1 #LyX 1.6.4svn 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 Typesetting isotopes and chemical symbols is described 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://www.lyx.org/trac/ticket/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
12505 within this box, because the box content will otherwise be treated as mathemati
12513 is used, a new formula is automatically created inside the frame.
12516 \begin_layout Standard
12523 is not suitable to frame displayed formulas because the formula will always
12524 be set in the size of the text.
12531 is in contrary not suitable to frame inline formulas, because the formula
12532 will always be set in the size of a displayed formula.
12535 \begin_layout Standard
12542 there is the command
12552 \begin_layout Plain Layout
12560 where additionally the frame width and the alignment can be specified.
12567 is used in the following scheme:
12570 \begin_layout Standard
12575 framebox[frame width][position]{box content}
12578 \begin_layout Standard
12579 The position can either be
12596 right aligns the formula in the box.
12597 When no position is given, the formula will be centered.
12598 \begin_inset Newline newline
12601 Is no width given, also no position can be given.
12602 In this case the frame width is adjusted to the box content like for
12611 \begin_layout Standard
12618 is inserted, a box appears containing three blue boxes.
12619 The first two boxes are surrounded by brackets and denote the two optional
12621 The third box is for formula parts like for
12630 \begin_layout Standard
12632 \begin_inset Tabular
12633 <lyxtabular version="3" rows="5" columns="2">
12635 <column alignment="center" valignment="top" width="0">
12636 <column alignment="center" valignment="top" width="0">
12638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12641 \begin_layout Plain Layout
12647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12650 \begin_layout Plain Layout
12652 \begin_inset Note Note
12655 \begin_layout Plain Layout
12662 is only used as spacer.
12674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12677 \begin_layout Plain Layout
12684 \begin_layout Plain Layout
12703 \begin_layout Plain Layout
12717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12720 \begin_layout Plain Layout
12721 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12734 \begin_layout Plain Layout
12741 \begin_layout Plain Layout
12756 \begin_layout Plain Layout
12770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12773 \begin_layout Plain Layout
12774 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12787 \begin_layout Plain Layout
12794 \begin_layout Plain Layout
12808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12811 \begin_layout Plain Layout
12812 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12825 \begin_layout Plain Layout
12832 \begin_layout Plain Layout
12842 \begin_inset Formula $\to$
12846 \begin_inset Formula $\to$
12859 \begin_layout Plain Layout
12869 \begin_inset Formula $\downarrow$
12877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12880 \begin_layout Plain Layout
12881 \begin_inset Formula $\raisebox{6mm}{}$
12885 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12889 \begin_inset Formula $\raisebox{-4mm}{}$
12905 \begin_layout Standard
12906 The frame thickness can also be adjusted.
12907 To do this the following commands have to be inserted in TeX-mode before
12911 \begin_layout Standard
12921 \begin_inset Quotes eld
12925 \begin_inset Quotes erd
12939 \begin_inset Quotes eld
12943 \begin_inset Quotes erd
12949 \begin_layout Standard
12950 \begin_inset Quotes eld
12954 \begin_inset Quotes erd
12957 specifies the minimal distance between the frame and the first character
12959 An example for this is the following framed formula:
12963 \begin_layout Plain Layout
12975 \begin_inset Formula \[
12980 Before this formula the commands
12983 \begin_layout Standard
13005 \begin_layout Standard
13006 were inserted in TeX-mode.
13007 The given values are used for all following boxes.
13010 \begin_layout Standard
13011 To return to the standard frame size, the command
13014 \begin_layout Standard
13039 \begin_layout Plain Layout
13053 \begin_layout Standard
13054 is inserted in TeX-mode before the next formula.
13057 \begin_layout Subsection
13058 Boxes without Frame
13059 \begin_inset CommandInset label
13061 name "sub:Boxes-without-Frame"
13069 \begin_layout Plain Layout
13070 Boxes ! without frame
13078 \begin_layout Standard
13079 For boxes without a frame there are the following box commands:
13089 \begin_layout Plain Layout
13107 \begin_layout Plain Layout
13125 \begin_layout Plain Layout
13136 \begin_layout Standard
13143 a box can be super- or subscripted.
13144 But in contrary to normal super- and subscripting, the characters in the
13145 box keep their font size.
13152 is used in the following scheme:
13155 \begin_layout Standard
13160 raisebox{height}{box content}
13163 \begin_layout Standard
13164 When the box should contain a formula, an extra formula is needed like for
13175 \begin_inset Note Greyedout
13178 \begin_layout Plain Layout
13189 this extra formula is created by pressing
13193 twice instead of once because LyX doesn't yet support
13207 \begin_layout Standard
13209 \begin_inset Tabular
13210 <lyxtabular version="3" rows="4" columns="2">
13212 <column alignment="center" valignment="top" width="0">
13213 <column alignment="center" valignment="top" width="0">
13215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13218 \begin_layout Plain Layout
13224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13227 \begin_layout Plain Layout
13235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13238 \begin_layout Plain Layout
13242 \begin_inset Formula $\to$
13248 \begin_inset Formula $\to$
13256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13259 \begin_layout Plain Layout
13260 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13273 \begin_layout Plain Layout
13277 \begin_inset Formula $\to$
13283 \begin_inset Formula $\to$
13291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13294 \begin_layout Plain Layout
13295 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13308 \begin_layout Plain Layout
13312 \begin_inset Formula $\to$
13331 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13348 \begin_layout Plain Layout
13349 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13365 \begin_layout Standard
13390 , with the difference that there is no frame.
13393 \begin_layout Subsection
13395 \begin_inset CommandInset label
13397 name "sub:Colored-Boxes"
13405 \begin_layout Plain Layout
13414 \begin_layout Standard
13415 To be able to use all commands explained in this section, the LaTeX-package
13424 \begin_layout Plain Layout
13429 is part of every LaTeX standard installation.
13438 \begin_layout Plain Layout
13444 has to be loaded in the LaTeX-preamble with the line
13448 \begin_layout Plain Layout
13449 When text is colored somewhere in the document with a predefined color,
13450 LyX loads the LaTeX-package
13455 Thus it is possible that the package is loaded twice, but this doesn't
13462 \begin_inset Note Note
13465 \begin_layout Plain Layout
13466 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13475 \begin_layout Standard
13483 \begin_layout Standard
13484 \begin_inset VSpace medskip
13487 To color boxes, the command
13497 \begin_layout Plain Layout
13505 is used in the following scheme:
13508 \begin_layout Standard
13513 colorbox{color}{box content}
13516 \begin_layout Standard
13517 The box content can also be a box and a
13523 can also be part of another box (see the 2nd and 3rd example).
13524 When the box should contain a formula, an extra formula has to be created,
13525 the same way as for
13535 \begin_layout Plain Layout
13536 This also applies for the command
13550 \begin_layout Standard
13551 One of the following predefined colors can be chosen:
13554 \begin_layout Standard
13588 \begin_layout Standard
13590 \begin_inset Tabular
13591 <lyxtabular version="3" rows="4" columns="2">
13593 <column alignment="center" valignment="top" width="0">
13594 <column alignment="center" valignment="top" width="0">
13596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13599 \begin_layout Plain Layout
13605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13608 \begin_layout Plain Layout
13610 \begin_inset Note Note
13613 \begin_layout Plain Layout
13620 is only used as spacer.
13632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13635 \begin_layout Plain Layout
13639 \begin_inset Formula $\to$
13649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13652 \begin_layout Plain Layout
13653 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13666 \begin_layout Plain Layout
13670 \begin_inset Formula $\to$
13681 \begin_layout Plain Layout
13695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13698 \begin_layout Plain Layout
13699 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13712 \begin_layout Plain Layout
13719 \begin_layout Plain Layout
13731 \begin_inset Formula $\to$
13750 \begin_layout Plain Layout
13764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13767 \begin_layout Plain Layout
13768 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13784 \begin_layout Standard
13791 only colors the box but not the characters in the box.
13792 To color all characters, the whole formula is highlighted and the wanted
13793 color is chosen in the
13796 \begin_inset space ~
13802 The dialog can be called with the toolbar button
13803 \begin_inset Graphics
13804 filename ../images/dialog-show_character.png
13811 Edit\SpecialChar \menuseparator
13813 \begin_inset space ~
13816 Style\SpecialChar \menuseparator
13820 The formula number has then the same color as the formula.
13821 When the formula number should get another color than the formula characters,
13822 the color must be changed within the formula.
13825 \begin_layout Standard
13829 \begin_layout Standard
13832 \begin_inset Formula \begin{equation}
13833 \int A=B\label{eq:red}\end{equation}
13840 \begin_inset Formula \begin{equation}
13841 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13848 \begin_layout Standard
13850 \begin_inset CommandInset ref
13856 is completely colored red.
13857 \begin_inset Newline newline
13861 \begin_inset CommandInset ref
13863 reference "eq:redgreen"
13867 was first completely colored green to set the color for the formula number.
13868 Subsequently the formula characters were colored red.
13871 \begin_layout Standard
13872 \begin_inset VSpace bigskip
13875 To color the frame different than the rest of the box, the command
13885 \begin_layout Plain Layout
13893 is used in the following scheme:
13896 \begin_layout Standard
13901 fcolorbox{frame color}{color}{box content}
13904 \begin_layout Standard
13911 is an extension of the command
13918 The frame width is set, like for
13941 \begin_layout Plain Layout
13953 \begin_inset Formula \[
13954 \fcolorbox{cyan}{magenta}{A=B}\]
13962 \begin_layout Plain Layout
13976 \begin_layout Standard
13977 This formula was created with the command
13978 \begin_inset Newline newline
13986 \begin_inset Formula $\to$
13992 \begin_inset Formula $\to$
14002 \begin_layout Standard
14003 \begin_inset VSpace bigskip
14006 To use other colors than the predefined ones, they have to be defined first.
14009 \begin_layout Standard
14010 One can for example define the color
14011 \begin_inset Quotes eld
14019 \begin_inset Quotes erd
14022 with the LaTeX-preamble line:
14025 \begin_layout Standard
14030 definecolor{darkgreen}{cmyk}{0.5,
14048 \begin_layout Plain Layout
14059 \begin_layout Standard
14064 is the color space that denotes the colors
14081 The four comma separated numbers are the portion factor for the corresponding
14082 colors of the color space.
14083 The factors can be in the range of 0
14084 \begin_inset space \thinspace{}
14088 \begin_inset space \thinspace{}
14096 also the color space
14100 can be used for definitions.
14117 , so that there are in this case three portion factors for the corresponding
14119 Furthermore there is the color space
14123 with one portion factor for the gray value.
14126 \begin_layout Standard
14127 As example a framed box with the new defined color
14131 where the characters have been colored
14136 \begin_inset Formula \begin{equation}
14137 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14144 \begin_layout Standard
14145 Self-defined colors can also be used for text with the help of the command
14156 \begin_layout Plain Layout
14165 \begin_layout Standard
14169 \begin_layout Plain Layout
14173 textcolor{darkgreen}{
14179 \begin_inset Quotes eld
14183 \begin_inset Quotes erd
14190 \begin_layout Plain Layout
14200 \begin_layout Standard
14211 \begin_layout Plain Layout
14219 is used in the scheme
14223 textcolor{color}{characters to color}
14228 \begin_layout Subsection
14230 \begin_inset CommandInset label
14232 name "sub:Paragraph-Boxes"
14240 \begin_layout Plain Layout
14241 Boxes ! as paragraph
14249 \begin_layout Standard
14250 A box that can contain several lines and paragraphs, a so called paragraph
14251 box (parbox), can be created with the menu
14253 Insert\SpecialChar \menuseparator
14256 or the toolbar button
14257 \begin_inset Graphics
14258 filename ../images/box-insert.png
14266 \begin_layout Standard
14267 The following example shows a framed parbox in a line:
14270 \begin_layout Standard
14271 \begin_inset VSpace medskip
14275 \begin_inset Box Boxed
14284 height_special "totalheight"
14287 \begin_layout Plain Layout
14288 This is a paragraph box.
14290 \begin_inset space \thinspace{}
14293 cm long and can also contain formulas:
14294 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14305 \begin_layout Standard
14306 \begin_inset VSpace medskip
14312 \begin_layout Standard
14313 Such a box is created by right-clicking on the gray box inset.
14314 A dialog pops up showing the box properties.
14328 \begin_inset space \thinspace{}
14333 Vertical Box Alignment
14338 \begin_layout Standard
14339 \begin_inset VSpace medskip
14342 In LaTeX a parbox is created with the command
14352 \begin_layout Plain Layout
14360 that has the following scheme:
14363 \begin_layout Standard
14368 parbox[position]{width}{box content}
14371 \begin_layout Standard
14385 for bottom means that the box is aligned within the surrounding text with
14391 for top this is done with the first line.
14392 When no position is given, the box will be vertically centered, see section
14400 \begin_inset space ~
14405 manual for examples.
14408 \begin_layout Standard
14409 \begin_inset VSpace bigskip
14412 To frame formulas completely, including the formula number, the formula
14413 must be set into a parbox.
14414 To do this, the command
14428 is inserted in TeX-mode before the formula.
14437 \begin_layout Plain Layout
14447 is hereby the line width set for the document.
14448 Because the frame is outside the parbox, 2
14449 \begin_inset space \thinspace{}
14452 times the frame separation and the frame thickness must be subtracted from
14454 As this is not automatically done by LyX due to a bug
14458 \begin_layout Plain Layout
14459 \begin_inset CommandInset href
14461 name "LyX-bug #4483"
14462 target "http://www.lyx.org/trac/ticket/4483"
14471 , TeX-mode has to be used.
14472 To be able to multiply and subtract in arguments, the LaTeX-package
14480 \begin_layout Plain Layout
14485 is part of every LaTeX standard installation.
14494 \begin_layout Plain Layout
14500 must be loaded in the LaTeX-preamble with the line
14503 \begin_layout Standard
14511 \begin_layout Standard
14512 Behind the formula both boxes are closed by entering
14517 Here is an example:
14521 \begin_layout Plain Layout
14535 \begin_layout Standard
14539 \begin_layout Plain Layout
14557 \begin_inset Formula \begin{equation}
14558 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14566 \begin_layout Plain Layout
14577 \begin_layout Plain Layout
14591 \begin_layout Standard
14592 \begin_inset VSpace medskip
14595 As a parbox is used as argument of
14601 , there is in this case no difference between
14616 \begin_layout Standard
14617 \begin_inset VSpace bigskip
14620 Paragraph boxes are very useful to comment formulas directly.
14627 is used in combination with the command
14641 \begin_inset CommandInset ref
14643 reference "sub:User-defined-Numbering"
14650 \begin_layout Standard
14651 An example of a formula commented with
14660 \begin_layout Standard
14664 \begin_layout Plain Layout
14677 This is a description.
14678 It is distinctly separated from the formula and multiline.
14682 \begin_layout Plain Layout
14694 \begin_layout Standard
14695 Such a formula must be inserted completely in TeX-mode because LyX does
14696 not yet support the command
14703 The formula is created with the following command sequence:
14706 \begin_layout Standard
14719 is inserted in TeX-mode.
14723 \begin_layout Plain Layout
14724 When the formula style
14736 can also be replaced by
14743 (formula styles see
14744 \begin_inset CommandInset ref
14746 reference "sec:Formula-Styles"
14755 Then the description follows as normal text, and finally
14761 is inserted in TeX-mode.
14774 hereby create a displayed formula.
14777 \begin_layout Standard
14784 can be seen in this example that was
14785 \begin_inset Quotes eld
14789 \begin_inset Quotes erd
14792 using the mathematical textmode:
14793 \begin_inset Formula \[
14794 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14801 \begin_layout Section
14806 \begin_layout Plain Layout
14815 \begin_layout Subsection
14817 \begin_inset CommandInset label
14819 name "sub:Big-Operators"
14827 \begin_layout Plain Layout
14837 \begin_layout Plain Layout
14847 \begin_layout Plain Layout
14856 \begin_layout Standard
14857 To be able to use all integral operators listed here, the option
14859 Use esint package automatically
14861 must be set in the document settings under
14864 \begin_inset space ~
14872 \begin_layout Standard
14873 \begin_inset space \hfill{}
14877 \begin_inset Tabular
14878 <lyxtabular version="3" rows="11" columns="2">
14880 <column alignment="center" valignment="top" width="0pt">
14881 <column alignment="center" valignment="top" width="0pt">
14883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14886 \begin_layout Plain Layout
14892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14895 \begin_layout Plain Layout
14903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14906 \begin_layout Plain Layout
14913 \begin_layout Plain Layout
14926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14929 \begin_layout Plain Layout
14930 \begin_inset Formula $\int$
14940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14943 \begin_layout Plain Layout
14951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14954 \begin_layout Plain Layout
14955 \begin_inset Formula $\oint$
14965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14968 \begin_layout Plain Layout
14976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14979 \begin_layout Plain Layout
14980 \begin_inset Formula $\ointctrclockwise$
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14993 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15005 \begin_inset Formula $\ointclockwise$
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15018 \begin_layout Plain Layout
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15029 \begin_layout Plain Layout
15030 \begin_inset Formula $\sqint$
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15043 \begin_layout Plain Layout
15051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15054 \begin_layout Plain Layout
15056 \begin_inset Formula $\fint$
15066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15069 \begin_layout Plain Layout
15077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15080 \begin_layout Plain Layout
15082 \begin_inset Formula $\landupint$
15092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15095 \begin_layout Plain Layout
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15106 \begin_layout Plain Layout
15108 \begin_inset Formula $\landdownint$
15118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15132 \begin_layout Plain Layout
15133 \begin_inset Formula $\bigcap$
15143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15157 \begin_layout Plain Layout
15158 \begin_inset Formula $\bigcup$
15172 \begin_inset space \hfill{}
15176 \begin_inset Tabular
15177 <lyxtabular version="3" rows="11" columns="2">
15179 <column alignment="center" valignment="top" width="0pt">
15180 <column alignment="center" valignment="top" width="0pt">
15182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15185 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15205 \begin_layout Plain Layout
15212 \begin_layout Plain Layout
15225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15228 \begin_layout Plain Layout
15229 \begin_inset Formula $\sum$
15239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15242 \begin_layout Plain Layout
15249 \begin_layout Plain Layout
15262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15265 \begin_layout Plain Layout
15266 \begin_inset Formula $\prod$
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15279 \begin_layout Plain Layout
15287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15290 \begin_layout Plain Layout
15291 \begin_inset Formula $\coprod$
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15304 \begin_layout Plain Layout
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15315 \begin_layout Plain Layout
15316 \begin_inset Formula $\bigodot$
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15329 \begin_layout Plain Layout
15337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15340 \begin_layout Plain Layout
15341 \begin_inset Formula $\bigotimes$
15351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15354 \begin_layout Plain Layout
15362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15365 \begin_layout Plain Layout
15366 \begin_inset Formula $\bigoplus$
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15379 \begin_layout Plain Layout
15387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15390 \begin_layout Plain Layout
15391 \begin_inset Formula $\bigwedge$
15401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15404 \begin_layout Plain Layout
15412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15415 \begin_layout Plain Layout
15416 \begin_inset Formula $\bigvee$
15426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15429 \begin_layout Plain Layout
15437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15440 \begin_layout Plain Layout
15441 \begin_inset Formula $\bigsqcup$
15451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15454 \begin_layout Plain Layout
15462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15465 \begin_layout Plain Layout
15466 \begin_inset Formula $\biguplus$
15480 \begin_inset space \hfill{}
15486 \begin_layout Standard
15487 All big operators can also be inserted via the math toolbar button
15488 \begin_inset Graphics
15489 filename ../images/math/intop.png
15497 \begin_layout Standard
15498 The operators are called big because they are bigger than the sometimes
15499 equal looking binary operators.
15500 All big operators can have limits as described in the next subsection.
15503 \begin_layout Standard
15504 For all integral operators there is a second version available, ending on
15522 These operators are different from
15529 \begin_inset space \space{}
15532 in the style the operator limits are displayed, see
15533 \begin_inset CommandInset ref
15535 reference "sub:Operator-Limits"
15543 \begin_layout Subsubsection*
15544 Advice for Integrals
15547 \begin_layout Standard
15552 in an integral is an operator, that therefore has to be set upright.
15553 This is done by highlighting the
15557 and using the keyboard shortcut
15567 \begin_layout Plain Layout
15573 \begin_inset CommandInset ref
15575 reference "sub:Font-Styles"
15585 Finally the smallest space is inserted before the
15589 , as this is usual for operators.
15593 \begin_layout Standard
15595 \begin_inset Formula $\int A(x)dx$
15599 \begin_inset Newline newline
15606 \begin_layout Plain Layout
15616 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15622 \begin_layout Standard
15623 For multiple integrals there are the following commands:
15624 \begin_inset VSpace medskip
15630 \begin_layout Standard
15631 \begin_inset space \hfill{}
15635 \begin_inset Tabular
15636 <lyxtabular version="3" rows="4" columns="2">
15638 <column alignment="center" valignment="top" width="0">
15639 <column alignment="center" valignment="top" width="0">
15641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15653 \begin_layout Plain Layout
15655 \begin_inset Note Note
15658 \begin_layout Plain Layout
15665 is only used as spacer.
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15680 \begin_layout Plain Layout
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15691 \begin_layout Plain Layout
15692 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15705 \begin_layout Plain Layout
15713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15716 \begin_layout Plain Layout
15717 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15730 \begin_layout Plain Layout
15738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15741 \begin_layout Plain Layout
15742 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15756 \begin_inset space \hfill{}
15760 \begin_inset Tabular
15761 <lyxtabular version="3" rows="4" columns="2">
15763 <column alignment="center" valignment="top" width="0">
15764 <column alignment="center" valignment="top" width="0">
15766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15769 \begin_layout Plain Layout
15775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15778 \begin_layout Plain Layout
15786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15789 \begin_layout Plain Layout
15797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15800 \begin_layout Plain Layout
15801 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15814 \begin_layout Plain Layout
15822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15825 \begin_layout Plain Layout
15826 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15839 \begin_layout Plain Layout
15847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15850 \begin_layout Plain Layout
15851 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15865 \begin_inset space \hfill{}
15871 \begin_layout Subsection
15873 \begin_inset CommandInset label
15875 name "sub:Operator-Limits"
15883 \begin_layout Plain Layout
15892 \begin_layout Standard
15893 Limits are created by super- and subscripts:
15896 \begin_layout Standard
15898 \begin_inset Tabular
15899 <lyxtabular version="3" rows="2" columns="2">
15901 <column alignment="center" valignment="top" width="0pt">
15902 <column alignment="center" valignment="top" width="0pt">
15904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15907 \begin_layout Plain Layout
15913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Plain Layout
15918 \begin_inset Note Note
15921 \begin_layout Plain Layout
15928 is only used as spacer.
15940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15943 \begin_layout Plain Layout
15952 \begin_layout Plain Layout
15962 \begin_inset Formula $\to$
15966 \begin_inset Formula $\to$
15974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15977 \begin_layout Plain Layout
15978 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15994 \begin_layout Standard
15995 Limits of inline formulas are set right beside the operator.
15996 Limits in displayed formulas are set above or below the operator, except
15997 for integral limits.
16000 \begin_layout Standard
16001 To force that the limits are set beside the operator, the cursor is set
16002 directly behind the operator and the limits type is changed with the menu
16005 Edit\SpecialChar \menuseparator
16006 Math\SpecialChar \menuseparator
16025 \begin_layout Standard
16026 The default limits type is this:
16027 \begin_inset Formula \[
16028 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16032 This is how it looks when the limits type was changed to
16039 \begin_inset Formula \[
16040 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16044 For integrals, except those ending with
16060 etc., the limits are by default set beside the operator.
16061 But for multiple integrals the limits are often set below the operator.
16062 In the following example the limits type was therefore set to
16066 and so set below the integrals:
16067 \begin_inset Formula \begin{equation}
16068 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16075 \begin_layout Standard
16076 \begin_inset VSpace medskip
16079 To specify conditions for limits, the commands
16089 \begin_layout Plain Layout
16107 \begin_layout Plain Layout
16116 To create for example this expression
16117 \begin_inset Formula \begin{equation}
16118 \sum_{\begin{subarray}{c}
16120 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16127 \begin_layout Standard
16128 the following has to be done:
16129 \begin_inset Newline newline
16144 \begin_layout Plain Layout
16156 One is now in a blue box under the summation operator and insert there
16165 \begin_layout Plain Layout
16177 The blue box is now within a purple box and now several lines can be written
16179 A new line is created by inserting a line break (
16182 arg "newline-insert newline"
16187 \begin_inset Newline newline
16192 0<k<1000 Ctrl+Return
16193 \begin_inset Newline newline
16198 is typed in, a new box appears below for the new line.
16201 \begin_layout Standard
16202 The alignment of the lines can be changed to left aligned with the
16212 Edit\SpecialChar \menuseparator
16216 To get right alignment,
16224 \begin_layout Plain Layout
16235 is inserted at the beginning of the line.
16238 \begin_layout Standard
16251 with the difference that the lines are always centered.
16254 \begin_layout Standard
16255 \begin_inset VSpace bigskip
16259 \begin_inset CommandInset ref
16261 reference "eq:substack"
16265 there can be too much space beside an operator, because the characters
16266 following the operator are set beside the limits.
16269 \begin_layout Standard
16270 To avoid this, the following macro can be used in the LaTeX-preamble:
16273 \begin_layout Standard
16287 \begin_inset Newline newline
16299 \begin_inset Newline newline
16306 mathclapinternal #1#2{
16310 mathsurround =0pt #1{#2}$}}
16313 \begin_layout Standard
16314 This defines the command
16324 \begin_layout Plain Layout
16332 that sets the width of the limit to 0
16333 \begin_inset space \thinspace{}
16337 The command scheme is
16340 \begin_layout Standard
16348 \begin_layout Standard
16349 where the limit can consist of several conditions.
16352 \begin_layout Standard
16354 \begin_inset CommandInset ref
16356 reference "eq:substack"
16360 , one uses the command
16363 \begin_layout Standard
16376 \begin_layout Plain Layout
16385 0<k<1000 Ctrl+Return
16388 \begin_layout Standard
16389 to create the lower limit.
16390 The summand is now directly behind the summation operator:
16391 \begin_inset Formula \[
16392 \sum_{\mathclap{\substack{0<k<1000\\
16393 \\k\,\in\,\mathbb{N}}
16401 \begin_layout Standard
16402 \begin_inset VSpace bigskip
16405 How to use one limit for several operators is described in
16406 \begin_inset CommandInset ref
16408 reference "sub:Self-defined-Operators"
16415 \begin_layout Subsection
16417 \begin_inset CommandInset label
16419 name "sub:Binary-Operators"
16427 \begin_layout Plain Layout
16436 \begin_layout Standard
16437 Binary operators are surrounded by space when there is a character before
16439 \begin_inset VSpace medskip
16445 \begin_layout Standard
16446 \begin_inset space \hfill{}
16450 \begin_inset Tabular
16451 <lyxtabular version="3" rows="13" columns="2">
16453 <column alignment="center" valignment="top" width="0pt">
16454 <column alignment="center" valignment="top" width="0pt">
16456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16459 \begin_layout Plain Layout
16461 \begin_inset Note Note
16464 \begin_layout Plain Layout
16471 is only used as spacer.
16481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16484 \begin_layout Plain Layout
16492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16495 \begin_layout Plain Layout
16501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16504 \begin_layout Plain Layout
16505 \begin_inset Formula $+$
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16518 \begin_layout Plain Layout
16524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16527 \begin_layout Plain Layout
16528 \begin_inset Formula $-$
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16541 \begin_layout Plain Layout
16549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16552 \begin_layout Plain Layout
16553 \begin_inset Formula $\pm$
16563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16566 \begin_layout Plain Layout
16574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16577 \begin_layout Plain Layout
16578 \begin_inset Formula $\mp$
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16591 \begin_layout Plain Layout
16599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16602 \begin_layout Plain Layout
16603 \begin_inset Formula $\cdot$
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16616 \begin_layout Plain Layout
16624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16627 \begin_layout Plain Layout
16628 \begin_inset Formula $\times$
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16641 \begin_layout Plain Layout
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Plain Layout
16653 \begin_inset Formula $\div$
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16666 \begin_layout Plain Layout
16670 \begin_layout Plain Layout
16683 \begin_layout Plain Layout
16695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16698 \begin_layout Plain Layout
16699 \begin_inset Formula $*$
16709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16712 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16723 \begin_layout Plain Layout
16724 \begin_inset Formula $\star$
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16737 \begin_layout Plain Layout
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16748 \begin_layout Plain Layout
16749 \begin_inset Formula $\circ$
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16762 \begin_layout Plain Layout
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16774 \begin_inset Formula $\diamond$
16784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16787 \begin_layout Plain Layout
16795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16798 \begin_layout Plain Layout
16799 \begin_inset Formula $\bullet$
16813 \begin_inset space \hfill{}
16817 \begin_inset Tabular
16818 <lyxtabular version="3" rows="13" columns="2">
16820 <column alignment="center" valignment="top" width="0pt">
16821 <column alignment="center" valignment="top" width="0pt">
16823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16826 \begin_layout Plain Layout
16832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16835 \begin_layout Plain Layout
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16846 \begin_layout Plain Layout
16854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16858 \begin_inset Formula $\nabla$
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16882 \begin_layout Plain Layout
16883 \begin_inset Formula $\bigtriangledown$
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16896 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $\bigtriangleup$
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\Box$
16943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\cap$
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\cup$
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\dagger$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\ddagger$
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\wr$
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\bigcirc$
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17096 \begin_layout Plain Layout
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17107 \begin_layout Plain Layout
17108 \begin_inset Formula $\wedge$
17118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17121 \begin_layout Plain Layout
17129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17132 \begin_layout Plain Layout
17133 \begin_inset Formula $\vee$
17147 \begin_inset space \hfill{}
17151 \begin_inset Tabular
17152 <lyxtabular version="3" rows="13" columns="2">
17154 <column alignment="center" valignment="top" width="0pt">
17155 <column alignment="center" valignment="top" width="0pt">
17157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17169 \begin_layout Plain Layout
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\oplus$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\ominus$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\otimes$
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\oslash$
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\odot$
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\amalg$
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\uplus$
17352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17355 \begin_layout Plain Layout
17363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17366 \begin_layout Plain Layout
17367 \begin_inset Formula $\setminus$
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17391 \begin_layout Plain Layout
17392 \begin_inset Formula $\sqcap$
17402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17405 \begin_layout Plain Layout
17413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17416 \begin_layout Plain Layout
17417 \begin_inset Formula $\sqcup$
17427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17430 \begin_layout Plain Layout
17438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17441 \begin_layout Plain Layout
17442 \begin_inset Formula $\triangleleft$
17452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17455 \begin_layout Plain Layout
17463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17466 \begin_layout Plain Layout
17467 \begin_inset Formula $\triangleright$
17481 \begin_inset space \hfill{}
17487 \begin_layout Standard
17488 All binary operators can also be inserted via the math toolbar button
17489 \begin_inset Graphics
17490 filename ../images/math/pm.png
17498 \begin_layout Standard
17499 To typeset the Laplace operator also
17516 \begin_inset Formula $\nabla^{2}$
17519 ) can be used instead of
17528 \begin_layout Standard
17535 Insert\SpecialChar \menuseparator
17547 \begin_layout Subsection
17548 Self-defined Operators
17549 \begin_inset CommandInset label
17551 name "sub:Self-defined-Operators"
17559 \begin_layout Plain Layout
17560 Operators ! self-defined
17568 \begin_layout Standard
17569 With the help of the command
17573 DeclareMathOperator
17579 \begin_layout Plain Layout
17584 DeclareMathOperator
17589 custom operators can be defined in the LaTeX-preamble.
17590 Its command scheme is:
17593 \begin_layout Standard
17598 DeclareMathOperator{new command}{display}
17601 \begin_layout Standard
17602 Display can be characters or symbols that define how the operator looks
17604 To define a big operator a * is set behind the command.
17605 All self-defined big operators can have limits as described in
17606 \begin_inset CommandInset ref
17608 reference "sub:Operator-Limits"
17615 \begin_layout Standard
17616 For example the LaTeX-preamble line
17619 \begin_layout Standard
17624 DeclareMathOperator*{
17631 \begin_layout Standard
17632 defines the command
17638 , that inserts a big operator consisting of the lozenge symbol from
17639 \begin_inset CommandInset ref
17641 reference "sub:Miscellaneous-Symbols"
17646 \begin_inset Formula \[
17647 \Lozenge_{n=1}^{\infty}\]
17651 The command for this formula is:
17662 \begin_inset Formula $\to$
17668 \begin_layout Standard
17669 \begin_inset VSpace bigskip
17672 When self-defined operators are not used several times in the document,
17673 they can also be defined with the commands
17683 \begin_layout Plain Layout
17701 \begin_layout Plain Layout
17709 , which have the following scheme:
17712 \begin_layout Standard
17726 \begin_layout Standard
17733 defines big operators,
17742 \begin_layout Standard
17750 \begin_inset space \thinspace{}
17754 \begin_inset space \space{}
17757 be used to use one limit for several operators:
17760 \begin_layout Standard
17761 \begin_inset Formula \[
17762 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17769 \begin_layout Standard
17770 The command for the formula above is:
17771 \begin_inset Newline newline
17790 \begin_layout Plain Layout
17802 \begin_inset Formula $\to$
17811 \begin_layout Plain Layout
17825 \begin_layout Section
17830 \begin_layout Plain Layout
17839 \begin_layout Subsection
17841 \begin_inset CommandInset label
17843 name "sub:Font-Styles"
17851 \begin_layout Plain Layout
17860 \begin_layout Standard
17861 Latin letters in formulas can be set in one of the following font styles:
17862 \begin_inset VSpace -2mm
17868 \begin_layout Standard
17870 \begin_inset Tabular
17871 <lyxtabular version="3" rows="6" columns="3">
17873 <column alignment="center" valignment="top" width="0">
17874 <column alignment="center" valignment="top" width="0">
17875 <column alignment="center" valignment="top" width="0">
17877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17880 \begin_layout Plain Layout
17886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17889 \begin_layout Plain Layout
17895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17898 \begin_layout Plain Layout
17906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17909 \begin_layout Plain Layout
17918 \begin_layout Plain Layout
17934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17937 \begin_layout Plain Layout
17938 \begin_inset Formula $\mathbb{ABC}$
17946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17949 \begin_layout Plain Layout
17962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17965 \begin_layout Plain Layout
17974 \begin_layout Plain Layout
17990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17993 \begin_layout Plain Layout
17994 \begin_inset Formula $\mathbf{AbC}$
18002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18005 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18021 \begin_layout Plain Layout
18030 \begin_layout Plain Layout
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18049 \begin_layout Plain Layout
18050 \begin_inset Formula $\boldsymbol{AbC}$
18058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18061 \begin_layout Plain Layout
18064 arg "font-boldsymbol"
18074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18077 \begin_layout Plain Layout
18086 \begin_layout Plain Layout
18102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18105 \begin_layout Plain Layout
18106 \begin_inset Formula $\mathcal{ABC}$
18114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18117 \begin_layout Plain Layout
18130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18133 \begin_layout Plain Layout
18142 \begin_layout Plain Layout
18158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18161 \begin_layout Plain Layout
18162 \begin_inset Formula $\mathfrak{AbC}$
18170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18173 \begin_layout Plain Layout
18187 \begin_layout Standard
18189 \begin_inset Tabular
18190 <lyxtabular version="3" rows="5" columns="3">
18192 <column alignment="center" valignment="top" width="0">
18193 <column alignment="center" valignment="top" width="0">
18194 <column alignment="center" valignment="top" width="0">
18196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18199 \begin_layout Plain Layout
18205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18208 \begin_layout Plain Layout
18214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18217 \begin_layout Plain Layout
18225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18228 \begin_layout Plain Layout
18237 \begin_layout Plain Layout
18253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18256 \begin_layout Plain Layout
18257 \begin_inset Formula $\mathit{AbC}$
18265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18268 \begin_layout Plain Layout
18276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18279 \begin_layout Plain Layout
18288 \begin_layout Plain Layout
18304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18307 \begin_layout Plain Layout
18308 \begin_inset Formula $\mathrm{AbC}$
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18319 \begin_layout Plain Layout
18332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18335 \begin_layout Plain Layout
18344 \begin_layout Plain Layout
18360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18363 \begin_layout Plain Layout
18364 \begin_inset Formula $\mathsf{AbC}$
18372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18375 \begin_layout Plain Layout
18388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18391 \begin_layout Plain Layout
18400 \begin_layout Plain Layout
18416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18419 \begin_layout Plain Layout
18420 \begin_inset Formula $\mathtt{AbC}$
18428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18431 \begin_layout Plain Layout
18434 arg "font-typewriter"
18450 \begin_layout Standard
18451 \begin_inset Note Greyedout
18454 \begin_layout Plain Layout
18471 can only be used for big letters.
18479 \begin_layout Standard
18480 Predefined is the style
18489 \begin_layout Standard
18490 The style commands work also for letters in mathematical constructs:
18491 \begin_inset Formula \[
18492 \mathfrak{A=\frac{b}{C}}\]
18499 \begin_layout Standard
18500 Characters in mathematical text don't appear in a math font style but in
18501 the text font style
18508 That their style can't be set correctly via the text style dialog is a
18513 \begin_layout Plain Layout
18514 \begin_inset CommandInset href
18516 name "LyX-bug #4629"
18517 target "http://www.lyx.org/trac/ticket/4629"
18529 \begin_layout Standard
18530 Instead of the style commands the dialog
18532 Edit\SpecialChar \menuseparator
18533 Math\SpecialChar \menuseparator
18536 or the toolbar button
18537 \begin_inset Graphics
18538 filename ../images/math/font.png
18546 \begin_layout Subsection
18548 \begin_inset CommandInset label
18550 name "sub:Bold-Formulas"
18558 \begin_layout Plain Layout
18567 \begin_layout Standard
18568 To make a complete formula bold, the command
18574 from the previous subsection cannot be used, because it doesn't work for
18575 small Greek letters.
18576 Furthermore it prints Latin letters always upright, like in the following
18580 \begin_layout Standard
18581 \begin_inset Formula \[
18582 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18589 \begin_layout Standard
18590 To display the formula correctly, the command
18597 \begin_inset Formula \[
18598 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18602 It is also possible to set the formula in a
18604 boldmath environment
18607 This environment is created by inserting the command
18615 \begin_layout Plain Layout
18626 To end the environment, the command
18634 \begin_layout Plain Layout
18644 is inserted in TeX-mode.
18648 \begin_layout Plain Layout
18658 \begin_inset Formula \[
18659 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18667 \begin_layout Plain Layout
18679 \begin_layout Subsection
18684 \begin_layout Plain Layout
18693 \begin_layout Standard
18694 Formulas can be colored like normal text: Highlight a formula or a formula
18700 Here is a formula in magenta:
18701 \begin_inset Formula \[
18702 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18709 \begin_layout Standard
18710 You can also define your own colors as described in
18711 \begin_inset CommandInset ref
18713 reference "sub:Colored-Boxes"
18718 They can be used with the TeX code command
18728 \begin_layout Plain Layout
18739 \begin_layout Standard
18744 textcolor{color}{characters or formula}
18747 \begin_layout Standard
18748 The following example was colored completely dark green and partly red:
18751 \begin_layout Standard
18755 \begin_layout Plain Layout
18759 textcolor{darkgreen}{
18765 \begin_inset Formula \[
18766 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18774 \begin_layout Plain Layout
18784 \begin_layout Standard
18785 Due to a bug in LyX only complete formulas can be colored with self-defined
18790 \begin_layout Plain Layout
18791 \begin_inset CommandInset href
18793 name "LyX-bug #5269"
18794 target "http://www.lyx.org/trac/ticket/5269"
18806 \begin_layout Subsection
18808 \begin_inset CommandInset label
18810 name "sub:Font-Sizes"
18818 \begin_layout Plain Layout
18827 \begin_layout Standard
18828 For characters in formulas there are, analog to characters in text, the
18829 following size commands:
18832 \begin_layout Standard
18876 \begin_inset Newline newline
18898 \begin_layout Standard
18899 The size produced by the commands depends on the document font size, that
18900 corresponds with the command
18907 The other commands produce smaller or larger sizes than
18914 The font size can however not exceed a certain value.
18915 Is for example the document font size 12
18916 \begin_inset space \thinspace{}
18925 switches to the same size as
18935 \begin_layout Standard
18936 A size command is inserted in TeX-mode before the formula and sets the size
18937 for all following formula and text characters.
18938 To switch back to the initial size, the command
18944 is inserted behind the formula in TeX-mode.
18947 \begin_layout Standard
18948 Within a formula the size can only be changed for symbols or letters in
18950 To do this, the size command is inserted in mathematical text.
18951 All following characters until the end of the mathematical text or until
18952 another size command will have the selected size.
18954 \begin_inset VSpace -2mm
18960 \begin_layout Standard
18964 \begin_layout Plain Layout
18974 \begin_inset Formula \[
18975 A=\frac{B}{c}\cdot\maltese\]
18980 \begin_inset Formula \[
18981 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18989 \begin_layout Plain Layout
19001 \begin_layout Standard
19002 \begin_inset VSpace medskip
19005 Before both formulas the command
19012 The command for the second formula is:
19013 \begin_inset Newline newline
19024 \begin_layout Plain Layout
19039 \begin_layout Plain Layout
19054 \begin_layout Plain Layout
19069 \begin_layout Plain Layout
19079 \begin_inset Formula $\to$
19083 \begin_inset Formula $\to$
19087 \begin_inset Newline newline
19091 \begin_inset space \hspace*{}
19105 \begin_layout Plain Layout
19120 \begin_layout Plain Layout
19135 \begin_layout Plain Layout
19147 \begin_layout Standard
19148 If a symbol cannot be displayed in different sizes, it will always be displayed
19149 in the default size.
19152 \begin_layout Section
19157 \begin_layout Plain Layout
19166 \begin_layout Standard
19167 All Greek letters can also be inserted via the toolbar button
19168 \begin_inset Graphics
19169 filename ../images/math/alpha.png
19177 \begin_layout Subsection
19182 \begin_layout Plain Layout
19183 Greek letters ! small
19191 \begin_layout Standard
19192 \begin_inset space \hfill{}
19196 \begin_inset Tabular
19197 <lyxtabular version="3" rows="11" columns="2">
19199 <column alignment="center" valignment="top" width="0pt">
19200 <column alignment="center" valignment="top" width="0pt">
19202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19205 \begin_layout Plain Layout
19211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19214 \begin_layout Plain Layout
19222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19225 \begin_layout Plain Layout
19233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19236 \begin_layout Plain Layout
19237 \begin_inset Formula $\alpha$
19247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19250 \begin_layout Plain Layout
19258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19261 \begin_layout Plain Layout
19262 \begin_inset Formula $\beta$
19272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19275 \begin_layout Plain Layout
19283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19286 \begin_layout Plain Layout
19287 \begin_inset Formula $\gamma$
19297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19300 \begin_layout Plain Layout
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19311 \begin_layout Plain Layout
19312 \begin_inset Formula $\delta$
19322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19325 \begin_layout Plain Layout
19333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19336 \begin_layout Plain Layout
19337 \begin_inset Formula $\epsilon$
19347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19350 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19362 \begin_inset Formula $\varepsilon$
19372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19375 \begin_layout Plain Layout
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19386 \begin_layout Plain Layout
19387 \begin_inset Formula $\zeta$
19397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19400 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19411 \begin_layout Plain Layout
19412 \begin_inset Formula $\eta$
19422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19425 \begin_layout Plain Layout
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19436 \begin_layout Plain Layout
19437 \begin_inset Formula $\theta$
19447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19461 \begin_layout Plain Layout
19462 \begin_inset Formula $\vartheta$
19476 \begin_inset space \hfill{}
19480 \begin_inset Tabular
19481 <lyxtabular version="3" rows="12" columns="2">
19483 <column alignment="center" valignment="top" width="0pt">
19484 <column alignment="center" valignment="top" width="0pt">
19486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19489 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19509 \begin_layout Plain Layout
19517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19520 \begin_layout Plain Layout
19521 \begin_inset Formula $\iota$
19531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19534 \begin_layout Plain Layout
19542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19545 \begin_layout Plain Layout
19546 \begin_inset Formula $\kappa$
19556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19559 \begin_layout Plain Layout
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19570 \begin_layout Plain Layout
19571 \begin_inset Formula $\varkappa$
19581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19584 \begin_layout Plain Layout
19592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19595 \begin_layout Plain Layout
19596 \begin_inset Formula $\lambda$
19606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19609 \begin_layout Plain Layout
19617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19620 \begin_layout Plain Layout
19621 \begin_inset Formula $\mu$
19631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19645 \begin_layout Plain Layout
19646 \begin_inset Formula $\nu$
19656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19659 \begin_layout Plain Layout
19667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19670 \begin_layout Plain Layout
19671 \begin_inset Formula $\xi$
19681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19684 \begin_layout Plain Layout
19690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19693 \begin_layout Plain Layout
19694 \begin_inset Formula $o$
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19707 \begin_layout Plain Layout
19715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19718 \begin_layout Plain Layout
19719 \begin_inset Formula $\pi$
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19732 \begin_layout Plain Layout
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19743 \begin_layout Plain Layout
19744 \begin_inset Formula $\varpi$
19754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19757 \begin_layout Plain Layout
19765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Plain Layout
19769 \begin_inset Formula $\rho$
19783 \begin_inset space \hfill{}
19787 \begin_inset Tabular
19788 <lyxtabular version="3" rows="11" columns="2">
19790 <column alignment="center" valignment="top" width="0pt">
19791 <column alignment="center" valignment="top" width="0pt">
19793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19796 \begin_layout Plain Layout
19802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19805 \begin_layout Plain Layout
19813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19816 \begin_layout Plain Layout
19824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19827 \begin_layout Plain Layout
19828 \begin_inset Formula $\varrho$
19838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19841 \begin_layout Plain Layout
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19852 \begin_layout Plain Layout
19853 \begin_inset Formula $\sigma$
19863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19866 \begin_layout Plain Layout
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19877 \begin_layout Plain Layout
19878 \begin_inset Formula $\varsigma$
19888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19891 \begin_layout Plain Layout
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19902 \begin_layout Plain Layout
19903 \begin_inset Formula $\tau$
19913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19916 \begin_layout Plain Layout
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19927 \begin_layout Plain Layout
19928 \begin_inset Formula $\upsilon$
19938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19941 \begin_layout Plain Layout
19949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19952 \begin_layout Plain Layout
19953 \begin_inset Formula $\phi$
19963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19966 \begin_layout Plain Layout
19974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19977 \begin_layout Plain Layout
19978 \begin_inset Formula $\varphi$
19988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20002 \begin_layout Plain Layout
20003 \begin_inset Formula $\chi$
20013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20016 \begin_layout Plain Layout
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20027 \begin_layout Plain Layout
20028 \begin_inset Formula $\psi$
20038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20041 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Plain Layout
20053 \begin_inset Formula $\omega$
20067 \begin_inset space \hfill{}
20073 \begin_layout Standard
20074 \begin_inset VSpace medskip
20080 \begin_layout Standard
20081 How to create upright Greek letters is explained in
20082 \begin_inset CommandInset ref
20084 reference "sub:Upright-small-Greek"
20091 \begin_layout Subsection
20096 \begin_layout Plain Layout
20097 Greek letters ! big
20105 \begin_layout Standard
20106 \begin_inset space \hfill{}
20110 \begin_inset Tabular
20111 <lyxtabular version="3" rows="7" columns="2">
20113 <column alignment="center" valignment="top" width="0pt">
20114 <column alignment="center" valignment="top" width="0pt">
20116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20119 \begin_layout Plain Layout
20125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20128 \begin_layout Plain Layout
20136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20139 \begin_layout Plain Layout
20147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20150 \begin_layout Plain Layout
20151 \begin_inset Formula $\Gamma$
20161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20164 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20175 \begin_layout Plain Layout
20176 \begin_inset Formula $\Delta$
20186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20189 \begin_layout Plain Layout
20197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20200 \begin_layout Plain Layout
20201 \begin_inset Formula $\Theta$
20211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $\Lambda$
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\Xi$
20261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20264 \begin_layout Plain Layout
20272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20275 \begin_layout Plain Layout
20276 \begin_inset Formula $\Pi$
20290 \begin_inset space \hfill{}
20294 \begin_inset Tabular
20295 <lyxtabular version="3" rows="6" columns="2">
20297 <column alignment="center" valignment="top" width="0pt">
20298 <column alignment="center" valignment="top" width="0pt">
20300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20303 \begin_layout Plain Layout
20309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20312 \begin_layout Plain Layout
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20335 \begin_inset Formula $\Sigma$
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20348 \begin_layout Plain Layout
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20359 \begin_layout Plain Layout
20360 \begin_inset Formula $\Upsilon$
20370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20373 \begin_layout Plain Layout
20381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20384 \begin_layout Plain Layout
20385 \begin_inset Formula $\Phi$
20395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\Psi$
20420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\Omega$
20449 \begin_inset space \hfill{}
20455 \begin_layout Standard
20456 \begin_inset VSpace medskip
20459 That the big Greek letters appear upright is caused by a design bug when
20461 To get correct italic big letters, begin every command with
20466 For example the command
20473 \begin_inset Formula $\varGamma$
20479 \begin_layout Subsection
20484 \begin_layout Plain Layout
20485 Greek letters ! bold
20493 \begin_layout Standard
20494 Greek letters cannot be set with different font styles like Latin letters.
20495 They can only be made bold with the command
20505 \begin_layout Plain Layout
20516 \begin_layout Standard
20518 \begin_inset Tabular
20519 <lyxtabular version="3" rows="3" columns="2">
20521 <column alignment="center" valignment="top" width="0">
20522 <column alignment="center" valignment="top" width="0">
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Plain Layout
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20562 \begin_layout Plain Layout
20563 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20576 \begin_layout Plain Layout
20588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Plain Layout
20592 \begin_inset Formula $\theta\boldsymbol{\theta}$
20608 \begin_layout Section
20613 \begin_layout Plain Layout
20626 \begin_layout Plain Layout
20627 A list with all symbols of most of the LaTeX-packages can be found in
20628 \begin_inset CommandInset citation
20643 \begin_layout Plain Layout
20651 \begin_inset Note Note
20654 \begin_layout Plain Layout
20657 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20660 \begin_layout Plain Layout
20663 texorpdfstring is in section
20664 \begin_inset CommandInset ref
20666 reference "sub:Formulas-in-Section"
20679 \begin_layout Plain Layout
20688 \begin_layout Standard
20689 Many of the symbols listed in this section can also be inserted via the
20691 \begin_inset Graphics
20692 filename ../images/math/nabla.png
20698 \begin_inset Graphics
20699 filename ../images/math/digamma.png
20707 \begin_layout Subsection
20708 Mathematical Symbols
20709 \begin_inset CommandInset label
20711 name "sub:Mathematical-Symbols"
20719 \begin_layout Plain Layout
20720 Symbols ! mathematical
20728 \begin_layout Standard
20729 \begin_inset space \hfill{}
20733 \begin_inset Tabular
20734 <lyxtabular version="3" rows="10" columns="2">
20736 <column alignment="center" valignment="top" width="0pt">
20737 <column alignment="center" valignment="top" width="0pt">
20739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20751 \begin_layout Plain Layout
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20762 \begin_layout Plain Layout
20770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20773 \begin_layout Plain Layout
20774 \begin_inset Formula $\neg$
20784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20787 \begin_layout Plain Layout
20795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20798 \begin_layout Plain Layout
20799 \begin_inset Formula $\Im$
20809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20812 \begin_layout Plain Layout
20820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20823 \begin_layout Plain Layout
20824 \begin_inset Formula $\Re$
20834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20837 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20849 \begin_inset Formula $\aleph$
20859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20862 \begin_layout Plain Layout
20870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20873 \begin_layout Plain Layout
20874 \begin_inset Formula $\partial$
20884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20887 \begin_layout Plain Layout
20895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20898 \begin_layout Plain Layout
20899 \begin_inset Formula $\infty$
20909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20912 \begin_layout Plain Layout
20920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20923 \begin_layout Plain Layout
20924 \begin_inset Formula $\wp$
20934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20937 \begin_layout Plain Layout
20945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20948 \begin_layout Plain Layout
20949 \begin_inset Formula $\imath$
20959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20962 \begin_layout Plain Layout
20970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20973 \begin_layout Plain Layout
20974 \begin_inset Formula $\jmath$
20988 \begin_inset space \hfill{}
20992 \begin_inset Tabular
20993 <lyxtabular version="3" rows="10" columns="2">
20995 <column alignment="center" valignment="top" width="0pt">
20996 <column alignment="center" valignment="top" width="0pt">
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21012 \begin_inset Note Note
21015 \begin_layout Plain Layout
21022 is only used as spacer.
21034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21037 \begin_layout Plain Layout
21045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21048 \begin_layout Plain Layout
21049 \begin_inset Formula $\forall$
21059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21062 \begin_layout Plain Layout
21070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21073 \begin_layout Plain Layout
21074 \begin_inset Formula $\exists$
21084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21087 \begin_layout Plain Layout
21095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21098 \begin_layout Plain Layout
21099 \begin_inset Formula $\nexists$
21109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21112 \begin_layout Plain Layout
21120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21123 \begin_layout Plain Layout
21124 \begin_inset Formula $\emptyset$
21134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21137 \begin_layout Plain Layout
21145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21148 \begin_layout Plain Layout
21149 \begin_inset Formula $\varnothing$
21159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21173 \begin_layout Plain Layout
21174 \begin_inset Formula $\dag$
21184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21187 \begin_layout Plain Layout
21195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21198 \begin_layout Plain Layout
21199 \begin_inset Formula $\ddag$
21209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21212 \begin_layout Plain Layout
21220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21223 \begin_layout Plain Layout
21227 \begin_layout Plain Layout
21237 \begin_inset Formula $\complement$
21244 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21261 \begin_layout Plain Layout
21269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21272 \begin_layout Plain Layout
21273 \begin_inset Formula $\Bbbk$
21287 \begin_inset space \hfill{}
21291 \begin_inset Tabular
21292 <lyxtabular version="3" rows="10" columns="2">
21294 <column alignment="center" valignment="top" width="0pt">
21295 <column alignment="center" valignment="top" width="0pt">
21297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21300 \begin_layout Plain Layout
21306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Plain Layout
21317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21320 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21332 \begin_inset Formula $\prime$
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\backprime$
21367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\mho$
21392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Plain Layout
21407 \begin_inset Formula $\triangle$
21417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Plain Layout
21432 \begin_inset Formula $\angle$
21442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\measuredangle$
21467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Plain Layout
21482 \begin_inset Formula $\sphericalangle$
21492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21495 \begin_layout Plain Layout
21503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Plain Layout
21507 \begin_inset Formula $\top$
21517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21520 \begin_layout Plain Layout
21528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21531 \begin_layout Plain Layout
21532 \begin_inset Formula $\bot$
21546 \begin_inset space \hfill{}
21552 \begin_layout Subsection
21553 Miscellaneous Symbols
21554 \begin_inset CommandInset label
21556 name "sub:Miscellaneous-Symbols"
21564 \begin_layout Plain Layout
21565 Symbols ! miscellaneous
21573 \begin_layout Standard
21576 \begin_inset Tabular
21577 <lyxtabular version="3" rows="10" columns="2">
21579 <column alignment="center" valignment="top" width="0pt">
21580 <column alignment="center" valignment="top" width="0pt">
21582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21585 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21605 \begin_layout Plain Layout
21613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21616 \begin_layout Plain Layout
21617 \begin_inset Formula $\flat$
21627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21630 \begin_layout Plain Layout
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21641 \begin_layout Plain Layout
21642 \begin_inset Formula $\natural$
21652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21655 \begin_layout Plain Layout
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21666 \begin_layout Plain Layout
21667 \begin_inset Formula $\sharp$
21677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\surd$
21702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21705 \begin_layout Plain Layout
21713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21716 \begin_layout Plain Layout
21717 \begin_inset Formula $\checkmark$
21727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21730 \begin_layout Plain Layout
21738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21741 \begin_layout Plain Layout
21742 \begin_inset Formula $\yen$
21752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21755 \begin_layout Plain Layout
21763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21766 \begin_layout Plain Layout
21767 \begin_inset Formula $\pounds$
21777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21780 \begin_layout Plain Layout
21786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21789 \begin_layout Plain Layout
21790 \begin_inset Formula $\$$
21800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21803 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21812 \begin_layout Plain Layout
21813 \begin_inset Formula $§$
21827 \begin_inset Tabular
21828 <lyxtabular version="3" rows="10" columns="2">
21830 <column alignment="center" valignment="top" width="0">
21831 <column alignment="center" valignment="top" width="0">
21833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21836 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21856 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21867 \begin_layout Plain Layout
21868 \begin_inset Formula $\hbar$
21878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21881 \begin_layout Plain Layout
21889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21892 \begin_layout Plain Layout
21893 \begin_inset Formula $\hslash$
21903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21906 \begin_layout Plain Layout
21914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21917 \begin_layout Plain Layout
21918 \begin_inset Formula $\clubsuit$
21928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21931 \begin_layout Plain Layout
21939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21942 \begin_layout Plain Layout
21943 \begin_inset Formula $\spadesuit$
21953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21956 \begin_layout Plain Layout
21964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21967 \begin_layout Plain Layout
21968 \begin_inset Formula $\bigstar$
21978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21981 \begin_layout Plain Layout
21989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21992 \begin_layout Plain Layout
21993 \begin_inset Formula $\blacklozenge$
22003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22006 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22017 \begin_layout Plain Layout
22018 \begin_inset Formula $\blacktriangle$
22028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22031 \begin_layout Plain Layout
22039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22042 \begin_layout Plain Layout
22043 \begin_inset Formula $\blacktriangledown$
22053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22056 \begin_layout Plain Layout
22064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22067 \begin_layout Plain Layout
22068 \begin_inset Formula $\bullet$
22082 \begin_inset Tabular
22083 <lyxtabular version="3" rows="10" columns="2">
22085 <column alignment="center" valignment="top" width="0pt">
22086 <column alignment="center" valignment="top" width="0pt">
22088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22091 \begin_layout Plain Layout
22097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22100 \begin_layout Plain Layout
22108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22111 \begin_layout Plain Layout
22119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22123 \begin_inset Formula $\diamondsuit$
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22136 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22148 \begin_inset Formula $\Diamond$
22158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22161 \begin_layout Plain Layout
22169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22173 \begin_inset Formula $\heartsuit$
22183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22186 \begin_layout Plain Layout
22194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22198 \begin_inset Formula $\P$
22208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22211 \begin_layout Plain Layout
22219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22222 \begin_layout Plain Layout
22223 \begin_inset Formula $\copyright$
22233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22236 \begin_layout Plain Layout
22244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22247 \begin_layout Plain Layout
22248 \begin_inset Formula $\circledR$
22258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\maltese$
22283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22298 \begin_inset Formula $\diagup$
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22322 \begin_layout Plain Layout
22323 \begin_inset Formula $\diagdown$
22339 \begin_layout Standard
22340 \begin_inset VSpace medskip
22343 More symbols are listed in
22344 \begin_inset CommandInset ref
22346 reference "sub:Miscellaneous-special-Characters"
22353 \begin_layout Standard
22354 Some symbols can be displayed in different sizes, see
22355 \begin_inset CommandInset ref
22357 reference "sub:Font-Sizes"
22364 \begin_layout Subsection
22369 \begin_layout Plain Layout
22370 Symbols ! Euro-symbol
22379 \begin_layout Plain Layout
22386 \begin_layout Plain Layout
22403 \begin_layout Standard
22404 To use the Euro symbol in formulas, the LaTeX-package
22412 \begin_layout Plain Layout
22418 must be installed and loaded with the LaTeX-preamble line
22421 \begin_layout Standard
22426 usepackage[gennarrow]{eurosym}
22429 \begin_layout Standard
22430 The Euro symbol can now be inserted with the command
22440 \begin_layout Plain Layout
22451 \begin_layout Standard
22452 The Euro symbol can directly be inserted with the € key in mathematical
22453 text, without having
22468 can also be inserted in TeX-mode.
22469 The official currency symbol can then be inserted with the command
22479 \begin_layout Plain Layout
22487 , that is only available in TeX-mode.
22490 \begin_layout Standard
22494 \begin_layout Plain Layout
22504 \begin_inset Note Note
22507 \begin_layout Plain Layout
22508 The following table will only be displayed when the LaTeX-package
22520 \begin_layout Standard
22521 An overview about the different Euro symbols:
22524 \begin_layout Standard
22526 \begin_inset Tabular
22527 <lyxtabular version="3" rows="4" columns="3">
22529 <column alignment="center" valignment="top" width="0pt">
22530 <column alignment="center" valignment="top" width="0pt">
22531 <column alignment="center" valignment="top" width="0pt">
22533 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22536 \begin_layout Plain Layout
22542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22565 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22574 \begin_layout Plain Layout
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22585 \begin_layout Plain Layout
22586 \begin_inset Formula $\euro$
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\mbox{€}$
22628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22655 \begin_layout Plain Layout
22677 \begin_layout Standard
22681 \begin_layout Plain Layout
22691 \begin_inset Note Note
22694 \begin_layout Plain Layout
22695 The following will be displayed when the LaTeX-package
22707 \begin_layout Standard
22708 You need to install the LaTeX-package
22712 to see the rest of this subsection in the output.
22715 \begin_layout Standard
22719 \begin_layout Plain Layout
22731 \begin_layout Standard
22732 \begin_inset Newpage newpage
22738 \begin_layout Section
22740 \begin_inset CommandInset label
22742 name "sec:Relations"
22750 \begin_layout Plain Layout
22760 \begin_layout Plain Layout
22765 \begin_layout Plain Layout
22776 \begin_layout Plain Layout
22791 \begin_layout Standard
22792 All relations can also be inserted via the toolbar button
22793 \begin_inset Graphics
22794 filename ../images/math/leq.png
22802 \begin_layout Standard
22803 \begin_inset space \hfill{}
22807 \begin_inset Tabular
22808 <lyxtabular version="3" rows="17" columns="2">
22810 <column alignment="center" valignment="top" width="0pt">
22811 <column alignment="center" valignment="top" width="0pt">
22813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22816 \begin_layout Plain Layout
22822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22825 \begin_layout Plain Layout
22833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22845 \begin_layout Plain Layout
22846 \begin_inset Formula $<$
22856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22859 \begin_layout Plain Layout
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22870 \begin_layout Plain Layout
22871 \begin_inset Formula $\le$
22881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22884 \begin_layout Plain Layout
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22895 \begin_layout Plain Layout
22896 \begin_inset Formula $\ll$
22906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22909 \begin_layout Plain Layout
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22920 \begin_layout Plain Layout
22921 \begin_inset Formula $\prec$
22931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22934 \begin_layout Plain Layout
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22945 \begin_layout Plain Layout
22946 \begin_inset Formula $\preceq$
22956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22959 \begin_layout Plain Layout
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22970 \begin_layout Plain Layout
22971 \begin_inset Formula $\subset$
22981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22995 \begin_layout Plain Layout
22996 \begin_inset Formula $\subseteq$
23006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23009 \begin_layout Plain Layout
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23020 \begin_layout Plain Layout
23021 \begin_inset Formula $\sqsubseteq$
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23034 \begin_layout Plain Layout
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23045 \begin_layout Plain Layout
23046 \begin_inset Formula $\in$
23056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23059 \begin_layout Plain Layout
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23070 \begin_layout Plain Layout
23071 \begin_inset Formula $\vdash$
23081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23084 \begin_layout Plain Layout
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23095 \begin_layout Plain Layout
23096 \begin_inset Formula $\smile$
23106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23109 \begin_layout Plain Layout
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23120 \begin_layout Plain Layout
23121 \begin_inset Formula $\lhd$
23131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23134 \begin_layout Plain Layout
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23145 \begin_layout Plain Layout
23146 \begin_inset Formula $\unlhd$
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23171 \begin_inset Formula $\gtrless$
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23195 \begin_layout Plain Layout
23196 \begin_inset Formula $\mid$
23206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23220 \begin_layout Plain Layout
23221 \begin_inset Formula $\nmid$
23235 \begin_inset space \hfill{}
23239 \begin_inset Tabular
23240 <lyxtabular version="3" rows="17" columns="2">
23242 <column alignment="center" valignment="top" width="0pt">
23243 <column alignment="center" valignment="top" width="0pt">
23245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23248 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23268 \begin_layout Plain Layout
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23277 \begin_layout Plain Layout
23278 \begin_inset Formula $=$
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23291 \begin_layout Plain Layout
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23302 \begin_layout Plain Layout
23303 \begin_inset Formula $\not=$
23313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23316 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23328 \begin_inset Formula $\equiv$
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23341 \begin_layout Plain Layout
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Plain Layout
23353 \begin_inset Formula $\sim$
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23378 \begin_inset Formula $\simeq$
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23391 \begin_layout Plain Layout
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Plain Layout
23403 \begin_inset Formula $\approx$
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23427 \begin_layout Plain Layout
23428 \begin_inset Formula $\cong$
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23441 \begin_layout Plain Layout
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23452 \begin_layout Plain Layout
23453 \begin_inset Formula $\bowtie$
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23466 \begin_layout Plain Layout
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23477 \begin_layout Plain Layout
23478 \begin_inset Formula $\notin$
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23491 \begin_layout Plain Layout
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23502 \begin_layout Plain Layout
23503 \begin_inset Formula $\perp$
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23516 \begin_layout Plain Layout
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23527 \begin_layout Plain Layout
23528 \begin_inset Formula $\propto$
23538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23541 \begin_layout Plain Layout
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23552 \begin_layout Plain Layout
23553 \begin_inset Formula $\asymp$
23563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23566 \begin_layout Plain Layout
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23577 \begin_layout Plain Layout
23578 \begin_inset Formula $\doteq$
23588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23591 \begin_layout Plain Layout
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23602 \begin_layout Plain Layout
23603 \begin_inset Formula $\circeq$
23613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23616 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23627 \begin_layout Plain Layout
23628 \begin_inset Formula $\models$
23638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\widehat{=}$
23667 \begin_inset space \hfill{}
23671 \begin_inset Tabular
23672 <lyxtabular version="3" rows="17" columns="2">
23674 <column alignment="center" valignment="top" width="0pt">
23675 <column alignment="center" valignment="top" width="0pt">
23677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23680 \begin_layout Plain Layout
23686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23689 \begin_layout Plain Layout
23697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23700 \begin_layout Plain Layout
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23709 \begin_layout Plain Layout
23710 \begin_inset Formula $>$
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23723 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23735 \begin_inset Formula $\ge$
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23759 \begin_layout Plain Layout
23760 \begin_inset Formula $\gg$
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23773 \begin_layout Plain Layout
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23784 \begin_layout Plain Layout
23785 \begin_inset Formula $\succ$
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23798 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23809 \begin_layout Plain Layout
23810 \begin_inset Formula $\succeq$
23820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23823 \begin_layout Plain Layout
23831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23834 \begin_layout Plain Layout
23835 \begin_inset Formula $\supset$
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23859 \begin_layout Plain Layout
23860 \begin_inset Formula $\supseteq$
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23873 \begin_layout Plain Layout
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23884 \begin_layout Plain Layout
23885 \begin_inset Formula $\sqsupseteq$
23895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23898 \begin_layout Plain Layout
23906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23909 \begin_layout Plain Layout
23910 \begin_inset Formula $\ni$
23920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23923 \begin_layout Plain Layout
23931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23934 \begin_layout Plain Layout
23935 \begin_inset Formula $\dashv$
23945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23948 \begin_layout Plain Layout
23956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23959 \begin_layout Plain Layout
23960 \begin_inset Formula $\frown$
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23984 \begin_layout Plain Layout
23985 \begin_inset Formula $\rhd$
23995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24009 \begin_layout Plain Layout
24010 \begin_inset Formula $\unrhd$
24020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24023 \begin_layout Plain Layout
24031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24034 \begin_layout Plain Layout
24035 \begin_inset Formula $\lessgtr$
24045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24048 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Plain Layout
24060 \begin_inset Formula $\parallel$
24070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24073 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24085 \begin_inset Formula $\nparallel$
24099 \begin_inset space \hfill{}
24105 \begin_layout Standard
24106 \begin_inset VSpace medskip
24121 are bigger than the equal looking operators
24136 \begin_layout Standard
24137 Relations are, in contrary to symbols, always surrounded by space.
24140 \begin_layout Standard
24141 Relations with labels can be created with the command
24151 \begin_layout Plain Layout
24162 \begin_layout Standard
24164 \begin_inset Tabular
24165 <lyxtabular version="3" rows="2" columns="2">
24167 <column alignment="center" valignment="top" width="0">
24168 <column alignment="center" valignment="top" width="0">
24170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24182 \begin_layout Plain Layout
24184 \begin_inset Note Note
24187 \begin_layout Plain Layout
24194 is only used as spacer.
24206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24216 \begin_layout Plain Layout
24233 \begin_layout Plain Layout
24243 \begin_inset Formula $\downarrow$
24252 \begin_layout Plain Layout
24265 \begin_layout Plain Layout
24279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24282 \begin_layout Plain Layout
24283 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24299 \begin_layout Section
24303 \begin_layout Subsection
24304 Predefined Functions
24305 \begin_inset CommandInset label
24307 name "sub:Predefined-Functions"
24315 \begin_layout Plain Layout
24316 Functions ! predefined
24324 \begin_layout Standard
24325 In general, variables are set
24329 in mathematical expressions, but not function names, because
24330 \begin_inset Formula $sin$
24333 could be misunderstood as
24334 \begin_inset Formula $s\cdot i\cdot n$
24338 Therefore there are predefined functions, that are additionally a bit separated
24340 They are inserted as commands starting with a backslash before their name.
24343 \begin_layout Standard
24345 \begin_inset Tabular
24346 <lyxtabular version="3" rows="2" columns="4">
24348 <column alignment="center" valignment="top" width="0pt">
24349 <column alignment="center" valignment="top" width="0pt">
24350 <column alignment="center" valignment="top" width="0pt">
24351 <column alignment="center" valignment="top" width="0pt">
24353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24403 \begin_layout Plain Layout
24404 \begin_inset Formula $Asin(x)+B$
24412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24415 \begin_layout Plain Layout
24423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24426 \begin_layout Plain Layout
24427 \begin_inset Formula $A\sin(x)+B$
24443 \begin_layout Standard
24444 The following functions are predefined:
24447 \begin_layout Standard
24448 \begin_inset VSpace -2mm
24454 \begin_layout Standard
24456 \begin_inset Tabular
24457 <lyxtabular version="3" rows="9" columns="4">
24459 <column alignment="center" valignment="top" width="0pt">
24460 <column alignment="center" valignment="top" width="0pt">
24461 <column alignment="center" valignment="top" width="0pt">
24462 <column alignment="center" valignment="top" width="0pt">
24464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24467 \begin_layout Plain Layout
24473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24476 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24485 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24505 \begin_layout Plain Layout
24513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24551 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24562 \begin_layout Plain Layout
24570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24573 \begin_layout Plain Layout
24581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24584 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24608 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24619 \begin_layout Plain Layout
24627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24630 \begin_layout Plain Layout
24640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24643 \begin_layout Plain Layout
24651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24654 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24665 \begin_layout Plain Layout
24673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24676 \begin_layout Plain Layout
24686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24689 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24700 \begin_layout Plain Layout
24708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24722 \begin_layout Plain Layout
24732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24735 \begin_layout Plain Layout
24743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24746 \begin_layout Plain Layout
24754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24768 \begin_layout Plain Layout
24778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24781 \begin_layout Plain Layout
24789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24792 \begin_layout Plain Layout
24800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24803 \begin_layout Plain Layout
24811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24814 \begin_layout Plain Layout
24824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24827 \begin_layout Plain Layout
24835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24838 \begin_layout Plain Layout
24846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24849 \begin_layout Plain Layout
24857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24860 \begin_layout Plain Layout
24876 \begin_layout Standard
24877 They can also be inserted with the math toolbar button
24878 \begin_inset Graphics
24879 filename ../images/math/functions.png
24887 \begin_layout Subsection
24888 Self-defined Functions
24892 \begin_layout Plain Layout
24893 Functions ! self-defined
24901 \begin_layout Standard
24902 To use a function that is not predefined, like for example the sign function
24903 sgn(x), there are two possibilities:
24906 \begin_layout Itemize
24907 Define the function by inserting the following line to the LaTeX-preamble
24911 \begin_layout Plain Layout
24916 DeclareMathOperator
24919 \begin_inset CommandInset ref
24921 reference "sub:Self-defined-Operators"
24931 \begin_inset Newline newline
24935 \begin_inset VSpace -3mm
24939 \begin_inset Newline newline
24946 DeclareMathOperator{
24954 \begin_layout Plain Layout
24959 DeclareMathOperator
24965 \begin_inset Newline newline
24969 \begin_inset VSpace -2mm
24973 \begin_inset Newline newline
24976 Now the new defined function can be called with the command
24985 \begin_layout Itemize
24986 Write the the formula as usual, mark the formula name, in our example the
24991 , and change it to mathematical text.
24992 At last a space is inserted between prefactor and function.
24995 \begin_layout Standard
24996 The result is the same with both methods as with a predefined function
25000 \begin_layout Plain Layout
25001 In LyX self-defined functions are displayed red, predefined ones black.
25009 \begin_layout Standard
25011 \begin_inset Tabular
25012 <lyxtabular version="3" rows="3" columns="2">
25014 <column alignment="center" valignment="top" width="0pt">
25015 <column alignment="center" valignment="top" width="0pt">
25017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25020 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25029 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25051 \begin_layout Plain Layout
25052 \begin_inset Formula $A\sgn(x)+B$
25062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25069 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25080 \begin_layout Plain Layout
25081 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25097 \begin_layout Standard
25098 The first method is more suitable when the self-defined function should
25099 be used several times.
25102 \begin_layout Subsection
25107 \begin_layout Plain Layout
25116 \begin_layout Standard
25117 For limits there are defined besides
25127 \begin_layout Plain Layout
25147 furthermore the following functions:
25150 \begin_layout Standard
25152 \begin_inset Tabular
25153 <lyxtabular version="3" rows="5" columns="2">
25155 <column alignment="center" valignment="top" width="0">
25156 <column alignment="center" valignment="top" width="0">
25158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25170 \begin_layout Plain Layout
25172 \begin_inset Note Note
25175 \begin_layout Plain Layout
25182 is only used as spacer.
25194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25197 \begin_layout Plain Layout
25205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25208 \begin_layout Plain Layout
25209 \begin_inset Formula $\varliminf$
25219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25233 \begin_layout Plain Layout
25234 \begin_inset Formula $\varlimsup$
25244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25247 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Plain Layout
25259 \begin_inset Formula $\varprojlim$
25269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25283 \begin_layout Plain Layout
25284 \begin_inset Formula $\varinjlim$
25288 \begin_inset Formula $\raisebox{-2.5mm}{}$
25304 \begin_layout Standard
25305 \begin_inset VSpace medskip
25308 The limit is created by inserting a subscript.
25309 It is set right beside the function in an inline formula:
25312 \begin_layout Standard
25314 \begin_inset Tabular
25315 <lyxtabular version="3" rows="2" columns="2">
25317 <column alignment="center" valignment="top" width="0pt">
25318 <column alignment="center" valignment="top" width="0pt">
25320 <cell alignment="center" valignment="top" usebox="none">
25323 \begin_layout Plain Layout
25329 <cell alignment="center" valignment="top" usebox="none">
25332 \begin_layout Plain Layout
25333 \begin_inset space \hspace{}
25338 \begin_inset Note Note
25341 \begin_layout Plain Layout
25348 are used here as spacer.
25360 <cell alignment="center" valignment="top" usebox="none">
25363 \begin_layout Plain Layout
25372 \begin_layout Plain Layout
25385 \begin_layout Plain Layout
25399 <cell alignment="center" valignment="top" usebox="none">
25402 \begin_layout Plain Layout
25403 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25419 \begin_layout Standard
25420 In a displayed formula the limit is set below the formula, as usual:
25421 \begin_inset Formula \[
25429 \begin_layout Subsection
25434 \begin_layout Plain Layout
25435 Functions ! modulo-
25443 \begin_layout Standard
25444 The modulo-function is special, because it exists in four variants.
25447 \begin_layout Standard
25448 The variants in a displayed formula:
25449 \begin_inset Formula \begin{align*}
25450 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25451 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25452 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25453 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25454 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25461 \begin_layout Standard
25462 In an inline formula less space is set before the function names for all
25466 \begin_layout Standard
25467 \begin_inset Newpage newpage
25473 \begin_layout Section
25478 \begin_layout Plain Layout
25487 \begin_layout Subsection
25488 Special Characters in Mathematical Text
25491 \begin_layout Standard
25492 The following commands can only be used in mathematical text or in TeX-mode:
25495 \begin_layout Standard
25496 \begin_inset space \hfill{}
25500 \begin_inset Tabular
25501 <lyxtabular version="3" rows="8" columns="2">
25503 <column alignment="block" valignment="top" width="0">
25504 <column alignment="block" valignment="top" width="0">
25506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25509 \begin_layout Plain Layout
25515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25518 \begin_layout Plain Layout
25526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25529 \begin_layout Plain Layout
25537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25540 \begin_layout Plain Layout
25541 \begin_inset Formula $\textrm{œ}$
25551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25554 \begin_layout Plain Layout
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25565 \begin_layout Plain Layout
25566 \begin_inset Formula $\textrm{Œ}$
25576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25579 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25590 \begin_layout Plain Layout
25591 \begin_inset Formula $\textrm{æ}$
25601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25604 \begin_layout Plain Layout
25612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25615 \begin_layout Plain Layout
25616 \begin_inset Formula $\textrm{Æ}$
25626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25629 \begin_layout Plain Layout
25637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25640 \begin_layout Plain Layout
25641 \begin_inset Formula $\textrm{\aa}$
25651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25654 \begin_layout Plain Layout
25661 \begin_layout Plain Layout
25668 \begin_layout Plain Layout
25689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25692 \begin_layout Plain Layout
25693 \begin_inset Formula $\textrm{Å}$
25703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25706 \begin_layout Plain Layout
25714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25717 \begin_layout Plain Layout
25718 \begin_inset Formula $\textrm{ı}$
25732 \begin_inset space \hfill{}
25736 \begin_inset Tabular
25737 <lyxtabular version="3" rows="8" columns="2">
25739 <column alignment="block" valignment="top" width="0">
25740 <column alignment="center" valignment="top" width="0">
25742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25745 \begin_layout Plain Layout
25747 \begin_inset Note Note
25750 \begin_layout Plain Layout
25752 \begin_inset space \thinspace{}
25755 mm is used for separation, because otherwise the output will be ¡ and ¿
25766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25769 \begin_layout Plain Layout
25777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25780 \begin_layout Plain Layout
25788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25791 \begin_layout Plain Layout
25792 \begin_inset Formula $\textrm{ø}$
25802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25805 \begin_layout Plain Layout
25813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25816 \begin_layout Plain Layout
25817 \begin_inset Formula $\textrm{Ø}$
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25830 \begin_layout Plain Layout
25838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25841 \begin_layout Plain Layout
25842 \begin_inset Formula $\textrm{ł}$
25852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25855 \begin_layout Plain Layout
25863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25866 \begin_layout Plain Layout
25867 \begin_inset Formula $\textrm{Ł}$
25877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25880 \begin_layout Plain Layout
25882 \begin_inset space \hspace{}
25890 \begin_layout Plain Layout
25904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25907 \begin_layout Plain Layout
25908 \begin_inset Formula $\textrm{!`}$
25918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25921 \begin_layout Plain Layout
25923 \begin_inset space \hspace{}
25931 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25949 \begin_inset Formula $\textrm{?`}$
25959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25962 \begin_layout Plain Layout
25970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25973 \begin_layout Plain Layout
25974 \begin_inset Formula $\textrm{ȷ}$
25988 \begin_inset space \hfill{}
25994 \begin_layout Standard
25996 \begin_inset Formula $\textrm{\textrm{Å}}$
26000 \begin_inset Formula $\textrm{\textrm{Ø}}$
26003 can also be inserted via the math toolbar button
26004 \begin_inset Graphics
26005 filename ../images/math/digamma.png
26013 \begin_layout Standard
26014 An exception are the commands
26017 \begin_inset space \hspace{}
26026 \begin_inset space \hspace{}
26032 , because they can be inserted in LyX directly to text.
26035 \begin_layout Subsection
26037 \begin_inset CommandInset label
26039 name "sub:Accents-in-Text"
26047 \begin_layout Plain Layout
26056 \begin_layout Standard
26057 With the following commands all letters can be accented.
26058 The commands must be inserted in TeX-mode.
26061 \begin_layout Standard
26062 \begin_inset space \hfill{}
26066 \begin_inset Tabular
26067 <lyxtabular version="3" rows="8" columns="2">
26069 <column alignment="block" valignment="top" width="0">
26070 <column alignment="block" valignment="top" width="0">
26072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26075 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26084 \begin_layout Plain Layout
26092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26095 \begin_layout Plain Layout
26099 \begin_inset Quotes grd
26107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26110 \begin_layout Plain Layout
26114 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26133 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26144 \begin_layout Plain Layout
26148 \begin_layout Plain Layout
26164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26167 \begin_layout Plain Layout
26174 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26195 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26214 \begin_layout Plain Layout
26222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26225 \begin_layout Plain Layout
26229 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26248 \begin_layout Plain Layout
26255 \begin_layout Plain Layout
26269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26272 \begin_layout Plain Layout
26276 \begin_layout Plain Layout
26292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26295 \begin_layout Plain Layout
26302 \begin_layout Plain Layout
26316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26319 \begin_layout Plain Layout
26323 \begin_layout Plain Layout
26339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26342 \begin_layout Plain Layout
26349 \begin_layout Plain Layout
26363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26366 \begin_layout Plain Layout
26370 \begin_layout Plain Layout
26390 \begin_inset space \hfill{}
26394 \begin_inset Tabular
26395 <lyxtabular version="3" rows="8" columns="2">
26397 <column alignment="block" valignment="top" width="0">
26398 <column alignment="center" valignment="top" width="0">
26400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26403 \begin_layout Plain Layout
26409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26412 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26430 \begin_layout Plain Layout
26444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26447 \begin_layout Plain Layout
26451 \begin_layout Plain Layout
26467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26470 \begin_layout Plain Layout
26478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26481 \begin_layout Plain Layout
26485 \begin_layout Plain Layout
26501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26504 \begin_layout Plain Layout
26511 \begin_layout Plain Layout
26522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26525 \begin_layout Plain Layout
26529 \begin_layout Plain Layout
26545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26548 \begin_layout Plain Layout
26556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26559 \begin_layout Plain Layout
26563 \begin_layout Plain Layout
26579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26582 \begin_layout Plain Layout
26589 \begin_layout Plain Layout
26603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26606 \begin_layout Plain Layout
26610 \begin_layout Plain Layout
26626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26629 \begin_layout Plain Layout
26636 \begin_layout Plain Layout
26650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26653 \begin_layout Plain Layout
26657 \begin_layout Plain Layout
26673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26676 \begin_layout Plain Layout
26683 \begin_layout Plain Layout
26697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26700 \begin_layout Plain Layout
26704 \begin_layout Plain Layout
26724 \begin_inset space \hfill{}
26730 \begin_layout Standard
26731 \begin_inset VSpace medskip
26740 also two different characters can be accented.
26749 \begin_layout Plain Layout
26764 \begin_layout Plain Layout
26776 \begin_layout Standard
26789 can in combination with vowels directly be inserted with the keyboard without
26791 The same applies for the tilde
26795 \begin_layout Plain Layout
26796 This only applies for keyboards where the tilde is defined as accent.
26805 in combination with
26820 \begin_layout Standard
26863 , and accents inserted directly with the keyboard are also available in
26865 For the other accents there are special math commands to be used in formulas,
26867 \begin_inset CommandInset ref
26869 reference "sub:Accents-for-one"
26876 \begin_layout Standard
26877 \begin_inset VSpace bigskip
26880 Furthermore, with the command
26890 \begin_layout Plain Layout
26898 all numbers and letters can be set into a circle, quasi accented with a
26899 circle, similar to the the copyright symbol.
26902 \begin_layout Standard
26904 \begin_inset Tabular
26905 <lyxtabular version="3" rows="3" columns="2">
26907 <column alignment="center" valignment="top" width="0">
26908 <column alignment="center" valignment="top" width="0">
26910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26913 \begin_layout Plain Layout
26919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26924 \begin_inset Note Note
26927 \begin_layout Plain Layout
26934 is only used as spacer.
26946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26949 \begin_layout Plain Layout
26957 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26960 \begin_layout Plain Layout
26964 \begin_layout Plain Layout
26980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26983 \begin_layout Plain Layout
26994 raisebox{-1.5pt}{W}}
26999 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27002 \begin_layout Plain Layout
27003 \begin_inset Formula $\raisebox{4.5mm}{}$
27010 \begin_layout Plain Layout
27028 \begin_inset Formula $\raisebox{-2mm}{}$
27044 \begin_layout Standard
27045 One has to take care that the character fits in the circle.
27056 \begin_layout Plain Layout
27058 \begin_inset CommandInset ref
27060 reference "sub:Font-Sizes"
27069 specifies thereby the size of the circle.
27080 \begin_layout Plain Layout
27082 \begin_inset CommandInset ref
27084 reference "sub:Boxes-without-Frame"
27093 the character can be centered.
27096 \begin_layout Subsection
27101 \begin_layout Plain Layout
27110 \begin_layout Standard
27111 Minuscule numbers are created with the command
27121 \begin_layout Plain Layout
27130 The command can be used in formulas and in TeX-mode.
27131 The command scheme is:
27134 \begin_layout Standard
27139 oldstylenums{number}
27142 \begin_layout Standard
27147 oldstylenums{0123456789
27150 \begin_inset Formula $\oldstylenums{0123456789}$
27156 \begin_layout Subsection
27157 Miscellaneous special Characters
27158 \begin_inset CommandInset label
27160 name "sub:Miscellaneous-special-Characters"
27168 \begin_layout Plain Layout
27169 Special characters ! miscellaneous
27177 \begin_layout Standard
27178 The following characters can only be inserted to formulas by using commands:
27181 \begin_layout Standard
27183 \begin_inset Tabular
27184 <lyxtabular version="3" rows="4" columns="2">
27186 <column alignment="center" valignment="top" width="0">
27187 <column alignment="center" valignment="top" width="0">
27189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27192 \begin_layout Plain Layout
27198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27201 \begin_layout Plain Layout
27209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27212 \begin_layout Plain Layout
27219 \begin_layout Plain Layout
27233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27236 \begin_layout Plain Layout
27237 \begin_inset Formula $\mathcircumflex$
27247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27250 \begin_layout Plain Layout
27258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27261 \begin_layout Plain Layout
27262 \begin_inset Formula $\_$
27272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27275 \begin_layout Plain Layout
27280 \begin_layout Plain Layout
27295 \begin_layout Plain Layout
27308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27311 \begin_layout Plain Layout
27312 \begin_inset Formula $^{\circ}$
27328 \begin_layout Standard
27329 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27330 contains the following line
27334 \begin_layout Plain Layout
27335 More about this is described in
27336 \begin_inset CommandInset ref
27338 reference "sub:Text-Characters-in"
27350 \begin_layout Standard
27355 DeclareInputtext{176}{
27368 \begin_layout Standard
27369 \begin_inset Newpage newpage
27375 \begin_layout Section
27377 \begin_inset CommandInset label
27379 name "sec:Formula-Styles"
27387 \begin_layout Plain Layout
27396 \begin_layout Itemize
27397 There are two different alignment styles:
27401 \begin_layout Description
27402 Centered is the predefined standard
27405 \begin_layout Description
27406 Indented for this the option
27410 must be inserted in the menu
27412 Document\SpecialChar \menuseparator
27418 \begin_inset space ~
27424 \begin_layout Standard
27429 is used, the indentation can be adjusted with the length
27439 \begin_layout Plain Layout
27448 Should the distance be 15
27449 \begin_inset space \thinspace{}
27452 mm, the following command line is inserted in the LaTeX-preamble
27455 \begin_layout Standard
27465 \begin_layout Standard
27466 When no length is specified, the predefined value of 30
27467 \begin_inset space \thinspace{}
27474 \begin_layout Itemize
27475 And two different numbering styles:
27479 \begin_layout Description
27480 Right is the predefined standard
27483 \begin_layout Description
27484 Left for this the option
27488 must be inserted in the menu
27490 Document\SpecialChar \menuseparator
27496 \begin_inset space ~
27503 \begin_layout Standard
27512 can also be used together.
27513 In this case both options are inserted, separated by a comma.
27516 \begin_layout Standard
27517 The chosen styles are used for all displayed formulas of the document.
27518 When both, centered and indented formulas should be created in a document,
27524 The indented formulas are then set in a flalign environment, see
27525 \begin_inset CommandInset ref
27527 reference "sub:Flalign-Environment"
27534 \begin_layout Section
27536 \begin_inset CommandInset label
27538 name "sec:Multiline-Formulas"
27546 \begin_layout Plain Layout
27547 Formula ! multiline
27555 \begin_layout Subsection
27559 \begin_layout Standard
27560 In LyX multiline formulas are created by pressing
27565 arg "newline-insert newline"
27571 This creates either an
27573 eqnarray environment
27575 that is described in
27576 \begin_inset CommandInset ref
27578 reference "sub:Eqnarray-Environment"
27582 or, when the option
27584 Use AMS math package
27586 in the document settings is selected, an
27590 that is described in
27591 \begin_inset CommandInset ref
27593 reference "sub:Standard-align-Environment"
27600 \begin_layout Standard
27601 There are other multiline formula environments that can be created via the
27604 Insert\SpecialChar \menuseparator
27608 These environments are described in the following sections.
27611 \begin_layout Standard
27612 In all multiline formula environments a new line is created by pressing
27616 arg "newline-insert newline"
27620 To add or delete lines, the math toolbar buttons
27621 \begin_inset Graphics
27622 filename ../images/tabular-feature_append-row.png
27628 \begin_inset Graphics
27629 filename ../images/tabular-feature_delete-row.png
27634 , respectively, or the menu
27636 Edit\SpecialChar \menuseparator
27642 \begin_layout Subsubsection
27644 \begin_inset CommandInset label
27646 name "sub:Line-Separation"
27654 \begin_layout Plain Layout
27655 Formula ! multiline ! Line separation
27663 \begin_layout Standard
27664 There is sometimes not enough space in multiline formulas between the lines:
27665 \begin_inset Formula \begin{eqnarray*}
27666 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}\\
27667 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*}
27674 \begin_layout Standard
27675 In LaTeX additional line space is specified as optional argument of the
27677 This is not yet possible in LyX
27681 \begin_layout Plain Layout
27683 \begin_inset CommandInset href
27685 name "LyX-bug #1505"
27686 target "http://www.lyx.org/trac/ticket/1505"
27695 , therefore the whole formula must be inserted in TeX-mode.
27696 To add in our example space, the command
27704 is inserted at the end of the first line.
27709 \begin_layout Plain Layout
27716 \begin_layout Plain Layout
27718 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27721 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27728 \begin_layout Plain Layout
27732 left(B^{2}+x_{0}^{2}
27740 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27745 \begin_layout Plain Layout
27757 \begin_layout Standard
27758 \begin_inset VSpace bigskip
27761 To set the the line separation for all lines in a formula, the length
27771 \begin_layout Plain Layout
27781 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27792 \begin_inset space \thinspace{}
27797 \begin_inset space \thinspace{}
27800 mm additional line separation as in the previous example, the command
27803 \begin_layout Standard
27813 \begin_layout Standard
27814 is inserted in TeX-mode before the formula.
27815 This requires that the LaTeX-package
27823 \begin_layout Plain Layout
27828 is part of every LaTeX standard installation.
27837 \begin_layout Plain Layout
27843 was loaded in LaTeX-preamble with the line
27846 \begin_layout Standard
27854 \begin_layout Standard
27859 \begin_layout Plain Layout
27871 \begin_inset Formula \begin{eqnarray*}
27872 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}\\
27873 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*}
27880 \begin_layout Standard
27884 \begin_layout Plain Layout
27895 To get back to the predefined distance,
27901 is set to the value 3
27902 \begin_inset space \thinspace{}
27908 \begin_layout Subsubsection
27910 \begin_inset CommandInset label
27912 name "sub:Column-Separation"
27920 \begin_layout Plain Layout
27921 Formula ! multiline ! Column separation
27929 \begin_layout Standard
27930 Multiline formulas form a matrix.
27931 A formula in the eqnarray environment is for example a matrix with three
27933 By changing the column separation in this environment, the space beside
27934 the relation sign can be changed.
27937 \begin_layout Standard
27938 The column separation is specified with the length
27948 \begin_layout Plain Layout
27957 \begin_inset Newline newline
27960 column separation = 2
27961 \begin_inset space \thinspace{}
27971 \begin_inset Newline newline
27977 \begin_layout Standard
27987 \begin_layout Standard
27988 inserted in TeX-mode, sets for all following formulas a column separation
27990 \begin_inset space \thinspace{}
27994 To get back to the predefined distance,
28001 \begin_inset space \thinspace{}
28007 \begin_layout Standard
28009 \begin_inset space \thinspace{}
28012 cm column separation:
28016 \begin_layout Plain Layout
28028 \begin_inset Formula \begin{eqnarray*}
28030 C & \ne & A\end{eqnarray*}
28034 A formula with the predefined column separation for matrices of 10
28035 \begin_inset space \thinspace{}
28042 \begin_layout Plain Layout
28054 \begin_inset Formula \begin{eqnarray*}
28056 C & \ne & A\end{eqnarray*}
28063 \begin_layout Subsubsection
28068 \begin_layout Plain Layout
28077 \begin_layout Standard
28078 Long formulas can be typeset using these methods:
28081 \begin_layout Itemize
28082 When one side of the equation is much shorther than the line width, this
28083 one is chosen for the left side and the right side is typeset over two
28085 \begin_inset Formula \begin{eqnarray}
28086 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 \\
28087 & & -\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}
28091 The minus sign at the beginning of the second line does normally not appear
28092 as operator because it is the first character of the line.
28093 Thus it would not be surrounded by space and could not be distinguished
28094 from the fraction bar.
28096 \begin_inset space \thinspace{}
28099 pt space was inserted behind the minus sign with the command
28109 \begin_layout Plain Layout
28117 \begin_inset CommandInset ref
28119 reference "sub:Variable-Space"
28132 \begin_layout Plain Layout
28143 \begin_layout Itemize
28144 When both sides of the equation are too long, the command
28154 \begin_layout Plain Layout
28163 It is inserted to the first column of the first line and effects that all
28164 further insertions overwrite the following columns:
28165 \begin_inset Formula \begin{eqnarray}
28166 \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 \\
28167 & & -\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 \\
28168 & & =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}
28172 After the insertion of
28178 , the cursor is in a purple box that is a bit shifted to the left from the
28180 In this the formula is inserted.
28181 \begin_inset Newline newline
28184 The content of the further lines is inserted to the second or another formula
28186 The greater the column number where it was inserted, the larger the indentation.
28187 \begin_inset VSpace medskip
28191 \begin_inset Newline newline
28195 \begin_inset Note Greyedout
28198 \begin_layout Plain Layout
28199 Note the following when using
28208 \begin_layout Itemize
28209 The formula doesn't use the full page width.
28211 \begin_inset space \thinspace{}
28215 \begin_inset space \space{}
28219 \begin_inset Formula $-B^{2}$
28222 is added to the first line in the above example, it would have been outside
28224 To better use the width, negative space can be inserted at the beginning
28228 \begin_layout Itemize
28229 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28234 \begin_layout Plain Layout
28235 \begin_inset CommandInset href
28237 name "LyX-bug #1429"
28238 target "http://www.lyx.org/trac/ticket/1429"
28247 One can only set the cursor at the beginning of the line and move it with
28256 \begin_layout Itemize
28257 Other methods to set long formulas are offered by the environments described
28259 \begin_inset CommandInset ref
28261 reference "sub:Multline-Environment"
28266 \begin_inset CommandInset ref
28268 reference "sub:Multiline-Formula-Parts"
28275 \begin_layout Subsubsection
28277 \begin_inset CommandInset label
28279 name "sub:Multiline-Brackets"
28287 \begin_layout Plain Layout
28288 Brackets ! for multiline expressions
28296 \begin_layout Standard
28297 For brackets spanning multiple lines the following problem occurs:
28298 \begin_inset Formula \begin{eqnarray*}
28299 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28300 & & \left.\cdots+B-D\right]\end{eqnarray*}
28307 \begin_layout Standard
28308 The closing bracket is smaller than the opening bracket because brackets
28309 with variable size may not span multiple lines.
28312 \begin_layout Standard
28313 To set the bracket size for the second line correctly, the first line is
28324 \begin_layout Plain Layout
28332 and the second line with
28340 \begin_layout Plain Layout
28354 \begin_inset CommandInset ref
28356 reference "sub:Automatic-Bracket-Size"
28371 \begin_layout Plain Layout
28397 \begin_layout Plain Layout
28416 \begin_layout Plain Layout
28435 \begin_layout Plain Layout
28447 \begin_inset Formula $\downarrow$
28456 \begin_layout Plain Layout
28464 is inserted, because the multiplication operator with its limits is the
28465 largest symbol in the first line and this should be the size for the bracket
28466 in the second line.
28469 \begin_layout Standard
28470 The result is this:
28471 \begin_inset Formula \begin{eqnarray*}
28472 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28473 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28480 \begin_layout Subsection
28484 \begin_layout Standard
28485 Align environments can be used for every kind of multiline formulas.
28486 They are specially useful to set several formulas side by side.
28489 \begin_layout Standard
28490 Align environments consist of columns.
28491 The odd columns are right aligned, the even ones left aligned.
28492 Every line in an Align environment can be numbered.
28495 \begin_layout Standard
28496 Align environments are created via the menu
28498 Insert\SpecialChar \menuseparator
28504 Edit\SpecialChar \menuseparator
28505 Math\SpecialChar \menuseparator
28506 Change Formula Type
28508 already existing formulas can be converted to Align environments.
28511 \begin_layout Standard
28512 To add or delete columns, the math toolbar buttons
28513 \begin_inset Graphics
28514 filename ../images/tabular-feature_append-column.png
28520 \begin_inset Graphics
28521 filename ../images/tabular-feature_delete-column.png
28526 , respectively, or the menu
28528 Edit\SpecialChar \menuseparator
28534 \begin_layout Subsubsection
28535 Standard align Environment
28536 \begin_inset CommandInset label
28538 name "sub:Standard-align-Environment"
28546 \begin_layout Plain Layout
28547 Formula ! multiline ! align environment
28555 \begin_layout Standard
28556 This Align environment is created by presssing
28559 arg "newline-insert newline"
28562 in a formula or by the menu
28564 Insert\SpecialChar \menuseparator
28565 Math\SpecialChar \menuseparator
28566 AMS align Environment
28571 \begin_layout Standard
28572 An example for two formulas set side by side, that are created with a four
28573 column align environment:
28574 \begin_inset Formula \begin{align*}
28575 A & =\sin(B) & C & =D\\
28576 C & \ne A & B & \ne D\end{align*}
28580 As it can be seen, the formulas in this environment are placed so as if
28589 \begin_layout Plain Layout
28597 \begin_inset CommandInset ref
28599 reference "sub:Variable-Space"
28610 before the first and after every even column.
28611 When the formula style
28617 \begin_layout Plain Layout
28619 \begin_inset CommandInset ref
28621 reference "sec:Formula-Styles"
28632 is used, the formula is set without the
28638 before the first column.
28641 \begin_layout Subsubsection
28642 Alignat Environment
28646 \begin_layout Plain Layout
28647 Formula ! multiline ! alignat environment
28655 \begin_layout Standard
28656 The alignat environment has no predefined column separation.
28657 It can be inserted manually with the spaces that are described
28658 \begin_inset CommandInset ref
28660 reference "sub:Space"
28667 \begin_layout Standard
28668 The above example in the alignat environment where 1
28669 \begin_inset space \thinspace{}
28672 cm space was inserted at the beginning of the second formula:
28673 \begin_inset Formula \begin{alignat*}{2}
28674 A & =\sin(B) & \hspace{1cm}C & =D\\
28675 C & \ne A & B & \ne D\end{alignat*}
28679 Because the column separation can be set separately for every column, this
28680 environment is especially suitable to set three and more formulas side
28684 \begin_layout Subsubsection
28685 Flalign Environment
28686 \begin_inset CommandInset label
28688 name "sub:Flalign-Environment"
28696 \begin_layout Plain Layout
28697 Formula ! multiline ! flalign environment
28705 \begin_layout Standard
28706 In this environment the first two columns are always set as much as possible
28707 to the left and the last two ones to the right.
28709 \begin_inset Formula \begin{flalign*}
28710 A & =1 & B & =2 & C & =3\\
28711 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28718 \begin_layout Standard
28719 By creating a flalign environment with an odd number of columns where an
28720 empty TeX-brace is inserted to the last column, several formulas in a document
28721 can be set to the left, although the formula style
28726 As example the indented formula
28727 \begin_inset CommandInset ref
28729 reference "eq:VolInt"
28734 \begin_inset Formula \begin{flalign}
28735 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28739 The first two columns contain the formula.
28740 To indent it as with the formula style
28745 \begin_inset space \thinspace{}
28748 pt space was inserted at the beginning of the first column.
28751 \begin_layout Subsection
28752 Eqnarray Environment
28753 \begin_inset CommandInset label
28755 name "sub:Eqnarray-Environment"
28763 \begin_layout Plain Layout
28764 Formula ! multiline ! eqnarray environment
28772 \begin_layout Standard
28773 When this environment has been created, three blue boxes appear.
28774 The content of the first box is right aligned, the content of the last
28776 The content of the middle box appears centered and a bit smaller, because
28777 it is designed to insert there only relation characters.
28778 \begin_inset Formula \begin{eqnarray*}
28779 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28781 A & = & A\end{eqnarray*}
28788 \begin_layout Subsection
28793 \begin_layout Plain Layout
28794 Formula ! multiline ! gather environment
28802 \begin_layout Standard
28803 This environment consists of only one centered column.
28804 Every line can be numbered.
28805 \begin_inset Formula \begin{gather}
28807 X=\textrm{-}1\end{gather}
28814 \begin_layout Subsection
28815 Multline Environment
28816 \begin_inset CommandInset label
28818 name "sub:Multline-Environment"
28826 \begin_layout Plain Layout
28827 Formula ! multiline ! multline environment
28835 \begin_layout Standard
28836 The multline environment consists, like the gather environment, of only
28838 But the first line is left aligned, the last one right aligned.
28839 All other lines are centered.
28840 Therefore this environment is suitable for long formulas.
28842 \begin_inset CommandInset ref
28844 reference "eq:lefteqn"
28848 in the multline environment:
28849 \begin_inset Formula \begin{multline}
28850 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}\\
28851 -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}\\
28852 =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}
28859 \begin_layout Standard
28860 In the output only the last (first) line of a multline environment appears
28861 numbered when the document numbering is right (left).
28865 \begin_layout Plain Layout
28866 numbering styles see
28867 \begin_inset CommandInset ref
28869 reference "sec:Formula-Styles"
28881 \begin_layout Standard
28890 \begin_layout Plain Layout
28908 \begin_layout Plain Layout
28918 a centered line can be right or left aligned, respectively.
28919 The commands are used as follows:
28922 \begin_layout Standard
28927 shoveright{line content}
28933 shoveleft{line content}
28936 \begin_layout Standard
28937 \begin_inset VSpace medskip
28948 \begin_layout Plain Layout
28958 specifies the distance of the first line from the left page margin.
28959 Predefined is the length 0
28960 \begin_inset space \thinspace{}
28966 \begin_layout Standard
28967 As example the above formula where the command
28970 \begin_layout Standard
28980 \begin_layout Standard
28981 was inserted in TeX-mode before:
28985 \begin_layout Plain Layout
28997 \begin_inset Formula \begin{multline}
28998 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}\\
28999 \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}}\\
29000 =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}
29008 \begin_layout Plain Layout
29019 The second line was left aligned using
29028 \begin_layout Subsection
29029 Multiline Formula Parts
29030 \begin_inset CommandInset label
29032 name "sub:Multiline-Formula-Parts"
29040 \begin_layout Plain Layout
29041 Formula ! multiline ! formula parts
29049 \begin_layout Standard
29050 To display only parts of a formula with multiple lines, one of the following
29051 environments are used:
29068 They can be inserted via the menu
29070 Insert\SpecialChar \menuseparator
29073 or by using the commands described in this section.
29076 \begin_layout Standard
29077 The first three have the same properties as the corresponding multiline
29078 formula environments, but it is possible to set further formula parts beside
29081 \begin_inset Formula \[
29082 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29083 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29084 \right\} \textrm{Uncertainty relations}\]
29091 \begin_layout Standard
29092 To get this formula, a displayed formula is created where the command
29100 \begin_layout Plain Layout
29111 A purple box appears around the blue formula box where now columns and
29112 lines can be added.
29113 Outside the multiline environment other formula parts can be set, like
29117 \begin_layout Standard
29118 The aligned environment is also suitable for long formulas whose lines are
29119 horizontally aligned.
29120 Using aligned in a displayed formula has the advantage that the formula
29121 number is vertically centered behind the lines.
29123 \begin_inset CommandInset ref
29125 reference "eq:shortlong"
29129 in the aligned environment:
29130 \begin_inset Formula \begin{equation}
29131 \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}|}\\
29132 & -\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}
29140 \begin_layout Standard
29141 To use the environments
29163 \begin_layout Plain Layout
29181 \begin_layout Plain Layout
29199 \begin_layout Plain Layout
29207 are inserted, respectively.
29208 The split environment has the same properties as the aligned environment
29209 but it can only have two columns.
29212 \begin_layout Subsection
29213 Text in multiline Formulas
29214 \begin_inset CommandInset label
29216 name "sub:Text-in-multiline"
29224 \begin_layout Plain Layout
29234 \begin_layout Plain Layout
29235 Formula ! multiline ! text
29243 \begin_layout Standard
29244 In the Align environments, and the multline and gather environment, text
29245 can be inserted that will appear in a separate line and doesn't affect
29246 the column alignment.
29247 To do this, the command
29255 \begin_layout Plain Layout
29265 is used in the following scheme:
29268 \begin_layout Standard
29276 \begin_layout Standard
29277 The text should not be longer than a line because it cannot be hyphenated.
29278 As LyX doesn't yet support
29284 directly, the text is written as mathematical text.
29291 must hereby be at the beginning of a line and appears in the output above
29293 An example where the text was inserted at the beginning of the second line:
29294 \begin_inset Formula \begin{align}
29295 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29296 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29303 \begin_layout Section
29308 \begin_layout Plain Layout
29318 \begin_layout Plain Layout
29319 Formula ! numbering|see
29323 \begin_layout Plain Layout
29334 \begin_layout Plain Layout
29349 \begin_layout Subsection
29353 \begin_layout Standard
29354 Numbered formulas can be created with the menu
29356 Insert\SpecialChar \menuseparator
29357 Math\SpecialChar \menuseparator
29359 \begin_inset space ~
29367 \begin_inset space ~
29373 Existing formulas can be numbered with the menu
29375 Edit\SpecialChar \menuseparator
29376 Math\SpecialChar \menuseparator
29378 \begin_inset space ~
29386 arg "math-number-toggle"
29390 The formula number is displayed in LyX behind the formula as number sign
29392 The number sign is replaced in the output by the formula number.
29395 \begin_layout Standard
29396 When numbering is turned on in multiline formulas, all lines will be numbered.
29397 But the numbering can be controlled with the menu
29399 Edit\SpecialChar \menuseparator
29400 Math\SpecialChar \menuseparator
29402 \begin_inset space ~
29406 \begin_inset space ~
29410 \begin_inset space ~
29418 arg "math-number-line-toggle"
29424 \begin_layout Standard
29425 Except for inline formulas, all formulas can be numbered with two different
29427 \begin_inset CommandInset ref
29429 reference "sec:Formula-Styles"
29436 \begin_layout Subsection
29441 \begin_layout Plain Layout
29442 Cross-references ! to formulas
29450 \begin_layout Standard
29451 All labeled formulas can be cross-referenced.
29452 A label is added by the menu
29454 Insert\SpecialChar \menuseparator
29457 or the toolbar button
29458 \begin_inset Graphics
29459 filename ../images/label-insert.png
29465 The cursor must hereby be inside a displayed formula.
29466 A dialog pops up displaying the prefix
29471 The label is inserted there behind the prefix.
29472 The predefined prefix means
29473 \begin_inset Quotes eld
29477 \begin_inset Quotes erd
29480 and makes it easier to find labels in large documents because it marks
29481 it as formula label to divide it from e.
29482 \begin_inset space \thinspace{}
29486 \begin_inset space \space{}
29490 To change a label, the menu
29492 Insert\SpecialChar \menuseparator
29498 \begin_layout Standard
29499 The name of the label is displayed in LyX within two parentheses behind
29501 A formula with a label is always numbered.
29504 \begin_layout Standard
29505 Cross-references are inserted via the menu
29507 Insert\SpecialChar \menuseparator
29510 or with the toolbar button
29511 \begin_inset Graphics
29512 filename ../images/dialog-show-new-inset_ref.png
29518 A formula cross-reference appears in the output as formula number.
29519 When in the cross-reference dialog window the format
29523 is chosen, the cross-reference appears in the output as formula number
29525 \begin_inset Newline newline
29528 By right-clicking on a cross-reference in LyX, one jumps to the formula
29529 that is referenced.
29532 \begin_layout Standard
29533 Here are as examples cross-references to formulas of the following subsections:
29534 \begin_inset Note Note
29537 \begin_layout Plain Layout
29538 Note the different cross-reference types.
29546 \begin_layout Standard
29548 \begin_inset CommandInset ref
29555 \begin_inset CommandInset ref
29563 \begin_inset CommandInset ref
29569 ) big Latin letters are used for the numbering in contrary to (
29570 \begin_inset CommandInset ref
29579 \begin_layout Standard
29580 \begin_inset VSpace medskip
29583 When the argument of
29591 \begin_layout Plain Layout
29599 \begin_inset CommandInset ref
29601 reference "sub:User-defined-Numbering"
29612 contains a box like in
29613 \begin_inset CommandInset ref
29615 reference "sub:Paragraph-Boxes"
29619 , the formula cannot be referenced.
29622 \begin_layout Subsection
29627 \begin_layout Plain Layout
29628 Formula numbering ! subnumbering
29636 \begin_layout Standard
29637 With the help of the commands
29641 begin{subequations}
29649 formulas can be subnumbered.
29650 Both commands are inserted in TeX-mode.
29653 \begin_layout Standard
29655 \begin_inset Formula \begin{equation}
29656 A=C-B\label{eq:a}\end{equation}
29664 \begin_layout Plain Layout
29668 addtocounter{equation}{-1}
29677 \begin_layout Plain Layout
29681 begin{subequations}
29687 \begin_inset VSpace -5mm
29691 \begin_inset Formula \begin{equation}
29692 B=C-A\label{eq:b}\end{equation}
29697 \begin_inset Formula \begin{equation}
29698 C=A+B\label{eq:c}\end{equation}
29705 \begin_layout Standard
29709 \begin_layout Plain Layout
29721 \begin_layout Standard
29722 To create the example, the following is done:
29725 \begin_layout Enumerate
29726 first formula is inserted
29729 \begin_layout Enumerate
29734 addtocounter{equation}{-1}
29736 begin{subequations}
29740 \begin_layout Plain Layout
29749 \begin_inset Newline newline
29754 is inserted after the first formula
29757 \begin_layout Enumerate
29758 second formula is inserted
29761 \begin_layout Enumerate
29762 third formula is inserted
29765 \begin_layout Enumerate
29772 is inserted after the third formula
29775 \begin_layout Standard
29776 Every formula between the commands
29788 is subnumbered as a, b,
29789 \begin_inset Newline linebreak
29792 c, \SpecialChar \ldots{}
29793 For multiline formulas every line will be subnumbered.
29794 All subnumbered formulas are treated as
29799 But as every numbered formula increases the counter
29803 by one, the command
29809 is needed to decrease it.
29810 Otherwise the formulas
29811 \begin_inset CommandInset ref
29818 \begin_inset CommandInset ref
29825 \begin_inset CommandInset ref
29831 would be numbered as
29832 \begin_inset CommandInset ref
29839 \begin_inset CommandInset ref
29846 \begin_inset CommandInset ref
29855 \begin_layout Standard
29856 By inserting the commands in TeX-mode, a space is created between the first
29859 \begin_inset space \thinspace{}
29862 mm vertical space is inserted after the command
29866 begin{subequations}
29869 When the formula style
29875 \begin_layout Plain Layout
29877 \begin_inset CommandInset ref
29879 reference "sec:Formula-Styles"
29891 \begin_inset space \thinspace{}
29894 mm space is inserted instead.
29897 \begin_layout Standard
29898 Here is an example for a multiline formula where the numbering was turned
29899 off for the second line:
29903 \begin_layout Plain Layout
29907 begin{subequations}
29913 \begin_inset Formula \begin{eqnarray}
29914 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29915 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29916 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29924 \begin_layout Plain Layout
29936 \begin_layout Subsection
29937 User-defined Numbering
29938 \begin_inset CommandInset label
29940 name "sub:User-defined-Numbering"
29948 \begin_layout Plain Layout
29949 Formula numbering ! user-defined
29957 \begin_layout Standard
29961 \begin_layout Plain Layout
29962 Formula numbering ! self-defined delimiters
29967 With the standard numbering parentheses are set around the formula number.
29968 To replace the parentheses for example by vertical bars, the following
29969 line is added to the LaTeX-preamble:
29972 \begin_layout Standard
29984 \begin_inset Note Note
29987 \begin_layout Plain Layout
29988 This macro is already declared in the LaTeX-preamble for testing.
29989 To activate it, remove the percent sign at the beginning.
29997 \begin_layout Standard
29998 To use other characters, the vertical bars besides the
30002 are replaced by one ore more characters.
30003 To get only the formula number the vertical bars are omitted.
30006 \begin_layout Standard
30007 \begin_inset VSpace bigskip
30010 When there should be an expression of your choice instead of the consecutive
30011 formula number in parentheses behind the formula, the command
30021 \begin_layout Plain Layout
30030 \begin_inset Formula \begin{equation}
30031 A+B=C\tag{something}\label{eq:tag}\end{equation}
30035 In this example the command
30043 \begin_layout Plain Layout
30054 was inserted to the formula.
30057 \begin_layout Standard
30066 \begin_layout Plain Layout
30077 is inserted instead, the star prevents the parentheses around the expression:
30078 \begin_inset Formula \[
30079 A+B=C\tag*{something}\]
30086 \begin_layout Standard
30087 \begin_inset VSpace bigskip
30090 To restart the formula numbering with new document parts or sections, the
30091 following command is used:
30094 \begin_layout Standard
30099 @addtoreset{equation}{part}
30105 \begin_layout Plain Layout
30110 \begin_layout Plain Layout
30121 \begin_layout Plain Layout
30134 \begin_layout Plain Layout
30145 \begin_layout Plain Layout
30158 \begin_inset Newline newline
30162 \begin_inset Newline newline
30169 @addtoreset{equation}{section}
30172 \begin_layout Standard
30173 To be able to use these commands in TeX-mode, the
30174 \begin_inset Quotes eld
30178 \begin_inset Quotes erd
30181 character has to be made
30182 \begin_inset Quotes eld
30186 \begin_inset Quotes erd
30189 for LaTeX using the command
30203 So the command sequence in TeX-mode is:
30206 \begin_layout Standard
30212 \begin_inset Newline newline
30217 @addtoreset{equation}{section}
30218 \begin_inset Newline newline
30226 \begin_layout Standard
30227 In the LaTeX-preamble
30239 can be omitted as they are automatically internally inserted by LyX.
30242 \begin_layout Standard
30257 \begin_layout Plain Layout
30262 is part of the LaTeX-package
30270 \begin_layout Plain Layout
30271 Packages ! carlisle
30276 that is part of every LaTeX standard installation.
30285 \begin_layout Plain Layout
30286 Packages ! remreset
30291 has to be loaded in the LaTeX-preamble with the line
30294 \begin_layout Standard
30299 usepackage{remreset}
30302 \begin_layout Standard
30313 \begin_layout Plain Layout
30318 \begin_layout Plain Layout
30329 \begin_layout Plain Layout
30342 \begin_layout Plain Layout
30353 \begin_layout Plain Layout
30365 can be used with the same scheme as
30374 \begin_layout Standard
30375 \begin_inset VSpace bigskip
30378 Sometimes formulas should be numbered in the following form:
30381 \begin_layout Standard
30384 (section number.formula number)
30387 \begin_layout Standard
30388 The formula number should start with every section with
30389 \begin_inset Quotes eld
30393 \begin_inset Quotes erd
30399 \begin_layout Standard
30400 For this case there is the command
30410 \begin_layout Plain Layout
30418 , which is used with the following scheme:
30421 \begin_layout Standard
30426 numberwithin{counter}{sectioning}
30429 \begin_layout Standard
30430 Counter denotes what kind of numbering is affected, sectioning denotes what
30431 number is before the dot.
30434 \begin_layout Standard
30435 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30438 \begin_layout Standard
30443 numberwithin{equation}{section}
30446 \begin_layout Standard
30447 This is the result:
30451 \begin_layout Plain Layout
30455 numberwithin{equation}{section}
30461 \begin_inset Formula \begin{equation}
30462 A+B=C\end{equation}
30469 \begin_layout Standard
30471 \begin_inset space \thinspace{}
30475 \begin_inset space \space{}
30478 tables so that the number of the part is the sectioning,
30479 \begin_inset Newline newline
30486 numberwithin{table}{part}
30491 \begin_layout Standard
30492 To go back to the standard numbering or to prevent this kind of numbering
30493 when it is defined by the document class, the following command is inserted
30494 as TeX-Code or to the LaTeX-preamble:
30497 \begin_layout Standard
30510 \begin_layout Plain Layout
30524 \begin_layout Plain Layout
30540 \begin_inset Newline newline
30548 \begin_inset Newline newline
30560 \begin_layout Standard
30567 uses internally the command
30573 , described above, that also needs to be reverted.
30577 \begin_layout Plain Layout
30584 \begin_layout Plain Layout
30588 @removefromreset{equation}{section}
30591 \begin_layout Plain Layout
30603 \begin_layout Subsection
30604 Numbering with Roman Numbers and Letters
30608 \begin_layout Plain Layout
30609 Formula numbering ! with letters
30618 \begin_layout Plain Layout
30619 Formula numbering ! with Roman numbers
30627 \begin_layout Standard
30628 Formulas can also be numbered with Roman numbers and Latin letters.
30629 To number for example with small Roman numbers, the command
30632 \begin_layout Standard
30644 \begin_layout Standard
30645 is inserted before the formula in TeX-mode.
30656 \begin_layout Plain Layout
30664 redefines the predefined command
30680 \begin_layout Plain Layout
30687 has the same scheme like the command
30693 that is described in
30694 \begin_inset CommandInset ref
30696 reference "sub:The-Command-newcommand"
30709 is the formula counter.
30716 is used as prefix for a counter, the value of the counter is output as
30718 When a formula is numbered, LaTeX sets internally the command
30724 behind the formula.
30733 \begin_layout Plain Layout
30743 outputs the counter as small Roman number.
30746 \begin_layout Standard
30747 All formulas behind the command
30757 are now numbered Roman.
30758 To switch to numbering with big Roman numbers, the command is inserted
30775 \begin_layout Plain Layout
30787 \begin_inset Quotes eld
30791 \begin_inset Quotes erd
30794 with small Latin letters there is the command
30804 \begin_layout Plain Layout
30812 , for big ones there is the command
30822 \begin_layout Plain Layout
30835 \begin_layout Standard
30836 \begin_inset Note Greyedout
30839 \begin_layout Plain Layout
30844 Only maximal 26 formulas can be numbered with Latin letters in one document.
30852 \begin_layout Standard
30853 \begin_inset Newpage pagebreak
30859 \begin_layout Standard
30863 \begin_layout Plain Layout
30879 \begin_layout Standard
30880 \begin_inset Formula \begin{equation}
30881 A=\textrm{small roman}\label{eq:rom}\end{equation}
30889 \begin_layout Plain Layout
30903 \begin_inset Formula \begin{equation}
30904 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30912 \begin_layout Plain Layout
30926 \begin_inset Formula \begin{equation}
30927 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30935 \begin_layout Plain Layout
30949 \begin_inset Formula \begin{equation}
30950 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30957 \begin_layout Standard
30958 To switch back to the default numbering, insert the command:
30961 \begin_layout Standard
30974 \begin_layout Plain Layout
30985 \begin_layout Standard
30989 \begin_layout Plain Layout
31003 \begin_inset Formula \begin{equation}
31004 E=\textrm{Arabic}\label{eq:arab}\end{equation}
31011 \begin_layout Standard
31012 \begin_inset VSpace medskip
31015 As you see, formulas are numbered serially independent from the numbering
31017 When then numbering should start with
31018 \begin_inset Quotes eld
31022 \begin_inset Quotes erd
31025 when the style is changed, new equation counters have to be defined.
31026 A description about this can be found in the file
31027 \begin_inset CommandInset href
31029 target "Formula-numbering.lyx"
31036 \begin_layout Section
31037 Chemical Symbols and Equations
31038 \begin_inset CommandInset label
31040 name "sub:Chemical-Symbols-and"
31048 \begin_layout Plain Layout
31049 Chemical characters ! Symbols
31058 \begin_layout Plain Layout
31068 \begin_layout Plain Layout
31077 \begin_layout Standard
31078 An example text from chemistry:
31081 \begin_layout Quote
31083 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31086 -ion reacts with two
31087 \begin_inset Formula $\mathrm{Na^{+}}$
31090 -ions to sodium sulfate
31091 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31095 The chemical equation for this is:
31096 \begin_inset Formula \begin{equation}
31097 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31104 \begin_layout Standard
31105 This chemical equation can directly be created as formula.
31106 To avoid that the symbols appear italic, everything is highlighted and
31107 changed by the shortcut
31113 to the upright font style.
31117 \begin_layout Plain Layout
31123 \begin_inset CommandInset ref
31125 reference "sub:Font-Styles"
31137 \begin_layout Standard
31138 A more convenient way to typeset chemical formulas is to use the command
31149 \begin_layout Plain Layout
31157 that is available when the LaTeX-package
31165 \begin_layout Plain Layout
31178 to a formula a new blue box appears where chemical formulas can be inserted
31179 in an intuitive way.
31182 \begin_layout Standard
31184 \begin_inset Tabular
31185 <lyxtabular version="3" rows="9" columns="2">
31187 <column alignment="center" valignment="top" width="0">
31188 <column alignment="center" valignment="top" width="0">
31190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31193 \begin_layout Plain Layout
31199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31202 \begin_layout Plain Layout
31204 \begin_inset Note Note
31207 \begin_layout Plain Layout
31214 is only used as spacer.
31226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31229 \begin_layout Plain Layout
31236 \begin_layout Plain Layout
31250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31253 \begin_layout Plain Layout
31254 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31267 \begin_layout Plain Layout
31274 \begin_layout Plain Layout
31288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31291 \begin_layout Plain Layout
31292 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31305 \begin_layout Plain Layout
31312 \begin_layout Plain Layout
31326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31329 \begin_layout Plain Layout
31330 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31343 \begin_layout Plain Layout
31350 \begin_layout Plain Layout
31364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31367 \begin_layout Plain Layout
31368 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31381 \begin_layout Plain Layout
31388 \begin_layout Plain Layout
31403 \begin_layout Plain Layout
31418 \begin_layout Plain Layout
31432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31435 \begin_layout Plain Layout
31436 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31449 \begin_layout Plain Layout
31456 \begin_layout Plain Layout
31466 \begin_inset Formula $\downarrow$
31470 \begin_inset Formula $\to$
31478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31481 \begin_layout Plain Layout
31482 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31495 \begin_layout Plain Layout
31502 \begin_layout Plain Layout
31515 \begin_layout Plain Layout
31528 \begin_layout Plain Layout
31541 \begin_layout Plain Layout
31554 \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 $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31585 \begin_layout Plain Layout
31592 \begin_layout Plain Layout
31605 \begin_layout Plain Layout
31618 \begin_layout Plain Layout
31631 \begin_layout Plain Layout
31648 \begin_layout Plain Layout
31662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31665 \begin_layout Plain Layout
31666 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31682 \begin_layout Standard
31683 \begin_inset Note Greyedout
31686 \begin_layout Plain Layout
31691 Inserting a formula to a
31697 box will lead to LaTeX errors.
31698 In this case TeX code has to be used like for
31712 \begin_layout Plain Layout
31733 \begin_layout Standard
31740 the command for equation
31741 \begin_inset space ~
31745 \begin_inset CommandInset ref
31747 reference "eq:chem-reaction"
31752 \begin_inset Newline newline
31763 \begin_layout Plain Layout
31776 \begin_layout Plain Layout
31789 \begin_layout Plain Layout
31802 \begin_layout Plain Layout
31815 \begin_layout Plain Layout
31828 \begin_layout Plain Layout
31840 \begin_layout Standard
31841 To create multiline chemical equations first a multiline formula is created
31843 \begin_inset CommandInset ref
31845 reference "sec:Multiline-Formulas"
31850 Afterwards the command
31856 is used in every small blue box of the formula.
31858 \begin_inset CommandInset ref
31860 reference "eq:TEOS-reaction-1"
31865 \begin_inset CommandInset ref
31867 reference "eq:TEOS-reaction-2"
31871 are an example of a multi-stage chemical reaction where every equation
31872 has its own number.
31873 \begin_inset Formula \begin{eqnarray}
31874 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31875 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
31882 \begin_layout Standard
31893 package provides the command
31903 \begin_layout Plain Layout
31911 that has to be used for special cases.
31912 For more information about
31918 and more examples have a look at the documentation of
31923 \begin_inset CommandInset citation
31932 \begin_layout Section
31936 \begin_layout Standard
31937 LyX supports two types of commutative diagrams:
31945 that are explained in the following.
31948 \begin_layout Subsection
31953 \begin_layout Plain Layout
31962 \begin_layout Standard
31963 Diagrams of this type visualize relations by vertical and horizontal lines
31965 \begin_inset Formula \[
31966 \begin{CD}A@>>>B@>>>C\\
31968 F@<<<E@<<<D\end{CD}\]
31975 \begin_layout Standard
31976 To get them, the command
31984 \begin_layout Plain Layout
31994 is inserted to a formula.
31995 A blue box appears with two dashed lines where further commands can be
32000 arg "newline-insert newline"
32003 a new line is created.
32004 Horizontal relations are inserted in odd, vertical in even formula lines.
32007 \begin_layout Standard
32008 To create the relations there are the following commands:
32011 \begin_layout Itemize
32016 creates a left arrow,
32027 \begin_layout Itemize
32032 creates an up arrow,
32040 a vertical equal sign
32043 \begin_layout Itemize
32049 is a placeholder for non-existent relations
32052 \begin_layout Standard
32053 All arrows can be labeled as follows:
32056 \begin_layout Itemize
32057 Is text inserted between the first and second < or >, resp., it is placed
32059 When it is inserted between the second and third one, it appears under
32063 \begin_layout Itemize
32064 When text for vertical arrows is inserted between the first and second A
32065 or V, resp., it is placed left beside the arrow.
32066 When it is inserted between the second and third one, it appears right
32068 If the text contains an A or V, these letters must be set into a TeX-brace.
32071 \begin_layout Standard
32072 As example a diagram with all possible relations:
32075 \begin_layout Standard
32076 \begin_inset Formula \[
32077 \begin{CD}A@>j>>B@>>k>C@=F\\
32079 D@<<j<E@>k>>F@=C\end{CD}\]
32086 \begin_layout Standard
32087 The command for this is:
32088 \begin_inset Newline newline
32099 \begin_layout Plain Layout
32108 A@>j>>B@>>k>C@=F Ctrl+Return
32109 \begin_inset Newline newline
32116 \begin_layout Plain Layout
32131 \begin_layout Plain Layout
32144 \begin_layout Plain Layout
32156 \begin_inset Formula $\to$
32162 \begin_inset Newline newline
32169 \begin_layout Plain Layout
32184 \begin_layout Plain Layout
32197 \begin_layout Plain Layout
32207 \begin_layout Subsection
32212 \begin_layout Plain Layout
32213 Diagrams ! xymatrix
32221 \begin_layout Standard
32222 To be able to use xymatrices, the LaTeX-package
32227 A xymatrix is created by inserting the command
32234 Then you are able to add new matrix columns and rows like for normal matrices,
32236 \begin_inset CommandInset ref
32238 reference "sec:Matrices"
32245 \begin_layout Standard
32246 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32248 All possibilities to create commutative diagrams and decorations are explained
32253 that you find in the menu
32255 Help\SpecialChar \menuseparator
32257 \begin_inset space ~
32260 Manuals\SpecialChar \menuseparator
32262 \begin_inset space ~
32270 \begin_layout Standard
32271 \begin_inset Newpage newpage
32277 \begin_layout Section
32278 User-defined Commands
32282 \begin_layout Plain Layout
32283 User-defined commands
32291 \begin_layout Standard
32292 \begin_inset Note Greyedout
32295 \begin_layout Plain Layout
32300 The names of user-defined commands and macros may only consist of Latin
32309 \begin_layout Subsection
32313 \begin_inset CommandInset label
32315 name "sub:The-Command-newcommand"
32323 \begin_layout Plain Layout
32324 User-defined commands !
32335 \begin_layout Plain Layout
32346 \begin_layout Standard
32347 Many LaTeX-commands are too long to be used frequently.
32348 But it is possible to define with the command
32354 new shorter commands.
32357 \begin_layout Standard
32358 The command scheme of
32367 \begin_layout Standard
32372 newcommand{new command name}[number of arguments][optional
32377 \begin_inset Newline newline
32384 \begin_layout Plain Layout
32399 \begin_layout Plain Layout
32406 {command definition}
32409 \begin_layout Standard
32410 \begin_inset Note Greyedout
32413 \begin_layout Plain Layout
32418 Assure that the name of the new command is not already used in your document
32419 or by LaTeX-packages that you use.
32420 When you for example define the command
32432 , you get an error message because
32438 is already defined as command for
32439 \begin_inset Quotes eld
32443 \begin_inset Formula $\le$
32447 \begin_inset Quotes erd
32458 \begin_layout Standard
32459 The number of arguments is an integer in the range 0
32460 \begin_inset space \thinspace{}
32464 \begin_inset space \thinspace{}
32467 9 and specifies how many arguments the new command should have.
32468 With the optional value a value for an optional argument can be predefined.
32469 When this is done, the
32477 rgument of the new command is automatically an optional one.
32480 \begin_layout Standard
32481 Here are some examples:
32484 \begin_layout Itemize
32485 To define the command
32497 , the LaTeX-preamble line is:
32498 \begin_inset VSpace medskip
32502 \begin_inset Newline newline
32516 \begin_layout Itemize
32517 To define the command
32529 , the argument (that should be underlined) must be taken into account.
32530 For this the preamble line is:
32531 \begin_inset VSpace medskip
32535 \begin_inset Newline newline
32549 \begin_inset VSpace medskip
32553 \begin_inset Newline newline
32560 acts as argument placeholder, the
32564 behind it denotes that it is the placeholder for the first argument.
32567 \begin_layout Itemize
32575 \begin_inset space \thinspace{}
32579 \begin_inset space \space{}
32589 \begin_inset VSpace medskip
32593 \begin_inset Newline newline
32604 framebox#1#2{$#3$}}
32607 \begin_inset VSpace medskip
32611 \begin_inset Newline newline
32614 The two Dollar signs creates the extra formula needed for
32621 \begin_inset CommandInset ref
32623 reference "sub:Boxes-with-Frame"
32630 \begin_layout Itemize
32631 To create a new command for
32637 where the color for the box needn't to be specified, the argument for the
32638 color is defined optional:
32639 \begin_inset VSpace medskip
32643 \begin_inset Newline newline
32654 fcolorbox{#2}{#1}{$#3$}}
32657 \begin_inset VSpace medskip
32661 \begin_inset Newline newline
32664 When the color is not specified when using
32670 , the predefined color
32677 \begin_layout Standard
32678 A test of the new defined commands:
32681 \begin_layout Standard
32683 \begin_inset Tabular
32684 <lyxtabular version="3" rows="6" columns="2">
32686 <column alignment="center" valignment="top" width="0">
32687 <column alignment="center" valignment="top" width="0">
32689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32692 \begin_layout Plain Layout
32698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32701 \begin_layout Plain Layout
32703 \begin_inset Note Note
32706 \begin_layout Plain Layout
32713 is only used as spacer.
32725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32728 \begin_layout Plain Layout
32735 \begin_layout Plain Layout
32749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32752 \begin_layout Plain Layout
32753 \begin_inset Formula $A\gr B$
32763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32766 \begin_layout Plain Layout
32774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32777 \begin_layout Plain Layout
32778 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32791 \begin_layout Plain Layout
32795 \begin_inset Formula $\to$
32801 \begin_inset Formula $\to$
32812 \begin_layout Plain Layout
32826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32829 \begin_layout Plain Layout
32830 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32843 \begin_layout Plain Layout
32847 \begin_inset Formula $\to$
32858 \begin_layout Plain Layout
32872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32875 \begin_layout Plain Layout
32876 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32889 \begin_layout Plain Layout
32895 \begin_inset Formula $\to$
32906 \begin_layout Plain Layout
32920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32923 \begin_layout Plain Layout
32924 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32940 \begin_layout Subsection
32945 \begin_layout Plain Layout
32946 User-defined commands! Math macros
32955 \begin_layout Plain Layout
32964 \begin_layout Standard
32965 User-defined commands are especially convenient for complex expressions.
32966 When you are for example dealing in a document with quadratic equations,
32967 the same solution type occurs several times.
32968 The general form of a quadratic equation is
32969 \begin_inset Formula \[
32970 0=\lambda^{2}+p\lambda+q\]
32974 The general form of the solution is
32975 \begin_inset Formula \[
32976 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
32983 \begin_layout Standard
32984 To define a command for the solution formula where only the three parameters
32986 \begin_inset Formula $\lambda$
32990 \begin_inset Formula $p$
32994 \begin_inset Formula $q$
32997 need to be specified and the index of
32998 \begin_inset Formula $\lambda$
33001 can be given optionally, the LaTeX-preamble line is
33002 \begin_inset Newline newline
33018 \begin_inset Newline newline
33025 \begin_layout Plain Layout
33040 \begin_layout Plain Layout
33051 frac{#3^{2}}{4}-#4}}
33054 \begin_layout Standard
33055 To create with this the solution formula, the command
33056 \begin_inset Newline newline
33066 \begin_inset Formula $\to$
33072 \begin_inset Formula $\to$
33079 is inserted to a formula
33084 \begin_layout Standard
33085 The definition of the new command is unintuitive because one has to know
33086 the schemes of all used LaTeX commands, e.
33087 \begin_inset space \thinspace{}
33091 \begin_inset space \space{}
33094 that a fraction is inserted in LaTeX as
33098 frac{numerator}{denominator}
33101 Furthermore one can easily forget a brace in the definition and cannot
33102 see in LyX what the new command is doing.
33103 To avoid these problems LyX offers the possibility to use math macros instead
33113 \begin_layout Standard
33114 A math macro is created by using the menu
33116 Insert\SpecialChar \menuseparator
33117 Math\SpecialChar \menuseparator
33120 or the toolbar button
33121 \begin_inset Graphics
33122 filename ../images/math-macro_newmacroname_newcommand.png
33128 The math macro toolbar appears together with the following box where the
33130 \begin_inset Newline newline
33134 \begin_inset space \hspace*{\fill}
33138 \begin_inset Graphics
33139 filename clipart/macrobox.png
33144 \begin_inset space \hspace*{\fill}
33148 \begin_inset Newline newline
33152 \begin_inset FormulaMacro
33153 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33158 newmacroname is the default name of the macro that should be changed to
33159 something sensible.
33160 The wanted formula is inserted in the first blue box.
33161 An argument placeholder is inserted with the command
33168 \begin_inset space \thinspace{}
33172 \begin_inset space \space{}
33181 or by using the macro toolbar button
33182 \begin_inset Graphics
33183 filename ../images/math-macro-add-param.png
33189 Argument placeholders are displayed red.
33190 Maximum 9 arguments are possible.
33191 Optional arguments are created with the toolbar button
33192 \begin_inset Graphics
33193 filename ../images/math-macro-add-optional-param.png
33199 The first non-optional argument can be transformed to an optional one with
33201 \begin_inset Graphics
33202 filename ../images/math-macro-make-optional.png
33208 In the second blue box the appearance of the macro in LyX can be defined.
33209 Normally you want to see it as it is defined, so the box is kept empty.
33210 But when you have created a macro that needs lot of space on the screen,
33211 you can insert in the box for example
33212 \begin_inset Newline newline
33242 \begin_inset Newline newline
33247 For the macro only the arguments with the macro name in front of them will
33248 then be displayed in LyX, leading to a better overview.
33249 The formula appears in the output as defined in the first box.
33250 \begin_inset Newline newline
33253 The appearance of macros in formulas can furthermore be changed for single
33254 macros by setting the cursor in the macro and using the menu
33256 View\SpecialChar \menuseparator
33258 \begin_inset space ~
33262 \begin_inset space ~
33270 \begin_layout Standard
33271 To use a macro, the macro name is inserted as command to a formula, in our
33279 Our macro looks in LyX like this:
33280 \begin_inset Newline newline
33284 \begin_inset space \hspace*{\fill}
33288 \begin_inset Graphics
33289 filename clipart/macrouse.png
33294 \begin_inset space \hspace*{\fill}
33298 \begin_inset Newline newline
33301 Here is our macro example with the arguments
33302 \begin_inset Formula $x$
33306 \begin_inset Formula $\ln(x)$
33310 \begin_inset Formula $B$
33316 \begin_layout Standard
33317 \begin_inset Formula \[
33325 \begin_layout Standard
33326 LyX offers in the menu
33328 Tools\SpecialChar \menuseparator
33329 Preferences\SpecialChar \menuseparator
33330 Editing\SpecialChar \menuseparator
33333 different styles to edit macros.
33334 To find the style that suits you the most, choose a style and set the cursor
33335 in a macro formula to see the difference.
33338 \begin_layout Standard
33339 A math macro is transformed internally to a
33345 command when exporting the document.
33352 command is not placed in the LaTeX-preamble, therefore macros can only
33353 be used in formulas that are in the document below the macro definition
33357 \begin_layout Standard
33358 Math macros can also be directly be created from a
33365 When writing for example the command
33368 \begin_inset Newline newline
33377 xleftarrow[#2]{#1}}
33378 \begin_inset Newline newline
33383 in LyX as normal text, highlighting it completely and using then the shortcut
33388 , the command will be transformed to a math macro.
33389 Using this method you need to be careful that the
33395 command is typed correctly, otherwise you get a faulty macro leading to
33399 \begin_layout Standard
33400 Math macros currently yet have the problem that further formulas in macro
33401 definitions are handled wrongly.
33402 Therefore the example
33409 \begin_inset CommandInset ref
33411 reference "sub:The-Command-newcommand"
33415 cannot be created as macro.
33418 \begin_layout Standard
33419 When the cursor is in a macro definition box, you will see the macro toolbar
33423 \begin_layout Standard
33424 \begin_inset VSpace defskip
33430 \begin_layout Standard
33431 \begin_inset Graphics
33432 filename clipart/MacroToolbar.png
33440 \begin_layout Plain Layout
33449 \begin_layout Standard
33450 \begin_inset VSpace defskip
33456 \begin_layout Standard
33457 The macro toolbar contains from left to right the following buttons:
33460 \begin_layout Standard
33461 \begin_inset VSpace defskip
33467 \begin_layout Standard
33468 \begin_inset Tabular
33469 <lyxtabular version="3" rows="9" columns="2">
33470 <features islongtable="true">
33471 <column alignment="left" valignment="top" width="0">
33472 <column alignment="left" valignment="top" width="85col%">
33473 <row interlinespace="2.5mm">
33474 <cell alignment="center" valignment="top" usebox="none">
33477 \begin_layout Plain Layout
33478 \begin_inset Graphics
33479 filename ../images/math-macro-remove-param.png
33480 BoundingBox 0bp 5bp 20bp 25bp
33481 rotateOrigin center
33490 <cell alignment="center" valignment="top" usebox="none">
33493 \begin_layout Plain Layout
33496 Edit\SpecialChar \menuseparator
33497 Math\SpecialChar \menuseparator
33499 \begin_inset space ~
33502 Definition\SpecialChar \menuseparator
33503 Remove Last Argument
33509 <row interlinespace="2.5mm">
33510 <cell alignment="center" valignment="top" usebox="none">
33513 \begin_layout Plain Layout
33514 \begin_inset Graphics
33515 filename ../images/math-macro-add-param.png
33516 BoundingBox 0bp 5bp 20bp 25bp
33517 rotateOrigin center
33526 <cell alignment="center" valignment="top" usebox="none">
33529 \begin_layout Plain Layout
33532 Edit\SpecialChar \menuseparator
33533 Math\SpecialChar \menuseparator
33535 \begin_inset space ~
33538 Definition\SpecialChar \menuseparator
33545 <row interlinespace="2.5mm">
33546 <cell alignment="center" valignment="top" usebox="none">
33549 \begin_layout Plain Layout
33550 \begin_inset Graphics
33551 filename ../images/math-macro-make-optional.png
33552 BoundingBox 0bp 5bp 20bp 25bp
33553 rotateOrigin center
33562 <cell alignment="center" valignment="top" usebox="none">
33565 \begin_layout Plain Layout
33568 Edit\SpecialChar \menuseparator
33569 Math\SpecialChar \menuseparator
33571 \begin_inset space ~
33574 Definition\SpecialChar \menuseparator
33575 Make First Non-Optional into
33576 \begin_inset Newline newline
33583 \begin_layout Plain Layout
33592 Edit\SpecialChar \menuseparator
33593 Math\SpecialChar \menuseparator
33595 \begin_inset space ~
33598 Definition\SpecialChar \menuseparator
33603 \begin_layout Plain Layout
33616 <row interlinespace="2.5mm">
33617 <cell alignment="center" valignment="top" usebox="none">
33620 \begin_layout Plain Layout
33621 \begin_inset Graphics
33622 filename ../images/math-macro-make-nonoptional.png
33623 BoundingBox 0bp 5bp 20bp 25bp
33624 rotateOrigin center
33633 <cell alignment="center" valignment="top" usebox="none">
33636 \begin_layout Plain Layout
33639 Edit\SpecialChar \menuseparator
33640 Math\SpecialChar \menuseparator
33642 \begin_inset space ~
33645 Definition\SpecialChar \menuseparator
33646 Make Last Optional into
33647 \begin_inset Newline newline
33654 \begin_layout Plain Layout
33663 Edit\SpecialChar \menuseparator
33664 Math\SpecialChar \menuseparator
33666 \begin_inset space ~
33669 Definition\SpecialChar \menuseparator
33674 \begin_layout Plain Layout
33681 Non-Optional Argument
33687 <row interlinespace="2.5mm">
33688 <cell alignment="center" valignment="top" usebox="none">
33691 \begin_layout Plain Layout
33692 \begin_inset Graphics
33693 filename ../images/math-macro-remove-optional-param.png
33694 BoundingBox 0bp 5bp 20bp 25bp
33695 rotateOrigin center
33704 <cell alignment="center" valignment="top" usebox="none">
33707 \begin_layout Plain Layout
33710 Edit\SpecialChar \menuseparator
33711 Math\SpecialChar \menuseparator
33713 \begin_inset space ~
33716 Definition\SpecialChar \menuseparator
33717 Remove Optional Argument
33723 <row interlinespace="2.5mm">
33724 <cell alignment="center" valignment="top" usebox="none">
33727 \begin_layout Plain Layout
33728 \begin_inset Graphics
33729 filename ../images/math-macro-add-optional-param.png
33730 BoundingBox 0bp 5bp 20bp 25bp
33731 rotateOrigin center
33740 <cell alignment="center" valignment="top" usebox="none">
33743 \begin_layout Plain Layout
33746 Edit\SpecialChar \menuseparator
33747 Math\SpecialChar \menuseparator
33749 \begin_inset space ~
33752 Definition\SpecialChar \menuseparator
33753 Insert Optional Argument
33759 <row interlinespace="2.5mm">
33760 <cell alignment="center" valignment="top" usebox="none">
33763 \begin_layout Plain Layout
33764 \begin_inset Graphics
33765 filename ../images/math-macro-remove-greedy-param.png
33766 BoundingBox 0bp 5bp 20bp 25bp
33767 rotateOrigin center
33776 <cell alignment="center" valignment="top" usebox="none">
33779 \begin_layout Plain Layout
33782 Edit\SpecialChar \menuseparator
33783 Math\SpecialChar \menuseparator
33785 \begin_inset space ~
33788 Definition\SpecialChar \menuseparator
33789 Remove Last Argument
33790 \begin_inset Newline newline
33797 \begin_layout Plain Layout
33806 Edit\SpecialChar \menuseparator
33807 Math\SpecialChar \menuseparator
33809 \begin_inset space ~
33812 Definition\SpecialChar \menuseparator
33817 \begin_layout Plain Layout
33824 Spitting Out To The Right
33830 <row interlinespace="2.5mm">
33831 <cell alignment="center" valignment="top" usebox="none">
33834 \begin_layout Plain Layout
33835 \begin_inset Graphics
33836 filename ../images/math-macro-append-greedy-param.png
33837 BoundingBox 0bp 5bp 20bp 25bp
33838 rotateOrigin center
33847 <cell alignment="center" valignment="top" usebox="none">
33850 \begin_layout Plain Layout
33853 Edit\SpecialChar \menuseparator
33854 Math\SpecialChar \menuseparator
33856 \begin_inset space ~
33859 Definition\SpecialChar \menuseparator
33861 \begin_inset Newline newline
33868 \begin_layout Plain Layout
33877 Edit\SpecialChar \menuseparator
33878 Math\SpecialChar \menuseparator
33880 \begin_inset space ~
33883 Definition\SpecialChar \menuseparator
33888 \begin_layout Plain Layout
33895 Eating From The Right
33901 <row interlinespace="2.5mm">
33902 <cell alignment="center" valignment="top" usebox="none">
33905 \begin_layout Plain Layout
33906 \begin_inset Graphics
33907 filename ../images/math-macro-add-greedy-optional-param.png
33908 BoundingBox 0bp 5bp 20bp 25bp
33909 rotateOrigin center
33918 <cell alignment="center" valignment="top" usebox="none">
33921 \begin_layout Plain Layout
33924 Edit\SpecialChar \menuseparator
33925 Math\SpecialChar \menuseparator
33927 \begin_inset space ~
33930 Definition\SpecialChar \menuseparator
33931 Append Optional Argument
33932 \begin_inset Newline newline
33939 \begin_layout Plain Layout
33948 Edit\SpecialChar \menuseparator
33949 Math\SpecialChar \menuseparator
33951 \begin_inset space ~
33954 Definition\SpecialChar \menuseparator
33959 \begin_layout Plain Layout
33966 Eating From The Right
33979 \begin_layout Standard
33980 \begin_inset Newpage newpage
33986 \begin_layout Section
33991 \begin_layout Plain Layout
34004 \begin_layout Plain Layout
34005 Other useful math tips can be found in
34006 \begin_inset CommandInset citation
34021 \begin_layout Plain Layout
34029 \begin_inset Note Note
34032 \begin_layout Plain Layout
34035 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
34038 \begin_layout Plain Layout
34041 texorpdfstring is in section
34042 \begin_inset CommandInset ref
34044 reference "sub:Formulas-in-Section"
34057 \begin_layout Plain Layout
34067 \begin_layout Plain Layout
34072 \begin_layout Plain Layout
34079 Chemical characters
34083 \begin_layout Plain Layout
34098 \begin_layout Subsection
34103 \begin_layout Plain Layout
34112 \begin_layout Standard
34113 Negative numbers often look ugly in formulas because the minus sign before
34114 the number is set with the same length as the minus operator sign.
34115 When writing the negative number in normal text, the minus sign appears
34119 \begin_layout Standard
34120 Thus, the problem disappears when converting the minus sign to mathematical
34124 \begin_layout Standard
34125 An example to visualize the problem:
34128 \begin_layout Standard
34130 \begin_inset Tabular
34131 <lyxtabular version="3" rows="3" columns="2">
34133 <column alignment="right" valignment="top" width="0">
34134 <column alignment="left" valignment="top" width="0">
34136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34139 \begin_layout Plain Layout
34145 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34148 \begin_layout Plain Layout
34156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34159 \begin_layout Plain Layout
34165 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34168 \begin_layout Plain Layout
34169 \begin_inset Formula $x=-2$
34179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34182 \begin_layout Plain Layout
34188 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34191 \begin_layout Plain Layout
34192 \begin_inset Formula $x=\textrm{-}2$
34208 \begin_layout Subsection
34209 Comma as decimal Separator
34213 \begin_layout Plain Layout
34222 \begin_layout Standard
34223 In LaTeX a comma inside a formula is used, according to the English convention,
34224 as number group separator.
34225 So there will be space added behind all commas in formulas.
34228 \begin_layout Standard
34229 To avoid this, the comma is highlighted and changed to mathematical text
34239 \begin_layout Standard
34240 To use all formula commas in the document as decimal separator, the file
34249 \begin_layout Plain Layout
34254 is part of the LaTeX-package
34262 \begin_layout Plain Layout
34267 \begin_layout Plain Layout
34290 \begin_layout Plain Layout
34296 is loaded with the LaTeX-preamble line
34299 \begin_layout Standard
34307 \begin_layout Subsection
34309 \begin_inset CommandInset label
34311 name "sub:Physical-Vectors"
34319 \begin_layout Plain Layout
34328 \begin_layout Standard
34329 Predefined vectors are offered by the LaTeX-package
34337 \begin_layout Plain Layout
34342 should be part of every LaTeX standard installation.
34351 \begin_layout Plain Layout
34357 that is loaded with the LaTeX-preamble line
34360 \begin_layout Standard
34368 \begin_layout Standard
34372 \begin_layout Plain Layout
34382 \begin_inset Note Note
34385 \begin_layout Plain Layout
34386 The following table will only be displayed when the LaTeX-package
34395 The following commands are defined:
34398 \begin_layout Standard
34400 \begin_inset Tabular
34401 <lyxtabular version="3" rows="4" columns="2">
34403 <column alignment="center" valignment="top" width="0">
34404 <column alignment="center" valignment="top" width="0">
34406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34409 \begin_layout Plain Layout
34415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34418 \begin_layout Plain Layout
34426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34429 \begin_layout Plain Layout
34439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34442 \begin_layout Plain Layout
34443 \begin_inset Formula $\Bra{\psi}$
34453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34456 \begin_layout Plain Layout
34466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34469 \begin_layout Plain Layout
34470 \begin_inset Formula $\Ket{\psi}$
34480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34483 \begin_layout Plain Layout
34495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34498 \begin_layout Plain Layout
34499 \begin_inset Formula $\Braket{\psi|\phi}$
34515 \begin_layout Standard
34522 assures that all vertical bars are set in the size of the surrounding brackets:
34523 \begin_inset Formula \[
34524 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34532 \begin_layout Plain Layout
34542 \begin_inset Note Note
34545 \begin_layout Plain Layout
34546 The following will be displayed when the LaTeX-package
34558 \begin_layout Standard
34559 You need to install the LaTeX-package
34563 to see the rest of this subsection in the output.
34566 \begin_layout Standard
34570 \begin_layout Plain Layout
34582 \begin_layout Standard
34589 can also be achieved using the command
34595 , that is described in
34596 \begin_inset CommandInset ref
34598 reference "sub:Automatic-Bracket-Size"
34605 \begin_layout Subsection
34606 Self-defined Fractions
34607 \begin_inset CommandInset label
34609 name "sub:Self-defined-Fractions"
34617 \begin_layout Plain Layout
34618 Fractions ! self-defined
34626 \begin_layout Standard
34627 To define custom commands for fractions, the command
34637 \begin_layout Plain Layout
34645 is used in the following scheme:
34648 \begin_layout Standard
34661 bracket}{fraction bar thickness}{style}
34662 \begin_inset Newline newline
34669 \begin_layout Plain Layout
34684 \begin_layout Plain Layout
34691 {numerator}{denominator}
34694 \begin_layout Standard
34695 The style is a number in the range of 0
34696 \begin_inset space \thinspace{}
34700 \begin_inset space \thinspace{}
34706 \begin_layout Standard
34708 \begin_inset Tabular
34709 <lyxtabular version="3" rows="5" columns="2">
34711 <column alignment="center" valignment="top" width="0">
34712 <column alignment="center" valignment="top" width="0">
34714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34717 \begin_layout Plain Layout
34723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34726 \begin_layout Plain Layout
34734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34737 \begin_layout Plain Layout
34743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34746 \begin_layout Plain Layout
34747 display style formula
34754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34757 \begin_layout Plain Layout
34763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34766 \begin_layout Plain Layout
34774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34777 \begin_layout Plain Layout
34783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34786 \begin_layout Plain Layout
34794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34797 \begin_layout Plain Layout
34803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34806 \begin_layout Plain Layout
34820 \begin_layout Standard
34821 When no style is given, the size is adjusted to the surrounding environment
34822 like for the command
34831 \begin_layout Standard
34832 When no fraction bar thickness is given, the predefined value of 0.4
34833 \begin_inset space \thinspace{}
34839 \begin_layout Standard
34840 \begin_inset VSpace medskip
34843 For example, the commands
34856 \begin_inset CommandInset ref
34858 reference "sub:Fractions"
34862 are defined with the commands
34865 \begin_layout Standard
34874 genfrac{}{}{}{0}{#1}{#2}}
34877 \begin_layout Standard
34881 \begin_layout Standard
34890 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34893 \begin_layout Standard
34894 \begin_inset VSpace medskip
34897 To define a fraction where the fraction bar thickness can be given as optional
34898 argument, the following line is inserted to the LaTeX-preamble:
34901 \begin_layout Standard
34910 genfrac{}{}{#1}{}{#2}{#3}}
34913 \begin_layout Standard
34915 \begin_inset Formula \begin{align*}
34916 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34917 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34921 As one can see, the distance of the numerator and the denominator to the
34922 fraction bar is round about three times the bar thickness.
34925 \begin_layout Subsection
34930 \begin_layout Plain Layout
34939 \begin_layout Standard
34940 To cancel formulas or formula parts, the LaTeX-package
34948 \begin_layout Plain Layout
34953 is part of every LaTeX standard installation.
34962 \begin_layout Plain Layout
34968 has to be loaded with the LaTeX-preamble line
34971 \begin_layout Standard
34976 usepackage[samesize]{cancel}
34979 \begin_layout Standard
34980 There are four ways to cancel formulas:
34983 \begin_layout Standard
34985 \begin_inset Tabular
34986 <lyxtabular version="3" rows="5" columns="2">
34988 <column alignment="center" valignment="top" width="0">
34989 <column alignment="center" valignment="top" width="0">
34991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34994 \begin_layout Plain Layout
35000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35003 \begin_layout Plain Layout
35005 \begin_inset Note Note
35008 \begin_layout Plain Layout
35015 are used here as spacer.
35027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35030 \begin_layout Plain Layout
35039 \begin_layout Plain Layout
35053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35056 \begin_layout Plain Layout
35057 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35070 \begin_layout Plain Layout
35079 \begin_layout Plain Layout
35093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35096 \begin_layout Plain Layout
35097 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35110 \begin_layout Plain Layout
35119 \begin_layout Plain Layout
35133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35136 \begin_layout Plain Layout
35137 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35150 \begin_layout Plain Layout
35154 \begin_inset Formula $\to$
35165 \begin_layout Plain Layout
35179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35182 \begin_layout Plain Layout
35183 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35199 \begin_layout Standard
35206 is especially suitable to visualize the reduction of fractions within formulas:
35207 \begin_inset Formula \[
35208 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35215 \begin_layout Subsection
35216 Formulas in Section Headings
35217 \begin_inset CommandInset label
35219 name "sub:Formulas-in-Section"
35227 \begin_layout Plain Layout
35228 Formula ! in section headings
35236 \begin_layout Standard
35237 When formulas are used in section headings, the following has to be taken
35241 \begin_layout Standard
35242 \begin_inset Note Greyedout
35245 \begin_layout Plain Layout
35254 \begin_layout Plain Layout
35255 Packages ! hyperref
35260 support is enabled in the document settings dialog under
35263 \begin_inset space ~
35268 , PDF-bookmarks are created for every section heading in the table of contents.
35269 If a section heading contains formulas, they are incorrectly displayed
35270 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35279 \begin_layout Standard
35280 Both problems can be solved by inserting at the end of the section heading
35281 a short title with the menu
35283 Insert\SpecialChar \menuseparator
35285 \begin_inset space ~
35291 Short titles are used as alternative for multiline section headings to
35292 keep the table of contents clearly arranged.
35293 Only the short title appears in the table of contents and therefore also
35294 in the PDF-bookmark.
35297 \begin_layout Standard
35298 When formulas should be used in the table of contents but
35302 is used, one can use the following command in TeX-mode:
35305 \begin_layout Standard
35310 texorpdfstring{part}{alternative}
35314 \begin_layout Plain Layout
35325 \begin_layout Standard
35326 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35327 This can be characters, formulas, footnotes, but also cross-references.
35328 The alternative is used instead of the part for the bookmark.
35331 \begin_layout Standard
35332 Here are two example headings:
35333 \begin_inset VSpace -3mm
35340 \begin_layout Plain Layout
35352 \begin_layout Subsubsection
35353 Heading without formula in table of contents
35354 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35358 \begin_inset OptArg
35361 \begin_layout Plain Layout
35362 Heading without formula in table of contents
35370 \begin_layout Subsubsection
35371 Heading with formula in table of contents
35375 \begin_layout Plain Layout
35385 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35392 \begin_layout Plain Layout
35402 \begin_layout Standard
35406 \begin_layout Plain Layout
35415 In the first heading a short title was used, in the second one
35424 \begin_layout Standard
35425 To get the same formatting as for the other headings, the complete heading
35434 \begin_layout Plain Layout
35436 \begin_inset CommandInset ref
35438 reference "sub:Bold-Formulas"
35450 \begin_layout Subsection
35451 Formulas in multi-column Text
35455 \begin_layout Plain Layout
35456 Formula ! in multi-column text
35464 \begin_layout Standard
35465 Formulas in multi-column text are often too wide to fit into a column and
35466 thus need to be set over the whole page width.
35467 This is done by using the LaTeX-package
35475 \begin_layout Plain Layout
35480 is part of every LaTeX standard installation.
35489 \begin_layout Plain Layout
35490 Packages ! multicol
35495 , that is loaded with the LaTeX-preamble line
35498 \begin_layout Standard
35503 usepackage{multicol}
35506 \begin_layout Standard
35507 \begin_inset Note Greyedout
35510 \begin_layout Plain Layout
35511 Note herby that the setting
35514 \begin_inset space ~
35521 Document\SpecialChar \menuseparator
35527 \begin_inset space ~
35547 \begin_layout Standard
35548 Before the multi-column text the command
35551 \begin_layout Standard
35556 begin{multicols}{column number}
35559 \begin_layout Standard
35560 is written in TeX-mode.
35561 The column number is a number in the range of 2
35562 \begin_inset space \thinspace{}
35566 \begin_inset space \thinspace{}
35570 Before the formula the multi-column text is ended by inserting the command
35573 \begin_layout Standard
35581 \begin_layout Standard
35585 \begin_layout Standard
35586 Due to the command some space is automatically added before the formula.
35588 \begin_inset space \thinspace{}
35591 mm vertical space is inserted before the formula.
35592 When the formula style
35598 \begin_layout Plain Layout
35600 \begin_inset CommandInset ref
35602 reference "sec:Formula-Styles"
35614 \begin_inset space \thinspace{}
35617 mm space is inserted instead.
35620 \begin_layout Standard
35621 As example a multi-column text with a displayed formula:
35624 \begin_layout Standard
35630 \begin_layout Plain Layout
35634 begin{multicols}{2}
35639 Das Spektrum wird fouriertransformiert.
35640 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35641 , Lösungsmittel) zu trennen.
35642 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35643 nun das Aussehen des Ausgangssignals.
35644 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35645 über alle Phasen integrieren muss.
35647 \begin_inset Formula $S$
35650 unser normiertes Ausgangssignal und
35651 \begin_inset Formula $P$
35654 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35658 \begin_layout Plain Layout
35668 \begin_inset VSpace -6mm
35672 \begin_inset Formula \begin{equation}
35673 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35681 \begin_layout Plain Layout
35685 begin{multicols}{2}
35691 \begin_inset Formula $S_{0}$
35694 das Signal ohne Gradient ist und die Normierungsbedingung
35695 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35699 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35701 \begin_inset Formula $\nicefrac{\pi}{2}$
35705 \begin_inset space \thinspace{}
35708 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35709 das Signal zusätzlich abschwächt.
35710 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35712 \begin_inset Formula $T_{2}$
35718 \begin_layout Standard
35724 \begin_layout Plain Layout
35736 \begin_layout Subsection
35737 Formulas with Description of Variables
35741 \begin_layout Plain Layout
35742 Formula ! with description of variables
35750 \begin_layout Standard
35751 To describe variables within a formula, like in formula
35752 \begin_inset CommandInset ref
35754 reference "eq:within"
35763 \begin_inset Formula $n$
35767 \begin_inset space ~
35770 matrix is used with left aligned columns for the
35771 \begin_inset Formula $n$
35778 \begin_layout Plain Layout
35780 \begin_inset CommandInset ref
35782 reference "sec:Matrices"
35791 To set the description in a smaller size, before the matrix e.
35792 \begin_inset space \thinspace{}
35796 \begin_inset space \space{}
35809 \begin_layout Plain Layout
35811 \begin_inset CommandInset ref
35813 reference "sub:Font-Sizes"
35825 \begin_layout Standard
35826 When the formula style
35832 \begin_layout Plain Layout
35834 \begin_inset CommandInset ref
35836 reference "sec:Formula-Styles"
35857 \begin_layout Plain Layout
35864 only works in formulas with the style
35869 \begin_inset CommandInset ref
35871 reference "sub:Variable-Space"
35880 is inserted before and after the matrix to have the same separation of
35881 the matrix from the equation and the side margin.
35884 \begin_layout Standard
35885 When the formula style
35889 is used, the method described in
35890 \begin_inset CommandInset ref
35892 reference "sub:Flalign-Environment"
35896 is used to indent formulas.
35898 \begin_inset CommandInset ref
35900 reference "eq:within"
35904 consists of five columns whereas in the first two columns contain the equation,
35905 the third the matrix, and the last one an empty TeX-brace.
35906 \begin_inset Formula \begin{flalign}
35907 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35908 \rho & \textrm{density}\\
35909 V & \textrm{volume}\\
35910 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35917 \begin_layout Subsection
35918 Upright small Greek Letters
35919 \begin_inset CommandInset label
35921 name "sub:Upright-small-Greek"
35929 \begin_layout Plain Layout
35930 Greek letters ! upright
35938 \begin_layout Standard
35939 Most of the math fonts only provide italic small Greek letters.
35940 But for symbols of elementary particles like pions and neutrinos, upright
35941 Greek letters are needed.
35950 \begin_layout Plain Layout
35955 is part of the LaTeX-package
35963 \begin_layout Plain Layout
35968 \begin_layout Plain Layout
35991 \begin_layout Plain Layout
35997 that is loaded with the LaTeX-preamble line
36000 \begin_layout Standard
36005 usepackage{upgreek}
36008 \begin_layout Standard
36014 \begin_layout Plain Layout
36024 \begin_inset Note Note
36027 \begin_layout Plain Layout
36028 The following table will only be displayed when the LaTeX-package
36037 They are created when the command for a small Greek letters is started
36043 For example the command
36050 \begin_inset Formula $\uptau$
36056 \begin_layout Standard
36057 With these commands reactions of elementary particles can be typeset:
36058 \begin_inset Formula \[
36059 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36066 \begin_layout Standard
36067 The upright letters are more bold and wider than the italic ones.
36068 They should therefore not be used for units like
36069 \begin_inset Quotes eld
36073 \begin_inset Quotes erd
36079 \begin_layout Standard
36083 \begin_layout Plain Layout
36093 \begin_inset Note Note
36096 \begin_layout Plain Layout
36097 The following will be displayed when the LaTeX-package
36109 \begin_layout Standard
36110 You need to install the LaTeX-package
36114 to see the rest of this subsection in the output.
36117 \begin_layout Standard
36121 \begin_layout Plain Layout
36133 \begin_layout Subsection
36134 Text Characters in Formulas
36135 \begin_inset CommandInset label
36137 name "sub:Text-Characters-in"
36145 \begin_layout Plain Layout
36154 \begin_layout Standard
36155 In some cases you might want to insert text characters directly into formulas.
36156 When for example the centered dot · is often used in formulas like
36157 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36160 , one would have to insert the command
36170 \begin_layout Plain Layout
36172 \begin_inset CommandInset ref
36174 reference "sub:Binary-Operators"
36183 all the time, because this character is defined in all encodings as text
36185 But the encoding can be changed by this LaTeX-preamble line:
36188 \begin_layout Standard
36193 Declare Inputtext{183}{
36203 f\SpecialChar \textcompwordmark{}
36207 \begin_layout Standard
36208 The character encoding (menu
36210 Document\SpecialChar \menuseparator
36211 Settings\SpecialChar \menuseparator
36214 ) specifies what character appears when a keyboard key is pressed.
36215 When the key for the character '·' is pressed, internally the command
36222 But this command is not available in a formula so that you would get LaTeX-erro
36224 With the changed encoding the right command is chosen automatically, depending
36225 on if the character was inserted into a formula or not.
36228 \begin_layout Standard
36229 The encoding of several characters is saved in definition files.
36230 Fore example the encoding
36234 is defined in the file
36238 that is in the installation folder of LaTeX.
36239 Encodings should only be changed via the LaTeX-preamble and not in the
36241 Otherwise own documents could not be edited by other LyX users working
36242 on other computers.
36245 \begin_layout Standard
36246 \begin_inset VSpace medskip
36249 Besides the centered dot, in this document the degree sign ° is defined
36250 with the following LaTeX-preamble line so that it can directly be inserted
36254 \begin_layout Standard
36259 DeclareInputtext{176}{
36269 f\SpecialChar \textcompwordmark{}
36273 \begin_layout Standard
36274 \begin_inset Newpage newpage
36280 \begin_layout Section
36286 \begin_layout Plain Layout
36295 \begin_layout Standard
36296 This section is a summary of the most important typographic rules, listed
36301 \begin_layout Plain Layout
36302 This collection was partly taken from the German semi-official dictionary
36304 \begin_inset Quotes eld
36308 \begin_inset Quotes erd
36312 \begin_inset CommandInset citation
36318 that lists some of the ISO rules.
36326 \begin_layout Itemize
36335 \begin_layout Plain Layout
36336 done with font styles, see
36337 \begin_inset CommandInset ref
36339 reference "sub:Font-Styles"
36349 \begin_inset space \thinspace{}
36353 \begin_inset Newline newline
36356 Between the value and the unit is the smallest space, see
36357 \begin_inset CommandInset ref
36359 reference "sub:Predefined-Space"
36364 \begin_inset Newline newline
36367 This convention is automatically fulfilled when the command
36374 When it is entered to a formula, two boxes appear.
36375 In the first one the value is inserted, in the second one the unit, and
36377 \begin_inset Formula $\unit[30]{km/h}$
36381 \begin_inset space \thinspace{}
36391 is not a real LaTeX command but the command
36397 , therefore you cannot use it in TeX code.
36400 \begin_layout Itemize
36401 Percent and perthousand signs are set like physical units:
36402 \begin_inset Newline newline
36406 \begin_inset space \thinspace{}
36412 \begin_layout Itemize
36413 The degree sign follows directly on the value: 15°, but not when it is used
36415 \begin_inset space \thinspace{}
36421 \begin_layout Itemize
36422 In numbers with more than four digits the smallest space is inserted before
36423 every third digit to group them:
36433 \begin_inset space \thinspace{}
36437 \begin_inset space \thinspace{}
36443 \begin_layout Itemize
36444 For dimensions like 120×90×40
36445 \begin_inset space \thinspace{}
36448 cm the multiplication sign
36449 \begin_inset Quotes eld
36453 \begin_inset Quotes erd
36457 It is available via the menu
36459 Insert\SpecialChar \menuseparator
36460 Special Character\SpecialChar \menuseparator
36464 With some keyboard definitions it can also be inserted directly.
36467 \begin_layout Itemize
36468 Functions with names consisting of several letters are set upright to avoid
36470 \begin_inset CommandInset ref
36472 reference "sub:Predefined-Functions"
36479 \begin_layout Itemize
36480 Indices consisting of several letters, are set upright:
36481 \begin_inset Formula $E_{\mathrm{kin}}$
36485 \begin_inset Newline newline
36488 Components of matrices are set italic:
36489 \begin_inset Formula $\hat{H}_{kl}$
36495 \begin_layout Itemize
36496 The differentiation/integration operator 'd', the Euler's number 'e', and
36497 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36501 \begin_layout Standard
36502 \begin_inset Newpage newpage
36508 \begin_layout Section
36513 \begin_layout Plain Layout
36522 \begin_layout Standard
36523 Some characters and symbols can be created with several commands.
36524 Here is a list of the synonym commands:
36527 \begin_layout Standard
36528 \begin_inset VSpace bigskip
36532 \begin_inset space \hfill{}
36536 \begin_inset Tabular
36537 <lyxtabular version="3" rows="12" columns="2">
36539 <column alignment="center" valignment="top" width="0pt">
36540 <column alignment="center" valignment="top" width="0pt">
36542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36545 \begin_layout Plain Layout
36551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36554 \begin_layout Plain Layout
36556 \begin_inset Note Note
36559 \begin_layout Plain Layout
36566 is only used as spacer.
36578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36581 \begin_layout Plain Layout
36589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36592 \begin_layout Plain Layout
36596 \begin_layout Plain Layout
36609 \begin_layout Plain Layout
36623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36626 \begin_layout Plain Layout
36634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36637 \begin_layout Plain Layout
36647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36650 \begin_layout Plain Layout
36658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36661 \begin_layout Plain Layout
36671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36674 \begin_layout Plain Layout
36682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36685 \begin_layout Plain Layout
36693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36696 \begin_layout Plain Layout
36704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36707 \begin_layout Plain Layout
36715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36718 \begin_layout Plain Layout
36726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36729 \begin_layout Plain Layout
36739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36742 \begin_layout Plain Layout
36750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36753 \begin_layout Plain Layout
36763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36766 \begin_layout Plain Layout
36774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36777 \begin_layout Plain Layout
36787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36790 \begin_layout Plain Layout
36798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36801 \begin_layout Plain Layout
36811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36814 \begin_layout Plain Layout
36822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36825 \begin_layout Plain Layout
36833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36836 \begin_layout Plain Layout
36844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36847 \begin_layout Plain Layout
36859 \begin_inset space \hfill{}
36863 \begin_inset Tabular
36864 <lyxtabular version="3" rows="12" columns="2">
36866 <column alignment="center" valignment="top" width="0pt">
36867 <column alignment="center" valignment="top" width="0pt">
36869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36872 \begin_layout Plain Layout
36878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36881 \begin_layout Plain Layout
36889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36892 \begin_layout Plain Layout
36900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36903 \begin_layout Plain Layout
36915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36918 \begin_layout Plain Layout
36926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36929 \begin_layout Plain Layout
36939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36942 \begin_layout Plain Layout
36950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36953 \begin_layout Plain Layout
36963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36966 \begin_layout Plain Layout
36974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36977 \begin_layout Plain Layout
36985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36988 \begin_layout Plain Layout
36996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36999 \begin_layout Plain Layout
37007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37010 \begin_layout Plain Layout
37018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37021 \begin_layout Plain Layout
37031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37034 \begin_layout Plain Layout
37042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37045 \begin_layout Plain Layout
37055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37058 \begin_layout Plain Layout
37066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37069 \begin_layout Plain Layout
37079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37082 \begin_layout Plain Layout
37090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37093 \begin_layout Plain Layout
37103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37106 \begin_layout Plain Layout
37114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37117 \begin_layout Plain Layout
37127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37130 \begin_layout Plain Layout
37138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37141 \begin_layout Plain Layout
37155 \begin_inset space \hfill{}
37161 \begin_layout Standard
37162 \begin_inset Newpage newpage
37168 \begin_layout Bibliography
37169 \begin_inset CommandInset bibitem
37170 LatexCommand bibitem
37182 The LaTeX Companion
37185 Addison Wesley, 2004
37188 \begin_layout Bibliography
37189 \begin_inset CommandInset bibitem
37190 LatexCommand bibitem
37196 \begin_inset CommandInset href
37199 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37203 of LaTeX's math abilities
37206 \begin_layout Bibliography
37207 \begin_inset CommandInset bibitem
37208 LatexCommand bibitem
37213 LaTeX tips and tricks-
37214 \begin_inset CommandInset href
37217 target "http://tug.org/TeXnik/"
37224 \begin_layout Bibliography
37225 \begin_inset CommandInset bibitem
37226 LatexCommand bibitem
37232 \begin_inset CommandInset href
37235 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37243 \begin_layout Plain Layout
37255 \begin_layout Bibliography
37256 \begin_inset CommandInset bibitem
37257 LatexCommand bibitem
37263 \begin_inset CommandInset href
37266 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37270 of all symbols available with LaTeX-packages
37273 \begin_layout Bibliography
37274 \begin_inset CommandInset bibitem
37275 LatexCommand bibitem
37281 \begin_inset CommandInset href
37283 name "Documentation"
37284 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37288 of the LaTeX-package
37296 \begin_layout Plain Layout
37297 Packages ! hyperref
37305 \begin_layout Bibliography
37306 \begin_inset CommandInset bibitem
37307 LatexCommand bibitem
37313 \begin_inset CommandInset href
37315 name "Documentation"
37316 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37320 of the LaTeX-package
37328 \begin_layout Plain Layout
37337 \begin_layout Bibliography
37338 \begin_inset CommandInset bibitem
37339 LatexCommand bibitem
37345 \begin_inset CommandInset href
37348 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37359 \begin_inset CommandInset ref
37361 reference "sub:Operator-Limits"
37369 \begin_layout Plain Layout
37380 \begin_layout Bibliography
37381 \begin_inset CommandInset bibitem
37382 LatexCommand bibitem
37393 Auflage, Duden 2001
37396 \begin_layout Subsubsection*
37397 \begin_inset CommandInset index_print
37398 LatexCommand printindex