28608 AMS align Environment
28613 \begin_layout Standard
28614 An example for two formulas set side by side, that are created with a four
28615 column align environment:
28616 \begin_inset Formula \begin{align*}
28617 A & =\sin(B) & C & =D\\
28618 C & \ne A & B & \ne D\end{align*}
28622 As it can be seen, the formulas in this environment are placed so as if
28631 \begin_layout Plain Layout
28639 \begin_inset CommandInset ref
28641 reference "sub:Variable-Space"
28652 before the first and after every even column.
28653 When the formula style
28659 \begin_layout Plain Layout
28661 \begin_inset CommandInset ref
28663 reference "sec:Formula-Styles"
28674 is used, the formula is set without the
28680 before the first column.
28683 \begin_layout Subsubsection
28684 Alignat Environment
28688 \begin_layout Plain Layout
28689 Formula ! multiline ! alignat environment
28697 \begin_layout Standard
28698 The alignat environment has no predefined column separation.
28699 It can be inserted manually with the spaces that are described
28700 \begin_inset CommandInset ref
28702 reference "sub:Space"
28709 \begin_layout Standard
28710 The above example in the alignat environment where 1
28711 \begin_inset space \thinspace{}
28714 cm space was inserted at the beginning of the second formula:
28715 \begin_inset Formula \begin{alignat*}{2}
28716 A & =\sin(B) & \hspace{1cm}C & =D\\
28717 C & \ne A & B & \ne D\end{alignat*}
28721 Because the column separation can be set separately for every column, this
28722 environment is especially suitable to set three and more formulas side
28726 \begin_layout Subsubsection
28727 Flalign Environment
28728 \begin_inset CommandInset label
28730 name "sub:Flalign-Environment"
28738 \begin_layout Plain Layout
28739 Formula ! multiline ! flalign environment
28747 \begin_layout Standard
28748 In this environment the first two columns are always set as much as possible
28749 to the left and the last two ones to the right.
28751 \begin_inset Formula \begin{flalign*}
28752 A & =1 & B & =2 & C & =3\\
28753 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28760 \begin_layout Standard
28761 By creating a flalign environment with an odd number of columns where an
28762 empty TeX-brace is inserted to the last column, several formulas in a document
28763 can be set to the left, although the formula style
28768 As example the indented formula
28769 \begin_inset CommandInset ref
28771 reference "eq:VolInt"
28776 \begin_inset Formula \begin{flalign}
28777 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28781 The first two columns contain the formula.
28782 To indent it as with the formula style
28787 \begin_inset space \thinspace{}
28790 pt space was inserted at the beginning of the first column.
28793 \begin_layout Subsection
28794 Eqnarray Environment
28795 \begin_inset CommandInset label
28797 name "sub:Eqnarray-Environment"
28805 \begin_layout Plain Layout
28806 Formula ! multiline ! eqnarray environment
28814 \begin_layout Standard
28815 When this environment has been created, three blue boxes appear.
28816 The content of the first box is right aligned, the content of the last
28818 The content of the middle box appears centered and a bit smaller, because
28819 it is designed to insert there only relation characters.
28820 \begin_inset Formula \begin{eqnarray*}
28821 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28823 A & = & A\end{eqnarray*}
28830 \begin_layout Subsection
28835 \begin_layout Plain Layout
28836 Formula ! multiline ! gather environment
28844 \begin_layout Standard
28845 This environment consists of only one centered column.
28846 Every line can be numbered.
28847 \begin_inset Formula \begin{gather}
28849 X=\textrm{-}1\end{gather}
28856 \begin_layout Subsection
28857 Multline Environment
28858 \begin_inset CommandInset label
28860 name "sub:Multline-Environment"
28868 \begin_layout Plain Layout
28869 Formula ! multiline ! multline environment
28877 \begin_layout Standard
28878 The multline environment consists, like the gather environment, of only
28880 But the first line is left aligned, the last one right aligned.
28881 All other lines are centered.
28882 Therefore this environment is suitable for long formulas.
28884 \begin_inset CommandInset ref
28886 reference "eq:lefteqn"
28890 in the multline environment:
28891 \begin_inset Formula \begin{multline}
28892 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}\\
28893 -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}\\
28894 =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}
28901 \begin_layout Standard
28902 In the output only the last (first) line of a multline environment appears
28903 numbered when the document numbering is right (left).
28907 \begin_layout Plain Layout
28908 numbering styles see
28909 \begin_inset CommandInset ref
28911 reference "sec:Formula-Styles"
28923 \begin_layout Standard
28932 \begin_layout Plain Layout
28950 \begin_layout Plain Layout
28960 a centered line can be right or left aligned, respectively.
28961 The commands are used as follows:
28964 \begin_layout Standard
28969 shoveright{line content}
28975 shoveleft{line content}
28978 \begin_layout Standard
28979 \begin_inset VSpace medskip
28990 \begin_layout Plain Layout
29000 specifies the distance of the first line from the left page margin.
29001 Predefined is the length 0
29002 \begin_inset space \thinspace{}
29008 \begin_layout Standard
29009 As example the above formula where the command
29012 \begin_layout Standard
29022 \begin_layout Standard
29023 was inserted in TeX-mode before:
29027 \begin_layout Plain Layout
29039 \begin_inset Formula \begin{multline}
29040 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}\\
29041 \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}}\\
29042 =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}
29050 \begin_layout Plain Layout
29061 The second line was left aligned using
29070 \begin_layout Subsection
29071 Multiline Formula Parts
29072 \begin_inset CommandInset label
29074 name "sub:Multiline-Formula-Parts"
29082 \begin_layout Plain Layout
29083 Formula ! multiline ! formula parts
29091 \begin_layout Standard
29092 To display only parts of a formula with multiple lines, one of the following
29093 environments are used:
29110 They can be inserted via the menu
29112 Insert\SpecialChar \menuseparator
29115 or by using the commands described in this section.
29118 \begin_layout Standard
29119 The first three have the same properties as the corresponding multiline
29120 formula environments, but it is possible to set further formula parts beside
29123 \begin_inset Formula \[
29124 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29125 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29126 \right\} \textrm{Uncertainty relations}\]
29133 \begin_layout Standard
29134 To get this formula, a displayed formula is created where the command
29142 \begin_layout Plain Layout
29153 A purple box appears around the blue formula box where now columns and
29154 lines can be added.
29155 Outside the multiline environment other formula parts can be set, like
29159 \begin_layout Standard
29160 The aligned environment is also suitable for long formulas whose lines are
29161 horizontally aligned.
29162 Using aligned in a displayed formula has the advantage that the formula
29163 number is vertically centered behind the lines.
29165 \begin_inset CommandInset ref
29167 reference "eq:shortlong"
29171 in the aligned environment:
29172 \begin_inset Formula \begin{equation}
29173 \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}|}\\
29174 & -\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}
29182 \begin_layout Standard
29183 To use the environments
29205 \begin_layout Plain Layout
29223 \begin_layout Plain Layout
29241 \begin_layout Plain Layout
29249 are inserted, respectively.
29250 The split environment has the same properties as the aligned environment
29251 but it can only have two columns.
29254 \begin_layout Subsection
29255 Text in multiline Formulas
29256 \begin_inset CommandInset label
29258 name "sub:Text-in-multiline"
29266 \begin_layout Plain Layout
29276 \begin_layout Plain Layout
29277 Formula ! multiline ! text
29285 \begin_layout Standard
29286 In the Align environments, and the multline and gather environment, text
29287 can be inserted that will appear in a separate line and doesn't affect
29288 the column alignment.
29289 To do this, the command
29297 \begin_layout Plain Layout
29307 is used in the following scheme:
29310 \begin_layout Standard
29318 \begin_layout Standard
29319 The text should not be longer than a line because it cannot be hyphenated.
29320 As LyX doesn't yet support
29326 directly, the text is written as mathematical text.
29333 must hereby be at the beginning of a line and appears in the output above
29335 An example where the text was inserted at the beginning of the second line:
29336 \begin_inset Formula \begin{align}
29337 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29338 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29345 \begin_layout Section
29350 \begin_layout Plain Layout
29360 \begin_layout Plain Layout
29361 Formula ! numbering|see
29365 \begin_layout Plain Layout
29376 \begin_layout Plain Layout
29391 \begin_layout Subsection
29395 \begin_layout Standard
29396 Numbered formulas can be created with the menu
29398 Insert\SpecialChar \menuseparator
29399 Math\SpecialChar \menuseparator
29401 \begin_inset space ~
29409 \begin_inset space ~
29415 Existing formulas can be numbered with the menu
29417 Edit\SpecialChar \menuseparator
29418 Math\SpecialChar \menuseparator
29420 \begin_inset space ~
29428 arg "math-number-toggle"
29432 The formula number is displayed in LyX behind the formula as number sign
29434 The number sign is replaced in the output by the formula number.
29437 \begin_layout Standard
29438 When numbering is turned on in multiline formulas, all lines will be numbered.
29439 But the numbering can be controlled with the menu
29441 Edit\SpecialChar \menuseparator
29442 Math\SpecialChar \menuseparator
29444 \begin_inset space ~
29448 \begin_inset space ~
29452 \begin_inset space ~
29460 arg "math-number-line-toggle"
29466 \begin_layout Standard
29467 Except for inline formulas, all formulas can be numbered with two different
29469 \begin_inset CommandInset ref
29471 reference "sec:Formula-Styles"
29478 \begin_layout Subsection
29483 \begin_layout Plain Layout
29484 Cross-references ! to formulas
29492 \begin_layout Standard
29493 All labeled formulas can be cross-referenced.
29494 A label is added by the menu
29496 Insert\SpecialChar \menuseparator
29499 or the toolbar button
29500 \begin_inset Graphics
29501 filename ../images/label-insert.png
29507 The cursor must hereby be inside a displayed formula.
29508 A dialog pops up displaying the prefix
29513 The label is inserted there behind the prefix.
29514 The predefined prefix means
29515 \begin_inset Quotes eld
29519 \begin_inset Quotes erd
29522 and makes it easier to find labels in large documents because it marks
29523 it as formula label to divide it from e.
29524 \begin_inset space \thinspace{}
29528 \begin_inset space \space{}
29532 To change a label, the menu
29534 Insert\SpecialChar \menuseparator
29540 \begin_layout Standard
29541 The name of the label is displayed in LyX within two parentheses behind
29543 A formula with a label is always numbered.
29546 \begin_layout Standard
29547 Cross-references are inserted via the menu
29549 Insert\SpecialChar \menuseparator
29552 or with the toolbar button
29553 \begin_inset Graphics
29554 filename ../images/dialog-show-new-inset_ref.png
29560 A formula cross-reference appears in the output as formula number.
29561 When in the cross-reference dialog window the format
29565 is chosen, the cross-reference appears in the output as formula number
29567 \begin_inset Newline newline
29570 By right-clicking on a cross-reference in LyX, one jumps to the formula
29571 that is referenced.
29574 \begin_layout Standard
29575 Here are as examples cross-references to formulas of the following subsections:
29576 \begin_inset Note Note
29579 \begin_layout Plain Layout
29580 Note the different cross-reference types.
29588 \begin_layout Standard
29590 \begin_inset CommandInset ref
29597 \begin_inset CommandInset ref
29605 \begin_inset CommandInset ref
29611 ) big Latin letters are used for the numbering in contrary to (
29612 \begin_inset CommandInset ref
29621 \begin_layout Standard
29622 \begin_inset VSpace medskip
29625 When the argument of
29633 \begin_layout Plain Layout
29641 \begin_inset CommandInset ref
29643 reference "sub:User-defined-Numbering"
29654 contains a box like in
29655 \begin_inset CommandInset ref
29657 reference "sub:Paragraph-Boxes"
29661 , the formula cannot be referenced.
29664 \begin_layout Subsection
29669 \begin_layout Plain Layout
29670 Formula numbering ! subnumbering
29678 \begin_layout Standard
29679 With the help of the commands
29683 begin{subequations}
29691 formulas can be subnumbered.
29692 Both commands are inserted in TeX-mode.
29695 \begin_layout Standard
29697 \begin_inset Formula \begin{equation}
29698 A=C-B\label{eq:a}\end{equation}
29706 \begin_layout Plain Layout
29710 addtocounter{equation}{-1}
29719 \begin_layout Plain Layout
29723 begin{subequations}
29729 \begin_inset VSpace -5mm
29733 \begin_inset Formula \begin{equation}
29734 B=C-A\label{eq:b}\end{equation}
29739 \begin_inset Formula \begin{equation}
29740 C=A+B\label{eq:c}\end{equation}
29747 \begin_layout Standard
29751 \begin_layout Plain Layout
29763 \begin_layout Standard
29764 To create the example, the following is done:
29767 \begin_layout Enumerate
29768 first formula is inserted
29771 \begin_layout Enumerate
29776 addtocounter{equation}{-1}
29778 begin{subequations}
29782 \begin_layout Plain Layout
29791 \begin_inset Newline newline
29796 is inserted after the first formula
29799 \begin_layout Enumerate
29800 second formula is inserted
29803 \begin_layout Enumerate
29804 third formula is inserted
29807 \begin_layout Enumerate
29814 is inserted after the third formula
29817 \begin_layout Standard
29818 Every formula between the commands
29830 is subnumbered as a, b,
29831 \begin_inset Newline linebreak
29834 c, \SpecialChar \ldots{}
29835 For multiline formulas every line will be subnumbered.
29836 All subnumbered formulas are treated as
29841 But as every numbered formula increases the counter
29845 by one, the command
29851 is needed to decrease it.
29852 Otherwise the formulas
29853 \begin_inset CommandInset ref
29860 \begin_inset CommandInset ref
29867 \begin_inset CommandInset ref
29873 would be numbered as
29874 \begin_inset CommandInset ref
29881 \begin_inset CommandInset ref
29888 \begin_inset CommandInset ref
29897 \begin_layout Standard
29898 By inserting the commands in TeX-mode, a space is created between the first
29901 \begin_inset space \thinspace{}
29904 mm vertical space is inserted after the command
29908 begin{subequations}
29911 When the formula style
29917 \begin_layout Plain Layout
29919 \begin_inset CommandInset ref
29921 reference "sec:Formula-Styles"
29933 \begin_inset space \thinspace{}
29936 mm space is inserted instead.
29939 \begin_layout Standard
29940 Here is an example for a multiline formula where the numbering was turned
29941 off for the second line:
29945 \begin_layout Plain Layout
29949 begin{subequations}
29955 \begin_inset Formula \begin{eqnarray}
29956 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29957 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29958 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29966 \begin_layout Plain Layout
29978 \begin_layout Subsection
29979 User-defined Numbering
29980 \begin_inset CommandInset label
29982 name "sub:User-defined-Numbering"
29990 \begin_layout Plain Layout
29991 Formula numbering ! user-defined
29999 \begin_layout Standard
30003 \begin_layout Plain Layout
30004 Formula numbering ! self-defined delimiters
30009 With the standard numbering parentheses are set around the formula number.
30010 To replace the parentheses for example by vertical bars, the following
30011 line is added to the LaTeX-preamble:
30014 \begin_layout Standard
30026 \begin_inset Note Note
30029 \begin_layout Plain Layout
30030 This macro is already declared in the LaTeX-preamble for testing.
30031 To activate it, remove the percent sign at the beginning.
30039 \begin_layout Standard
30040 To use other characters, the vertical bars besides the
30044 are replaced by one ore more characters.
30045 To get only the formula number the vertical bars are omitted.
30048 \begin_layout Standard
30049 \begin_inset VSpace bigskip
30052 When there should be an expression of your choice instead of the consecutive
30053 formula number in parentheses behind the formula, the command
30063 \begin_layout Plain Layout
30072 \begin_inset Formula \begin{equation}
30073 A+B=C\tag{something}\label{eq:tag}\end{equation}
30077 In this example the command
30085 \begin_layout Plain Layout
30096 was inserted to the formula.
30099 \begin_layout Standard
30108 \begin_layout Plain Layout
30119 is inserted instead, the star prevents the parentheses around the expression:
30120 \begin_inset Formula \[
30121 A+B=C\tag*{something}\]
30128 \begin_layout Standard
30129 \begin_inset VSpace bigskip
30132 To restart the formula numbering with new document parts or sections, the
30133 following command is used:
30136 \begin_layout Standard
30141 @addtoreset{equation}{part}
30147 \begin_layout Plain Layout
30152 \begin_layout Plain Layout
30163 \begin_layout Plain Layout
30176 \begin_layout Plain Layout
30187 \begin_layout Plain Layout
30200 \begin_inset Newline newline
30204 \begin_inset Newline newline
30211 @addtoreset{equation}{section}
30214 \begin_layout Standard
30215 To be able to use these commands in TeX-mode, the
30216 \begin_inset Quotes eld
30220 \begin_inset Quotes erd
30223 character has to be made
30224 \begin_inset Quotes eld
30228 \begin_inset Quotes erd
30231 for LaTeX using the command
30245 So the command sequence in TeX-mode is:
30248 \begin_layout Standard
30254 \begin_inset Newline newline
30259 @addtoreset{equation}{section}
30260 \begin_inset Newline newline
30268 \begin_layout Standard
30269 In the LaTeX-preamble
30281 can be omitted as they are automatically internally inserted by LyX.
30284 \begin_layout Standard
30299 \begin_layout Plain Layout
30304 is part of the LaTeX-package
30312 \begin_layout Plain Layout
30313 Packages ! carlisle
30318 that is part of every LaTeX standard installation.
30327 \begin_layout Plain Layout
30328 Packages ! remreset
30333 has to be loaded in the LaTeX-preamble with the line
30336 \begin_layout Standard
30341 usepackage{remreset}
30344 \begin_layout Standard
30355 \begin_layout Plain Layout
30360 \begin_layout Plain Layout
30371 \begin_layout Plain Layout
30384 \begin_layout Plain Layout
30395 \begin_layout Plain Layout
30407 can be used with the same scheme as
30416 \begin_layout Standard
30417 \begin_inset VSpace bigskip
30420 Sometimes formulas should be numbered in the following form:
30423 \begin_layout Standard
30426 (section number.formula number)
30429 \begin_layout Standard
30430 The formula number should start with every section with
30431 \begin_inset Quotes eld
30435 \begin_inset Quotes erd
30441 \begin_layout Standard
30442 For this case there is the command
30452 \begin_layout Plain Layout
30460 , which is used with the following scheme:
30463 \begin_layout Standard
30468 numberwithin{counter}{sectioning}
30471 \begin_layout Standard
30472 Counter denotes what kind of numbering is affected, sectioning denotes what
30473 number is before the dot.
30476 \begin_layout Standard
30477 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30480 \begin_layout Standard
30485 numberwithin{equation}{section}
30488 \begin_layout Standard
30489 This is the result:
30493 \begin_layout Plain Layout
30497 numberwithin{equation}{section}
30503 \begin_inset Formula \begin{equation}
30504 A+B=C\end{equation}
30511 \begin_layout Standard
30513 \begin_inset space \thinspace{}
30517 \begin_inset space \space{}
30520 tables so that the number of the part is the sectioning,
30521 \begin_inset Newline newline
30528 numberwithin{table}{part}
30533 \begin_layout Standard
30534 To go back to the standard numbering or to prevent this kind of numbering
30535 when it is defined by the document class, the following command is inserted
30536 as TeX-Code or to the LaTeX-preamble:
30539 \begin_layout Standard
30552 \begin_layout Plain Layout
30566 \begin_layout Plain Layout
30582 \begin_inset Newline newline
30590 \begin_inset Newline newline
30602 \begin_layout Standard
30609 uses internally the command
30615 , described above, that also needs to be reverted.
30619 \begin_layout Plain Layout
30626 \begin_layout Plain Layout
30630 @removefromreset{equation}{section}
30633 \begin_layout Plain Layout
30645 \begin_layout Subsection
30646 Numbering with Roman Numbers and Letters
30650 \begin_layout Plain Layout
30651 Formula numbering ! with letters
30660 \begin_layout Plain Layout
30661 Formula numbering ! with Roman numbers
30669 \begin_layout Standard
30670 Formulas can also be numbered with Roman numbers and Latin letters.
30671 To number for example with small Roman numbers, the command
30674 \begin_layout Standard
30686 \begin_layout Standard
30687 is inserted before the formula in TeX-mode.
30698 \begin_layout Plain Layout
30706 redefines the predefined command
30722 \begin_layout Plain Layout
30729 has the same scheme like the command
30735 that is described in
30736 \begin_inset CommandInset ref
30738 reference "sub:The-Command-newcommand"
30751 is the formula counter.
30758 is used as prefix for a counter, the value of the counter is output as
30760 When a formula is numbered, LaTeX sets internally the command
30766 behind the formula.
30775 \begin_layout Plain Layout
30785 outputs the counter as small Roman number.
30788 \begin_layout Standard
30789 All formulas behind the command
30799 are now numbered Roman.
30800 To switch to numbering with big Roman numbers, the command is inserted
30817 \begin_layout Plain Layout
30829 \begin_inset Quotes eld
30833 \begin_inset Quotes erd
30836 with small Latin letters there is the command
30846 \begin_layout Plain Layout
30854 , for big ones there is the command
30864 \begin_layout Plain Layout
30877 \begin_layout Standard
30878 \begin_inset Note Greyedout
30881 \begin_layout Plain Layout
30886 Only maximal 26 formulas can be numbered with Latin letters in one document.
30894 \begin_layout Standard
30898 \begin_layout Plain Layout
30914 \begin_layout Standard
30915 \begin_inset Formula \begin{equation}
30916 A=\textrm{small roman}\label{eq:rom}\end{equation}
30924 \begin_layout Plain Layout
30938 \begin_inset Formula \begin{equation}
30939 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30947 \begin_layout Plain Layout
30961 \begin_inset Formula \begin{equation}
30962 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30970 \begin_layout Plain Layout
30984 \begin_inset Formula \begin{equation}
30985 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30992 \begin_layout Standard
30993 To switch back to the default numbering, insert the command:
30996 \begin_layout Standard
31009 \begin_layout Plain Layout
31020 \begin_layout Standard
31024 \begin_layout Plain Layout
31038 \begin_inset Formula \begin{equation}
31039 E=\textrm{Arabic}\label{eq:arab}\end{equation}
31046 \begin_layout Standard
31047 \begin_inset VSpace medskip
31050 As you see, formulas are numbered serially independent from the numbering
31052 When then numbering should start with
31053 \begin_inset Quotes eld
31057 \begin_inset Quotes erd
31060 when the style is changed, new equation counters have to be defined.
31061 A description about this can be found in the file
31062 \begin_inset CommandInset href
31064 target "Formula-numbering.lyx"
31071 \begin_layout Section
31072 User-defined Commands
31076 \begin_layout Plain Layout
31077 User-defined commands
31085 \begin_layout Standard
31086 \begin_inset Note Greyedout
31089 \begin_layout Plain Layout
31094 The names of user-defined commands and macros may only consist of Latin
31103 \begin_layout Subsection
31107 \begin_inset CommandInset label
31109 name "sub:The-Command-newcommand"
31117 \begin_layout Plain Layout
31118 User-defined commands !
31129 \begin_layout Plain Layout
31140 \begin_layout Standard
31141 Many LaTeX-commands are too long to be used frequently.
31142 But it is possible to define with the command
31148 new shorter commands.
31151 \begin_layout Standard
31152 The command scheme of
31161 \begin_layout Standard
31166 newcommand{new command name}[number of arguments][optional
31171 \begin_inset Newline newline
31178 \begin_layout Plain Layout
31193 \begin_layout Plain Layout
31200 {command definition}
31203 \begin_layout Standard
31204 \begin_inset Note Greyedout
31207 \begin_layout Plain Layout
31212 Assure that the name of the new command is not already used in your document
31213 or by LaTeX-packages that you use.
31214 When you for example define the command
31226 , you get an error message because
31232 is already defined as command for
31233 \begin_inset Quotes eld
31237 \begin_inset Formula $\le$
31241 \begin_inset Quotes erd
31252 \begin_layout Standard
31253 The number of arguments is an integer in the range 0
31254 \begin_inset space \thinspace{}
31258 \begin_inset space \thinspace{}
31261 9 and specifies how many arguments the new command should have.
31262 With the optional value a value for an optional argument can be predefined.
31263 When this is done, the
31271 rgument of the new command is automatically an optional one.
31274 \begin_layout Standard
31275 Here are some examples:
31278 \begin_layout Itemize
31279 To define the command
31291 , the LaTeX-preamble line is:
31292 \begin_inset VSpace medskip
31296 \begin_inset Newline newline
31310 \begin_layout Itemize
31311 To define the command
31323 , the argument (that should be underlined) must be taken into account.
31324 For this the preamble line is:
31325 \begin_inset VSpace medskip
31329 \begin_inset Newline newline
31343 \begin_inset VSpace medskip
31347 \begin_inset Newline newline
31354 acts as argument placeholder, the
31358 behind it denotes that it is the placeholder for the first argument.
31361 \begin_layout Itemize
31369 \begin_inset space \thinspace{}
31373 \begin_inset space \space{}
31383 \begin_inset VSpace medskip
31387 \begin_inset Newline newline
31398 framebox#1#2{$#3$}}
31401 \begin_inset VSpace medskip
31405 \begin_inset Newline newline
31408 The two Dollar signs creates the extra formula needed for
31415 \begin_inset CommandInset ref
31417 reference "sub:Boxes-with-Frame"
31424 \begin_layout Itemize
31425 To create a new command for
31431 where the color for the box needn't to be specified, the argument for the
31432 color is defined optional:
31433 \begin_inset VSpace medskip
31437 \begin_inset Newline newline
31448 fcolorbox{#2}{#1}{$#3$}}
31451 \begin_inset VSpace medskip
31455 \begin_inset Newline newline
31458 When the color is not specified when using
31464 , the predefined color
31471 \begin_layout Standard
31472 A test of the new defined commands:
31475 \begin_layout Standard
31477 \begin_inset Tabular
31478 <lyxtabular version="3" rows="6" columns="2">
31480 <column alignment="center" valignment="top" width="0">
31481 <column alignment="center" valignment="top" width="0">
31483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31486 \begin_layout Plain Layout
31492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31495 \begin_layout Plain Layout
31497 \begin_inset Note Note
31500 \begin_layout Plain Layout
31507 is only used as spacer.
31519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31522 \begin_layout Plain Layout
31529 \begin_layout Plain Layout
31543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31546 \begin_layout Plain Layout
31547 \begin_inset Formula $A\gr B$
31557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31560 \begin_layout Plain Layout
31568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31571 \begin_layout Plain Layout
31572 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31585 \begin_layout Plain Layout
31589 \begin_inset Formula $\to$
31595 \begin_inset Formula $\to$
31606 \begin_layout Plain Layout
31620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31623 \begin_layout Plain Layout
31624 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31637 \begin_layout Plain Layout
31641 \begin_inset Formula $\to$
31652 \begin_layout Plain Layout
31666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31669 \begin_layout Plain Layout
31670 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31683 \begin_layout Plain Layout
31689 \begin_inset Formula $\to$
31700 \begin_layout Plain Layout
31714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31717 \begin_layout Plain Layout
31718 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31734 \begin_layout Subsection
31739 \begin_layout Plain Layout
31740 User-defined commands! Math macros
31749 \begin_layout Plain Layout
31758 \begin_layout Standard
31759 User-defined commands are especially convenient for complex expressions.
31760 When you are for example dealing in a document with quadratic equations,
31761 the same solution type occurs several times.
31762 The general form of a quadratic equation is
31763 \begin_inset Formula \[
31764 0=\lambda^{2}+p\lambda+q\]
31768 The general form of the solution is
31769 \begin_inset Formula \[
31770 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31777 \begin_layout Standard
31778 To define a command for the solution formula where only the three parameters
31780 \begin_inset Formula $\lambda$
31784 \begin_inset Formula $p$
31788 \begin_inset Formula $q$
31791 need to be specified and the index of
31792 \begin_inset Formula $\lambda$
31795 can be given optionally, the LaTeX-preamble line is
31796 \begin_inset Newline newline
31812 \begin_inset Newline newline
31819 \begin_layout Plain Layout
31834 \begin_layout Plain Layout
31845 frac{#3^{2}}{4}-#4}}
31848 \begin_layout Standard
31849 To create with this the solution formula, the command
31850 \begin_inset Newline newline
31860 \begin_inset Formula $\to$
31866 \begin_inset Formula $\to$
31873 is inserted to a formula
31878 \begin_layout Standard
31879 The definition of the new command is unintuitive because one has to know
31880 the schemes of all used LaTeX commands, e.
31881 \begin_inset space \thinspace{}
31885 \begin_inset space \space{}
31888 that a fraction is inserted in LaTeX as
31892 frac{numerator}{denominator}
31895 Furthermore one can easily forget a brace in the definition and cannot
31896 see in LyX what the new command is doing.
31897 To avoid these problems LyX offers the possibility to use math macros instead
31907 \begin_layout Standard
31908 A math macro is created by using the menu
31910 Insert\SpecialChar \menuseparator
31911 Math\SpecialChar \menuseparator
31914 or the toolbar button
31915 \begin_inset Graphics
31916 filename ../images/math-macro_newmacroname_newcommand.png
31922 The math macro toolbar appears together with the following box where the
31924 \begin_inset Newline newline
31928 \begin_inset space \hspace*{\fill}
31932 \begin_inset Graphics
31933 filename clipart/macrobox.png
31938 \begin_inset space \hspace*{\fill}
31942 \begin_inset Newline newline
31946 \begin_inset FormulaMacro
31947 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31952 newmacroname is the default name of the macro that should be changed to
31953 something sensible.
31954 The wanted formula is inserted in the first blue box.
31955 An argument placeholder is inserted with the command
31962 \begin_inset space \thinspace{}
31966 \begin_inset space \space{}
31975 or by using the macro toolbar button
31976 \begin_inset Graphics
31977 filename ../images/math-macro-add-param.png
31983 Argument placeholders are displayed red.
31984 Maximum 9 arguments are possible.
31985 Optional arguments are created with the toolbar button
31986 \begin_inset Graphics
31987 filename ../images/math-macro-add-optional-param.png
31993 The first non-optional argument can be transformed to an optional one with
31995 \begin_inset Graphics
31996 filename ../images/math-macro-make-optional.png
32002 In the second blue box the appearance of the macro in LyX can be defined.
32003 Normally you want to see it as it is defined, so the box is kept empty.
32004 But when you have created a macro that needs lot of space on the screen,
32005 you can insert in the box for example
32006 \begin_inset Newline newline
32036 \begin_inset Newline newline
32041 For the macro only the arguments with the macro name in front of them will
32042 then be displayed in LyX, leading to a better overview.
32043 The formula appears in the output as defined in the first box.
32044 \begin_inset Newline newline
32047 The appearance of macros in formulas can furthermore be changed for single
32048 macros by setting the cursor in the macro and using the menu
32050 View\SpecialChar \menuseparator
32052 \begin_inset space ~
32056 \begin_inset space ~
32064 \begin_layout Standard
32065 To use a macro, the macro name is inserted as command to a formula, in our
32073 Our macro looks in LyX like this:
32074 \begin_inset Newline newline
32078 \begin_inset space \hspace*{\fill}
32082 \begin_inset Graphics
32083 filename clipart/macrouse.png
32088 \begin_inset space \hspace*{\fill}
32092 \begin_inset Newline newline
32095 Here is our macro example with the arguments
32096 \begin_inset Formula $x$
32100 \begin_inset Formula $\ln(x)$
32104 \begin_inset Formula $B$
32110 \begin_layout Standard
32111 \begin_inset Formula \[
32119 \begin_layout Standard
32120 A math macro is transformed internally to a
32126 command when exporting the document.
32133 command is not placed in the LaTeX-preamble, therefore macros can only
32134 be used in formulas that are in the document below the macro definition
32138 \begin_layout Standard
32139 Math macros can also be directly be created from a
32146 When writing for example the command
32149 \begin_inset Newline newline
32158 xleftarrow[#2]{#1}}
32159 \begin_inset Newline newline
32164 in LyX as normal text, highlighting it completely and using then the shortcut
32169 , the command will be transformed to a math macro.
32170 Using this method you need to be careful that the
32176 command is typed correctly, otherwise you get a faulty macro leading to
32180 \begin_layout Standard
32181 Math macros currently yet have the problem that further formulas in macro
32182 definitions are handled wrongly.
32183 Therefore the example
32190 \begin_inset CommandInset ref
32192 reference "sub:The-Command-newcommand"
32196 cannot be created as macro.
32199 \begin_layout Standard
32200 When the cursor is in a macro definition box, you will see the macro toolbar
32204 \begin_layout Standard
32205 \begin_inset VSpace defskip
32211 \begin_layout Standard
32212 \begin_inset Graphics
32213 filename clipart/MacroToolbar.png
32221 \begin_layout Plain Layout
32230 \begin_layout Standard
32231 \begin_inset VSpace defskip
32237 \begin_layout Standard
32238 The macro toolbar contains from left to right the following buttons:
32241 \begin_layout Standard
32242 \begin_inset VSpace defskip
32248 \begin_layout Standard
32249 \begin_inset Tabular
32250 <lyxtabular version="3" rows="9" columns="2">
32251 <features islongtable="true">
32252 <column alignment="left" valignment="top" width="0">
32253 <column alignment="left" valignment="top" width="85col%">
32254 <row interlinespace="2.5mm">
32255 <cell alignment="center" valignment="top" usebox="none">
32258 \begin_layout Plain Layout
32259 \begin_inset Graphics
32260 filename ../images/math-macro-remove-param.png
32261 BoundingBox 0bp 5bp 20bp 25bp
32262 rotateOrigin center
32271 <cell alignment="center" valignment="top" usebox="none">
32274 \begin_layout Plain Layout
32277 Edit\SpecialChar \menuseparator
32278 Math\SpecialChar \menuseparator
32280 \begin_inset space ~
32283 Definition\SpecialChar \menuseparator
32284 Remove Last Argument
32290 <row interlinespace="2.5mm">
32291 <cell alignment="center" valignment="top" usebox="none">
32294 \begin_layout Plain Layout
32295 \begin_inset Graphics
32296 filename ../images/math-macro-add-param.png
32297 BoundingBox 0bp 5bp 20bp 25bp
32298 rotateOrigin center
32307 <cell alignment="center" valignment="top" usebox="none">
32310 \begin_layout Plain Layout
32313 Edit\SpecialChar \menuseparator
32314 Math\SpecialChar \menuseparator
32316 \begin_inset space ~
32319 Definition\SpecialChar \menuseparator
32326 <row interlinespace="2.5mm">
32327 <cell alignment="center" valignment="top" usebox="none">
32330 \begin_layout Plain Layout
32331 \begin_inset Graphics
32332 filename ../images/math-macro-make-optional.png
32333 BoundingBox 0bp 5bp 20bp 25bp
32334 rotateOrigin center
32343 <cell alignment="center" valignment="top" usebox="none">
32346 \begin_layout Plain Layout
32349 Edit\SpecialChar \menuseparator
32350 Math\SpecialChar \menuseparator
32352 \begin_inset space ~
32355 Definition\SpecialChar \menuseparator
32356 Make First Non-Optional into
32357 \begin_inset Newline newline
32364 \begin_layout Plain Layout
32373 Edit\SpecialChar \menuseparator
32374 Math\SpecialChar \menuseparator
32376 \begin_inset space ~
32379 Definition\SpecialChar \menuseparator
32384 \begin_layout Plain Layout
32397 <row interlinespace="2.5mm">
32398 <cell alignment="center" valignment="top" usebox="none">
32401 \begin_layout Plain Layout
32402 \begin_inset Graphics
32403 filename ../images/math-macro-make-nonoptional.png
32404 BoundingBox 0bp 5bp 20bp 25bp
32405 rotateOrigin center
32414 <cell alignment="center" valignment="top" usebox="none">
32417 \begin_layout Plain Layout
32420 Edit\SpecialChar \menuseparator
32421 Math\SpecialChar \menuseparator
32423 \begin_inset space ~
32426 Definition\SpecialChar \menuseparator
32427 Make Last Optional into
32428 \begin_inset Newline newline
32435 \begin_layout Plain Layout
32444 Edit\SpecialChar \menuseparator
32445 Math\SpecialChar \menuseparator
32447 \begin_inset space ~
32450 Definition\SpecialChar \menuseparator
32455 \begin_layout Plain Layout
32462 Non-Optional Argument
32468 <row interlinespace="2.5mm">
32469 <cell alignment="center" valignment="top" usebox="none">
32472 \begin_layout Plain Layout
32473 \begin_inset Graphics
32474 filename ../images/math-macro-remove-optional-param.png
32475 BoundingBox 0bp 5bp 20bp 25bp
32476 rotateOrigin center
32485 <cell alignment="center" valignment="top" usebox="none">
32488 \begin_layout Plain Layout
32491 Edit\SpecialChar \menuseparator
32492 Math\SpecialChar \menuseparator
32494 \begin_inset space ~
32497 Definition\SpecialChar \menuseparator
32498 Remove Optional Argument
32504 <row interlinespace="2.5mm">
32505 <cell alignment="center" valignment="top" usebox="none">
32508 \begin_layout Plain Layout
32509 \begin_inset Graphics
32510 filename ../images/math-macro-add-optional-param.png
32511 BoundingBox 0bp 5bp 20bp 25bp
32512 rotateOrigin center
32521 <cell alignment="center" valignment="top" usebox="none">
32524 \begin_layout Plain Layout
32527 Edit\SpecialChar \menuseparator
32528 Math\SpecialChar \menuseparator
32530 \begin_inset space ~
32533 Definition\SpecialChar \menuseparator
32534 Insert Optional Argument
32540 <row interlinespace="2.5mm">
32541 <cell alignment="center" valignment="top" usebox="none">
32544 \begin_layout Plain Layout
32545 \begin_inset Graphics
32546 filename ../images/math-macro-remove-greedy-param.png
32547 BoundingBox 0bp 5bp 20bp 25bp
32548 rotateOrigin center
32557 <cell alignment="center" valignment="top" usebox="none">
32560 \begin_layout Plain Layout
32563 Edit\SpecialChar \menuseparator
32564 Math\SpecialChar \menuseparator
32566 \begin_inset space ~
32569 Definition\SpecialChar \menuseparator
32570 Remove Last Argument
32571 \begin_inset Newline newline
32578 \begin_layout Plain Layout
32587 Edit\SpecialChar \menuseparator
32588 Math\SpecialChar \menuseparator
32590 \begin_inset space ~
32593 Definition\SpecialChar \menuseparator
32598 \begin_layout Plain Layout
32605 Spitting Out To The Right
32611 <row interlinespace="2.5mm">
32612 <cell alignment="center" valignment="top" usebox="none">
32615 \begin_layout Plain Layout
32616 \begin_inset Graphics
32617 filename ../images/math-macro-append-greedy-param.png
32618 BoundingBox 0bp 5bp 20bp 25bp
32619 rotateOrigin center
32628 <cell alignment="center" valignment="top" usebox="none">
32631 \begin_layout Plain Layout
32634 Edit\SpecialChar \menuseparator
32635 Math\SpecialChar \menuseparator
32637 \begin_inset space ~
32640 Definition\SpecialChar \menuseparator
32642 \begin_inset Newline newline
32649 \begin_layout Plain Layout
32658 Edit\SpecialChar \menuseparator
32659 Math\SpecialChar \menuseparator
32661 \begin_inset space ~
32664 Definition\SpecialChar \menuseparator
32669 \begin_layout Plain Layout
32676 Eating From The Right
32682 <row interlinespace="2.5mm">
32683 <cell alignment="center" valignment="top" usebox="none">
32686 \begin_layout Plain Layout
32687 \begin_inset Graphics
32688 filename ../images/math-macro-add-greedy-optional-param.png
32689 BoundingBox 0bp 5bp 20bp 25bp
32690 rotateOrigin center
32699 <cell alignment="center" valignment="top" usebox="none">
32702 \begin_layout Plain Layout
32705 Edit\SpecialChar \menuseparator
32706 Math\SpecialChar \menuseparator
32708 \begin_inset space ~
32711 Definition\SpecialChar \menuseparator
32712 Append Optional Argument
32713 \begin_inset Newline newline
32720 \begin_layout Plain Layout
32729 Edit\SpecialChar \menuseparator
32730 Math\SpecialChar \menuseparator
32732 \begin_inset space ~
32735 Definition\SpecialChar \menuseparator
32740 \begin_layout Plain Layout
32747 Eating From The Right
32760 \begin_layout Standard
32761 \begin_inset Newpage newpage
32767 \begin_layout Section
32771 \begin_layout Standard
32772 LyX supports two types of commutative diagrams:
32780 that are explained in the following.
32783 \begin_layout Subsection
32788 \begin_layout Plain Layout
32797 \begin_layout Standard
32798 Diagrams of this type visualize relations by vertical and horizontal lines
32800 \begin_inset Formula \[
32801 \begin{CD}A@>>>B@>>>C\\
32803 F@<<<E@<<<D\end{CD}\]
32810 \begin_layout Standard
32811 To get them, the command
32819 \begin_layout Plain Layout
32829 is inserted to a formula.
32830 A blue box appears with two dashed lines where further commands can be
32835 arg "newline-insert newline"
32838 a new line is created.
32839 Horizontal relations are inserted in odd, vertical in even formula lines.
32842 \begin_layout Standard
32843 To create the relations there are the following commands:
32846 \begin_layout Itemize
32851 creates a left arrow,
32862 \begin_layout Itemize
32867 creates an up arrow,
32875 a vertical equal sign
32878 \begin_layout Itemize
32884 is a placeholder for non-existent relations
32887 \begin_layout Standard
32888 All arrows can be labeled as follows:
32891 \begin_layout Itemize
32892 Is text inserted between the first and second < or >, resp., it is placed
32894 When it is inserted between the second and third one, it appears under
32898 \begin_layout Itemize
32899 When text for vertical arrows is inserted between the first and second A
32900 or V, resp., it is placed left beside the arrow.
32901 When it is inserted between the second and third one, it appears right
32903 If the text contains an A or V, these letters must be set into a TeX-brace.
32906 \begin_layout Standard
32907 As example a diagram with all possible relations:
32910 \begin_layout Standard
32911 \begin_inset Formula \[
32912 \begin{CD}A@>j>>B@>>k>C@=F\\
32914 D@<<j<E@>k>>F@=C\end{CD}\]
32921 \begin_layout Standard
32922 The command for this is:
32923 \begin_inset Newline newline
32934 \begin_layout Plain Layout
32943 A@>j>>B@>>k>C@=F Ctrl+Return
32944 \begin_inset Newline newline
32951 \begin_layout Plain Layout
32966 \begin_layout Plain Layout
32979 \begin_layout Plain Layout
32991 \begin_inset Formula $\to$
32997 \begin_inset Newline newline
33004 \begin_layout Plain Layout
33019 \begin_layout Plain Layout
33032 \begin_layout Plain Layout
33042 \begin_layout Subsection
33047 \begin_layout Plain Layout
33048 Diagrams ! xymatrix
33056 \begin_layout Standard
33057 To be able to use xymatrices, the LaTeX-package
33062 A xymatrix is created by inserting the command
33069 Then you are able to add new matrix columns and rows like for normal matrices,
33071 \begin_inset CommandInset ref
33073 reference "sec:Matrices"
33080 \begin_layout Standard
33081 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33083 All possibilities to create commutative diagrams and decorations are explained
33088 that you find in the menu
33090 Help\SpecialChar \menuseparator
33092 \begin_inset space ~
33095 Manuals\SpecialChar \menuseparator
33097 \begin_inset space ~
33105 \begin_layout Standard
33106 \begin_inset Newpage newpage
33112 \begin_layout Section
33117 \begin_layout Plain Layout
33130 \begin_layout Plain Layout
33131 Other useful math tips can be found in
33132 \begin_inset CommandInset citation
33147 \begin_layout Plain Layout
33155 \begin_inset Note Note
33158 \begin_layout Plain Layout
33161 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33164 \begin_layout Plain Layout
33167 texorpdfstring is in section
33168 \begin_inset CommandInset ref
33170 reference "sub:Formulas-in-Section"
33183 \begin_layout Plain Layout
33193 \begin_layout Plain Layout
33198 \begin_layout Plain Layout
33205 Chemical characters
33209 \begin_layout Plain Layout
33224 \begin_layout Subsection
33225 Chemical Symbols and Equations
33226 \begin_inset CommandInset label
33228 name "sub:Chemical-Symbols-and"
33236 \begin_layout Plain Layout
33237 Chemical characters ! Symbols
33246 \begin_layout Plain Layout
33256 \begin_layout Plain Layout
33265 \begin_layout Standard
33266 An example text from chemistry:
33269 \begin_layout Quote
33271 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33274 -ion reacts with two
33275 \begin_inset Formula $\mathrm{Na^{+}}$
33278 -ions to sodium sulfate
33279 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33283 The chemical equation for this is:
33284 \begin_inset Formula \[
33285 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33292 \begin_layout Standard
33293 This chemical equation can directly be created as formula.
33294 To avoid that the symbols appear italic, everything is highlighted and
33295 changed by the shortcut
33301 to the upright font style.
33305 \begin_layout Plain Layout
33311 \begin_inset CommandInset ref
33313 reference "sub:Font-Styles"
33325 \begin_layout Subsection
33330 \begin_layout Plain Layout
33339 \begin_layout Standard
33340 Negative numbers often look ugly in formulas because the minus sign before
33341 the number is set with the same length as the minus operator sign.
33342 When writing the negative number in normal text, the minus sign appears
33346 \begin_layout Standard
33347 Thus, the problem disappears when converting the minus sign to mathematical
33351 \begin_layout Standard
33352 An example to visualize the problem:
33355 \begin_layout Standard
33357 \begin_inset Tabular
33358 <lyxtabular version="3" rows="3" columns="2">
33360 <column alignment="right" valignment="top" width="0">
33361 <column alignment="left" valignment="top" width="0">
33363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33366 \begin_layout Plain Layout
33372 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33375 \begin_layout Plain Layout
33383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33386 \begin_layout Plain Layout
33392 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33395 \begin_layout Plain Layout
33396 \begin_inset Formula $x=-2$
33406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33409 \begin_layout Plain Layout
33415 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33418 \begin_layout Plain Layout
33419 \begin_inset Formula $x=\textrm{-}2$
33435 \begin_layout Subsection
33436 Comma as decimal Separator
33440 \begin_layout Plain Layout
33449 \begin_layout Standard
33450 In LaTeX a comma inside a formula is used, according to the English convention,
33451 as number group separator.
33452 So there will be space added behind all commas in formulas.
33455 \begin_layout Standard
33456 To avoid this, the comma is highlighted and changed to mathematical text
33466 \begin_layout Standard
33467 To use all formula commas in the document as decimal separator, the file
33476 \begin_layout Plain Layout
33481 is part of the LaTeX-package
33489 \begin_layout Plain Layout
33494 \begin_layout Plain Layout
33517 \begin_layout Plain Layout
33523 is loaded with the LaTeX-preamble line
33526 \begin_layout Standard
33534 \begin_layout Subsection
33536 \begin_inset CommandInset label
33538 name "sub:Physical-Vectors"
33546 \begin_layout Plain Layout
33555 \begin_layout Standard
33556 Predefined vectors are offered by the LaTeX-package
33564 \begin_layout Plain Layout
33569 should be part of every LaTeX standard installation.
33578 \begin_layout Plain Layout
33584 that is loaded with the LaTeX-preamble line
33587 \begin_layout Standard
33595 \begin_layout Standard
33599 \begin_layout Plain Layout
33609 \begin_inset Note Note
33612 \begin_layout Plain Layout
33613 The following table will only be displayed when the LaTeX-package
33622 The following commands are defined:
33625 \begin_layout Standard
33627 \begin_inset Tabular
33628 <lyxtabular version="3" rows="4" columns="2">
33630 <column alignment="center" valignment="top" width="0">
33631 <column alignment="center" valignment="top" width="0">
33633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33636 \begin_layout Plain Layout
33642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33645 \begin_layout Plain Layout
33653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33656 \begin_layout Plain Layout
33666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33669 \begin_layout Plain Layout
33670 \begin_inset Formula $\Bra{\psi}$
33680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33683 \begin_layout Plain Layout
33693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33696 \begin_layout Plain Layout
33697 \begin_inset Formula $\Ket{\psi}$
33707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33710 \begin_layout Plain Layout
33722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33725 \begin_layout Plain Layout
33726 \begin_inset Formula $\Braket{\psi|\phi}$
33742 \begin_layout Standard
33749 assures that all vertical bars are set in the size of the surrounding brackets:
33750 \begin_inset Formula \[
33751 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33759 \begin_layout Plain Layout
33769 \begin_inset Note Note
33772 \begin_layout Plain Layout
33773 The following will be displayed when the LaTeX-package
33785 \begin_layout Standard
33786 You need to install the LaTeX-package
33790 to see the rest of this subsection in the output.
33793 \begin_layout Standard
33797 \begin_layout Plain Layout
33809 \begin_layout Standard
33816 can also be achieved using the command
33822 , that is described in
33823 \begin_inset CommandInset ref
33825 reference "sub:Automatic-Bracket-Size"
33832 \begin_layout Subsection
33833 Self-defined Fractions
33834 \begin_inset CommandInset label
33836 name "sub:Self-defined-Fractions"
33844 \begin_layout Plain Layout
33845 Fractions ! self-defined
33853 \begin_layout Standard
33854 To define custom commands for fractions, the command
33864 \begin_layout Plain Layout
33872 is used in the following scheme:
33875 \begin_layout Standard
33888 bracket}{fraction bar thickness}{style}
33889 \begin_inset Newline newline
33896 \begin_layout Plain Layout
33911 \begin_layout Plain Layout
33918 {numerator}{denominator}
33921 \begin_layout Standard
33922 The style is a number in the range of 0
33923 \begin_inset space \thinspace{}
33927 \begin_inset space \thinspace{}
33933 \begin_layout Standard
33935 \begin_inset Tabular
33936 <lyxtabular version="3" rows="5" columns="2">
33938 <column alignment="center" valignment="top" width="0">
33939 <column alignment="center" valignment="top" width="0">
33941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33944 \begin_layout Plain Layout
33950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33953 \begin_layout Plain Layout
33961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33964 \begin_layout Plain Layout
33970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33973 \begin_layout Plain Layout
33974 display style formula
33981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33984 \begin_layout Plain Layout
33990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33993 \begin_layout Plain Layout
34001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34004 \begin_layout Plain Layout
34010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34013 \begin_layout Plain Layout
34021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34024 \begin_layout Plain Layout
34030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34033 \begin_layout Plain Layout
34047 \begin_layout Standard
34048 When no style is given, the size is adjusted to the surrounding environment
34049 like for the command
34058 \begin_layout Standard
34059 When no fraction bar thickness is given, the predefined value of 0.4
34060 \begin_inset space \thinspace{}
34066 \begin_layout Standard
34067 \begin_inset VSpace medskip
34070 For example, the commands
34083 \begin_inset CommandInset ref
34085 reference "sub:Fractions"
34089 are defined with the commands
34092 \begin_layout Standard
34101 genfrac{}{}{}{0}{#1}{#2}}
34104 \begin_layout Standard
34108 \begin_layout Standard
34117 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34120 \begin_layout Standard
34121 \begin_inset VSpace medskip
34124 To define a fraction where the fraction bar thickness can be given as optional
34125 argument, the following line is inserted to the LaTeX-preamble:
34128 \begin_layout Standard
34137 genfrac{}{}{#1}{}{#2}{#3}}
34140 \begin_layout Standard
34142 \begin_inset Formula \begin{align*}
34143 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34144 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34148 As one can see, the distance of the numerator and the denominator to the
34149 fraction bar is round about three times the bar thickness.
34152 \begin_layout Subsection
34157 \begin_layout Plain Layout
34166 \begin_layout Standard
34167 To cancel formulas or formula parts, the LaTeX-package
34175 \begin_layout Plain Layout
34180 is part of every LaTeX standard installation.
34189 \begin_layout Plain Layout
34195 has to be loaded with the LaTeX-preamble line
34198 \begin_layout Standard
34203 usepackage[samesize]{cancel}
34206 \begin_layout Standard
34207 There are four ways to cancel formulas:
34210 \begin_layout Standard
34212 \begin_inset Tabular
34213 <lyxtabular version="3" rows="5" columns="2">
34215 <column alignment="center" valignment="top" width="0">
34216 <column alignment="center" valignment="top" width="0">
34218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34221 \begin_layout Plain Layout
34227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34230 \begin_layout Plain Layout
34232 \begin_inset Note Note
34235 \begin_layout Plain Layout
34242 are used here as spacer.
34254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34257 \begin_layout Plain Layout
34266 \begin_layout Plain Layout
34280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34283 \begin_layout Plain Layout
34284 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34297 \begin_layout Plain Layout
34306 \begin_layout Plain Layout
34320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34323 \begin_layout Plain Layout
34324 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34337 \begin_layout Plain Layout
34346 \begin_layout Plain Layout
34360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34363 \begin_layout Plain Layout
34364 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34377 \begin_layout Plain Layout
34381 \begin_inset Formula $\to$
34392 \begin_layout Plain Layout
34406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34409 \begin_layout Plain Layout
34410 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34426 \begin_layout Standard
34433 is especially suitable to visualize the reduction of fractions within formulas:
34434 \begin_inset Formula \[
34435 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34442 \begin_layout Subsection
34443 Formulas in Section Headings
34444 \begin_inset CommandInset label
34446 name "sub:Formulas-in-Section"
34454 \begin_layout Plain Layout
34455 Formula ! in section headings
34463 \begin_layout Standard
34464 When formulas are used in section headings, the following has to be taken
34468 \begin_layout Standard
34469 \begin_inset Note Greyedout
34472 \begin_layout Plain Layout
34481 \begin_layout Plain Layout
34482 Packages ! hyperref
34487 support is enabled in the document settings dialog under
34490 \begin_inset space ~
34495 , PDF-bookmarks are created for every section heading in the table of contents.
34496 If a section heading contains formulas, they are incorrectly displayed
34497 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34506 \begin_layout Standard
34507 Both problems can be solved by inserting at the end of the section heading
34508 a short title with the menu
34510 Insert\SpecialChar \menuseparator
34512 \begin_inset space ~
34518 Short titles are used as alternative for multiline section headings to
34519 keep the table of contents clearly arranged.
34520 Only the short title appears in the table of contents and therefore also
34521 in the PDF-bookmark.
34524 \begin_layout Standard
34525 When formulas should be used in the table of contents but
34529 is used, one can use the following command in TeX-mode:
34532 \begin_layout Standard
34537 texorpdfstring{part}{alternative}
34541 \begin_layout Plain Layout
34552 \begin_layout Standard
34553 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34554 This can be characters, formulas, footnotes, but also cross-references.
34555 The alternative is used instead of the part for the bookmark.
34558 \begin_layout Standard
34559 Here are two example headings:
34560 \begin_inset VSpace -3mm
34567 \begin_layout Plain Layout
34579 \begin_layout Subsubsection
34580 Heading without formula in table of contents
34581 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34585 \begin_inset OptArg
34588 \begin_layout Plain Layout
34589 Heading without formula in table of contents
34597 \begin_layout Subsubsection
34598 Heading with formula in table of contents
34602 \begin_layout Plain Layout
34612 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34619 \begin_layout Plain Layout
34629 \begin_layout Standard
34633 \begin_layout Plain Layout
34642 In the first heading a short title was used, in the second one
34651 \begin_layout Standard
34652 To get the same formatting as for the other headings, the complete heading
34661 \begin_layout Plain Layout
34663 \begin_inset CommandInset ref
34665 reference "sub:Bold-Formulas"
34677 \begin_layout Subsection
34678 Formulas in multi-column Text
34682 \begin_layout Plain Layout
34683 Formula ! in multi-column text
34691 \begin_layout Standard
34692 Formulas in multi-column text are often too wide to fit into a column and
34693 thus need to be set over the whole page width.
34694 This is done by using the LaTeX-package
34702 \begin_layout Plain Layout
34707 is part of every LaTeX standard installation.
34716 \begin_layout Plain Layout
34717 Packages ! multicol
34722 , that is loaded with the LaTeX-preamble line
34725 \begin_layout Standard
34730 usepackage{multicol}
34733 \begin_layout Standard
34734 \begin_inset Note Greyedout
34737 \begin_layout Plain Layout
34738 Note herby that the setting
34741 \begin_inset space ~
34748 Document\SpecialChar \menuseparator
34754 \begin_inset space ~
34774 \begin_layout Standard
34775 Before the multi-column text the command
34778 \begin_layout Standard
34783 begin{multicols}{column number}
34786 \begin_layout Standard
34787 is written in TeX-mode.
34788 The column number is a number in the range of 2
34789 \begin_inset space \thinspace{}
34793 \begin_inset space \thinspace{}
34797 Before the formula the multi-column text is ended by inserting the command
34800 \begin_layout Standard
34808 \begin_layout Standard
34812 \begin_layout Standard
34813 Due to the command some space is automatically added before the formula.
34815 \begin_inset space \thinspace{}
34818 mm vertical space is inserted before the formula.
34819 When the formula style
34825 \begin_layout Plain Layout
34827 \begin_inset CommandInset ref
34829 reference "sec:Formula-Styles"
34841 \begin_inset space \thinspace{}
34844 mm space is inserted instead.
34847 \begin_layout Standard
34848 As example a multi-column text with a displayed formula:
34851 \begin_layout Standard
34855 \begin_layout Plain Layout
34859 begin{multicols}{2}
34864 Das Spektrum wird fouriertransformiert.
34865 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34866 , Lösungsmittel) zu trennen.
34867 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34868 nun das Aussehen des Ausgangssignals.
34869 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34870 über alle Phasen integrieren muss.
34872 \begin_inset Formula $S$
34875 unser normiertes Ausgangssignal and
34876 \begin_inset Formula $P$
34879 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34883 \begin_layout Plain Layout
34893 \begin_inset VSpace -6mm
34897 \begin_inset Formula \begin{equation}
34898 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34906 \begin_layout Plain Layout
34910 begin{multicols}{2}
34916 \begin_inset Formula $S_{0}$
34919 das Signal ohne Gradient ist and the Normierungsbedingung
34920 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34924 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34926 \begin_inset Formula $\nicefrac{\pi}{2}$
34930 \begin_inset space \thinspace{}
34933 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34934 das Signal zusätzlich abschwächt.
34935 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34937 \begin_inset Formula $T_{2}$
34943 \begin_layout Standard
34947 \begin_layout Plain Layout
34959 \begin_layout Subsection
34960 Formulas with Description of Variables
34964 \begin_layout Plain Layout
34965 Formula ! with description of variables
34973 \begin_layout Standard
34974 To describe variables within a formula, like in formula
34975 \begin_inset CommandInset ref
34977 reference "eq:within"
34986 \begin_inset Formula $n$
34990 \begin_inset space ~
34993 matrix is used with left aligned columns for the
34994 \begin_inset Formula $n$
35001 \begin_layout Plain Layout
35003 \begin_inset CommandInset ref
35005 reference "sec:Matrices"
35014 To set the description in a smaller size, before the matrix e.
35015 \begin_inset space \thinspace{}
35019 \begin_inset space \space{}
35032 \begin_layout Plain Layout
35034 \begin_inset CommandInset ref
35036 reference "sub:Font-Sizes"
35048 \begin_layout Standard
35049 When the formula style
35055 \begin_layout Plain Layout
35057 \begin_inset CommandInset ref
35059 reference "sec:Formula-Styles"
35080 \begin_layout Plain Layout
35087 only works in formulas with the style
35092 \begin_inset CommandInset ref
35094 reference "sub:Variable-Space"
35103 is inserted before and after the matrix to have the same separation of
35104 the matrix from the equation and the side margin.
35107 \begin_layout Standard
35108 When the formula style
35112 is used, the method described in
35113 \begin_inset CommandInset ref
35115 reference "sub:Flalign-Environment"
35119 is used to indent formulas.
35121 \begin_inset CommandInset ref
35123 reference "eq:within"
35127 consists of five columns whereas in the first two columns contain the equation,
35128 the third the matrix, and the last one an empty TeX-brace.
35129 \begin_inset Formula \begin{flalign}
35130 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35131 \rho & \textrm{density}\\
35132 V & \textrm{volume}\\
35133 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35140 \begin_layout Subsection
35141 Upright small Greek Letters
35142 \begin_inset CommandInset label
35144 name "sub:Upright-small-Greek"
35152 \begin_layout Plain Layout
35153 Greek letters ! upright
35161 \begin_layout Standard
35162 Most of the math fonts only provide italic small Greek letters.
35163 But for symbols of elementary particles like pions and neutrinos, upright
35164 Greek letters are needed.
35173 \begin_layout Plain Layout
35178 is part of the LaTeX-package
35186 \begin_layout Plain Layout
35191 \begin_layout Plain Layout
35214 \begin_layout Plain Layout
35220 that is loaded with the LaTeX-preamble line
35223 \begin_layout Standard
35228 usepackage{upgreek}
35231 \begin_layout Standard
35237 \begin_layout Plain Layout
35247 \begin_inset Note Note
35250 \begin_layout Plain Layout
35251 The following table will only be displayed when the LaTeX-package
35260 They are created when the command for a small Greek letters is started
35266 For example the command
35273 \begin_inset Formula $\uptau$
35279 \begin_layout Standard
35280 With these commands reactions of elementary particles can be typeset:
35281 \begin_inset Formula \[
35282 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35289 \begin_layout Standard
35290 The upright letters are more bold and wider than the italic ones.
35291 They should therefore not be used for units like
35292 \begin_inset Quotes eld
35296 \begin_inset Quotes erd
35302 \begin_layout Standard
35306 \begin_layout Plain Layout
35316 \begin_inset Note Note
35319 \begin_layout Plain Layout
35320 The following will be displayed when the LaTeX-package
35332 \begin_layout Standard
35333 You need to install the LaTeX-package
35337 to see the rest of this subsection in the output.
35340 \begin_layout Standard
35344 \begin_layout Plain Layout
35356 \begin_layout Subsection
35357 Text Characters in Formulas
35358 \begin_inset CommandInset label
35360 name "sub:Text-Characters-in"
35368 \begin_layout Plain Layout
35377 \begin_layout Standard
35378 In some cases you might want to insert text characters directly into formulas.
35379 When for example the centered dot · is often used in formulas like
35380 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35383 , one would have to insert the command
35393 \begin_layout Plain Layout
35395 \begin_inset CommandInset ref
35397 reference "sub:Binary-Operators"
35406 all the time, because this character is defined in all encodings as text
35408 But the encoding can be changed by this LaTeX-preamble line:
35411 \begin_layout Standard
35416 Declare Inputtext{183}{
35426 f\SpecialChar \textcompwordmark{}
35430 \begin_layout Standard
35431 The character encoding (menu
35433 Document\SpecialChar \menuseparator
35434 Settings\SpecialChar \menuseparator
35437 ) specifies what character appears when a keyboard key is pressed.
35438 When the key for the character '·' is pressed, internally the command
35445 But this command is not available in a formula so that you would get LaTeX-erro
35447 With the changed encoding the right command is chosen automatically, depending
35448 on if the character was inserted into a formula or not.
35451 \begin_layout Standard
35452 The encoding of several characters is saved in definition files.
35453 Fore example the encoding
35457 is defined in the file
35461 that is in the installation folder of LaTeX.
35462 Encodings should only be changed via the LaTeX-preamble and not in the
35464 Otherwise own documents could not be edited by other LyX users working
35465 on other computers.
35468 \begin_layout Standard
35469 \begin_inset VSpace medskip
35472 Besides the centered dot, in this document the degree sign ° is defined
35473 with the following LaTeX-preamble line so that it can directly be inserted
35477 \begin_layout Standard
35482 DeclareInputtext{176}{
35492 f\SpecialChar \textcompwordmark{}
35496 \begin_layout Standard
35497 \begin_inset Newpage newpage
35503 \begin_layout Section
35509 \begin_layout Plain Layout
35518 \begin_layout Standard
35519 This section is a summary of the most important typographic rules, listed
35524 \begin_layout Plain Layout
35525 This collection was partly taken from the German semi-official dictionary
35527 \begin_inset Quotes eld
35531 \begin_inset Quotes erd
35535 \begin_inset CommandInset citation
35541 that lists some of the ISO rules.
35549 \begin_layout Itemize
35558 \begin_layout Plain Layout
35559 done with font styles, see
35560 \begin_inset CommandInset ref
35562 reference "sub:Font-Styles"
35572 \begin_inset space \thinspace{}
35576 \begin_inset Newline newline
35579 Between the value and the unit is the smallest space, see
35580 \begin_inset CommandInset ref
35582 reference "sub:Predefined-Space"
35587 \begin_inset Newline newline
35590 This convention is automatically fulfilled when the command
35597 When it is entered to a formula, two boxes appear.
35598 In the first one the value is inserted, in the second one the unit, and
35600 \begin_inset Formula $\unit[30]{km/h}$
35604 \begin_inset space \thinspace{}
35614 is not a real LaTeX command but the command
35620 , therefore you cannot use it in TeX code.
35623 \begin_layout Itemize
35624 Percent and perthousand signs are set like physical units:
35625 \begin_inset Newline newline
35629 \begin_inset space \thinspace{}
35635 \begin_layout Itemize
35636 The degree sign follows directly on the value: 15°, but not when it is used
35638 \begin_inset space \thinspace{}
35644 \begin_layout Itemize
35645 In numbers with more than four digits the smallest space is inserted before
35646 every third digit to group them:
35656 \begin_inset space \thinspace{}
35660 \begin_inset space \thinspace{}
35666 \begin_layout Itemize
35667 For dimensions like 120×90×40
35668 \begin_inset space \thinspace{}
35671 cm the multiplication sign
35672 \begin_inset Quotes eld
35676 \begin_inset Quotes erd
35680 It is available via the menu
35682 Insert\SpecialChar \menuseparator
35683 Special Character\SpecialChar \menuseparator
35687 With some keyboard definitions it can also be inserted directly.
35690 \begin_layout Itemize
35691 Functions with names consisting of several letters are set upright to avoid
35693 \begin_inset CommandInset ref
35695 reference "sub:Predefined-Functions"
35702 \begin_layout Itemize
35703 Indices consisting of several letters, are set upright:
35704 \begin_inset Formula $E_{\mathrm{kin}}$
35708 \begin_inset Newline newline
35711 Components of matrices are set italic:
35712 \begin_inset Formula $\hat{H}_{kl}$
35718 \begin_layout Itemize
35719 The differentiation/integration operator 'd', the Euler's number 'e', and
35720 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35724 \begin_layout Standard
35725 \begin_inset Newpage newpage
35731 \begin_layout Section
35736 \begin_layout Plain Layout
35745 \begin_layout Standard
35746 Some characters and symbols can be created with several commands.
35747 Here is a list of the synonym commands:
35750 \begin_layout Standard
35751 \begin_inset VSpace bigskip
35755 \begin_inset space \hfill{}
35759 \begin_inset Tabular
35760 <lyxtabular version="3" rows="12" columns="2">
35762 <column alignment="center" valignment="top" width="0pt">
35763 <column alignment="center" valignment="top" width="0pt">
35765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35768 \begin_layout Plain Layout
35774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35777 \begin_layout Plain Layout
35779 \begin_inset Note Note
35782 \begin_layout Plain Layout
35789 is only used as spacer.
35801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35804 \begin_layout Plain Layout
35812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35815 \begin_layout Plain Layout
35819 \begin_layout Plain Layout
35832 \begin_layout Plain Layout
35846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35849 \begin_layout Plain Layout
35857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35860 \begin_layout Plain Layout
35870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35873 \begin_layout Plain Layout
35881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35884 \begin_layout Plain Layout
35894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35897 \begin_layout Plain Layout
35905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35908 \begin_layout Plain Layout
35916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35919 \begin_layout Plain Layout
35927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35930 \begin_layout Plain Layout
35938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35941 \begin_layout Plain Layout
35949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35952 \begin_layout Plain Layout
35962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35965 \begin_layout Plain Layout
35973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35976 \begin_layout Plain Layout
35986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35989 \begin_layout Plain Layout
35997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36000 \begin_layout Plain Layout
36010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36013 \begin_layout Plain Layout
36021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36024 \begin_layout Plain Layout
36034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36037 \begin_layout Plain Layout
36045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36048 \begin_layout Plain Layout
36056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36059 \begin_layout Plain Layout
36067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36070 \begin_layout Plain Layout
36082 \begin_inset space \hfill{}
36086 \begin_inset Tabular
36087 <lyxtabular version="3" rows="12" columns="2">
36089 <column alignment="center" valignment="top" width="0pt">
36090 <column alignment="center" valignment="top" width="0pt">
36092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36095 \begin_layout Plain Layout
36101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36104 \begin_layout Plain Layout
36112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36115 \begin_layout Plain Layout
36123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36126 \begin_layout Plain Layout
36138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36141 \begin_layout Plain Layout
36149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36152 \begin_layout Plain Layout
36162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36165 \begin_layout Plain Layout
36173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36176 \begin_layout Plain Layout
36186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36189 \begin_layout Plain Layout
36197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36200 \begin_layout Plain Layout
36208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36211 \begin_layout Plain Layout
36219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36222 \begin_layout Plain Layout
36230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36233 \begin_layout Plain Layout
36241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36244 \begin_layout Plain Layout
36254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36257 \begin_layout Plain Layout
36265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36268 \begin_layout Plain Layout
36278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36281 \begin_layout Plain Layout
36289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36292 \begin_layout Plain Layout
36302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36305 \begin_layout Plain Layout
36313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36316 \begin_layout Plain Layout
36326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36329 \begin_layout Plain Layout
36337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36340 \begin_layout Plain Layout
36350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36353 \begin_layout Plain Layout
36361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36364 \begin_layout Plain Layout
36378 \begin_inset space \hfill{}
36384 \begin_layout Standard
36385 \begin_inset Newpage newpage
36391 \begin_layout Bibliography
36392 \begin_inset CommandInset bibitem
36393 LatexCommand bibitem
36405 The LaTeX Companion
36408 Addison Wesley, 2004
36411 \begin_layout Bibliography
36412 \begin_inset CommandInset bibitem
36413 LatexCommand bibitem
36419 \begin_inset CommandInset href
36422 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36426 of LaTeX's math abilities
36429 \begin_layout Bibliography
36430 \begin_inset CommandInset bibitem
36431 LatexCommand bibitem
36436 LaTeX tips and tricks-
36437 \begin_inset CommandInset href
36440 target "http://tug.org/TeXnik/"
36447 \begin_layout Bibliography
36448 \begin_inset CommandInset bibitem
36449 LatexCommand bibitem
36455 \begin_inset CommandInset href
36458 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36466 \begin_layout Plain Layout
36478 \begin_layout Bibliography
36479 \begin_inset CommandInset bibitem
36480 LatexCommand bibitem
36486 \begin_inset CommandInset href
36489 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36493 of all symbols available with LaTeX-packages
36496 \begin_layout Bibliography
36497 \begin_inset CommandInset bibitem
36498 LatexCommand bibitem
36504 \begin_inset CommandInset href
36506 name "Documentation"
36507 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36511 of the LaTeX-package
36519 \begin_layout Plain Layout
36520 Packages ! hyperref
36528 \begin_layout Bibliography
36529 \begin_inset CommandInset bibitem
36530 LatexCommand bibitem
36536 \begin_inset CommandInset href
36539 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36550 \begin_inset CommandInset ref
36552 reference "sub:Operator-Limits"
36560 \begin_layout Plain Layout
36571 \begin_layout Bibliography
36572 \begin_inset CommandInset bibitem
36573 LatexCommand bibitem
36584 Auflage, Duden 2001
36587 \begin_layout Subsubsection*
36588 \begin_inset CommandInset index_print
36589 LatexCommand printindex