1 #LyX 1.6.3svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % center multirows (e.g. in sec. 13.3)
86 \renewcommand{\multirowsetup}{\centering}
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % redefine the greyed out note
113 \renewenvironment{lyxgreyedout}
114 {\textcolor{blue}\bgroup}{\egroup}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % needed for math macros
129 % check for package xargs
131 \IfFileExists{xargs.sty}
133 \setboolean{xargs}{true}}
134 {\setboolean{xargs}{false}}
136 % needed in sec. 22.4
137 % check for package braket
139 \IfFileExists{braket.sty}
141 \setboolean{braket}{true}}
142 {\setboolean{braket}{false}}
144 % needed in sec. 22.10
145 % check for package upgreek
147 \IfFileExists{upgreek.sty}
148 {\usepackage{upgreek}
149 \setboolean{upgreek}{true}}
150 {\setboolean{upgreek}{false}}
152 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
153 \use_default_options false
158 \font_typewriter default
159 \font_default_family default
169 \pdf_title "LyX's Math Manual"
170 \pdf_author "LyX Team, Uwe Stöhr"
171 \pdf_subject "LyX-documentation about math"
172 \pdf_keywords "LyX, Mathed"
174 \pdf_bookmarksnumbered true
175 \pdf_bookmarksopen true
176 \pdf_bookmarksopenlevel 1
177 \pdf_breaklinks false
181 \pdf_pdfusetitle false
182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
189 \paperorientation portrait
192 \paragraph_separation skip
194 \quotes_language english
197 \paperpagestyle plain
201 \tracking_changes false
202 \output_changes false
210 LyX's detailed Math manual
218 \begin_layout Plain Layout
220 If you have comments or error corrections, please send them to the LyX Documenta
224 \begin_inset CommandInset href
226 name "lyx-docs@lists.lyx.org"
227 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
238 \begin_inset Note Note
241 \begin_layout Plain Layout
248 \begin_inset Newline newline
252 \begin_inset Newline newline
260 \begin_layout Standard
261 \begin_inset CommandInset toc
262 LatexCommand tableofcontents
269 \begin_layout Standard
270 \begin_inset Note Note
273 \begin_layout Plain Layout
274 To export this document to PDF, PS, or DVI the LaTeX-packages
287 If they are not installed you can export the document anyway but the sections
288 where the packages are required won't appear in the output.
291 \begin_layout Plain Layout
292 The latest PDF-version of this document can be found here:
293 \begin_inset Newline newline
298 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
306 \begin_layout Standard
307 \begin_inset Newpage newpage
313 \begin_layout Section
317 \begin_layout Standard
318 This document explains LyX's math features and is furthermore a collection
319 of LaTeX-commands used for mathematical characters and constructs.
320 The explanations are designed for the usage of commands.
321 It is therefore required that you have read the section
332 \begin_layout Standard
333 Most of the characters and many constructs explained in this manual are
334 also accessible via the menu
338 \SpecialChar \menuseparator
354 But everybody who has to write lots of formulas will notice that it is
355 much faster to use commands instead of the math toolbar.
356 Therefore this manual is focused on commands but also mentions the correspondin
357 g toolbar buttons when available.
360 \begin_layout Standard
361 If not specially mentioned the commands are only available within formulas.
362 To be able to use all commands explained in this document, the option
366 must be used in the document settings (menu
368 Document\SpecialChar \menuseparator
369 Settings\SpecialChar \menuseparator
380 \begin_layout Plain Layout
383 Use AMS math package automatically
389 \begin_layout Plain Layout
398 -math when math constructs are found that are supported by LyX.
406 \begin_layout Standard
407 This document doesn't list all
411 \begin_layout Plain Layout
424 \begin_layout Plain Layout
429 \begin_layout Plain Layout
438 -math commands is in the file
441 \begin_inset CommandInset href
444 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
450 , which is part of every LaTeX standard installation.
455 for lucidity reasons.
458 \begin_layout Section
462 \begin_layout Standard
463 To create an inline formula
467 \begin_layout Plain Layout
473 that is embedded into a text line, use one of the shortcuts
479 or the toolbar button
480 \begin_inset Graphics
481 filename ../images/math-mode.png
487 \begin_inset Newline newline
490 To create a display style formula
494 \begin_layout Plain Layout
495 Formula ! display style
500 that will appear bigger and in an own paragraph, use one of these shortcuts:
510 \begin_layout Standard
511 To change a display style formula to an inline formula, set the cursor into
512 the formula and use one of the shortcuts
520 Edit\SpecialChar \menuseparator
521 Math\SpecialChar \menuseparator
525 The same way is used to change an inline formula to a display style formula.
528 \begin_layout Standard
529 To display parts of an inline formula in the size of a display style formula,
538 \begin_layout Plain Layout
549 Then a new blue box appears in which the desired formula part is inserted.
552 \begin_layout Standard
553 Only inline formulas are allowed inside tables.
556 \begin_layout Standard
561 can be turned on in the menu
563 View\SpecialChar \menuseparator
567 When you click there on
568 \begin_inset Quotes eld
572 \begin_inset Quotes erd
575 the toolbar will be shown permanently at the bottom; this state is visualized
580 menu with a checkmark.
581 When you click in this state again on
582 \begin_inset Quotes eld
586 \begin_inset Quotes erd
597 is only shown when the cursor is within a formula; this state is visualized
598 by the renaming of the menu entry from
599 \begin_inset Quotes eld
603 \begin_inset Quotes erd
607 \begin_inset Quotes eld
615 \begin_inset Quotes erd
621 \begin_layout Standard
626 \begin_layout Plain Layout
632 is invoked by pressing the toolbar button
633 \begin_inset Graphics
634 filename ../images/ert-insert.png
641 Insert\SpecialChar \menuseparator
646 \begin_layout Plain Layout
662 \begin_inset Note Note
665 \begin_layout Plain Layout
666 In LyX there are three
667 \begin_inset Quotes eld
671 \begin_inset Quotes erd
674 that appear in the output with sub- and superscript letters: TeX, LaTeX,
678 \begin_layout Plain Layout
679 To avoid that these names are recognized as proper names, a TeX-brace pair
688 \begin_layout Standard
689 To change the LaTeX-preamble
693 \begin_layout Plain Layout
701 Document\SpecialChar \menuseparator
702 Settings\SpecialChar \menuseparator
707 \begin_layout Plain Layout
723 \begin_layout Standard
724 To edit matrices, case differentiations, and multiline formulas subsequently,
727 Edit\SpecialChar \menuseparator
732 Edit\SpecialChar \menuseparator
734 \begin_inset space \thinspace{}
738 \begin_inset space \thinspace{}
748 When lines and columns are swapped via the menu, the column or line where
749 the cursor is in is exchanged with the column to the right or the line
751 Is the cursor in the last column or row, the exchange is done with the
752 column to the left or the line above.
755 \begin_layout Standard
756 To write text in formulas
760 \begin_layout Plain Layout
761 For multiline formulas the command
768 \begin_inset CommandInset ref
770 reference "sub:Text-in-multiline"
787 \begin_layout Plain Layout
797 \begin_layout Plain Layout
804 This mode is invoked with the the shortcut
810 or by the insertion of the command
818 \begin_layout Plain Layout
829 The text appears black in LyX and can therefore be distinguished from the
830 other formula parts that appear blue.
831 In the output mathematical text is set upright, in contrary to other formula
835 \begin_layout Subsection*
839 \begin_layout Standard
840 Most of the LaTeX-commands for math constructs have the following scheme:
843 \begin_layout Standard
859 \begin_layout Standard
860 A command starts always with a backslash
861 \begin_inset Quotes gld
871 \begin_inset Quotes grd
875 To omit optional arguments, also omit the associated brackets.
876 The braces around the required arguments are named in this document as
881 \begin_layout Plain Layout
888 If you add in a formula a left brace to a command name, LyX creates automatical
890 In all other cases TeX-braces are created in formulas with the command
898 TeX-braces appear red in LyX, in contrary to normal braces that appear
900 In TeX-mode no command is needed to get TeX-braces.
901 TeX-braces don't appear in the output.
904 \begin_layout Standard
905 When commands without arguments, like commands for symbols are entered in
906 TeX-mode, a space character must
910 be behind the command to end it.
911 This space doesn't appear in the output.
912 When the space should appear in the output, the space must be followed
913 by a protected space in normal text.
916 \begin_layout Standard
917 A protected space is inserted with
920 arg "space-insert protected"
926 \begin_layout Subsection*
927 \begin_inset Newpage newpage
933 \begin_layout Itemize
938 \begin_layout Plain Layout
939 This visible space character can be created with the command
949 \begin_layout Plain Layout
957 , inserted in TeX-mode.
966 \begin_layout Plain Layout
979 denotes a space character to be input.
982 \begin_layout Itemize
984 \begin_inset Formula $\to$
987 denotes the usage of the corresponding arrow key on the keyboard.
990 \begin_layout Subsection*
994 \begin_layout Standard
996 \begin_inset Float table
1002 \begin_layout Plain Layout
1004 \begin_inset Caption
1006 \begin_layout Plain Layout
1007 \begin_inset CommandInset label
1009 name "tab:Available-units"
1021 \begin_layout Plain Layout
1023 \begin_inset Tabular
1024 <lyxtabular version="3" rows="13" columns="2">
1026 <column alignment="center" valignment="top" width="0">
1027 <column alignment="center" valignment="top" width="0">
1029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1032 \begin_layout Plain Layout
1038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1041 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1092 \begin_layout Plain Layout
1098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1101 \begin_layout Plain Layout
1103 \begin_inset space \thinspace{}
1107 \begin_inset space \thinspace{}
1117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1120 \begin_layout Plain Layout
1126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1129 \begin_layout Plain Layout
1131 \begin_inset space \thinspace{}
1135 \begin_inset space \thinspace{}
1145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1148 \begin_layout Plain Layout
1154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1157 \begin_layout Plain Layout
1159 \begin_inset space \thinspace{}
1163 \begin_inset space \thinspace{}
1173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1176 \begin_layout Plain Layout
1182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1185 \begin_layout Plain Layout
1187 \begin_inset space \thinspace{}
1191 \begin_inset space \thinspace{}
1201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1204 \begin_layout Plain Layout
1210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1213 \begin_layout Plain Layout
1215 \begin_inset space \thinspace{}
1219 \begin_inset space \thinspace{}
1229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1232 \begin_layout Plain Layout
1238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1241 \begin_layout Plain Layout
1243 \begin_inset space \thinspace{}
1247 \begin_inset Formula $\approx$
1251 \begin_inset space \thinspace{}
1261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1264 \begin_layout Plain Layout
1270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1273 \begin_layout Plain Layout
1275 \begin_inset space \thinspace{}
1279 \begin_inset space \thinspace{}
1289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1292 \begin_layout Plain Layout
1298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1301 \begin_layout Plain Layout
1305 \begin_inset Quotes eld
1311 \begin_inset Quotes erd
1321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1324 \begin_layout Plain Layout
1330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1333 \begin_layout Plain Layout
1335 \begin_inset Quotes eld
1343 \begin_inset Quotes erd
1353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1356 \begin_layout Plain Layout
1362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1365 \begin_layout Plain Layout
1367 \begin_inset space \thinspace{}
1371 \begin_inset Formula $\nicefrac{1}{18}$
1375 \begin_inset space \thinspace{}
1396 \begin_layout Standard
1397 \begin_inset Newpage newpage
1403 \begin_layout Section
1407 \begin_layout Subsection
1412 \begin_layout Plain Layout
1422 \begin_layout Plain Layout
1432 \begin_layout Plain Layout
1437 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1464 \begin_layout Plain Layout
1469 \begin_layout Plain Layout
1480 \begin_layout Plain Layout
1495 \begin_layout Standard
1496 Indices are created with an underscore
1497 \begin_inset Quotes eld
1501 \begin_inset Quotes erd
1504 or via the math toolbar button
1505 \begin_inset Graphics
1506 filename ../images/math-subscript.png
1511 , exponents with a caret
1512 \begin_inset Quotes eld
1516 \begin_inset Quotes erd
1519 or via the math toolbar button
1520 \begin_inset Graphics
1521 filename ../images/math-superscript.png
1529 \begin_layout Standard
1531 \begin_inset Tabular
1532 <lyxtabular version="3" rows="4" columns="2">
1534 <column alignment="center" valignment="top" width="0pt">
1535 <column alignment="center" valignment="top" width="0pt">
1537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1540 \begin_layout Plain Layout
1546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1549 \begin_layout Plain Layout
1551 \begin_inset Note Note
1554 \begin_layout Plain Layout
1561 is only used as spacer.
1573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1576 \begin_layout Plain Layout
1582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1585 \begin_layout Plain Layout
1586 \begin_inset Formula $B_{V}$
1596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1599 \begin_layout Plain Layout
1605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1608 \begin_layout Plain Layout
1609 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1622 \begin_layout Plain Layout
1627 \begin_layout Plain Layout
1641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1644 \begin_layout Plain Layout
1645 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1661 \begin_layout Standard
1662 As the caret is in some languages an accent, vowels will be accentuated
1663 in this case and not set as exponents
1667 \begin_layout Plain Layout
1668 Depending on the used keyboard settings this can also happen for other character
1675 To get in this case exponents, press
1679 after the caret as in the last example.
1682 \begin_layout Subsection
1684 \begin_inset CommandInset label
1686 name "sub:Fractions"
1694 \begin_layout Plain Layout
1703 \begin_layout Standard
1704 Fractions are generated with the command
1714 \begin_layout Plain Layout
1722 or via the math toolbar button
1723 \begin_inset Graphics
1724 filename ../images/math/frac.png
1730 The font size is adjusted automatically, depending on whether the fraction
1731 is in an inline or display style formula.
1732 With the math toolbar button
1733 \begin_inset Graphics
1734 filename ../images/math/frac-square.png
1739 you can select different fraction types.
1742 \begin_layout Standard
1751 \begin_layout Plain Layout
1761 a fraction can be created that has in any case the size of a display style
1771 \begin_layout Plain Layout
1781 the fraction appears always with the size of an inline formula.
1785 \begin_layout Standard
1786 A line with the fraction
1787 \begin_inset Formula $\frac{1}{2}$
1790 that was created with the command
1799 \begin_layout Standard
1800 A line with the fraction
1801 \begin_inset Formula $\dfrac{1}{2}$
1804 that was created with the command
1813 \begin_layout Standard
1815 \begin_inset Tabular
1816 <lyxtabular version="3" rows="4" columns="2">
1818 <column alignment="center" valignment="top" width="0pt">
1819 <column alignment="center" valignment="top" width="0pt">
1821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1824 \begin_layout Plain Layout
1830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1833 \begin_layout Plain Layout
1835 \begin_inset Note Note
1838 \begin_layout Plain Layout
1845 is only used as spacer.
1857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1860 \begin_layout Plain Layout
1867 \begin_layout Plain Layout
1877 \begin_inset Formula $\downarrow$
1885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1888 \begin_layout Plain Layout
1889 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1902 \begin_layout Plain Layout
1909 \begin_layout Plain Layout
1919 \begin_inset Formula $\downarrow$
1927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1930 \begin_layout Plain Layout
1931 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1944 \begin_layout Plain Layout
1951 \begin_layout Plain Layout
1964 \begin_layout Plain Layout
1979 \begin_layout Plain Layout
1989 \begin_inset Formula $\downarrow$
1993 \begin_inset Formula $\downarrow\downarrow$
2001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2004 \begin_layout Plain Layout
2005 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2021 \begin_layout Standard
2022 \begin_inset VSpace bigskip
2026 \begin_inset Newpage newpage
2029 For nested fractions the command
2039 \begin_layout Plain Layout
2049 \begin_inset VSpace -3mm
2055 \begin_layout Standard
2056 \begin_inset Formula \begin{align*}
2057 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2058 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2065 \begin_layout Standard
2066 The command for the example above is:
2069 \begin_layout Standard
2075 \begin_inset Formula $\to$
2085 \begin_inset Formula $\to$
2091 \begin_inset Formula $\to\to$
2099 \begin_layout Standard
2100 \begin_inset VSpace medskip
2106 \begin_layout Standard
2113 sets the fraction always in the size of a displayed formula, also when
2114 it is part of another fraction.
2121 has the following command scheme:
2124 \begin_layout Standard
2129 cfrac[numerator position]{numerator}{denominator}
2132 \begin_layout Standard
2133 The numerator position can be
2146 l or r aligns the numerator to the left or right, resp.
2147 \begin_inset space ~
2150 with the fraction stroke.
2155 or no position is given, the numerator appears centered.
2156 These fractions demonstrate the different alignments:
2157 \begin_inset Newline newline
2163 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2167 \begin_inset Formula $\cfrac{A}{B+C}$
2171 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2177 \begin_layout Standard
2178 \begin_inset VSpace medskip
2181 It is often advantageous to combine
2194 \begin_inset Formula \[
2195 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2202 \begin_layout Standard
2203 For inline fractions with a sloped fraction stroke you can use the command
2214 \begin_layout Plain Layout
2223 \begin_inset Formula $\nicefrac{5}{31}$
2236 \begin_layout Plain Layout
2245 \begin_inset Formula $\unitfrac{5}{31}$
2248 There is furthermore the command
2254 that offers to write a fraction in combination with a number:
2255 \begin_inset Formula $\unitfrac[2]{1}{3}$
2259 \begin_inset Newline newline
2268 is not a real LaTeX command but the command
2269 \begin_inset Newline newline
2276 unitfrac[number]{numerator}{denominator}
2278 , therefore you cannot use it in TeX code.
2281 \begin_layout Standard
2282 How to define own fractions where the fraction stroke can be changed, is
2284 \begin_inset CommandInset ref
2286 reference "sub:Self-defined-Fractions"
2293 \begin_layout Subsection
2298 \begin_layout Plain Layout
2307 \begin_layout Standard
2308 Square roots are created with
2318 \begin_layout Plain Layout
2326 or the math toolbar button
2327 \begin_inset Graphics
2328 filename ../images/math/sqrt.png
2333 , all other roots with the command
2343 \begin_layout Plain Layout
2351 or with the math toolbar button
2352 \begin_inset Graphics
2353 filename ../images/math/root.png
2361 \begin_layout Standard
2363 \begin_inset Tabular
2364 <lyxtabular version="3" rows="3" columns="2">
2366 <column alignment="center" valignment="top" width="0pt">
2367 <column alignment="center" valignment="top" width="0pt">
2369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2372 \begin_layout Plain Layout
2378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2381 \begin_layout Plain Layout
2383 \begin_inset Note Note
2386 \begin_layout Plain Layout
2393 is only used as spacer.
2405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2408 \begin_layout Plain Layout
2415 \begin_layout Plain Layout
2429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2432 \begin_layout Plain Layout
2433 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2446 \begin_layout Plain Layout
2453 \begin_layout Plain Layout
2463 \begin_inset Formula $\downarrow$
2471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2474 \begin_layout Plain Layout
2475 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2491 \begin_layout Standard
2492 A square root can also be created with
2498 when the root index field is left empty.
2501 \begin_layout Standard
2502 With certain indices the distance to the root is too small, like in this
2504 \begin_inset Formula $\sqrt[\beta]{B}$
2508 \begin_inset Newline newline
2512 \begin_inset Formula $\beta$
2516 To avoid this, the commands
2526 \begin_layout Plain Layout
2544 \begin_layout Plain Layout
2552 are used with the following scheme:
2555 \begin_layout Standard
2569 \begin_layout Standard
2570 Distance is the number of Big Points (unit bp;
2571 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2574 ), that the index should be moved to the left or top, resp..
2575 The commands are written to the index.
2576 This way the command
2577 \begin_inset Newline newline
2587 \begin_inset Formula $\to$
2593 \begin_inset Formula $\to$
2602 \begin_layout Plain Layout
2612 \begin_inset Formula $\to$
2616 \begin_inset Newline newline
2621 produces a correct typeset formula:
2622 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2628 \begin_layout Subsection
2629 Binomial Coefficients
2633 \begin_layout Plain Layout
2634 Binomial coefficients
2642 \begin_layout Standard
2643 Binomial coefficients are inserted with the command
2653 \begin_layout Plain Layout
2661 or with the submenu of the math toolbar button
2662 \begin_inset Graphics
2663 filename ../images/math/frac-square.png
2669 Analog to fractions (
2689 \begin_layout Plain Layout
2709 \begin_layout Plain Layout
2718 For other brackets around binomial coeficients there are the commands
2728 \begin_layout Plain Layout
2746 \begin_layout Plain Layout
2757 \begin_layout Standard
2759 \begin_inset Tabular
2760 <lyxtabular version="3" rows="6" columns="2">
2762 <column alignment="center" valignment="top" width="0pt">
2763 <column alignment="center" valignment="top" width="0pt">
2765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2768 \begin_layout Plain Layout
2774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2777 \begin_layout Plain Layout
2779 \begin_inset Note Note
2782 \begin_layout Plain Layout
2789 is only used as spacer.
2801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2804 \begin_layout Plain Layout
2811 \begin_layout Plain Layout
2821 \begin_inset Formula $\downarrow$
2829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2832 \begin_layout Plain Layout
2833 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2846 \begin_layout Plain Layout
2853 \begin_layout Plain Layout
2863 \begin_inset Formula $\downarrow$
2871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2874 \begin_layout Plain Layout
2875 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2888 \begin_layout Plain Layout
2895 \begin_layout Plain Layout
2905 \begin_inset Formula $\downarrow$
2913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2916 \begin_layout Plain Layout
2917 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2930 \begin_layout Plain Layout
2937 \begin_layout Plain Layout
2947 \begin_inset Formula $\downarrow$
2955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2958 \begin_layout Plain Layout
2959 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2972 \begin_layout Plain Layout
2979 \begin_layout Plain Layout
2989 \begin_inset Formula $\downarrow$
2997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3017 \begin_layout Subsection
3018 Case Differentiations
3022 \begin_layout Plain Layout
3023 Case differentiations
3031 \begin_layout Standard
3033 \begin_inset Tabular
3034 <lyxtabular version="3" rows="3" columns="2">
3036 <column alignment="center" valignment="top" width="0pt">
3037 <column alignment="center" valignment="top" width="0pt">
3039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3042 \begin_layout Plain Layout
3048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3051 \begin_layout Plain Layout
3059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3062 \begin_layout Plain Layout
3069 \begin_layout Plain Layout
3079 \begin_inset Formula $\to$
3086 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3102 \begin_layout Plain Layout
3103 \begin_inset Formula $\begin{cases}
3114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3117 \begin_layout Plain Layout
3124 \begin_layout Plain Layout
3136 arg "newline-insert newline"
3144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3147 \begin_layout Plain Layout
3148 \begin_inset Formula $\begin{cases}
3149 A & \textrm{for }x>0\\
3150 B & \textrm{for }x=0\end{cases}$
3166 \begin_layout Standard
3173 or the usage of the math toolbar button
3174 \begin_inset Graphics
3175 filename ../images/math/cases.png
3180 you can create new lines with the shortcut
3183 arg "newline-insert newline"
3186 or the table toolbar button
3187 \begin_inset Graphics
3188 filename ../images/tabular-feature_append-row.png
3196 \begin_layout Standard
3203 is also available via the menu
3205 Insert\SpecialChar \menuseparator
3206 Math\SpecialChar \menuseparator
3212 \begin_layout Subsection
3217 \begin_layout Plain Layout
3226 \begin_layout Standard
3237 \begin_layout Plain Layout
3245 every character can be displayed canceled.
3246 The characters are quasi accentuated by a slash.
3249 \begin_layout Standard
3251 \begin_inset Tabular
3252 <lyxtabular version="3" rows="4" columns="2">
3254 <column alignment="center" valignment="top" width="0pt">
3255 <column alignment="center" valignment="top" width="0pt">
3257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3260 \begin_layout Plain Layout
3266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3269 \begin_layout Plain Layout
3277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3280 \begin_layout Plain Layout
3288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3291 \begin_layout Plain Layout
3292 \begin_inset Formula $\not=$
3302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3305 \begin_layout Plain Layout
3315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3318 \begin_layout Plain Layout
3319 \begin_inset Formula $\not\le$
3329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3332 \begin_layout Plain Layout
3342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3345 \begin_layout Plain Layout
3346 \begin_inset Formula $\not\parallel$
3362 \begin_layout Standard
3363 The last example shows, that not all negations look good.
3364 Therefore there are for some negations special commands (see
3365 \begin_inset CommandInset ref
3367 reference "sub:Mathematical-Symbols"
3372 \begin_inset CommandInset ref
3374 reference "sec:Relations"
3381 \begin_layout Subsection
3383 \begin_inset CommandInset label
3385 name "sub:Placeholders"
3393 \begin_layout Plain Layout
3403 \begin_layout Plain Layout
3404 Chemical characters ! Isotopes
3413 \begin_layout Plain Layout
3418 \begin_layout Plain Layout
3429 \begin_layout Plain Layout
3444 \begin_layout Standard
3446 \begin_inset space \thinspace{}
3450 \begin_inset space \space{}
3457 \begin_layout Plain Layout
3458 More about chemical symbols is written in
3459 \begin_inset CommandInset ref
3461 reference "sub:Chemical-Symbols-and"
3470 the following problem occurs:
3473 \begin_layout Standard
3475 \begin_inset Tabular
3476 <lyxtabular version="3" rows="2" columns="2">
3478 <column alignment="center" valignment="top" width="0pt">
3479 <column alignment="center" valignment="top" width="0pt">
3481 <cell alignment="center" valignment="top" usebox="none">
3484 \begin_layout Plain Layout
3485 Indices created with sub- and superscripts:
3490 <cell alignment="center" valignment="top" usebox="none">
3493 \begin_layout Plain Layout
3494 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3504 <cell alignment="center" valignment="top" usebox="none">
3507 \begin_layout Plain Layout
3513 <cell alignment="center" valignment="top" usebox="none">
3516 \begin_layout Plain Layout
3517 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3531 \begin_inset Note Note
3534 \begin_layout Plain Layout
3541 is only used as spacer.
3549 \begin_layout Standard
3550 The shorter index is by default placed below or above the first character
3551 of the longer index.
3552 To avoid this there is the command
3562 \begin_layout Plain Layout
3570 or the math toolbar button
3571 \begin_inset space \thinspace{}
3578 \begin_layout Plain Layout
3579 can be found in the submenu of the toolbar button
3580 \begin_inset Graphics
3581 filename ../images/math/space.png
3592 \begin_inset Graphics
3593 filename ../images/math/phantom.png
3598 that creates one or more phantom characters.
3605 a small blue box appears that is superposed with two red arrows.
3606 The arrows indicate that the complete width and height of the box content
3607 will be created as placeholder.
3608 Phantom characters are accordingly placeholders with the size of the characters.
3611 \begin_layout Standard
3613 \begin_inset Tabular
3614 <lyxtabular version="3" rows="4" columns="2">
3616 <column alignment="center" valignment="top" width="0">
3617 <column alignment="center" valignment="top" width="0">
3619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3622 \begin_layout Plain Layout
3628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3631 \begin_layout Plain Layout
3633 \begin_inset Note Note
3636 \begin_layout Plain Layout
3643 is only used as spacer.
3655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3658 \begin_layout Plain Layout
3663 \begin_layout Plain Layout
3678 \begin_layout Plain Layout
3688 \begin_inset Formula $\to$
3695 \begin_layout Plain Layout
3709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3712 \begin_layout Plain Layout
3713 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3726 \begin_layout Plain Layout
3731 \begin_layout Plain Layout
3746 \begin_layout Plain Layout
3756 \begin_inset Formula $\to$
3763 \begin_layout Plain Layout
3777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3780 \begin_layout Plain Layout
3781 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3794 \begin_layout Plain Layout
3801 \begin_layout Plain Layout
3816 \begin_layout Plain Layout
3826 \begin_inset Formula $\to$
3833 \begin_layout Plain Layout
3847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3850 \begin_layout Plain Layout
3851 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3867 \begin_layout Standard
3868 Furthermore there are the commands
3878 \begin_layout Plain Layout
3887 \begin_inset space ~
3891 \begin_inset Graphics
3892 filename ../images/math/vphantom.png
3907 \begin_layout Plain Layout
3916 \begin_inset space ~
3920 \begin_inset Graphics
3921 filename ../images/math/hphantom.png
3933 creates only space for the maximal height of the characters in the box
3934 but not for its width.
3941 creates only space for the width of the box content.
3942 Therefore the boxes of both commands have only one red arrow.
3945 \begin_layout Standard
3956 \begin_layout Plain Layout
3971 space for the height of the integral sign,
3975 \begin_layout Plain Layout
3982 creates an integral sign, see
3983 \begin_inset CommandInset ref
3985 reference "sub:Big-Operators"
3994 because this is the larger character.
3995 An example application is in
3996 \begin_inset CommandInset ref
3998 reference "sub:Multiline-Brackets"
4005 \begin_layout Subsection
4010 \begin_layout Plain Layout
4020 \begin_layout Plain Layout
4021 Formula ! underlined
4029 \begin_layout Standard
4031 \begin_inset Tabular
4032 <lyxtabular version="3" rows="4" columns="2">
4034 <column alignment="center" valignment="top" width="0pt">
4035 <column alignment="center" valignment="top" width="0pt">
4037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4040 \begin_layout Plain Layout
4046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4049 \begin_layout Plain Layout
4051 \begin_inset Note Note
4054 \begin_layout Plain Layout
4061 is only used as spacer.
4073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4076 \begin_layout Plain Layout
4083 \begin_layout Plain Layout
4096 \begin_layout Plain Layout
4109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4112 \begin_layout Plain Layout
4113 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4126 \begin_layout Plain Layout
4133 \begin_layout Plain Layout
4146 \begin_layout Plain Layout
4159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4162 \begin_layout Plain Layout
4163 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4176 \begin_layout Plain Layout
4183 \begin_layout Plain Layout
4198 \begin_layout Plain Layout
4212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4215 \begin_layout Plain Layout
4216 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4232 \begin_layout Standard
4233 In the last example it doesn't matter if first
4248 \begin_layout Standard
4249 To double underline e.
4250 \begin_inset space \thinspace{}
4254 \begin_inset space \space{}
4266 \begin_layout Standard
4267 It is possible to place up to 6 lines above or below characters.
4270 \begin_layout Standard
4271 \begin_inset VSpace bigskip
4274 Custom lines can be created using the command
4284 \begin_layout Plain Layout
4292 which has the following scheme:
4295 \begin_layout Standard
4300 rule[vertical offset]{length}{thickness}
4303 \begin_layout Standard
4304 The optional vertical offset shifts the line upwards (or downwards, when
4305 the value is negative).
4307 \begin_inset CommandInset ref
4309 reference "tab:Available-units"
4313 can be used for the values.
4314 Here are two example lines created with the commands
4315 \begin_inset Newline newline
4322 rule[-2ex]{3cm}{2pt}
4333 \begin_layout Standard
4335 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4341 \begin_layout Standard
4348 can also be used for text when it is inserted in TeX-mode.
4351 \begin_layout Subsection
4353 \begin_inset CommandInset label
4363 \begin_layout Plain Layout
4372 \begin_layout Standard
4373 There are different types of ellipses available.
4377 \begin_layout Plain Layout
4378 In the math toolbar in the submenu of the button
4379 \begin_inset Graphics
4380 filename ../images/math/ldots.png
4390 For listings dots at the baseline are used (
4400 \begin_layout Plain Layout
4408 ), while for operations dots are needed that are on the same height as the
4419 \begin_layout Plain Layout
4428 When using the command
4438 \begin_layout Plain Layout
4446 , LaTeX decides on the basis of the next character what type is used.
4449 \begin_layout Standard
4451 \begin_inset Tabular
4452 <lyxtabular version="3" rows="8" columns="2">
4454 <column alignment="center" valignment="top" width="0pt">
4455 <column alignment="center" valignment="top" width="0pt">
4457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4460 \begin_layout Plain Layout
4466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4469 \begin_layout Plain Layout
4477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4480 \begin_layout Plain Layout
4485 \begin_layout Plain Layout
4500 \begin_layout Plain Layout
4514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4517 \begin_layout Plain Layout
4518 \begin_inset Formula $A_{1},\dots,A_{n}$
4528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4531 \begin_layout Plain Layout
4536 \begin_layout Plain Layout
4551 \begin_layout Plain Layout
4565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4568 \begin_layout Plain Layout
4569 \begin_inset Formula $A_{1}+\dots+A_{n}$
4579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4582 \begin_layout Plain Layout
4587 \begin_layout Plain Layout
4602 \begin_layout Plain Layout
4616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4619 \begin_layout Plain Layout
4620 \begin_inset Formula $A_{1},\ldots,A_{n}$
4630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4633 \begin_layout Plain Layout
4638 \begin_layout Plain Layout
4653 \begin_layout Plain Layout
4667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4670 \begin_layout Plain Layout
4671 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4684 \begin_layout Plain Layout
4692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4695 \begin_layout Plain Layout
4696 \begin_inset Formula $\vdots$
4706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4709 \begin_layout Plain Layout
4717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4720 \begin_layout Plain Layout
4721 \begin_inset Formula $\ddots$
4731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4734 \begin_layout Plain Layout
4736 \begin_inset space \thinspace{}
4739 matrix with the different dots
4744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4747 \begin_layout Plain Layout
4748 \begin_inset Formula $\begin{array}{ccc}
4749 A_{11} & \cdots & A_{1m}\\
4750 \vdots & \ddots & \vdots\\
4751 A_{n1} & \cdots & A_{nm}\end{array}$
4767 \begin_layout Standard
4768 The ellipses available in menu
4770 Insert\SpecialChar \menuseparator
4772 \begin_inset space ~
4786 \begin_layout Standard
4787 \begin_inset VSpace medskip
4790 Specially for matrices there are ellipses that span over several columns.
4791 They are created with the command
4801 \begin_layout Plain Layout
4809 , that has the following scheme:
4812 \begin_layout Standard
4817 hdotsfor[distance]{number of columns}
4820 \begin_layout Standard
4821 The number of columns specifies how many columns should be spanned.
4822 Distance is a factor for the distance between the dots.
4825 \begin_layout Standard
4826 In the following matrix the command
4832 was inserted in the first box of the second line, to get an ellipsis with
4833 a dot distance twice as long as with the command
4840 \begin_inset Formula \[
4841 \left(\begin{array}{cccc}
4844 q & w & e & r\end{array}\right)\]
4848 Note that the matrix fields that should be spanned must be empty, otherwise
4849 you get LaTeX-errors.
4852 \begin_layout Standard
4853 \begin_inset VSpace bigskip
4856 Furthermore you can fill with the command
4866 \begin_layout Plain Layout
4874 the rest of a line with dots.
4875 The effect of these commands is the same like with
4882 \begin_inset CommandInset ref
4884 reference "sub:Variable-Space"
4891 \begin_layout Standard
4892 For example the command
4900 \begin_layout Plain Layout
4914 \begin_layout Standard
4915 \begin_inset Formula $A\dotfill B$
4921 \begin_layout Standard
4928 there is for a line the command
4938 \begin_layout Plain Layout
4949 \begin_layout Standard
4950 \begin_inset Formula $A\hrulefill B$
4956 \begin_layout Standard
4957 To use the commands for text, they have to be inserted in TeX-mode.
4960 \begin_layout Section
4962 \begin_inset CommandInset label
4972 \begin_layout Plain Layout
4981 \begin_layout Standard
4982 Matrices can be inserted via the math toolbar button
4983 \begin_inset Graphics
4984 filename ../images/dialog-show_mathmatrix.png
4991 Insert\SpecialChar \menuseparator
4992 Math\SpecialChar \menuseparator
4996 You will be asked for the number of matrix columns and rows, and the alignment.
4997 The vertical alignment is hereby only of importance for matrices in inline
5001 \begin_layout Standard
5002 The first matrix is top
5003 \begin_inset Formula $\begin{array}[t]{cccc}
5006 C & F & I & L\end{array}$
5010 \begin_inset Formula $\begin{array}{cccc}
5013 C & F & I & L\end{array}$
5016 , and the third bottom
5017 \begin_inset Formula $\begin{array}[b]{cccc}
5020 C & F & I & L\end{array}$
5026 \begin_layout Standard
5027 The horizontal alignment specifies how the column entries should be aligned.
5028 It is set by entering a letter for every column.
5033 denotes left aligned,
5042 To create for example a 4
5047 \begin_inset space ~
5050 matrix where the first column is left aligned, the second and third are
5051 centered, and the last one is right aligned, one enters for the horizontal
5057 Normally are in a matrix all columns centered, therefore the default is
5058 for every column is a
5065 \begin_layout Standard
5066 Horizontal alignment:
5069 \begin_layout Standard
5075 \begin_inset Formula $\begin{array}{lll}
5078 C & F & 10000\end{array}$
5086 \begin_inset Formula $\begin{array}{ccc}
5089 C & F & 10000\end{array}$
5097 \begin_inset Formula $\begin{array}{rrr}
5100 C & F & 10000\end{array}$
5106 \begin_layout Standard
5107 To add or delete rows and columns subsequently, the math toolbar buttons
5109 \begin_inset Graphics
5110 filename ../images/tabular-feature_append-row.png
5116 \begin_inset Graphics
5117 filename ../images/tabular-feature_delete-row.png
5123 \begin_inset space \thinspace{}
5128 Edit\SpecialChar \menuseparator
5132 New rows can also be created with
5135 arg "newline-insert newline"
5141 \begin_layout Standard
5142 \begin_inset VSpace bigskip
5145 Parentheses around a matrix can can either be created with the commands
5156 \begin_layout Plain Layout
5174 \begin_layout Plain Layout
5185 \begin_inset space ~
5191 \begin_inset CommandInset ref
5193 reference "sub:Automatic-Bracket-Size"
5197 , or by using the following commands:
5198 \begin_inset VSpace medskip
5204 \begin_layout Standard
5205 \begin_inset space \hfill{}
5209 \begin_inset Tabular
5210 <lyxtabular version="3" rows="4" columns="2">
5212 <column alignment="center" valignment="top" width="0">
5213 <column alignment="center" valignment="top" width="0">
5215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5218 \begin_layout Plain Layout
5224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5227 \begin_layout Plain Layout
5229 \begin_inset Note Note
5232 \begin_layout Plain Layout
5239 is only used as spacer.
5251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5254 \begin_layout Plain Layout
5261 \begin_layout Plain Layout
5275 \begin_inset space \thinspace{}
5283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5286 \begin_layout Plain Layout
5287 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5288 0 & \textrm{-}\mathrm{i}\\
5289 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5302 \begin_layout Plain Layout
5309 \begin_layout Plain Layout
5323 \begin_inset space \thinspace{}
5331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5334 \begin_layout Plain Layout
5335 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5336 0 & \textrm{-}\mathrm{i}\\
5337 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5350 \begin_layout Plain Layout
5357 \begin_layout Plain Layout
5371 \begin_inset space \thinspace{}
5379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5382 \begin_layout Plain Layout
5383 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5384 0 & \textrm{-}\mathrm{i}\\
5385 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5399 \begin_inset space \hfill{}
5403 \begin_inset Tabular
5404 <lyxtabular version="3" rows="4" columns="2">
5406 <column alignment="center" valignment="top" width="0">
5407 <column alignment="center" valignment="top" width="0">
5409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5412 \begin_layout Plain Layout
5418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5421 \begin_layout Plain Layout
5429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5432 \begin_layout Plain Layout
5439 \begin_layout Plain Layout
5453 \begin_inset space \thinspace{}
5461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5464 \begin_layout Plain Layout
5465 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5466 0 & \textrm{-}\mathrm{i}\\
5467 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5480 \begin_layout Plain Layout
5487 \begin_layout Plain Layout
5501 \begin_inset space \thinspace{}
5509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5512 \begin_layout Plain Layout
5513 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5514 0 & \textrm{-}\mathrm{i}\\
5515 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5528 \begin_layout Plain Layout
5535 \begin_layout Plain Layout
5549 \begin_inset space \thinspace{}
5557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5560 \begin_layout Plain Layout
5561 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5562 0 & \textrm{-}\mathrm{i}\\
5563 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5577 \begin_inset space \hfill{}
5583 \begin_layout Standard
5584 \begin_inset VSpace medskip
5588 \begin_inset space \thinspace{}
5592 \begin_inset space \space{}
5601 is inserted, a blue box appears between two vertical lines where the matrix
5605 \begin_layout Standard
5606 \begin_inset VSpace bigskip
5609 As all multiline formulas are matrices, the length
5619 \begin_layout Plain Layout
5627 that is described in
5628 \begin_inset CommandInset ref
5630 reference "sub:Column-Separation"
5634 can also be used to change the column separation of matrices.
5637 \begin_layout Standard
5638 To change the row separation, the command
5648 \begin_layout Plain Layout
5657 It is used as follows:
5660 \begin_layout Standard
5667 arraystretch}{stretch factor}
5671 \begin_layout Plain Layout
5682 \begin_layout Standard
5689 assigns the stretch factor to the predefined command
5697 \begin_inset space \thinspace{}
5701 \begin_inset space \space{}
5704 the row separation, use the factor 2.
5705 This is then used for all following matrices.
5706 To go back to the original separation, assign the factor 1 to
5715 \begin_layout Standard
5716 To set matrices into a text line, the command
5726 \begin_layout Plain Layout
5735 When it is inserted a blue box with two dashed lines appears.
5736 In this box the matrix is inserted.
5739 \begin_layout Standard
5741 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5742 C & D\end{smallmatrix}\right)$
5748 \begin_layout Section
5749 Brackets and Delimiters
5753 \begin_layout Plain Layout
5763 \begin_layout Plain Layout
5772 \begin_layout Subsection
5773 Vertical Brackets and Delimiters
5777 \begin_layout Plain Layout
5786 \begin_layout Standard
5787 \begin_inset space \hfill{}
5791 \begin_inset Tabular
5792 <lyxtabular version="3" rows="9" columns="2">
5794 <column alignment="center" valignment="top" width="0pt">
5795 <column alignment="center" valignment="top" width="0pt">
5797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5800 \begin_layout Plain Layout
5806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5809 \begin_layout Plain Layout
5817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5820 \begin_layout Plain Layout
5826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5829 \begin_layout Plain Layout
5830 \begin_inset Formula $($
5840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5843 \begin_layout Plain Layout
5849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5852 \begin_layout Plain Layout
5853 \begin_inset Formula $\{$
5863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5866 \begin_layout Plain Layout
5872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5875 \begin_layout Plain Layout
5876 \begin_inset Formula $[$
5886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5889 \begin_layout Plain Layout
5897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5900 \begin_layout Plain Layout
5901 \begin_inset Formula $\langle$
5911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5914 \begin_layout Plain Layout
5922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5925 \begin_layout Plain Layout
5926 \begin_inset Formula $\lceil$
5936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5939 \begin_layout Plain Layout
5947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5950 \begin_layout Plain Layout
5951 \begin_inset Formula $\lfloor$
5961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5964 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Plain Layout
5974 \begin_inset Formula $/$
5984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5987 \begin_layout Plain Layout
5993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5996 \begin_layout Plain Layout
5997 \begin_inset Formula $|$
6011 \begin_inset space \hfill{}
6015 \begin_inset Tabular
6016 <lyxtabular version="3" rows="9" columns="2">
6018 <column alignment="center" valignment="top" width="0pt">
6019 <column alignment="center" valignment="top" width="0pt">
6021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6024 \begin_layout Plain Layout
6030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6033 \begin_layout Plain Layout
6041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6044 \begin_layout Plain Layout
6050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6053 \begin_layout Plain Layout
6054 \begin_inset Formula $)$
6064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6067 \begin_layout Plain Layout
6073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6076 \begin_layout Plain Layout
6077 \begin_inset Formula $\}$
6087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6090 \begin_layout Plain Layout
6096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6099 \begin_layout Plain Layout
6100 \begin_inset Formula $]$
6110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6113 \begin_layout Plain Layout
6121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6124 \begin_layout Plain Layout
6125 \begin_inset Formula $\rangle$
6135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6138 \begin_layout Plain Layout
6146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6149 \begin_layout Plain Layout
6150 \begin_inset Formula $\rceil$
6160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6163 \begin_layout Plain Layout
6171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6174 \begin_layout Plain Layout
6175 \begin_inset Formula $\rfloor$
6185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6188 \begin_layout Plain Layout
6198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6201 \begin_layout Plain Layout
6202 \begin_inset Formula $\backslash$
6212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6215 \begin_layout Plain Layout
6223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6226 \begin_layout Plain Layout
6227 \begin_inset Formula $\|$
6241 \begin_inset space \hfill{}
6247 \begin_layout Standard
6250 \begin_inset Note Greyedout
6253 \begin_layout Plain Layout
6258 In TeX-mode the command
6268 \begin_layout Plain Layout
6276 must be used for the backslash, because the command
6284 produces there a line break.
6292 \begin_layout Standard
6293 For all characters listed above the size can be adjusted with the commands
6294 described in the following two subsections.
6295 When using these commands, the characters < and > can directly be used
6296 instead of the commands
6311 \begin_layout Subsubsection
6313 \begin_inset CommandInset label
6315 name "sub:Manual-Bracket-Size"
6323 \begin_layout Plain Layout
6324 Bracket size ! manual
6332 \begin_layout Standard
6333 The bracket size can be specified manually by the LaTeX-commands
6343 \begin_layout Plain Layout
6376 denotes the smallest and
6382 the largest bracket size.
6385 \begin_layout Standard
6386 These commands are used to emphasize levels of brackets:
6389 \begin_layout Standard
6391 \begin_inset Tabular
6392 <lyxtabular version="3" rows="2" columns="2">
6394 <column alignment="center" valignment="top" width="0pt">
6395 <column alignment="center" valignment="top" width="0pt">
6397 <cell alignment="center" valignment="top" usebox="none">
6400 \begin_layout Plain Layout
6401 all brackets in the same size:
6406 <cell alignment="center" valignment="top" usebox="none">
6409 \begin_layout Plain Layout
6410 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6420 <cell alignment="center" valignment="top" usebox="none">
6423 \begin_layout Plain Layout
6429 <cell alignment="center" valignment="top" usebox="none">
6432 \begin_layout Plain Layout
6433 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6447 \begin_inset Note Note
6450 \begin_layout Plain Layout
6457 is only used as spacer.
6465 \begin_layout Standard
6466 For the second formula the command
6476 \begin_layout Plain Layout
6490 \begin_layout Standard
6491 Here is an overview about all bracket sizes:
6494 \begin_layout Standard
6514 \begin_layout Plain Layout
6531 \begin_layout Plain Layout
6544 \begin_layout Plain Layout
6560 \begin_layout Standard
6562 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6568 \begin_layout Standard
6575 -commands there is the variant
6585 \begin_layout Plain Layout
6593 that adds a bit more space between the bracket and its content, and the
6610 \begin_layout Plain Layout
6620 , that don't add additional space.
6625 at the end of the command
6631 is for a left bracket; for a right bracket this will be replaced by an
6637 A left or right bracket can each be an opening or closing bracket.
6640 \begin_layout Standard
6641 In the following table is a comparison of the variants:
6644 \begin_layout Standard
6646 \begin_inset Tabular
6647 <lyxtabular version="3" rows="5" columns="2">
6649 <column alignment="center" valignment="middle" width="0">
6650 <column alignment="center" valignment="middle" width="0">
6652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6655 \begin_layout Plain Layout
6661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6664 \begin_layout Plain Layout
6666 \begin_inset Note Note
6669 \begin_layout Plain Layout
6676 is only used as spacer.
6688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6691 \begin_layout Plain Layout
6706 \begin_layout Plain Layout
6724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6727 \begin_layout Plain Layout
6728 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6741 \begin_layout Plain Layout
6756 \begin_layout Plain Layout
6774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6777 \begin_layout Plain Layout
6778 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6791 \begin_layout Plain Layout
6806 \begin_layout Plain Layout
6824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6827 \begin_layout Plain Layout
6828 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6841 \begin_layout Plain Layout
6853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6856 \begin_layout Plain Layout
6857 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6873 \begin_layout Subsubsection
6874 Automatic Bracket Size
6875 \begin_inset CommandInset label
6877 name "sub:Automatic-Bracket-Size"
6885 \begin_layout Plain Layout
6886 Bracket size ! automatic
6894 \begin_layout Standard
6895 Brackets with variable size can be inserted with the commands
6905 \begin_layout Plain Layout
6923 \begin_layout Plain Layout
6931 or via the math toolbar button
6932 \begin_inset Graphics
6933 filename ../images/dialog-show_mathdelimiter.png
6951 the wanted bracket must be inserted.
6952 The bracket size will then automatically be calculated for the output.
6955 \begin_layout Standard
6957 normal bracket: The command
6967 \begin_layout Plain Layout
6977 \begin_inset Formula $\downarrow$
6984 \begin_layout Plain Layout
6996 \begin_inset Formula \[
7004 \begin_layout Standard
7006 multiline bracket: The command
7018 \begin_layout Plain Layout
7028 \begin_inset Formula $\downarrow$
7035 \begin_layout Plain Layout
7049 \begin_inset Formula \[
7050 \ln\left(\frac{A}{C}\right)\]
7057 \begin_layout Standard
7073 \begin_inset space ~
7079 This has the advantage that you can see in LyX immediately the real bracket
7080 size and that the matching right bracket will be created too.
7081 \begin_inset Newline newline
7084 The command for the last example would then be:
7098 \begin_layout Plain Layout
7108 \begin_inset Formula $\downarrow$
7114 \begin_layout Standard
7115 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7116 For example the command
7126 \begin_layout Plain Layout
7136 \begin_inset Formula $\downarrow$
7143 \begin_layout Plain Layout
7159 \begin_inset Formula \[
7160 \left.\frac{A}{B}\right\} \]
7178 will be converted by LyX to brackets in the right size when the document
7179 is reloaded and an omitted bracket will appear as dashed line.
7182 \begin_layout Standard
7183 \begin_inset VSpace bigskip
7186 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7197 \begin_layout Plain Layout
7205 is additionally available for all brackets and limits.
7206 With this command the height of the following character is adapted to the
7207 one of the surrounding brackets, what is e.
7208 \begin_inset space \thinspace{}
7212 \begin_inset space \space{}
7215 needed for physical vectors:
7216 \begin_inset Formula \[
7217 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7221 For physical vectors there is a special LaTeX-package, described in
7222 \begin_inset CommandInset ref
7224 reference "sub:Physical-Vectors"
7231 \begin_layout Subsection
7236 \begin_layout Plain Layout
7237 Brackets ! horizontal
7245 \begin_layout Standard
7247 \begin_inset Tabular
7248 <lyxtabular version="3" rows="4" columns="2">
7250 <column alignment="center" valignment="top" width="0pt">
7251 <column alignment="center" valignment="top" width="0pt">
7253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7256 \begin_layout Plain Layout
7258 \begin_inset Note Note
7261 \begin_layout Plain Layout
7268 is only used as spacer.
7278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7281 \begin_layout Plain Layout
7289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7292 \begin_layout Plain Layout
7296 \begin_layout Plain Layout
7311 \begin_layout Plain Layout
7324 \begin_layout Plain Layout
7337 \begin_layout Plain Layout
7350 \begin_layout Plain Layout
7361 \begin_layout Plain Layout
7374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7377 \begin_layout Plain Layout
7378 \begin_inset Formula $\overbrace{A+B}^{3}$
7388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7391 \begin_layout Plain Layout
7395 \begin_layout Plain Layout
7410 \begin_layout Plain Layout
7423 \begin_layout Plain Layout
7436 \begin_layout Plain Layout
7447 \begin_layout Plain Layout
7460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7463 \begin_layout Plain Layout
7464 \begin_inset Formula $\underbrace{A+B}_{5}$
7474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7477 \begin_layout Plain Layout
7484 \begin_layout Plain Layout
7499 \begin_layout Plain Layout
7512 \begin_layout Plain Layout
7525 \begin_layout Plain Layout
7538 \begin_layout Plain Layout
7551 \begin_layout Plain Layout
7564 \begin_layout Plain Layout
7578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7581 \begin_layout Plain Layout
7582 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7598 \begin_layout Standard
7599 In the last example it doesn't matter if
7611 is inserted at first.
7614 \begin_layout Standard
7615 \begin_inset VSpace bigskip
7618 When brackets are needed that overlap each other, multiline formulas, as
7620 \begin_inset CommandInset ref
7622 reference "sec:Multiline-Formulas"
7627 \begin_inset Formula \begin{eqnarray*}
7628 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7629 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7633 In the first row the formula is inserted together with the first brace.
7634 It is hereby important that the space command
7638 \begin_layout Plain Layout
7639 Space commands are explained in
7640 \begin_inset CommandInset ref
7642 reference "sub:Predefined-Space"
7657 is inserted before the first
7658 \begin_inset Formula $d$
7661 , because the brace that ends behind the
7662 \begin_inset Formula $q$
7665 prevents that the following
7666 \begin_inset Quotes eld
7670 \begin_inset Quotes erd
7673 is surrounded by space.
7677 \begin_layout Plain Layout
7678 because a bracket is not handled as character, see
7679 \begin_inset CommandInset ref
7681 reference "sub:Binary-Operators"
7690 In the second row the second brace is inserted.
7691 As it should begin before the
7692 \begin_inset Formula $b$
7707 \begin_layout Plain Layout
7715 \begin_inset CommandInset ref
7717 reference "sub:Placeholders"
7726 This space is needed because the
7727 \begin_inset Quotes eld
7731 \begin_inset Quotes erd
7734 is also surrounded by space in the formula.
7735 The brace is placed under the command
7744 \begin_layout Standard
7745 It gets more complicated when brackets overlap each other, like in the following
7750 \begin_layout Plain Layout
7762 \begin_inset Formula \begin{eqnarray*}
7763 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7764 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7772 \begin_layout Plain Layout
7783 The first formula row is the same as the second row of the previous example,
7784 with the difference that the brace is above.
7785 The second row contains the formula together with the second brace.
7786 To avoid that there is space between the upper brace in the first row and
7787 the formula, the row spacing need to be reduced.
7788 This is not easily possible due to a bug in LyX
7792 \begin_layout Plain Layout
7793 \begin_inset CommandInset href
7795 name "LyX-bug #1505"
7796 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7806 As solution for the problem, the global formula row separation
7816 \begin_layout Plain Layout
7824 must be changed to -6
7825 \begin_inset space \thinspace{}
7828 pt before the formula with the command
7843 is set back after the formula to the standard value of 3
7844 \begin_inset space \thinspace{}
7847 pt using the same command.
7848 More about the row separation in formulas is explained in
7849 \begin_inset CommandInset ref
7851 reference "sub:Line-Separation"
7858 \begin_layout Section
7863 \begin_layout Plain Layout
7872 \begin_layout Standard
7873 Arrows can be inserted via the math toolbar button
7874 \begin_inset Graphics
7875 filename ../images/math/leftarrow.png
7880 or the commands listed in the following subsections.
7883 \begin_layout Standard
7884 \begin_inset Newpage newpage
7890 \begin_layout Subsection
7895 \begin_layout Plain Layout
7904 \begin_layout Standard
7905 \begin_inset space \hfill{}
7909 \begin_inset Tabular
7910 <lyxtabular version="3" rows="8" columns="2">
7912 <column alignment="center" valignment="top" width="0pt">
7913 <column alignment="center" valignment="top" width="0pt">
7915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7918 \begin_layout Plain Layout
7924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7927 \begin_layout Plain Layout
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7938 \begin_layout Plain Layout
7946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7949 \begin_layout Plain Layout
7950 \begin_inset Formula $\gets$
7960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7963 \begin_layout Plain Layout
7971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7974 \begin_layout Plain Layout
7975 \begin_inset Formula $\Leftarrow$
7985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7988 \begin_layout Plain Layout
7996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7999 \begin_layout Plain Layout
8000 \begin_inset Formula $\longleftarrow$
8010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8013 \begin_layout Plain Layout
8021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8024 \begin_layout Plain Layout
8025 \begin_inset Formula $\Longleftarrow$
8035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8038 \begin_layout Plain Layout
8046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8049 \begin_layout Plain Layout
8050 \begin_inset Formula $\leftharpoonup$
8060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8063 \begin_layout Plain Layout
8071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8074 \begin_layout Plain Layout
8075 \begin_inset Formula $\leftharpoondown$
8085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8088 \begin_layout Plain Layout
8096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8099 \begin_layout Plain Layout
8100 \begin_inset Formula $\hookleftarrow$
8114 \begin_inset space \hfill{}
8118 \begin_inset Tabular
8119 <lyxtabular version="3" rows="8" columns="2">
8121 <column alignment="center" valignment="top" width="0pt">
8122 <column alignment="center" valignment="top" width="0pt">
8124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8127 \begin_layout Plain Layout
8133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8136 \begin_layout Plain Layout
8144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8147 \begin_layout Plain Layout
8155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8158 \begin_layout Plain Layout
8159 \begin_inset Formula $\to$
8169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8172 \begin_layout Plain Layout
8180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8183 \begin_layout Plain Layout
8184 \begin_inset Formula $\Rightarrow$
8194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8197 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8208 \begin_layout Plain Layout
8209 \begin_inset Formula $\longrightarrow$
8219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\Longrightarrow$
8244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8247 \begin_layout Plain Layout
8255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8258 \begin_layout Plain Layout
8259 \begin_inset Formula $\rightharpoonup$
8269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8272 \begin_layout Plain Layout
8280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8283 \begin_layout Plain Layout
8284 \begin_inset Formula $\rightharpoondown$
8294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8297 \begin_layout Plain Layout
8305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8308 \begin_layout Plain Layout
8309 \begin_inset Formula $\hookrightarrow$
8323 \begin_inset space \hfill{}
8329 \begin_layout Standard
8330 \begin_inset space \hfill{}
8334 \begin_inset Tabular
8335 <lyxtabular version="3" rows="6" columns="2">
8337 <column alignment="center" valignment="top" width="0pt">
8338 <column alignment="center" valignment="top" width="0pt">
8340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8343 \begin_layout Plain Layout
8349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8363 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8374 \begin_layout Plain Layout
8375 \begin_inset Formula $\leftrightarrow$
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8388 \begin_layout Plain Layout
8396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8399 \begin_layout Plain Layout
8400 \begin_inset Formula $\Leftrightarrow$
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8413 \begin_layout Plain Layout
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8424 \begin_layout Plain Layout
8425 \begin_inset Formula $\longleftrightarrow$
8435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8438 \begin_layout Plain Layout
8446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8449 \begin_layout Plain Layout
8450 \begin_inset Formula $\Longleftrightarrow$
8460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8463 \begin_layout Plain Layout
8471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8474 \begin_layout Plain Layout
8475 \begin_inset Formula $\rightleftharpoons$
8489 \begin_inset space \hspace{}
8494 \begin_inset space \hfill{}
8498 \begin_inset Tabular
8499 <lyxtabular version="3" rows="5" columns="2">
8501 <column alignment="center" valignment="top" width="0pt">
8502 <column alignment="center" valignment="top" width="0pt">
8504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8507 \begin_layout Plain Layout
8513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8516 \begin_layout Plain Layout
8524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8527 \begin_layout Plain Layout
8535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $\mapsto$
8549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8552 \begin_layout Plain Layout
8560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8563 \begin_layout Plain Layout
8564 \begin_inset Formula $\longmapsto$
8574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8577 \begin_layout Plain Layout
8585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8588 \begin_layout Plain Layout
8589 \begin_inset Formula $\leadsto$
8599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8602 \begin_layout Plain Layout
8610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8613 \begin_layout Plain Layout
8614 \begin_inset Formula $\dasharrow$
8628 \begin_inset space \hfill{}
8634 \begin_layout Standard
8635 \begin_inset VSpace medskip
8638 Arrows used as accent like e.
8639 \begin_inset space \thinspace{}
8643 \begin_inset space \space{}
8646 vector arrows are listed in
8647 \begin_inset CommandInset ref
8649 reference "sec:Accents"
8656 \begin_layout Standard
8657 \begin_inset VSpace bigskip
8660 Furthermore there are the labeled arrows
8664 \begin_layout Plain Layout
8680 \begin_layout Plain Layout
8698 \begin_layout Plain Layout
8705 \begin_layout Plain Layout
8720 When inserting one of these commands in a formula, an arrow with two blue
8721 boxes appear where the label can be inserted.
8722 The length of the arrow adapts to the label width.
8725 \begin_layout Standard
8727 \begin_inset Tabular
8728 <lyxtabular version="3" rows="3" columns="2">
8730 <column alignment="center" valignment="top" width="0pt">
8731 <column alignment="center" valignment="top" width="0pt">
8733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8736 \begin_layout Plain Layout
8742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8745 \begin_layout Plain Layout
8747 \begin_inset Note Note
8750 \begin_layout Plain Layout
8757 is only used as spacer.
8769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8772 \begin_layout Plain Layout
8779 \begin_layout Plain Layout
8789 \begin_inset Formula $\downarrow$
8793 \begin_inset Formula $\to$
8801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8804 \begin_layout Plain Layout
8805 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8818 \begin_layout Plain Layout
8825 \begin_layout Plain Layout
8835 \begin_inset Formula $\downarrow$
8839 \begin_inset Formula $\to$
8847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8850 \begin_layout Plain Layout
8851 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8867 \begin_layout Subsection
8868 Vertical and diagonal Arrows
8872 \begin_layout Plain Layout
8882 \begin_layout Plain Layout
8891 \begin_layout Standard
8892 \begin_inset space \hfill{}
8896 \begin_inset Tabular
8897 <lyxtabular version="3" rows="7" columns="2">
8899 <column alignment="center" valignment="top" width="0pt">
8900 <column alignment="center" valignment="top" width="0pt">
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8905 \begin_layout Plain Layout
8911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8914 \begin_layout Plain Layout
8922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8925 \begin_layout Plain Layout
8933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8936 \begin_layout Plain Layout
8937 \begin_inset Formula $\uparrow$
8947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8950 \begin_layout Plain Layout
8958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8961 \begin_layout Plain Layout
8962 \begin_inset Formula $\Uparrow$
8972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8975 \begin_layout Plain Layout
8983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8986 \begin_layout Plain Layout
8987 \begin_inset Formula $\updownarrow$
8997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9000 \begin_layout Plain Layout
9008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9011 \begin_layout Plain Layout
9012 \begin_inset Formula $\Updownarrow$
9022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9025 \begin_layout Plain Layout
9033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9036 \begin_layout Plain Layout
9037 \begin_inset Formula $\Downarrow$
9047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9050 \begin_layout Plain Layout
9058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9061 \begin_layout Plain Layout
9062 \begin_inset Formula $\downarrow$
9076 \begin_inset space \hfill{}
9080 \begin_inset Tabular
9081 <lyxtabular version="3" rows="5" columns="2">
9083 <column alignment="center" valignment="top" width="0pt">
9084 <column alignment="center" valignment="top" width="0pt">
9086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9089 \begin_layout Plain Layout
9095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9098 \begin_layout Plain Layout
9106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9109 \begin_layout Plain Layout
9117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9120 \begin_layout Plain Layout
9121 \begin_inset Formula $\nearrow$
9131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9134 \begin_layout Plain Layout
9142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9145 \begin_layout Plain Layout
9146 \begin_inset Formula $\searrow$
9156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9159 \begin_layout Plain Layout
9167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9170 \begin_layout Plain Layout
9171 \begin_inset Formula $\swarrow$
9181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9184 \begin_layout Plain Layout
9192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9195 \begin_layout Plain Layout
9196 \begin_inset Formula $\nwarrow$
9210 \begin_inset space \hfill{}
9216 \begin_layout Standard
9217 \begin_inset VSpace medskip
9220 Vertical arrows can be used also as delimiter together with the commands
9222 \begin_inset CommandInset ref
9224 reference "sub:Manual-Bracket-Size"
9229 \begin_inset CommandInset ref
9231 reference "sub:Automatic-Bracket-Size"
9238 \begin_layout Standard
9239 \begin_inset Newpage newpage
9245 \begin_layout Section
9247 \begin_inset CommandInset label
9257 \begin_layout Plain Layout
9266 \begin_layout Standard
9267 Accents can be inserted via the math toolbar button
9268 \begin_inset Graphics
9269 filename ../images/math/hat.png
9274 or the commands listed in the following subsections.
9277 \begin_layout Subsection
9278 Accents for one Character
9282 \begin_layout Plain Layout
9295 \begin_layout Plain Layout
9297 \begin_inset CommandInset ref
9299 reference "sub:Accents-in-Text"
9312 \begin_layout Plain Layout
9320 \begin_inset Note Note
9323 \begin_layout Plain Layout
9326 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9329 \begin_layout Plain Layout
9332 texorpdfstring is in section
9333 \begin_inset CommandInset ref
9335 reference "sub:Formulas-in-Section"
9345 \begin_inset CommandInset label
9347 name "sub:Accents-for-one"
9355 \begin_layout Plain Layout
9356 Accents ! for one character
9364 \begin_layout Standard
9365 \begin_inset space \hfill{}
9369 \begin_inset Tabular
9370 <lyxtabular version="3" rows="8" columns="2">
9372 <column alignment="center" valignment="top" width="0pt">
9373 <column alignment="center" valignment="top" width="0pt">
9375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9378 \begin_layout Plain Layout
9384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9387 \begin_layout Plain Layout
9389 \begin_inset Note Note
9392 \begin_layout Plain Layout
9399 is only used as spacer.
9411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9414 \begin_layout Plain Layout
9421 \begin_layout Plain Layout
9435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9438 \begin_layout Plain Layout
9439 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9452 \begin_layout Plain Layout
9459 \begin_layout Plain Layout
9473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9476 \begin_layout Plain Layout
9477 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9490 \begin_layout Plain Layout
9497 \begin_layout Plain Layout
9511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9514 \begin_layout Plain Layout
9515 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9528 \begin_layout Plain Layout
9536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9539 \begin_layout Plain Layout
9540 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9553 \begin_layout Plain Layout
9560 \begin_layout Plain Layout
9573 \begin_layout Plain Layout
9584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9587 \begin_layout Plain Layout
9588 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9601 \begin_layout Plain Layout
9608 \begin_layout Plain Layout
9622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9625 \begin_layout Plain Layout
9626 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9639 \begin_layout Plain Layout
9646 \begin_layout Plain Layout
9660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9663 \begin_layout Plain Layout
9664 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9678 \begin_inset space \hfill{}
9682 \begin_inset Tabular
9683 <lyxtabular version="3" rows="7" columns="2">
9685 <column alignment="center" valignment="top" width="0pt">
9686 <column alignment="center" valignment="top" width="0pt">
9688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9691 \begin_layout Plain Layout
9697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9700 \begin_layout Plain Layout
9708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9711 \begin_layout Plain Layout
9718 \begin_layout Plain Layout
9732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9735 \begin_layout Plain Layout
9736 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9749 \begin_layout Plain Layout
9756 \begin_layout Plain Layout
9770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9773 \begin_layout Plain Layout
9774 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9787 \begin_layout Plain Layout
9794 \begin_layout Plain Layout
9808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9811 \begin_layout Plain Layout
9812 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9825 \begin_layout Plain Layout
9832 \begin_layout Plain Layout
9846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9849 \begin_layout Plain Layout
9850 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9863 \begin_layout Plain Layout
9870 \begin_layout Plain Layout
9884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9887 \begin_layout Plain Layout
9888 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9901 \begin_layout Plain Layout
9908 \begin_layout Plain Layout
9922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9925 \begin_layout Plain Layout
9926 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9940 \begin_inset space \hfill{}
9946 \begin_layout Standard
9947 \begin_inset VSpace bigskip
9953 \begin_layout Standard
9954 You can directly insert accents like é to formulas.
9955 LyX will transform them to the corresponding accent command.
9960 \begin_layout Plain Layout
9966 it is better to insert a quotation mark before the vowel.
9967 These two characters are then treated by LaTeX as
9971 character when the formula part with the umlaut is marked as German.
9979 \begin_inset Quotes eld
9983 \begin_inset Quotes erd
9986 umlauts are created as demonstrated in the following example:
9989 \begin_layout Standard
9990 \begin_inset VSpace -2mm
9996 \begin_layout Standard
9998 \begin_inset Tabular
9999 <lyxtabular version="3" rows="3" columns="2">
10001 <column alignment="center" valignment="top" width="0">
10002 <column alignment="center" valignment="top" width="0">
10004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10007 \begin_layout Plain Layout
10013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10016 \begin_layout Plain Layout
10018 \begin_inset Note Note
10021 \begin_layout Plain Layout
10029 \begin_inset space \thinspace{}
10032 pt space are only used as spacer.
10044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10047 \begin_layout Plain Layout
10050 \begin_inset Quotes grd
10058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10061 \begin_layout Plain Layout
10062 \begin_inset space \hspace{}
10069 \begin_inset Formula $"i$
10079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10082 \begin_layout Plain Layout
10089 \begin_layout Plain Layout
10103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10106 \begin_layout Plain Layout
10107 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10123 \begin_layout Standard
10124 Another advantage to
10130 is that umlauts can directly be converted to mathematical text because
10131 the accent commands above are
10137 in mathematical text
10140 To convert an accented character to mathematical text, only the character
10141 under the accent may be converted.
10142 This applies also for all other conversions, e.
10143 \begin_inset space \thinspace{}
10147 \begin_inset space \space{}
10153 \begin_layout Standard
10154 In mathematical text, umlauts and other accented characters can directly
10158 \begin_layout Subsection
10159 Accents for Operators
10163 \begin_layout Plain Layout
10164 Accents ! for operators
10172 \begin_layout Standard
10183 \begin_layout Plain Layout
10201 \begin_layout Plain Layout
10209 characters can be placed above or below an operator, respectively, to accent
10221 \begin_layout Plain Layout
10229 characters can be set before and behind an operator.
10230 The command scheme is:
10233 \begin_layout Standard
10249 \begin_layout Standard
10256 must always be before the operator that should be accented.
10257 You can accent with several characters and even with other operators and
10265 for example only characters behind an operator, write nothing between the
10266 first braces but don't omit the braces.
10269 \begin_layout Standard
10270 For example the command
10275 \begin_inset Formula $\to$
10285 \begin_inset Formula $\to$
10294 \begin_layout Plain Layout
10310 \begin_inset Formula \[
10311 \sideset{}{'}\sum_{k=1}^{n}\]
10318 \begin_layout Standard
10327 \begin_layout Plain Layout
10342 \begin_layout Plain Layout
10354 \begin_inset Formula $\uparrow$
10362 \begin_inset Formula \[
10363 \overset{a}{\maltese}\]
10367 As seen in the last example, with
10379 also symbols and characters can be accented; with
10385 this is not possible.
10388 \begin_layout Subsection
10389 Accents for several Characters
10393 \begin_layout Plain Layout
10394 Accents ! for several characters
10402 \begin_layout Standard
10403 \begin_inset space \hfill{}
10407 \begin_inset Tabular
10408 <lyxtabular version="3" rows="5" columns="2">
10410 <column alignment="center" valignment="top" width="0pt">
10411 <column alignment="center" valignment="top" width="0pt">
10413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10416 \begin_layout Plain Layout
10422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10425 \begin_layout Plain Layout
10427 \begin_inset Note Note
10430 \begin_layout Plain Layout
10437 is only used as spacer.
10449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10452 \begin_layout Plain Layout
10459 \begin_layout Plain Layout
10473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10476 \begin_layout Plain Layout
10477 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10490 \begin_layout Plain Layout
10497 \begin_layout Plain Layout
10511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10514 \begin_layout Plain Layout
10515 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10528 \begin_layout Plain Layout
10535 \begin_layout Plain Layout
10549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10552 \begin_layout Plain Layout
10553 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10566 \begin_layout Plain Layout
10569 underleftrightarrow
10573 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10590 \begin_layout Plain Layout
10591 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10605 \begin_inset space \hfill{}
10609 \begin_inset Tabular
10610 <lyxtabular version="3" rows="5" columns="2">
10612 <column alignment="center" valignment="top" width="0pt">
10613 <column alignment="center" valignment="top" width="0pt">
10615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10618 \begin_layout Plain Layout
10624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10627 \begin_layout Plain Layout
10635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10638 \begin_layout Plain Layout
10645 \begin_layout Plain Layout
10659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10662 \begin_layout Plain Layout
10663 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10676 \begin_layout Plain Layout
10683 \begin_layout Plain Layout
10697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10700 \begin_layout Plain Layout
10701 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10714 \begin_layout Plain Layout
10721 \begin_layout Plain Layout
10735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10738 \begin_layout Plain Layout
10739 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10752 \begin_layout Plain Layout
10759 \begin_layout Plain Layout
10773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10776 \begin_layout Plain Layout
10777 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10791 \begin_inset space \hfill{}
10797 \begin_layout Standard
10798 \begin_inset VSpace medskip
10801 With these commands as many characters as you like can be accented.
10814 will only be set in the output with a length of three characters, as shown
10815 in the following example:
10816 \begin_inset Formula \[
10817 \widetilde{A+B=C-D}\]
10824 \begin_layout Standard
10835 \begin_layout Plain Layout
10853 \begin_layout Plain Layout
10861 described in the previous subsection it is also possible to accent several
10871 \begin_layout Plain Layout
10881 \begin_inset Formula $\downarrow$
10887 \begin_inset Formula \[
10888 \underset{***}{A=B}\]
10895 \begin_layout Section
10897 \begin_inset CommandInset label
10907 \begin_layout Plain Layout
10916 \begin_layout Subsection
10918 \begin_inset CommandInset label
10920 name "sub:Predefined-Space"
10928 \begin_layout Plain Layout
10929 Space ! horizontal ! predefined
10937 \begin_layout Standard
10938 Sometimes it is necessary to insert horizontal space to a formula.
10939 This is done by inserting a protected space (shortcut
10942 arg "space-insert protected"
10947 \begin_inset Quotes eld
10956 \begin_layout Plain Layout
10968 \begin_inset Quotes erd
10971 appears and by pressing
10975 several times one can select one of eight different space sizes.
10976 The spaces can also be inserted using the math toolbar button
10977 \begin_inset Graphics
10978 filename ../images/math/space.png
10983 or special commands.
10984 Independent from the inserted command, one can select the size again by
10992 \begin_layout Standard
10995 \begin_inset VSpace -5mm
10999 \begin_inset Tabular
11000 <lyxtabular version="3" rows="3" columns="7">
11002 <column alignment="center" valignment="middle" width="6.8cm">
11003 <column alignment="center" valignment="top" width="0">
11004 <column alignment="center" valignment="top" width="0">
11005 <column alignment="center" valignment="top" width="0">
11006 <column alignment="center" valignment="top" width="0">
11007 <column alignment="center" valignment="top" width="0">
11008 <column alignment="center" valignment="top" width="0">
11010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11013 \begin_layout Plain Layout
11019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11022 \begin_layout Plain Layout
11030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11033 \begin_layout Plain Layout
11041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11044 \begin_layout Plain Layout
11052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11055 \begin_layout Plain Layout
11063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11077 \begin_layout Plain Layout
11087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11090 \begin_layout Plain Layout
11095 keystrokes after inserting the protected space
11100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11103 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11121 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11139 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11148 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11159 \begin_layout Plain Layout
11165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11169 \begin_inset Formula $A\, B$
11177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11181 \begin_inset Formula $A\: B$
11189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\; B$
11201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11205 \begin_inset Formula $A\quad B$
11213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11216 \begin_layout Plain Layout
11217 \begin_inset Formula $A\qquad B$
11225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11228 \begin_layout Plain Layout
11229 \begin_inset Formula $A\! B$
11245 \begin_layout Standard
11246 The last size seem to produce no space.
11247 It is displayed red in LyX contrary to the other sizes, because it is a
11249 There are two more negative spaces:
11252 \begin_layout Standard
11254 \begin_inset Tabular
11255 <lyxtabular version="3" rows="3" columns="3">
11257 <column alignment="center" valignment="middle" width="6.8cm">
11258 <column alignment="center" valignment="top" width="0pt">
11259 <column alignment="center" valignment="top" width="0pt">
11261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11264 \begin_layout Plain Layout
11270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11284 \begin_layout Plain Layout
11294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11297 \begin_layout Plain Layout
11302 keystrokes after inserting the protected space
11307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11319 \begin_layout Plain Layout
11327 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11339 \begin_layout Plain Layout
11340 \begin_inset Formula $A\negmedspace B$
11348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11351 \begin_layout Plain Layout
11352 \begin_inset Formula $A\negthickspace B$
11368 \begin_layout Standard
11369 Negative spaces can lead to characters overlapping each other.
11370 Thus they can be used to enforce ligatures, what is e.
11371 \begin_inset space \thinspace{}
11375 \begin_inset space \space{}
11378 useful for summation operators:
11381 \begin_layout Standard
11383 \begin_inset Tabular
11384 <lyxtabular version="3" rows="3" columns="2">
11386 <column alignment="center" valignment="top" width="0">
11387 <column alignment="center" valignment="top" width="0">
11389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11392 \begin_layout Plain Layout
11398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11401 \begin_layout Plain Layout
11403 \begin_inset Note Note
11406 \begin_layout Plain Layout
11413 is only used as spacer.
11425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11428 \begin_layout Plain Layout
11437 \begin_layout Plain Layout
11451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11454 \begin_layout Plain Layout
11455 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11468 \begin_layout Plain Layout
11479 \begin_layout Plain Layout
11493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11496 \begin_layout Plain Layout
11497 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11513 \begin_layout Standard
11514 Relations like for example equal signs, are always surrounded by space.
11515 To suppress this, the equal sign is placed into a TeX-brace.
11516 The following example demonstrates this:
11519 \begin_layout Standard
11521 \begin_inset Tabular
11522 <lyxtabular version="3" rows="2" columns="2">
11524 <column alignment="center" valignment="top" width="0pt">
11525 <column alignment="center" valignment="top" width="0pt">
11527 <cell alignment="center" valignment="top" usebox="none">
11530 \begin_layout Plain Layout
11536 <cell alignment="center" valignment="top" usebox="none">
11539 \begin_layout Plain Layout
11540 \begin_inset Formula $A=B$
11550 <cell alignment="center" valignment="top" usebox="none">
11553 \begin_layout Plain Layout
11554 \begin_inset Note Note
11557 \begin_layout Plain Layout
11564 is only used as spacer.
11570 \begin_inset Formula $\raisebox{5mm}{}$
11573 equation without space
11578 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11581 \begin_layout Plain Layout
11582 \begin_inset Formula $A{=}B$
11598 \begin_layout Standard
11600 The command for the last formula is:
11605 \begin_inset Formula $\to$
11611 \begin_layout Standard
11612 \begin_inset VSpace bigskip
11615 Spaces are needed for physical units, because the space between the value
11616 and the unit is the smallest one and not a normal space.
11617 For units in text, the smallest space is inserted via the menu
11619 Insert\SpecialChar \menuseparator
11620 Formatting\SpecialChar \menuseparator
11622 \begin_inset space ~
11630 arg "space-insert thin"
11636 \begin_layout Standard
11637 An example to visualize the difference:
11640 \begin_layout Standard
11641 \begin_inset Tabular
11642 <lyxtabular version="3" rows="2" columns="2">
11644 <column alignment="left" valignment="top" width="0">
11645 <column alignment="left" valignment="top" width="0">
11647 <cell alignment="center" valignment="top" usebox="none">
11650 \begin_layout Plain Layout
11652 \begin_inset Formula $\cdot$
11660 <cell alignment="center" valignment="top" usebox="none">
11663 \begin_layout Plain Layout
11664 space between value and unit
11671 <cell alignment="center" valignment="top" usebox="none">
11674 \begin_layout Plain Layout
11676 \begin_inset space \thinspace{}
11680 \begin_inset Formula $\cdot$
11688 <cell alignment="center" valignment="top" usebox="none">
11691 \begin_layout Plain Layout
11692 smallest space between value and unit
11705 \begin_layout Subsection
11710 \begin_layout Plain Layout
11723 \begin_layout Plain Layout
11724 for vertical space in formulas see
11725 \begin_inset CommandInset ref
11727 reference "sub:Line-Separation"
11740 \begin_layout Plain Layout
11748 \begin_inset Note Note
11751 \begin_layout Plain Layout
11754 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11757 \begin_layout Plain Layout
11760 texorpdfstring is in section
11761 \begin_inset CommandInset ref
11763 reference "sub:Formulas-in-Section"
11773 \begin_inset CommandInset label
11775 name "sub:Variable-Space"
11783 \begin_layout Plain Layout
11784 Space ! horizontal ! variable
11792 \begin_layout Standard
11793 Space with a defined length can be inserted with the command
11803 \begin_layout Plain Layout
11813 \begin_inset Quotes eld
11822 \begin_layout Plain Layout
11834 \begin_inset Quotes erd
11838 The length can be specified by left-clicking on the
11839 \begin_inset Quotes eld
11848 \begin_layout Plain Layout
11860 \begin_inset Quotes erd
11864 The length may also be negative.
11865 To insert so many space that the formula uses all available space, the
11876 \begin_layout Plain Layout
11887 \begin_layout Standard
11888 \begin_inset VSpace -1mm
11894 \begin_layout Standard
11896 \begin_inset Tabular
11897 <lyxtabular version="3" rows="4" columns="2">
11899 <column alignment="center" valignment="top" width="0">
11900 <column alignment="center" valignment="top" width="0">
11902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11905 \begin_layout Plain Layout
11913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11916 \begin_layout Plain Layout
11924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11927 \begin_layout Plain Layout
11934 \begin_layout Plain Layout
11944 \begin_inset Formula $\to$
11950 \begin_inset space \thinspace{}
11958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11961 \begin_layout Plain Layout
11962 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11975 \begin_layout Plain Layout
11982 \begin_layout Plain Layout
11992 \begin_inset Formula $\to$
11998 \begin_inset space \thinspace{}
12006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12009 \begin_layout Plain Layout
12010 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12023 \begin_layout Plain Layout
12030 \begin_layout Plain Layout
12044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12047 \begin_layout Plain Layout
12048 \begin_inset Formula $A=A\hfill B=B$
12064 \begin_layout Standard
12065 In the last example the available space is given by the longest column entry
12067 In an inline formula the space depends on the length of the line in which
12075 Thus, when the line uses the full width, no space will be created.
12082 only has an effect on displayed formulas when the formula style
12087 (Formula styles are explained in
12088 \begin_inset CommandInset ref
12090 reference "sec:Formula-Styles"
12097 \begin_layout Standard
12104 , there are the commands
12116 that fill the space with a pattern, see
12117 \begin_inset CommandInset ref
12119 reference "sub:Ellipses"
12126 \begin_layout Standard
12127 For text, variable space can be inserted via the menu
12129 Insert\SpecialChar \menuseparator
12130 Formatting\SpecialChar \menuseparator
12132 \begin_inset space ~
12140 \begin_layout Standard
12141 This is a line with
12142 \begin_inset space \hspace{}
12147 \begin_inset space \thinspace{}
12153 \begin_layout Standard
12154 This is a line with
12155 \begin_inset space \hfill{}
12161 \begin_layout Subsection
12162 Space besides inline Formulas
12166 \begin_layout Plain Layout
12167 Space ! besides inline formulas
12175 \begin_layout Standard
12176 The space that surrounds inline formulas can be adjusted with the length
12185 \begin_layout Plain Layout
12196 The value of a length is set with the command
12204 \begin_layout Plain Layout
12214 that has the following scheme:
12217 \begin_layout Standard
12222 setlength{length name}{value}
12225 \begin_layout Standard
12233 \begin_inset space \thinspace{}
12239 \begin_layout Standard
12249 \begin_layout Standard
12250 is inserted in TeX-mode.
12252 \begin_inset space \thinspace{}
12255 mm space will now be set around all inline formulas:
12259 \begin_layout Plain Layout
12273 \begin_layout Standard
12274 This is a line with an inline formula
12275 \begin_inset Formula $A=B$
12279 \begin_inset space \thinspace{}
12282 mm surrounding space.
12286 \begin_layout Plain Layout
12300 \begin_layout Standard
12301 To return to the predefined value,
12307 is set to the value 0
12308 \begin_inset space \thinspace{}
12314 \begin_layout Section
12319 \begin_layout Plain Layout
12329 \begin_layout Plain Layout
12334 \begin_layout Plain Layout
12345 \begin_layout Plain Layout
12360 \begin_layout Standard
12361 Boxes for text are described in chapter
12368 \begin_inset space ~
12376 \begin_layout Subsection
12378 \begin_inset CommandInset label
12380 name "sub:Boxes-with-Frame"
12388 \begin_layout Plain Layout
12397 \begin_layout Standard
12398 It is possible to frame formulas or parts of it with the commands
12408 \begin_layout Plain Layout
12426 \begin_layout Plain Layout
12437 \begin_layout Standard
12438 When one of these commands is inserted to a formula, a blue box appears
12439 within a frame to enter formula parts.
12446 an additional formula has to be created by
12454 \begin_layout Plain Layout
12455 Due to a bug in LyX it is not possible to create a new formula with
12460 \begin_inset CommandInset href
12462 name "LyX-bug #1435"
12463 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12472 , because the box content will otherwise be treated as mathematical text.
12479 is used, a new formula is automatically created inside the frame.
12482 \begin_layout Standard
12489 is not suitable to frame displayed formulas, because the formula will always
12490 be set in the size of the text.
12497 is in contrary not suitable to frame inline formulas, because the formula
12498 will always be set in the size of a displayed formula.
12501 \begin_layout Standard
12508 there is the command
12518 \begin_layout Plain Layout
12526 where additionally the frame width and the alignment can be specified.
12533 is used in the following scheme:
12536 \begin_layout Standard
12541 framebox[frame width][position]{box content}
12544 \begin_layout Standard
12545 The position can either be
12562 right aligns the formula in the box.
12563 When no position is given, the formula will be centered.
12564 \begin_inset Newline newline
12567 Is no width given, also no position can be given.
12568 In this case the frame width is adjusted to the box content like for
12577 \begin_layout Standard
12584 is inserted, a box appears containing three blue boxes.
12585 The first two boxes are surrounded by brackets and denote the two optional
12587 The third box is for formula parts like for
12596 \begin_layout Standard
12598 \begin_inset Note Note
12601 \begin_layout Plain Layout
12602 The table has been set into a minipage to make the footnote appearing.
12603 Otherwise the footnote text would not be displayed.
12609 \begin_inset Box Frameless
12618 height_special "totalheight"
12621 \begin_layout Plain Layout
12623 \begin_inset Tabular
12624 <lyxtabular version="3" rows="5" columns="2">
12626 <column alignment="center" valignment="top" width="0">
12627 <column alignment="center" valignment="top" width="0">
12629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12632 \begin_layout Plain Layout
12637 \begin_layout Plain Layout
12638 Due to a bug in LyX it is not possible to create a new formula with
12643 \begin_inset CommandInset href
12645 name "LyX-bug #1435"
12646 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12663 \begin_layout Plain Layout
12665 \begin_inset Note Note
12668 \begin_layout Plain Layout
12675 is only used as spacer.
12687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12690 \begin_layout Plain Layout
12697 \begin_layout Plain Layout
12716 \begin_layout Plain Layout
12730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12733 \begin_layout Plain Layout
12734 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12747 \begin_layout Plain Layout
12754 \begin_layout Plain Layout
12769 \begin_layout Plain Layout
12783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12786 \begin_layout Plain Layout
12787 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12800 \begin_layout Plain Layout
12807 \begin_layout Plain Layout
12821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12824 \begin_layout Plain Layout
12825 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12838 \begin_layout Plain Layout
12845 \begin_layout Plain Layout
12855 \begin_inset Formula $\to$
12859 \begin_inset Formula $\to$
12872 \begin_layout Plain Layout
12882 \begin_inset Formula $\downarrow$
12890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12893 \begin_layout Plain Layout
12894 \begin_inset Formula $\raisebox{6mm}{}$
12898 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12902 \begin_inset Formula $\raisebox{-4mm}{}$
12923 \begin_layout Standard
12924 The frame thickness can also be adjusted.
12925 To do this the following commands have to be inserted in TeX-mode before
12929 \begin_layout Standard
12939 \begin_inset Quotes eld
12943 \begin_inset Quotes erd
12957 \begin_inset Quotes eld
12961 \begin_inset Quotes erd
12967 \begin_layout Standard
12968 \begin_inset Quotes eld
12972 \begin_inset Quotes erd
12975 specifies the minimal distance between the frame and the first character
12977 An example for this is the following framed formula:
12981 \begin_layout Plain Layout
12993 \begin_inset Formula \[
12998 Before this formula the commands
13001 \begin_layout Standard
13023 \begin_layout Standard
13024 were inserted in TeX-mode.
13025 The given values are used for all following boxes.
13028 \begin_layout Standard
13029 To return to the standard frame size, the command
13032 \begin_layout Standard
13057 \begin_layout Plain Layout
13071 \begin_layout Standard
13072 is inserted in TeX-mode before the next formula.
13075 \begin_layout Subsection
13076 Boxes without Frame
13077 \begin_inset CommandInset label
13079 name "sub:Boxes-without-Frame"
13087 \begin_layout Plain Layout
13088 Boxes ! without frame
13096 \begin_layout Standard
13097 For boxes without a frame there are the following box commands:
13107 \begin_layout Plain Layout
13125 \begin_layout Plain Layout
13143 \begin_layout Plain Layout
13154 \begin_layout Standard
13161 a box can be super- or subscripted.
13162 But in contrary to normal super- and subscripting, the characters in the
13163 box keep their font size.
13170 is used in the following scheme:
13173 \begin_layout Standard
13178 raisebox{height}{box content}
13181 \begin_layout Standard
13182 When the box should contain a formula, an extra formula is needed like for
13192 \begin_layout Standard
13194 \begin_inset Tabular
13195 <lyxtabular version="3" rows="4" columns="2">
13197 <column alignment="center" valignment="top" width="0">
13198 <column alignment="center" valignment="top" width="0">
13200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13203 \begin_layout Plain Layout
13209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13212 \begin_layout Plain Layout
13220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13223 \begin_layout Plain Layout
13227 \begin_inset Formula $\to$
13233 \begin_inset Formula $\to$
13241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13244 \begin_layout Plain Layout
13245 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13258 \begin_layout Plain Layout
13262 \begin_inset Formula $\to$
13268 \begin_inset Formula $\to$
13276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13279 \begin_layout Plain Layout
13280 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13293 \begin_layout Plain Layout
13297 \begin_inset Formula $\to$
13312 \begin_layout Plain Layout
13326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13329 \begin_layout Plain Layout
13333 \begin_layout Plain Layout
13357 \begin_layout Standard
13358 The last formula can currently only be created using TeX-mode because LyX
13359 inserts a box instead of the needed extra formula.
13363 \begin_layout Plain Layout
13365 \begin_inset CommandInset href
13367 name "LyX-bug #1435"
13368 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13380 \begin_layout Standard
13405 , with the difference that there is no frame.
13408 \begin_layout Subsection
13410 \begin_inset CommandInset label
13412 name "sub:Colored-Boxes"
13420 \begin_layout Plain Layout
13429 \begin_layout Standard
13430 To be able to use all commands explained in this section, the LaTeX-package
13439 \begin_layout Plain Layout
13444 is part of every LaTeX standard installation.
13453 \begin_layout Plain Layout
13459 has to be loaded in the LaTeX-preamble with the line
13463 \begin_layout Plain Layout
13464 When text is colored somewhere in the document with a predefined color,
13465 LyX loads the LaTeX-package
13470 Thus it is possible that the package is loaded twice, but this doesn't
13477 \begin_inset Note Note
13480 \begin_layout Plain Layout
13481 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13490 \begin_layout Standard
13498 \begin_layout Standard
13499 \begin_inset VSpace medskip
13502 To color boxes, the command
13512 \begin_layout Plain Layout
13520 is used in the following scheme:
13523 \begin_layout Standard
13528 colorbox{color}{box content}
13531 \begin_layout Standard
13532 The box content can also be a box and a
13538 can also be part of another box (see the 2nd and 3rd example).
13539 When the box should contain a formula, an extra formula has to be created,
13550 \begin_layout Plain Layout
13551 This also applies for the command
13559 \begin_inset CommandInset href
13561 name "LyX-bug #1435"
13562 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13574 \begin_layout Standard
13575 One of the following predefined colors can be chosen:
13578 \begin_layout Standard
13612 \begin_layout Standard
13614 \begin_inset Tabular
13615 <lyxtabular version="3" rows="4" columns="2">
13617 <column alignment="center" valignment="top" width="0">
13618 <column alignment="center" valignment="top" width="0">
13620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13623 \begin_layout Plain Layout
13629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13632 \begin_layout Plain Layout
13634 \begin_inset Note Note
13637 \begin_layout Plain Layout
13644 is only used as spacer.
13656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13659 \begin_layout Plain Layout
13663 \begin_inset Formula $\to$
13673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13676 \begin_layout Plain Layout
13677 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13690 \begin_layout Plain Layout
13694 \begin_inset Formula $\to$
13705 \begin_layout Plain Layout
13719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13722 \begin_layout Plain Layout
13723 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13736 \begin_layout Plain Layout
13743 \begin_layout Plain Layout
13755 \begin_inset Formula $\to$
13765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13768 \begin_layout Plain Layout
13769 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13785 \begin_layout Standard
13792 only colors the box but not the characters in the box.
13793 To color all characters, the whole formula is highlighted and the wanted
13794 color is chosen in the
13797 \begin_inset space ~
13803 The dialog can be called with the toolbar button
13804 \begin_inset Graphics
13805 filename ../images/dialog-show_character.png
13812 Edit\SpecialChar \menuseparator
13814 \begin_inset space ~
13817 Style\SpecialChar \menuseparator
13821 The formula number has then the same color as the formula.
13822 When the formula number should get another color than the formula characters,
13823 the color must be changed within the formula.
13826 \begin_layout Standard
13830 \begin_layout Standard
13833 \begin_inset Formula \begin{equation}
13834 \int A=B\label{eq:red}\end{equation}
13841 \begin_inset Formula \begin{equation}
13842 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13849 \begin_layout Standard
13851 \begin_inset CommandInset ref
13857 is completely colored red.
13858 \begin_inset Newline newline
13862 \begin_inset CommandInset ref
13864 reference "eq:redgreen"
13868 was first completely colored green to set the color for the formula number.
13869 Subsequently the formula characters were colored red.
13872 \begin_layout Standard
13873 \begin_inset VSpace bigskip
13876 To color the frame different than the rest of the box, the command
13886 \begin_layout Plain Layout
13894 is used in the following scheme:
13897 \begin_layout Standard
13902 fcolorbox{frame color}{color}{box content}
13905 \begin_layout Standard
13912 is an extension of the command
13919 The frame width is set, like for
13942 \begin_layout Plain Layout
13954 \begin_inset Formula \[
13955 \fcolorbox{cyan}{magenta}{A=B}\]
13963 \begin_layout Plain Layout
13977 \begin_layout Standard
13978 This formula was created with the command
13979 \begin_inset Newline newline
13987 \begin_inset Formula $\to$
13993 \begin_inset Formula $\to$
14003 \begin_layout Standard
14004 \begin_inset VSpace bigskip
14007 To use other colors than the predefined ones, they have to be defined first.
14010 \begin_layout Standard
14011 One can for example define the color
14012 \begin_inset Quotes eld
14020 \begin_inset Quotes erd
14023 with the LaTeX-preamble line:
14026 \begin_layout Standard
14031 definecolor{darkgreen}{cmyk}{0.5,
14049 \begin_layout Plain Layout
14060 \begin_layout Standard
14065 is the color space that denotes the colors
14082 The four comma separated numbers are the portion factor for the corresponding
14083 colors of the color space.
14084 The factors can be in the range of 0
14085 \begin_inset space \thinspace{}
14089 \begin_inset space \thinspace{}
14097 also the color space
14101 can be used for definitions.
14118 , so that there are in this case three portion factors for the corresponding
14120 Furthermore there is the color space
14124 with one portion factor for the gray value.
14127 \begin_layout Standard
14128 As example a framed box with the new defined color
14132 where the characters have been colored
14137 \begin_inset Formula \begin{equation}
14138 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14145 \begin_layout Standard
14146 Self-defined colors can also be used for text with the help of the command
14157 \begin_layout Plain Layout
14166 \begin_layout Standard
14170 \begin_layout Plain Layout
14174 textcolor{darkgreen}{
14180 \begin_inset Quotes eld
14184 \begin_inset Quotes erd
14191 \begin_layout Plain Layout
14201 \begin_layout Standard
14212 \begin_layout Plain Layout
14220 is used in the scheme
14224 textcolor{color}{characters to color}
14229 \begin_layout Subsection
14231 \begin_inset CommandInset label
14233 name "sub:Paragraph-Boxes"
14241 \begin_layout Plain Layout
14242 Boxes ! as paragraph
14250 \begin_layout Standard
14251 A box that can contain several lines and paragraphs, a so called paragraph
14252 box (parbox), can be created with the menu
14254 Insert\SpecialChar \menuseparator
14257 or the toolbar button
14258 \begin_inset Graphics
14259 filename ../images/box-insert.png
14267 \begin_layout Standard
14268 The following example shows a framed parbox in a line:
14271 \begin_layout Standard
14272 \begin_inset VSpace medskip
14276 \begin_inset Box Boxed
14285 height_special "totalheight"
14288 \begin_layout Plain Layout
14289 This is a paragraph box.
14291 \begin_inset space \thinspace{}
14294 cm long and can also contain formulas:
14295 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14306 \begin_layout Standard
14307 \begin_inset VSpace medskip
14313 \begin_layout Standard
14314 Such a box is created by right-clicking on the gray box inset.
14315 A dialog pops up showing the box properties.
14329 \begin_inset space \thinspace{}
14334 Vertical Box Alignment
14339 \begin_layout Standard
14340 \begin_inset VSpace medskip
14343 In LaTeX a parbox is created with the command
14353 \begin_layout Plain Layout
14361 that has the following scheme:
14364 \begin_layout Standard
14369 parbox[position]{width}{box content}
14372 \begin_layout Standard
14386 for bottom means that the box is aligned within the surrounding text with
14392 for top this is done with the first line.
14393 When no position is given, the box will be vertically centered, see section
14401 \begin_inset space ~
14406 manual for examples.
14409 \begin_layout Standard
14410 \begin_inset VSpace bigskip
14413 To frame formulas completely, including the formula number, the formula
14414 must be set into a parbox.
14415 To do this, the command
14429 is inserted in TeX-mode before the formula.
14438 \begin_layout Plain Layout
14448 is hereby the line width set for the document.
14449 Because the frame is outside the parbox, 2
14450 \begin_inset space \thinspace{}
14453 times the frame separation and the frame thickness must be subtracted from
14455 As this is not automatically done by LyX due to a bug
14459 \begin_layout Plain Layout
14460 \begin_inset CommandInset href
14462 name "LyX-bug #4483"
14463 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14472 , TeX-mode has to be used.
14473 To be able to multiply and subtract in arguments, the LaTeX-package
14481 \begin_layout Plain Layout
14486 is part of every LaTeX standard installation.
14495 \begin_layout Plain Layout
14501 must be loaded in the LaTeX-preamble with the line
14504 \begin_layout Standard
14512 \begin_layout Standard
14513 Behind the formula both boxes are closed by entering
14518 Here is an example:
14522 \begin_layout Plain Layout
14536 \begin_layout Standard
14540 \begin_layout Plain Layout
14558 \begin_inset Formula \begin{equation}
14559 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14567 \begin_layout Plain Layout
14578 \begin_layout Plain Layout
14592 \begin_layout Standard
14593 \begin_inset VSpace medskip
14596 As a parbox is used as argument of
14602 , there is in this case no difference between
14617 \begin_layout Standard
14618 \begin_inset VSpace bigskip
14621 Paragraph boxes are very useful to comment formulas directly.
14628 is used in combination with the command
14642 \begin_inset CommandInset ref
14644 reference "sub:User-defined-Numbering"
14651 \begin_layout Standard
14652 An example of a formula commented with
14661 \begin_layout Standard
14665 \begin_layout Plain Layout
14678 This is a description.
14679 It is distinctly separated from the formula and multiline.
14683 \begin_layout Plain Layout
14695 \begin_layout Standard
14696 Such a formula must be inserted completely in TeX-mode because LyX does
14697 not yet support the command
14704 The formula is created with the following command sequence:
14707 \begin_layout Standard
14720 is inserted in TeX-mode.
14724 \begin_layout Plain Layout
14725 When the formula style
14737 can also be replaced by
14744 (formula styles see
14745 \begin_inset CommandInset ref
14747 reference "sec:Formula-Styles"
14756 Then the description follows as normal text, and finally
14762 is inserted in TeX-mode.
14775 hereby create a displayed formula.
14778 \begin_layout Standard
14785 can be seen in this example that was
14786 \begin_inset Quotes eld
14790 \begin_inset Quotes erd
14793 using the mathematical textmode:
14794 \begin_inset Formula \[
14795 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14802 \begin_layout Section
14807 \begin_layout Plain Layout
14816 \begin_layout Subsection
14818 \begin_inset CommandInset label
14820 name "sub:Big-Operators"
14828 \begin_layout Plain Layout
14838 \begin_layout Plain Layout
14848 \begin_layout Plain Layout
14857 \begin_layout Standard
14858 To be able to use all integral operators listed here, the option
14860 Use esint package automatically
14862 must be set in the document settings under
14865 \begin_inset space ~
14873 \begin_layout Standard
14874 \begin_inset space \hfill{}
14878 \begin_inset Tabular
14879 <lyxtabular version="3" rows="11" columns="2">
14881 <column alignment="center" valignment="top" width="0pt">
14882 <column alignment="center" valignment="top" width="0pt">
14884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14887 \begin_layout Plain Layout
14893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14896 \begin_layout Plain Layout
14904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14907 \begin_layout Plain Layout
14914 \begin_layout Plain Layout
14927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14930 \begin_layout Plain Layout
14931 \begin_inset Formula $\int$
14941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14944 \begin_layout Plain Layout
14952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14955 \begin_layout Plain Layout
14956 \begin_inset Formula $\oint$
14966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14969 \begin_layout Plain Layout
14977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14980 \begin_layout Plain Layout
14981 \begin_inset Formula $\ointctrclockwise$
14991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14994 \begin_layout Plain Layout
15002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15005 \begin_layout Plain Layout
15006 \begin_inset Formula $\ointclockwise$
15016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15019 \begin_layout Plain Layout
15027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15030 \begin_layout Plain Layout
15031 \begin_inset Formula $\sqint$
15041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15044 \begin_layout Plain Layout
15052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15055 \begin_layout Plain Layout
15057 \begin_inset Formula $\fint$
15067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15070 \begin_layout Plain Layout
15078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15081 \begin_layout Plain Layout
15083 \begin_inset Formula $\landupint$
15093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15096 \begin_layout Plain Layout
15104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15107 \begin_layout Plain Layout
15109 \begin_inset Formula $\landdownint$
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15134 \begin_inset Formula $\bigcap$
15144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15147 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\bigcup$
15173 \begin_inset space \hfill{}
15177 \begin_inset Tabular
15178 <lyxtabular version="3" rows="11" columns="2">
15180 <column alignment="center" valignment="top" width="0pt">
15181 <column alignment="center" valignment="top" width="0pt">
15183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15186 \begin_layout Plain Layout
15192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15195 \begin_layout Plain Layout
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15206 \begin_layout Plain Layout
15213 \begin_layout Plain Layout
15226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15229 \begin_layout Plain Layout
15230 \begin_inset Formula $\sum$
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15250 \begin_layout Plain Layout
15263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15266 \begin_layout Plain Layout
15267 \begin_inset Formula $\prod$
15277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15280 \begin_layout Plain Layout
15288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15291 \begin_layout Plain Layout
15292 \begin_inset Formula $\coprod$
15302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15305 \begin_layout Plain Layout
15313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15316 \begin_layout Plain Layout
15317 \begin_inset Formula $\bigodot$
15327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15330 \begin_layout Plain Layout
15338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15341 \begin_layout Plain Layout
15342 \begin_inset Formula $\bigotimes$
15352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15355 \begin_layout Plain Layout
15363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15366 \begin_layout Plain Layout
15367 \begin_inset Formula $\bigoplus$
15377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15380 \begin_layout Plain Layout
15388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15391 \begin_layout Plain Layout
15392 \begin_inset Formula $\bigwedge$
15402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15405 \begin_layout Plain Layout
15413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15416 \begin_layout Plain Layout
15417 \begin_inset Formula $\bigvee$
15427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15430 \begin_layout Plain Layout
15438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15441 \begin_layout Plain Layout
15442 \begin_inset Formula $\bigsqcup$
15452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15455 \begin_layout Plain Layout
15463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15466 \begin_layout Plain Layout
15467 \begin_inset Formula $\biguplus$
15481 \begin_inset space \hfill{}
15487 \begin_layout Standard
15488 All big operators can also be inserted via the math toolbar button
15489 \begin_inset Graphics
15490 filename ../images/math/intop.png
15498 \begin_layout Standard
15499 The operators are called big because they are bigger than the sometimes
15500 equal looking binary operators.
15501 All big operators can have limits as described in the next subsection.
15504 \begin_layout Standard
15505 For all integral operators there is a second version available, ending on
15523 These operators are different from
15530 \begin_inset space \space{}
15533 in the style the operator limits are displayed, see
15534 \begin_inset CommandInset ref
15536 reference "sub:Operator-Limits"
15544 \begin_layout Subsubsection*
15545 Advices for Integrals
15548 \begin_layout Standard
15553 in an integral is an operator, that therefore has to be set upright.
15554 This is done by highlighting the
15558 and using the keyboard shortcut
15568 \begin_layout Plain Layout
15574 \begin_inset CommandInset ref
15576 reference "sub:Font-Styles"
15586 Finally the smallest space is inserted before the
15590 , as this is usual for operators.
15594 \begin_layout Standard
15596 \begin_inset Formula $\int A(x)dx$
15600 \begin_inset Newline newline
15607 \begin_layout Plain Layout
15617 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15623 \begin_layout Standard
15624 For multiple integrals there are the following commands:
15625 \begin_inset VSpace medskip
15631 \begin_layout Standard
15632 \begin_inset space \hfill{}
15636 \begin_inset Tabular
15637 <lyxtabular version="3" rows="4" columns="2">
15639 <column alignment="center" valignment="top" width="0">
15640 <column alignment="center" valignment="top" width="0">
15642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15645 \begin_layout Plain Layout
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15654 \begin_layout Plain Layout
15656 \begin_inset Note Note
15659 \begin_layout Plain Layout
15666 is only used as spacer.
15678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15681 \begin_layout Plain Layout
15689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15692 \begin_layout Plain Layout
15693 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15706 \begin_layout Plain Layout
15714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15717 \begin_layout Plain Layout
15718 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15731 \begin_layout Plain Layout
15739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15742 \begin_layout Plain Layout
15743 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15757 \begin_inset space \hfill{}
15761 \begin_inset Tabular
15762 <lyxtabular version="3" rows="4" columns="2">
15764 <column alignment="center" valignment="top" width="0">
15765 <column alignment="center" valignment="top" width="0">
15767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15770 \begin_layout Plain Layout
15776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15779 \begin_layout Plain Layout
15787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15790 \begin_layout Plain Layout
15798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15801 \begin_layout Plain Layout
15802 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15815 \begin_layout Plain Layout
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15826 \begin_layout Plain Layout
15827 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15840 \begin_layout Plain Layout
15848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15851 \begin_layout Plain Layout
15852 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15866 \begin_inset space \hfill{}
15872 \begin_layout Subsection
15874 \begin_inset CommandInset label
15876 name "sub:Operator-Limits"
15884 \begin_layout Plain Layout
15893 \begin_layout Standard
15894 Limits are created by super- and subscripts:
15897 \begin_layout Standard
15899 \begin_inset Tabular
15900 <lyxtabular version="3" rows="2" columns="2">
15902 <column alignment="center" valignment="top" width="0pt">
15903 <column alignment="center" valignment="top" width="0pt">
15905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15908 \begin_layout Plain Layout
15914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15917 \begin_layout Plain Layout
15919 \begin_inset Note Note
15922 \begin_layout Plain Layout
15929 is only used as spacer.
15941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15944 \begin_layout Plain Layout
15953 \begin_layout Plain Layout
15963 \begin_inset Formula $\to$
15967 \begin_inset Formula $\to$
15975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15978 \begin_layout Plain Layout
15979 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15995 \begin_layout Standard
15996 Limits of inline formulas are set right beside the operator.
15997 Limits in displayed formulas are set above or below the operator, except
15998 for integral limits.
16001 \begin_layout Standard
16002 To force that the limits are set beside the operator, the cursor is set
16003 directly behind the operator and the limits type is changed with the menu
16006 Edit\SpecialChar \menuseparator
16007 Math\SpecialChar \menuseparator
16026 \begin_layout Standard
16027 The default limits type is this:
16028 \begin_inset Formula \[
16029 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16033 This is how it looks when the limits type was changed to
16040 \begin_inset Formula \[
16041 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16045 For integrals, except those ending with
16061 etc., the limits are by default set beside the operator.
16062 But for multiple integrals the limits are often set below the operator.
16063 In the following example the limits type was therefore set to
16067 and so set below the integrals:
16068 \begin_inset Formula \begin{equation}
16069 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16076 \begin_layout Standard
16077 \begin_inset VSpace medskip
16080 To specify conditions for limits, the commands
16090 \begin_layout Plain Layout
16108 \begin_layout Plain Layout
16117 To create for example this expression
16118 \begin_inset Formula \begin{equation}
16119 \sum_{\begin{subarray}{c}
16121 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16128 \begin_layout Standard
16129 the following has to be done:
16130 \begin_inset Newline newline
16145 \begin_layout Plain Layout
16157 One is now in a blue box under the summation operator and insert there
16166 \begin_layout Plain Layout
16178 The blue box is now within a purple box and now several lines can be written
16180 A new line is created by inserting a line break (
16183 arg "newline-insert newline"
16188 \begin_inset Newline newline
16193 0<k<1000 Ctrl+Return
16194 \begin_inset Newline newline
16199 is typed in, a new box appears below for the new line.
16202 \begin_layout Standard
16203 The alignment of the lines can be changed to left aligned with the
16213 Edit\SpecialChar \menuseparator
16217 To get right alignment,
16225 \begin_layout Plain Layout
16236 is inserted at the beginning of the line.
16239 \begin_layout Standard
16252 with the difference that the lines are always centered.
16255 \begin_layout Standard
16256 \begin_inset VSpace bigskip
16260 \begin_inset CommandInset ref
16262 reference "eq:substack"
16266 there can be too much space beside an operator, because the characters
16267 following the operator are set beside the limits.
16270 \begin_layout Standard
16271 To avoid this, the following macro can be used in the LaTeX-preamble:
16274 \begin_layout Standard
16288 \begin_inset Newline newline
16300 \begin_inset Newline newline
16307 mathclapinternal #1#2{
16311 mathsurround =0pt #1{#2}$}}
16314 \begin_layout Standard
16315 This defines the command
16325 \begin_layout Plain Layout
16333 that sets the width of the limit to 0
16334 \begin_inset space \thinspace{}
16338 The command scheme is
16341 \begin_layout Standard
16349 \begin_layout Standard
16350 where the limit can consist of several conditions.
16353 \begin_layout Standard
16355 \begin_inset CommandInset ref
16357 reference "eq:substack"
16361 , one uses the command
16364 \begin_layout Standard
16377 \begin_layout Plain Layout
16386 0<k<1000 Ctrl+Return
16389 \begin_layout Standard
16390 to create the lower limit.
16391 The summand is now directly behind the summation operator:
16392 \begin_inset Formula \[
16393 \sum_{\mathclap{\substack{0<k<1000\\
16394 \\k\,\in\,\mathbb{N}}
16402 \begin_layout Standard
16403 \begin_inset VSpace bigskip
16406 How to use one limit for several operators is described in
16407 \begin_inset CommandInset ref
16409 reference "sub:Self-defined-Operators"
16416 \begin_layout Standard
16417 \begin_inset Newpage newpage
16423 \begin_layout Subsection
16425 \begin_inset CommandInset label
16427 name "sub:Binary-Operators"
16435 \begin_layout Plain Layout
16444 \begin_layout Standard
16445 Binary operators are surrounded by space when there is a character before
16447 \begin_inset VSpace medskip
16453 \begin_layout Standard
16454 \begin_inset space \hfill{}
16458 \begin_inset Tabular
16459 <lyxtabular version="3" rows="13" columns="2">
16461 <column alignment="center" valignment="top" width="0pt">
16462 <column alignment="center" valignment="top" width="0pt">
16464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16467 \begin_layout Plain Layout
16469 \begin_inset Note Note
16472 \begin_layout Plain Layout
16479 is only used as spacer.
16489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16492 \begin_layout Plain Layout
16500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16503 \begin_layout Plain Layout
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16512 \begin_layout Plain Layout
16513 \begin_inset Formula $+$
16523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16526 \begin_layout Plain Layout
16532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16535 \begin_layout Plain Layout
16536 \begin_inset Formula $-$
16546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16549 \begin_layout Plain Layout
16557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16560 \begin_layout Plain Layout
16561 \begin_inset Formula $\pm$
16571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16574 \begin_layout Plain Layout
16582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16585 \begin_layout Plain Layout
16586 \begin_inset Formula $\mp$
16596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16599 \begin_layout Plain Layout
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16610 \begin_layout Plain Layout
16611 \begin_inset Formula $\cdot$
16621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16624 \begin_layout Plain Layout
16632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16635 \begin_layout Plain Layout
16636 \begin_inset Formula $\times$
16646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16649 \begin_layout Plain Layout
16657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16660 \begin_layout Plain Layout
16661 \begin_inset Formula $\div$
16671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16674 \begin_layout Plain Layout
16678 \begin_layout Plain Layout
16691 \begin_layout Plain Layout
16703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16706 \begin_layout Plain Layout
16707 \begin_inset Formula $*$
16717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16720 \begin_layout Plain Layout
16728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16731 \begin_layout Plain Layout
16732 \begin_inset Formula $\star$
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16745 \begin_layout Plain Layout
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16756 \begin_layout Plain Layout
16757 \begin_inset Formula $\circ$
16767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16770 \begin_layout Plain Layout
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16781 \begin_layout Plain Layout
16782 \begin_inset Formula $\diamond$
16792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16795 \begin_layout Plain Layout
16803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16806 \begin_layout Plain Layout
16807 \begin_inset Formula $\bullet$
16821 \begin_inset space \hfill{}
16825 \begin_inset Tabular
16826 <lyxtabular version="3" rows="13" columns="2">
16828 <column alignment="center" valignment="top" width="0pt">
16829 <column alignment="center" valignment="top" width="0pt">
16831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16834 \begin_layout Plain Layout
16840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16843 \begin_layout Plain Layout
16851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16854 \begin_layout Plain Layout
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16865 \begin_layout Plain Layout
16866 \begin_inset Formula $\nabla$
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16879 \begin_layout Plain Layout
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16890 \begin_layout Plain Layout
16891 \begin_inset Formula $\bigtriangledown$
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16904 \begin_layout Plain Layout
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16915 \begin_layout Plain Layout
16916 \begin_inset Formula $\bigtriangleup$
16926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16929 \begin_layout Plain Layout
16937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16940 \begin_layout Plain Layout
16941 \begin_inset Formula $\Box$
16951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16954 \begin_layout Plain Layout
16962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16965 \begin_layout Plain Layout
16966 \begin_inset Formula $\cap$
16976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16979 \begin_layout Plain Layout
16987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16990 \begin_layout Plain Layout
16991 \begin_inset Formula $\cup$
17001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17004 \begin_layout Plain Layout
17012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17015 \begin_layout Plain Layout
17016 \begin_inset Formula $\dagger$
17026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17029 \begin_layout Plain Layout
17037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17040 \begin_layout Plain Layout
17041 \begin_inset Formula $\ddagger$
17051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17054 \begin_layout Plain Layout
17062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17065 \begin_layout Plain Layout
17066 \begin_inset Formula $\wr$
17076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17079 \begin_layout Plain Layout
17087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17090 \begin_layout Plain Layout
17091 \begin_inset Formula $\bigcirc$
17101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17104 \begin_layout Plain Layout
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17115 \begin_layout Plain Layout
17116 \begin_inset Formula $\wedge$
17126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17129 \begin_layout Plain Layout
17137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17140 \begin_layout Plain Layout
17141 \begin_inset Formula $\vee$
17155 \begin_inset space \hfill{}
17159 \begin_inset Tabular
17160 <lyxtabular version="3" rows="13" columns="2">
17162 <column alignment="center" valignment="top" width="0pt">
17163 <column alignment="center" valignment="top" width="0pt">
17165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17168 \begin_layout Plain Layout
17174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17177 \begin_layout Plain Layout
17185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17188 \begin_layout Plain Layout
17196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17199 \begin_layout Plain Layout
17200 \begin_inset Formula $\oplus$
17210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17213 \begin_layout Plain Layout
17221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17224 \begin_layout Plain Layout
17225 \begin_inset Formula $\ominus$
17235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17238 \begin_layout Plain Layout
17246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17249 \begin_layout Plain Layout
17250 \begin_inset Formula $\otimes$
17260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17263 \begin_layout Plain Layout
17271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17274 \begin_layout Plain Layout
17275 \begin_inset Formula $\oslash$
17285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17288 \begin_layout Plain Layout
17296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17299 \begin_layout Plain Layout
17300 \begin_inset Formula $\odot$
17310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17313 \begin_layout Plain Layout
17321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17324 \begin_layout Plain Layout
17325 \begin_inset Formula $\amalg$
17335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17338 \begin_layout Plain Layout
17346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17349 \begin_layout Plain Layout
17350 \begin_inset Formula $\uplus$
17360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17363 \begin_layout Plain Layout
17371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17374 \begin_layout Plain Layout
17375 \begin_inset Formula $\setminus$
17385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17388 \begin_layout Plain Layout
17396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17399 \begin_layout Plain Layout
17400 \begin_inset Formula $\sqcap$
17410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17413 \begin_layout Plain Layout
17421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17424 \begin_layout Plain Layout
17425 \begin_inset Formula $\sqcup$
17435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17438 \begin_layout Plain Layout
17446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17449 \begin_layout Plain Layout
17450 \begin_inset Formula $\triangleleft$
17460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17474 \begin_layout Plain Layout
17475 \begin_inset Formula $\triangleright$
17489 \begin_inset space \hfill{}
17495 \begin_layout Standard
17496 All binary operators can also be inserted via the math toolbar button
17497 \begin_inset Graphics
17498 filename ../images/math/pm.png
17506 \begin_layout Standard
17507 To typeset the Laplace operator also
17524 \begin_inset Formula $\nabla^{2}$
17527 ) can be used instead of
17536 \begin_layout Standard
17543 Insert\SpecialChar \menuseparator
17555 \begin_layout Subsection
17556 Self-defined Operators
17557 \begin_inset CommandInset label
17559 name "sub:Self-defined-Operators"
17567 \begin_layout Plain Layout
17568 Operators ! self-defined
17576 \begin_layout Standard
17577 With the help of the command
17581 DeclareMathOperator
17587 \begin_layout Plain Layout
17592 DeclareMathOperator
17597 custom operators can be defined in the LaTeX-preamble.
17598 Its command scheme is:
17601 \begin_layout Standard
17606 DeclareMathOperator{new command}{display}
17609 \begin_layout Standard
17610 Display can be characters or symbols that define how the operator looks
17612 To define a big operator a * is set behind the command.
17613 All self-defined big operators can have limits as described in
17614 \begin_inset CommandInset ref
17616 reference "sub:Operator-Limits"
17623 \begin_layout Standard
17624 For example the LaTeX-preamble line
17627 \begin_layout Standard
17632 DeclareMathOperator*{
17639 \begin_layout Standard
17640 defines the command
17646 , that inserts a big operator consisting of the lozenge symbol from
17647 \begin_inset CommandInset ref
17649 reference "sub:Miscellaneous-Symbols"
17654 \begin_inset Formula \[
17655 \Lozenge_{n=1}^{\infty}\]
17659 The command for this formula is:
17670 \begin_inset Formula $\to$
17676 \begin_layout Standard
17677 \begin_inset VSpace bigskip
17680 When self-defined operators are not used several times in the document,
17681 they can also be defined with the commands
17691 \begin_layout Plain Layout
17709 \begin_layout Plain Layout
17717 , which have the following scheme:
17720 \begin_layout Standard
17734 \begin_layout Standard
17741 defines big operators,
17750 \begin_layout Standard
17758 \begin_inset space \thinspace{}
17762 \begin_inset space \space{}
17765 be used to use one limit for several operators:
17768 \begin_layout Standard
17769 \begin_inset Formula \[
17770 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17777 \begin_layout Standard
17778 The command for the formula above is:
17779 \begin_inset Newline newline
17798 \begin_layout Plain Layout
17810 \begin_inset Formula $\to$
17819 \begin_layout Plain Layout
17833 \begin_layout Section
17838 \begin_layout Plain Layout
17847 \begin_layout Subsection
17849 \begin_inset CommandInset label
17851 name "sub:Font-Styles"
17859 \begin_layout Plain Layout
17868 \begin_layout Standard
17869 Latin letters in formulas can be set in one of the following font styles:
17870 \begin_inset VSpace -2mm
17876 \begin_layout Standard
17878 \begin_inset Tabular
17879 <lyxtabular version="3" rows="6" columns="3">
17881 <column alignment="center" valignment="top" width="0">
17882 <column alignment="center" valignment="top" width="0">
17883 <column alignment="center" valignment="top" width="0">
17885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17888 \begin_layout Plain Layout
17894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17897 \begin_layout Plain Layout
17903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17906 \begin_layout Plain Layout
17914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17917 \begin_layout Plain Layout
17926 \begin_layout Plain Layout
17942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17945 \begin_layout Plain Layout
17946 \begin_inset Formula $\mathbb{ABC}$
17954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17957 \begin_layout Plain Layout
17970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17973 \begin_layout Plain Layout
17982 \begin_layout Plain Layout
17998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18001 \begin_layout Plain Layout
18002 \begin_inset Formula $\mathbf{AbC}$
18010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18013 \begin_layout Plain Layout
18026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18029 \begin_layout Plain Layout
18038 \begin_layout Plain Layout
18054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18057 \begin_layout Plain Layout
18058 \begin_inset Formula $\boldsymbol{AbC}$
18066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18069 \begin_layout Plain Layout
18072 arg "font-boldsymbol"
18082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18085 \begin_layout Plain Layout
18094 \begin_layout Plain Layout
18110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18113 \begin_layout Plain Layout
18114 \begin_inset Formula $\mathcal{ABC}$
18122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18125 \begin_layout Plain Layout
18138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18141 \begin_layout Plain Layout
18150 \begin_layout Plain Layout
18166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18169 \begin_layout Plain Layout
18170 \begin_inset Formula $\mathfrak{AbC}$
18178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18181 \begin_layout Plain Layout
18195 \begin_layout Standard
18197 \begin_inset Tabular
18198 <lyxtabular version="3" rows="5" columns="3">
18200 <column alignment="center" valignment="top" width="0">
18201 <column alignment="center" valignment="top" width="0">
18202 <column alignment="center" valignment="top" width="0">
18204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18207 \begin_layout Plain Layout
18213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18216 \begin_layout Plain Layout
18222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18225 \begin_layout Plain Layout
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18236 \begin_layout Plain Layout
18245 \begin_layout Plain Layout
18261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18264 \begin_layout Plain Layout
18265 \begin_inset Formula $\mathit{AbC}$
18273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18276 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18296 \begin_layout Plain Layout
18312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18315 \begin_layout Plain Layout
18316 \begin_inset Formula $\mathrm{AbC}$
18324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18327 \begin_layout Plain Layout
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18343 \begin_layout Plain Layout
18352 \begin_layout Plain Layout
18368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18371 \begin_layout Plain Layout
18372 \begin_inset Formula $\mathsf{AbC}$
18380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18383 \begin_layout Plain Layout
18396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18399 \begin_layout Plain Layout
18408 \begin_layout Plain Layout
18424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18427 \begin_layout Plain Layout
18428 \begin_inset Formula $\mathtt{AbC}$
18436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18439 \begin_layout Plain Layout
18442 arg "font-typewriter"
18458 \begin_layout Standard
18459 \begin_inset Note Greyedout
18462 \begin_layout Plain Layout
18479 can only be used for big letters.
18487 \begin_layout Standard
18488 Predefined is the style
18497 \begin_layout Standard
18498 The style commands work also for letters in mathematical constructs:
18499 \begin_inset Formula \[
18500 \mathfrak{A=\frac{b}{C}}\]
18507 \begin_layout Standard
18508 Characters in mathematical text don't appear in a math font style but in
18509 the text font style
18516 That their style can't be set correctly via the text style dialog is a
18521 \begin_layout Plain Layout
18522 \begin_inset CommandInset href
18524 name "LyX-bug #4091"
18525 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18537 \begin_layout Standard
18538 Instead of the style commands the dialog
18540 Edit\SpecialChar \menuseparator
18541 Math\SpecialChar \menuseparator
18544 or the toolbar button
18545 \begin_inset Graphics
18546 filename ../images/math/font.png
18554 \begin_layout Subsection
18556 \begin_inset CommandInset label
18558 name "sub:Bold-Formulas"
18566 \begin_layout Plain Layout
18575 \begin_layout Standard
18576 To make a complete formula bold, the command
18582 from the previous subsection cannot be used, because it doesn't work for
18583 small Greek letters.
18584 Furthermore it prints Latin letters always upright, like in the following
18588 \begin_layout Standard
18589 \begin_inset Formula \[
18590 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18597 \begin_layout Standard
18598 To display the formula correctly, the command
18605 \begin_inset Formula \[
18606 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18610 It is also possible to set the formula in a
18612 boldmath environment
18615 This environment is created by inserting the command
18623 \begin_layout Plain Layout
18634 To end the environment, the command
18642 \begin_layout Plain Layout
18652 is inserted in TeX-mode.
18656 \begin_layout Plain Layout
18666 \begin_inset Formula \[
18667 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18675 \begin_layout Plain Layout
18687 \begin_layout Subsection
18692 \begin_layout Plain Layout
18701 \begin_layout Standard
18702 Formulas can be colored like normal text: Highlight a formula or a formula
18708 Here is a formula in magenta:
18709 \begin_inset Formula \[
18710 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18717 \begin_layout Standard
18718 You can also define your own colors as described in
18719 \begin_inset CommandInset ref
18721 reference "sub:Colored-Boxes"
18726 They can be used with the TeX code command
18736 \begin_layout Plain Layout
18747 \begin_layout Standard
18752 textcolor{color}{characters or formula}
18755 \begin_layout Standard
18756 The following example was colored completely dark green and partly red:
18759 \begin_layout Standard
18763 \begin_layout Plain Layout
18767 textcolor{darkgreen}{
18773 \begin_inset Formula \[
18774 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18782 \begin_layout Plain Layout
18792 \begin_layout Standard
18793 Due to a bug in LyX only complete formulas can be colored with self-defined
18798 \begin_layout Plain Layout
18799 \begin_inset CommandInset href
18801 name "LyX-bug #5269"
18802 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18814 \begin_layout Subsection
18816 \begin_inset CommandInset label
18818 name "sub:Font-Sizes"
18826 \begin_layout Plain Layout
18835 \begin_layout Standard
18836 For characters in formulas there are, analog to characters in text, the
18837 following size commands:
18840 \begin_layout Standard
18884 \begin_inset Newline newline
18906 \begin_layout Standard
18907 The size produced by the commands depends on the document font size, that
18908 corresponds with the command
18915 The other commands produce smaller or larger sizes than
18922 The font size can however not exceed a certain value.
18923 Is for example the document font size 12
18924 \begin_inset space \thinspace{}
18933 switches to the same size as
18943 \begin_layout Standard
18944 A size command is inserted in TeX-mode before the formula and sets the size
18945 for all following formula and text characters.
18946 To switch back to the initial size, the command
18952 is inserted behind the formula in TeX-mode.
18955 \begin_layout Standard
18956 Within a formula the size can only be changed for symbols or letters in
18958 To do this, the size command is inserted in mathematical text.
18959 All following characters until the end of the mathematical text or until
18960 another size command will have the selected size.
18962 \begin_inset VSpace -2mm
18968 \begin_layout Standard
18972 \begin_layout Plain Layout
18982 \begin_inset Formula \[
18983 A=\frac{B}{c}\cdot\maltese\]
18988 \begin_inset Formula \[
18989 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18997 \begin_layout Plain Layout
19009 \begin_layout Standard
19010 \begin_inset VSpace medskip
19013 Before both formulas the command
19020 The command for the second formula is:
19021 \begin_inset Newline newline
19032 \begin_layout Plain Layout
19047 \begin_layout Plain Layout
19062 \begin_layout Plain Layout
19077 \begin_layout Plain Layout
19087 \begin_inset Formula $\to$
19091 \begin_inset Formula $\to$
19095 \begin_inset Newline newline
19099 \begin_inset space \hspace*{}
19113 \begin_layout Plain Layout
19128 \begin_layout Plain Layout
19143 \begin_layout Plain Layout
19155 \begin_layout Standard
19156 If a symbol cannot be displayed in different sizes, it will always be displayed
19157 in the default size.
19160 \begin_layout Section
19165 \begin_layout Plain Layout
19174 \begin_layout Standard
19175 All Greek letters can also be inserted via the toolbar button
19176 \begin_inset Graphics
19177 filename ../images/math/alpha.png
19185 \begin_layout Subsection
19190 \begin_layout Plain Layout
19191 Greek letters ! small
19199 \begin_layout Standard
19200 \begin_inset space \hfill{}
19204 \begin_inset Tabular
19205 <lyxtabular version="3" rows="11" columns="2">
19207 <column alignment="center" valignment="top" width="0pt">
19208 <column alignment="center" valignment="top" width="0pt">
19210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19213 \begin_layout Plain Layout
19219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19222 \begin_layout Plain Layout
19230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19233 \begin_layout Plain Layout
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19244 \begin_layout Plain Layout
19245 \begin_inset Formula $\alpha$
19255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19258 \begin_layout Plain Layout
19266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19269 \begin_layout Plain Layout
19270 \begin_inset Formula $\beta$
19280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19283 \begin_layout Plain Layout
19291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19294 \begin_layout Plain Layout
19295 \begin_inset Formula $\gamma$
19305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19308 \begin_layout Plain Layout
19316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19319 \begin_layout Plain Layout
19320 \begin_inset Formula $\delta$
19330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19333 \begin_layout Plain Layout
19341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19344 \begin_layout Plain Layout
19345 \begin_inset Formula $\epsilon$
19355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19358 \begin_layout Plain Layout
19366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19369 \begin_layout Plain Layout
19370 \begin_inset Formula $\varepsilon$
19380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19383 \begin_layout Plain Layout
19391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19394 \begin_layout Plain Layout
19395 \begin_inset Formula $\zeta$
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19408 \begin_layout Plain Layout
19416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19419 \begin_layout Plain Layout
19420 \begin_inset Formula $\eta$
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19433 \begin_layout Plain Layout
19441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19444 \begin_layout Plain Layout
19445 \begin_inset Formula $\theta$
19455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19458 \begin_layout Plain Layout
19466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19469 \begin_layout Plain Layout
19470 \begin_inset Formula $\vartheta$
19484 \begin_inset space \hfill{}
19488 \begin_inset Tabular
19489 <lyxtabular version="3" rows="12" columns="2">
19491 <column alignment="center" valignment="top" width="0pt">
19492 <column alignment="center" valignment="top" width="0pt">
19494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19497 \begin_layout Plain Layout
19503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19506 \begin_layout Plain Layout
19514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19517 \begin_layout Plain Layout
19525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19528 \begin_layout Plain Layout
19529 \begin_inset Formula $\iota$
19539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19542 \begin_layout Plain Layout
19550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19553 \begin_layout Plain Layout
19554 \begin_inset Formula $\kappa$
19564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19567 \begin_layout Plain Layout
19575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19578 \begin_layout Plain Layout
19579 \begin_inset Formula $\varkappa$
19589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19592 \begin_layout Plain Layout
19600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19603 \begin_layout Plain Layout
19604 \begin_inset Formula $\lambda$
19614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19617 \begin_layout Plain Layout
19625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19628 \begin_layout Plain Layout
19629 \begin_inset Formula $\mu$
19639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19642 \begin_layout Plain Layout
19650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19653 \begin_layout Plain Layout
19654 \begin_inset Formula $\nu$
19664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19667 \begin_layout Plain Layout
19675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19678 \begin_layout Plain Layout
19679 \begin_inset Formula $\xi$
19689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19692 \begin_layout Plain Layout
19698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19701 \begin_layout Plain Layout
19702 \begin_inset Formula $o$
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19715 \begin_layout Plain Layout
19723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19726 \begin_layout Plain Layout
19727 \begin_inset Formula $\pi$
19737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19740 \begin_layout Plain Layout
19748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19751 \begin_layout Plain Layout
19752 \begin_inset Formula $\varpi$
19762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19765 \begin_layout Plain Layout
19773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19776 \begin_layout Plain Layout
19777 \begin_inset Formula $\rho$
19791 \begin_inset space \hfill{}
19795 \begin_inset Tabular
19796 <lyxtabular version="3" rows="11" columns="2">
19798 <column alignment="center" valignment="top" width="0pt">
19799 <column alignment="center" valignment="top" width="0pt">
19801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19804 \begin_layout Plain Layout
19810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19813 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\varrho$
19846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19849 \begin_layout Plain Layout
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19860 \begin_layout Plain Layout
19861 \begin_inset Formula $\sigma$
19871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19874 \begin_layout Plain Layout
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19885 \begin_layout Plain Layout
19886 \begin_inset Formula $\varsigma$
19896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19899 \begin_layout Plain Layout
19907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19910 \begin_layout Plain Layout
19911 \begin_inset Formula $\tau$
19921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19924 \begin_layout Plain Layout
19932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19935 \begin_layout Plain Layout
19936 \begin_inset Formula $\upsilon$
19946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19949 \begin_layout Plain Layout
19957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19960 \begin_layout Plain Layout
19961 \begin_inset Formula $\phi$
19971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19974 \begin_layout Plain Layout
19982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19985 \begin_layout Plain Layout
19986 \begin_inset Formula $\varphi$
19996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19999 \begin_layout Plain Layout
20007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20010 \begin_layout Plain Layout
20011 \begin_inset Formula $\chi$
20021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20024 \begin_layout Plain Layout
20032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20035 \begin_layout Plain Layout
20036 \begin_inset Formula $\psi$
20046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20049 \begin_layout Plain Layout
20057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20060 \begin_layout Plain Layout
20061 \begin_inset Formula $\omega$
20075 \begin_inset space \hfill{}
20081 \begin_layout Standard
20082 \begin_inset VSpace medskip
20088 \begin_layout Standard
20089 How to create upright Greek letters is explained in
20090 \begin_inset CommandInset ref
20092 reference "sub:Upright-small-Greek"
20099 \begin_layout Subsection
20104 \begin_layout Plain Layout
20105 Greek letters ! big
20113 \begin_layout Standard
20114 \begin_inset space \hfill{}
20118 \begin_inset Tabular
20119 <lyxtabular version="3" rows="7" columns="2">
20121 <column alignment="center" valignment="top" width="0pt">
20122 <column alignment="center" valignment="top" width="0pt">
20124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20127 \begin_layout Plain Layout
20133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20136 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20147 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20158 \begin_layout Plain Layout
20159 \begin_inset Formula $\Gamma$
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20172 \begin_layout Plain Layout
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20183 \begin_layout Plain Layout
20184 \begin_inset Formula $\Delta$
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20197 \begin_layout Plain Layout
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20208 \begin_layout Plain Layout
20209 \begin_inset Formula $\Theta$
20219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20222 \begin_layout Plain Layout
20230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20233 \begin_layout Plain Layout
20234 \begin_inset Formula $\Lambda$
20244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20247 \begin_layout Plain Layout
20255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20258 \begin_layout Plain Layout
20259 \begin_inset Formula $\Xi$
20269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20272 \begin_layout Plain Layout
20280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20283 \begin_layout Plain Layout
20284 \begin_inset Formula $\Pi$
20298 \begin_inset space \hfill{}
20302 \begin_inset Tabular
20303 <lyxtabular version="3" rows="6" columns="2">
20305 <column alignment="center" valignment="top" width="0pt">
20306 <column alignment="center" valignment="top" width="0pt">
20308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20311 \begin_layout Plain Layout
20317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20320 \begin_layout Plain Layout
20328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20331 \begin_layout Plain Layout
20339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20342 \begin_layout Plain Layout
20343 \begin_inset Formula $\Sigma$
20353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20356 \begin_layout Plain Layout
20364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20367 \begin_layout Plain Layout
20368 \begin_inset Formula $\Upsilon$
20378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20381 \begin_layout Plain Layout
20389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20392 \begin_layout Plain Layout
20393 \begin_inset Formula $\Phi$
20403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20406 \begin_layout Plain Layout
20414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20417 \begin_layout Plain Layout
20418 \begin_inset Formula $\Psi$
20428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20431 \begin_layout Plain Layout
20439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20442 \begin_layout Plain Layout
20443 \begin_inset Formula $\Omega$
20457 \begin_inset space \hfill{}
20463 \begin_layout Standard
20464 \begin_inset VSpace medskip
20467 That the big Greek letters appear upright is caused by a design bug when
20469 To get correct italic big letters, begin every command with
20474 For example the command
20481 \begin_inset Formula $\varGamma$
20487 \begin_layout Subsection
20492 \begin_layout Plain Layout
20493 Greek letters ! bold
20501 \begin_layout Standard
20502 Greek letters cannot be set with different font styles like Latin letters.
20503 They can only be made bold with the command
20513 \begin_layout Plain Layout
20524 \begin_layout Standard
20526 \begin_inset Tabular
20527 <lyxtabular version="3" rows="3" columns="2">
20529 <column alignment="center" valignment="top" width="0">
20530 <column alignment="center" valignment="top" width="0">
20532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20535 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20555 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\theta\boldsymbol{\theta}$
20616 \begin_layout Section
20621 \begin_layout Plain Layout
20634 \begin_layout Plain Layout
20635 A list with all symbols of most of the LaTeX-packages can be found in
20636 \begin_inset CommandInset citation
20651 \begin_layout Plain Layout
20659 \begin_inset Note Note
20662 \begin_layout Plain Layout
20665 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20668 \begin_layout Plain Layout
20671 texorpdfstring is in section
20672 \begin_inset CommandInset ref
20674 reference "sub:Formulas-in-Section"
20687 \begin_layout Plain Layout
20696 \begin_layout Standard
20697 Many of the symbols listed in this section can also be inserted via the
20699 \begin_inset Graphics
20700 filename ../images/math/nabla.png
20706 \begin_inset Graphics
20707 filename ../images/math/digamma.png
20715 \begin_layout Subsection
20716 Mathematical Symbols
20717 \begin_inset CommandInset label
20719 name "sub:Mathematical-Symbols"
20727 \begin_layout Plain Layout
20728 Symbols ! mathematical
20736 \begin_layout Standard
20737 \begin_inset space \hfill{}
20741 \begin_inset Tabular
20742 <lyxtabular version="3" rows="10" columns="2">
20744 <column alignment="center" valignment="top" width="0pt">
20745 <column alignment="center" valignment="top" width="0pt">
20747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\neg$
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20795 \begin_layout Plain Layout
20803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20806 \begin_layout Plain Layout
20807 \begin_inset Formula $\Im$
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20820 \begin_layout Plain Layout
20828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20831 \begin_layout Plain Layout
20832 \begin_inset Formula $\Re$
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20845 \begin_layout Plain Layout
20853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20856 \begin_layout Plain Layout
20857 \begin_inset Formula $\aleph$
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20870 \begin_layout Plain Layout
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20881 \begin_layout Plain Layout
20882 \begin_inset Formula $\partial$
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20895 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20906 \begin_layout Plain Layout
20907 \begin_inset Formula $\infty$
20917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20920 \begin_layout Plain Layout
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20931 \begin_layout Plain Layout
20932 \begin_inset Formula $\wp$
20942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20957 \begin_inset Formula $\imath$
20967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20970 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\jmath$
20996 \begin_inset space \hfill{}
21000 \begin_inset Tabular
21001 <lyxtabular version="3" rows="10" columns="2">
21003 <column alignment="center" valignment="top" width="0pt">
21004 <column alignment="center" valignment="top" width="0pt">
21006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21009 \begin_layout Plain Layout
21015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21018 \begin_layout Plain Layout
21020 \begin_inset Note Note
21023 \begin_layout Plain Layout
21030 is only used as spacer.
21042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21045 \begin_layout Plain Layout
21053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21056 \begin_layout Plain Layout
21057 \begin_inset Formula $\forall$
21067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21070 \begin_layout Plain Layout
21078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21081 \begin_layout Plain Layout
21082 \begin_inset Formula $\exists$
21092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21095 \begin_layout Plain Layout
21103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21106 \begin_layout Plain Layout
21107 \begin_inset Formula $\nexists$
21117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21120 \begin_layout Plain Layout
21128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21131 \begin_layout Plain Layout
21132 \begin_inset Formula $\emptyset$
21142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21145 \begin_layout Plain Layout
21153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21156 \begin_layout Plain Layout
21157 \begin_inset Formula $\varnothing$
21167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21170 \begin_layout Plain Layout
21178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21181 \begin_layout Plain Layout
21182 \begin_inset Formula $\dag$
21192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21195 \begin_layout Plain Layout
21203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21206 \begin_layout Plain Layout
21207 \begin_inset Formula $\ddag$
21217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21220 \begin_layout Plain Layout
21228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21231 \begin_layout Plain Layout
21235 \begin_layout Plain Layout
21245 \begin_inset Formula $\complement$
21252 \begin_layout Plain Layout
21266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21269 \begin_layout Plain Layout
21277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21280 \begin_layout Plain Layout
21281 \begin_inset Formula $\Bbbk$
21295 \begin_inset space \hfill{}
21299 \begin_inset Tabular
21300 <lyxtabular version="3" rows="10" columns="2">
21302 <column alignment="center" valignment="top" width="0pt">
21303 <column alignment="center" valignment="top" width="0pt">
21305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21308 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21328 \begin_layout Plain Layout
21336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21339 \begin_layout Plain Layout
21340 \begin_inset Formula $\prime$
21350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21353 \begin_layout Plain Layout
21361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21364 \begin_layout Plain Layout
21365 \begin_inset Formula $\backprime$
21375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21378 \begin_layout Plain Layout
21386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21389 \begin_layout Plain Layout
21390 \begin_inset Formula $\mho$
21400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21403 \begin_layout Plain Layout
21411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21414 \begin_layout Plain Layout
21415 \begin_inset Formula $\triangle$
21425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21428 \begin_layout Plain Layout
21436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21439 \begin_layout Plain Layout
21440 \begin_inset Formula $\angle$
21450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21453 \begin_layout Plain Layout
21461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21464 \begin_layout Plain Layout
21465 \begin_inset Formula $\measuredangle$
21475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21478 \begin_layout Plain Layout
21486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21489 \begin_layout Plain Layout
21490 \begin_inset Formula $\sphericalangle$
21500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21503 \begin_layout Plain Layout
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Plain Layout
21515 \begin_inset Formula $\top$
21525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21528 \begin_layout Plain Layout
21536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21539 \begin_layout Plain Layout
21540 \begin_inset Formula $\bot$
21554 \begin_inset space \hfill{}
21560 \begin_layout Subsection
21561 Miscellaneous Symbols
21562 \begin_inset CommandInset label
21564 name "sub:Miscellaneous-Symbols"
21572 \begin_layout Plain Layout
21573 Symbols ! miscellaneous
21581 \begin_layout Standard
21584 \begin_inset Tabular
21585 <lyxtabular version="3" rows="10" columns="2">
21587 <column alignment="center" valignment="top" width="0pt">
21588 <column alignment="center" valignment="top" width="0pt">
21590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21593 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21613 \begin_layout Plain Layout
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21624 \begin_layout Plain Layout
21625 \begin_inset Formula $\flat$
21635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21638 \begin_layout Plain Layout
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21649 \begin_layout Plain Layout
21650 \begin_inset Formula $\natural$
21660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21663 \begin_layout Plain Layout
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21674 \begin_layout Plain Layout
21675 \begin_inset Formula $\sharp$
21685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21688 \begin_layout Plain Layout
21696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21699 \begin_layout Plain Layout
21700 \begin_inset Formula $\surd$
21710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21713 \begin_layout Plain Layout
21721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21724 \begin_layout Plain Layout
21725 \begin_inset Formula $\checkmark$
21735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21738 \begin_layout Plain Layout
21746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21749 \begin_layout Plain Layout
21750 \begin_inset Formula $\yen$
21760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21763 \begin_layout Plain Layout
21771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21774 \begin_layout Plain Layout
21775 \begin_inset Formula $\pounds$
21785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21788 \begin_layout Plain Layout
21794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Plain Layout
21798 \begin_inset Formula $\$$
21808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21811 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $§$
21835 \begin_inset Tabular
21836 <lyxtabular version="3" rows="10" columns="2">
21838 <column alignment="center" valignment="top" width="0">
21839 <column alignment="center" valignment="top" width="0">
21841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21844 \begin_layout Plain Layout
21850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21853 \begin_layout Plain Layout
21861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\hbar$
21886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\hslash$
21911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\clubsuit$
21936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\spadesuit$
21961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21964 \begin_layout Plain Layout
21972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21975 \begin_layout Plain Layout
21976 \begin_inset Formula $\bigstar$
21986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21989 \begin_layout Plain Layout
21997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22000 \begin_layout Plain Layout
22001 \begin_inset Formula $\blacklozenge$
22011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22014 \begin_layout Plain Layout
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22025 \begin_layout Plain Layout
22026 \begin_inset Formula $\blacktriangle$
22036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22039 \begin_layout Plain Layout
22047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22050 \begin_layout Plain Layout
22051 \begin_inset Formula $\blacktriangledown$
22061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22064 \begin_layout Plain Layout
22072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22075 \begin_layout Plain Layout
22076 \begin_inset Formula $\bullet$
22090 \begin_inset Tabular
22091 <lyxtabular version="3" rows="10" columns="2">
22093 <column alignment="center" valignment="top" width="0pt">
22094 <column alignment="center" valignment="top" width="0pt">
22096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22099 \begin_layout Plain Layout
22105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22108 \begin_layout Plain Layout
22116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22119 \begin_layout Plain Layout
22127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22131 \begin_inset Formula $\diamondsuit$
22141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22144 \begin_layout Plain Layout
22152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22155 \begin_layout Plain Layout
22156 \begin_inset Formula $\Diamond$
22166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22169 \begin_layout Plain Layout
22177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22180 \begin_layout Plain Layout
22181 \begin_inset Formula $\heartsuit$
22191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22194 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22206 \begin_inset Formula $\P$
22216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22219 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22231 \begin_inset Formula $\copyright$
22241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22244 \begin_layout Plain Layout
22252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22255 \begin_layout Plain Layout
22256 \begin_inset Formula $\circledR$
22266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\maltese$
22291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22305 \begin_layout Plain Layout
22306 \begin_inset Formula $\diagup$
22316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\diagdown$
22347 \begin_layout Standard
22348 \begin_inset VSpace medskip
22351 More symbols are listed in
22352 \begin_inset CommandInset ref
22354 reference "sub:Miscellaneous-special-Characters"
22361 \begin_layout Standard
22362 Some symbols can be displayed in different sizes, see
22363 \begin_inset CommandInset ref
22365 reference "sub:Font-Sizes"
22372 \begin_layout Subsection
22377 \begin_layout Plain Layout
22378 Symbols ! Euro-symbol
22387 \begin_layout Plain Layout
22394 \begin_layout Plain Layout
22411 \begin_layout Standard
22412 To use the Euro symbol in formulas, the LaTeX-package
22420 \begin_layout Plain Layout
22426 must be installed and loaded with the LaTeX-preamble line
22429 \begin_layout Standard
22434 usepackage[gennarrow]{eurosym}
22437 \begin_layout Standard
22438 The Euro symbol can now be inserted with the command
22448 \begin_layout Plain Layout
22459 \begin_layout Standard
22460 The Euro symbol can directly be inserted with the € key in mathematical
22461 text, without having
22476 can also be inserted in TeX-mode.
22477 The official currency symbol can then be inserted with the command
22487 \begin_layout Plain Layout
22495 , that is only available in TeX-mode.
22498 \begin_layout Standard
22502 \begin_layout Plain Layout
22512 \begin_inset Note Note
22515 \begin_layout Plain Layout
22516 The following table will only be displayed when the LaTeX-package
22528 \begin_layout Standard
22529 An overview about the different Euro symbols:
22532 \begin_layout Standard
22534 \begin_inset Tabular
22535 <lyxtabular version="3" rows="4" columns="3">
22537 <column alignment="center" valignment="top" width="0pt">
22538 <column alignment="center" valignment="top" width="0pt">
22539 <column alignment="center" valignment="top" width="0pt">
22541 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22544 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22553 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22573 \begin_layout Plain Layout
22579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22582 \begin_layout Plain Layout
22590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22593 \begin_layout Plain Layout
22594 \begin_inset Formula $\euro$
22604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22607 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22616 \begin_layout Plain Layout
22622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22625 \begin_layout Plain Layout
22626 \begin_inset Formula $\mbox{€}$
22636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22639 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22648 \begin_layout Plain Layout
22656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22659 \begin_layout Plain Layout
22663 \begin_layout Plain Layout
22685 \begin_layout Standard
22689 \begin_layout Plain Layout
22699 \begin_inset Note Note
22702 \begin_layout Plain Layout
22703 The following will be displayed when the LaTeX-package
22715 \begin_layout Standard
22716 You need to install the LaTeX-package
22720 to see the rest of this subsection in the output.
22723 \begin_layout Standard
22727 \begin_layout Plain Layout
22739 \begin_layout Section
22741 \begin_inset CommandInset label
22743 name "sec:Relations"
22751 \begin_layout Plain Layout
22761 \begin_layout Plain Layout
22766 \begin_layout Plain Layout
22777 \begin_layout Plain Layout
22792 \begin_layout Standard
22793 All relations can also be inserted via the toolbar button
22794 \begin_inset Graphics
22795 filename ../images/math/leq.png
22803 \begin_layout Standard
22804 \begin_inset space \hfill{}
22808 \begin_inset Tabular
22809 <lyxtabular version="3" rows="17" columns="2">
22811 <column alignment="center" valignment="top" width="0pt">
22812 <column alignment="center" valignment="top" width="0pt">
22814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22837 \begin_layout Plain Layout
22843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22846 \begin_layout Plain Layout
22847 \begin_inset Formula $<$
22857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22860 \begin_layout Plain Layout
22868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22871 \begin_layout Plain Layout
22872 \begin_inset Formula $\le$
22882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22885 \begin_layout Plain Layout
22893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22896 \begin_layout Plain Layout
22897 \begin_inset Formula $\ll$
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22921 \begin_layout Plain Layout
22922 \begin_inset Formula $\prec$
22932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22935 \begin_layout Plain Layout
22943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22946 \begin_layout Plain Layout
22947 \begin_inset Formula $\preceq$
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22971 \begin_layout Plain Layout
22972 \begin_inset Formula $\subset$
22982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22985 \begin_layout Plain Layout
22993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22996 \begin_layout Plain Layout
22997 \begin_inset Formula $\subseteq$
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23010 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23021 \begin_layout Plain Layout
23022 \begin_inset Formula $\sqsubseteq$
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\in$
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23072 \begin_inset Formula $\vdash$
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23096 \begin_layout Plain Layout
23097 \begin_inset Formula $\smile$
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23110 \begin_layout Plain Layout
23118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23121 \begin_layout Plain Layout
23122 \begin_inset Formula $\lhd$
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23135 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23147 \begin_inset Formula $\unlhd$
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23172 \begin_inset Formula $\gtrless$
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23185 \begin_layout Plain Layout
23193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23196 \begin_layout Plain Layout
23197 \begin_inset Formula $\mid$
23207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23210 \begin_layout Plain Layout
23218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23221 \begin_layout Plain Layout
23222 \begin_inset Formula $\nmid$
23236 \begin_inset space \hfill{}
23240 \begin_inset Tabular
23241 <lyxtabular version="3" rows="17" columns="2">
23243 <column alignment="center" valignment="top" width="0pt">
23244 <column alignment="center" valignment="top" width="0pt">
23246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23269 \begin_layout Plain Layout
23275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23278 \begin_layout Plain Layout
23279 \begin_inset Formula $=$
23289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23292 \begin_layout Plain Layout
23300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23303 \begin_layout Plain Layout
23304 \begin_inset Formula $\not=$
23314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23317 \begin_layout Plain Layout
23325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23328 \begin_layout Plain Layout
23329 \begin_inset Formula $\equiv$
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23342 \begin_layout Plain Layout
23350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23353 \begin_layout Plain Layout
23354 \begin_inset Formula $\sim$
23364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23367 \begin_layout Plain Layout
23375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23378 \begin_layout Plain Layout
23379 \begin_inset Formula $\simeq$
23389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23392 \begin_layout Plain Layout
23400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23403 \begin_layout Plain Layout
23404 \begin_inset Formula $\approx$
23414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23417 \begin_layout Plain Layout
23425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23428 \begin_layout Plain Layout
23429 \begin_inset Formula $\cong$
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23442 \begin_layout Plain Layout
23450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23453 \begin_layout Plain Layout
23454 \begin_inset Formula $\bowtie$
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23467 \begin_layout Plain Layout
23475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23478 \begin_layout Plain Layout
23479 \begin_inset Formula $\notin$
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23492 \begin_layout Plain Layout
23500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23503 \begin_layout Plain Layout
23504 \begin_inset Formula $\perp$
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23517 \begin_layout Plain Layout
23525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23528 \begin_layout Plain Layout
23529 \begin_inset Formula $\propto$
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23542 \begin_layout Plain Layout
23550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23553 \begin_layout Plain Layout
23554 \begin_inset Formula $\asymp$
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23567 \begin_layout Plain Layout
23575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23578 \begin_layout Plain Layout
23579 \begin_inset Formula $\doteq$
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23592 \begin_layout Plain Layout
23600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23603 \begin_layout Plain Layout
23604 \begin_inset Formula $\circeq$
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23617 \begin_layout Plain Layout
23625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23628 \begin_layout Plain Layout
23629 \begin_inset Formula $\models$
23639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23642 \begin_layout Plain Layout
23650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23653 \begin_layout Plain Layout
23654 \begin_inset Formula $\widehat{=}$
23668 \begin_inset space \hfill{}
23672 \begin_inset Tabular
23673 <lyxtabular version="3" rows="17" columns="2">
23675 <column alignment="center" valignment="top" width="0pt">
23676 <column alignment="center" valignment="top" width="0pt">
23678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23701 \begin_layout Plain Layout
23707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23710 \begin_layout Plain Layout
23711 \begin_inset Formula $>$
23721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23724 \begin_layout Plain Layout
23732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23735 \begin_layout Plain Layout
23736 \begin_inset Formula $\ge$
23746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23749 \begin_layout Plain Layout
23757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23760 \begin_layout Plain Layout
23761 \begin_inset Formula $\gg$
23771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23774 \begin_layout Plain Layout
23782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23785 \begin_layout Plain Layout
23786 \begin_inset Formula $\succ$
23796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23799 \begin_layout Plain Layout
23807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23810 \begin_layout Plain Layout
23811 \begin_inset Formula $\succeq$
23821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23824 \begin_layout Plain Layout
23832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23835 \begin_layout Plain Layout
23836 \begin_inset Formula $\supset$
23846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23849 \begin_layout Plain Layout
23857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23860 \begin_layout Plain Layout
23861 \begin_inset Formula $\supseteq$
23871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23874 \begin_layout Plain Layout
23882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23885 \begin_layout Plain Layout
23886 \begin_inset Formula $\sqsupseteq$
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23899 \begin_layout Plain Layout
23907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23910 \begin_layout Plain Layout
23911 \begin_inset Formula $\ni$
23921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23924 \begin_layout Plain Layout
23932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23935 \begin_layout Plain Layout
23936 \begin_inset Formula $\dashv$
23946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23949 \begin_layout Plain Layout
23957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23960 \begin_layout Plain Layout
23961 \begin_inset Formula $\frown$
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23974 \begin_layout Plain Layout
23982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23985 \begin_layout Plain Layout
23986 \begin_inset Formula $\rhd$
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23999 \begin_layout Plain Layout
24007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24010 \begin_layout Plain Layout
24011 \begin_inset Formula $\unrhd$
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24035 \begin_layout Plain Layout
24036 \begin_inset Formula $\lessgtr$
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24049 \begin_layout Plain Layout
24057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24060 \begin_layout Plain Layout
24061 \begin_inset Formula $\parallel$
24071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24074 \begin_layout Plain Layout
24082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24085 \begin_layout Plain Layout
24086 \begin_inset Formula $\nparallel$
24100 \begin_inset space \hfill{}
24106 \begin_layout Standard
24107 \begin_inset VSpace medskip
24122 are bigger than the equal looking operators
24137 \begin_layout Standard
24138 Relations are, in contrary to symbols, always surrounded by space.
24141 \begin_layout Standard
24142 Relations with labels can be created with the command
24152 \begin_layout Plain Layout
24163 \begin_layout Standard
24165 \begin_inset Tabular
24166 <lyxtabular version="3" rows="2" columns="2">
24168 <column alignment="center" valignment="top" width="0">
24169 <column alignment="center" valignment="top" width="0">
24171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24174 \begin_layout Plain Layout
24180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24183 \begin_layout Plain Layout
24185 \begin_inset Note Note
24188 \begin_layout Plain Layout
24195 is only used as spacer.
24207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24210 \begin_layout Plain Layout
24217 \begin_layout Plain Layout
24234 \begin_layout Plain Layout
24244 \begin_inset Formula $\downarrow$
24253 \begin_layout Plain Layout
24266 \begin_layout Plain Layout
24280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24283 \begin_layout Plain Layout
24284 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24300 \begin_layout Section
24304 \begin_layout Subsection
24305 Predefined Functions
24306 \begin_inset CommandInset label
24308 name "sub:Predefined-Functions"
24316 \begin_layout Plain Layout
24317 Functions ! predefined
24325 \begin_layout Standard
24326 In general, variables are set
24330 in mathematical expressions, but not function names, because
24331 \begin_inset Formula $sin$
24334 could be misunderstood as
24335 \begin_inset Formula $s\cdot i\cdot n$
24339 Therefore there are predefined functions, that are additionally a bit separated
24341 They are inserted as commands starting with a backslash before their name.
24344 \begin_layout Standard
24346 \begin_inset Tabular
24347 <lyxtabular version="3" rows="2" columns="4">
24349 <column alignment="center" valignment="top" width="0pt">
24350 <column alignment="center" valignment="top" width="0pt">
24351 <column alignment="center" valignment="top" width="0pt">
24352 <column alignment="center" valignment="top" width="0pt">
24354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24366 \begin_layout Plain Layout
24372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24384 \begin_layout Plain Layout
24392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24404 \begin_layout Plain Layout
24405 \begin_inset Formula $Asin(x)+B$
24413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24427 \begin_layout Plain Layout
24428 \begin_inset Formula $A\sin(x)+B$
24444 \begin_layout Standard
24445 The following functions are predefined:
24448 \begin_layout Standard
24449 \begin_inset VSpace -2mm
24455 \begin_layout Standard
24457 \begin_inset Tabular
24458 <lyxtabular version="3" rows="9" columns="4">
24460 <column alignment="center" valignment="top" width="0pt">
24461 <column alignment="center" valignment="top" width="0pt">
24462 <column alignment="center" valignment="top" width="0pt">
24463 <column alignment="center" valignment="top" width="0pt">
24465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24468 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24506 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24517 \begin_layout Plain Layout
24525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24528 \begin_layout Plain Layout
24536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24539 \begin_layout Plain Layout
24549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24552 \begin_layout Plain Layout
24560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24563 \begin_layout Plain Layout
24571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24574 \begin_layout Plain Layout
24582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24585 \begin_layout Plain Layout
24595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24598 \begin_layout Plain Layout
24606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24609 \begin_layout Plain Layout
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24620 \begin_layout Plain Layout
24628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24631 \begin_layout Plain Layout
24641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24644 \begin_layout Plain Layout
24652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24655 \begin_layout Plain Layout
24663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24666 \begin_layout Plain Layout
24674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24677 \begin_layout Plain Layout
24687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24690 \begin_layout Plain Layout
24698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24701 \begin_layout Plain Layout
24709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24712 \begin_layout Plain Layout
24720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24723 \begin_layout Plain Layout
24733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24736 \begin_layout Plain Layout
24744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24747 \begin_layout Plain Layout
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24769 \begin_layout Plain Layout
24779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24782 \begin_layout Plain Layout
24790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24793 \begin_layout Plain Layout
24801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24804 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24828 \begin_layout Plain Layout
24836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24839 \begin_layout Plain Layout
24847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24850 \begin_layout Plain Layout
24858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24861 \begin_layout Plain Layout
24877 \begin_layout Standard
24878 They can also be inserted with the math toolbar button
24879 \begin_inset Graphics
24880 filename ../images/math/functions.png
24888 \begin_layout Subsection
24889 Self-defined Functions
24893 \begin_layout Plain Layout
24894 Functions ! self-defined
24902 \begin_layout Standard
24903 To use a function that is not predefined, like for example the sign function
24904 sgn(x), there are two possibilities:
24907 \begin_layout Itemize
24908 Define the function by inserting the following line to the LaTeX-preamble
24912 \begin_layout Plain Layout
24917 DeclareMathOperator
24920 \begin_inset CommandInset ref
24922 reference "sub:Self-defined-Operators"
24932 \begin_inset Newline newline
24936 \begin_inset VSpace -3mm
24940 \begin_inset Newline newline
24947 DeclareMathOperator{
24955 \begin_layout Plain Layout
24960 DeclareMathOperator
24966 \begin_inset Newline newline
24970 \begin_inset VSpace -2mm
24974 \begin_inset Newline newline
24977 Now the new defined function can be called with the command
24986 \begin_layout Itemize
24987 Write the the formula as usual, mark the formula name, in our example the
24992 , and change it to mathematical text.
24993 At last a space is inserted between prefactor and function.
24996 \begin_layout Standard
24997 The result is the same with both methods as with a predefined function
25001 \begin_layout Plain Layout
25002 In LyX self-defined functions are displayed red, predefined ones black.
25010 \begin_layout Standard
25012 \begin_inset Tabular
25013 <lyxtabular version="3" rows="3" columns="2">
25015 <column alignment="center" valignment="top" width="0pt">
25016 <column alignment="center" valignment="top" width="0pt">
25018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25021 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25030 \begin_layout Plain Layout
25038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25041 \begin_layout Plain Layout
25049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25052 \begin_layout Plain Layout
25053 \begin_inset Formula $A\sgn(x)+B$
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25070 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25081 \begin_layout Plain Layout
25082 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25098 \begin_layout Standard
25099 The first method is more suitable when the self-defined function should
25100 be used several times.
25103 \begin_layout Subsection
25108 \begin_layout Plain Layout
25117 \begin_layout Standard
25118 For limits there are defined besides
25128 \begin_layout Plain Layout
25148 furthermore the following functions:
25151 \begin_layout Standard
25153 \begin_inset Tabular
25154 <lyxtabular version="3" rows="5" columns="2">
25156 <column alignment="center" valignment="top" width="0">
25157 <column alignment="center" valignment="top" width="0">
25159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25162 \begin_layout Plain Layout
25168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25171 \begin_layout Plain Layout
25173 \begin_inset Note Note
25176 \begin_layout Plain Layout
25183 is only used as spacer.
25195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25198 \begin_layout Plain Layout
25206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25209 \begin_layout Plain Layout
25210 \begin_inset Formula $\varliminf$
25220 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25223 \begin_layout Plain Layout
25231 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25234 \begin_layout Plain Layout
25235 \begin_inset Formula $\varlimsup$
25245 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25248 \begin_layout Plain Layout
25256 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25259 \begin_layout Plain Layout
25260 \begin_inset Formula $\varprojlim$
25270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25273 \begin_layout Plain Layout
25281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25284 \begin_layout Plain Layout
25285 \begin_inset Formula $\varinjlim$
25289 \begin_inset Formula $\raisebox{-2.5mm}{}$
25305 \begin_layout Standard
25306 \begin_inset VSpace medskip
25309 The limit is created by inserting a subscript.
25310 It is set right beside the function in an inline formula:
25313 \begin_layout Standard
25315 \begin_inset Tabular
25316 <lyxtabular version="3" rows="2" columns="2">
25318 <column alignment="center" valignment="top" width="0pt">
25319 <column alignment="center" valignment="top" width="0pt">
25321 <cell alignment="center" valignment="top" usebox="none">
25324 \begin_layout Plain Layout
25330 <cell alignment="center" valignment="top" usebox="none">
25333 \begin_layout Plain Layout
25334 \begin_inset space \hspace{}
25339 \begin_inset Note Note
25342 \begin_layout Plain Layout
25349 are used here as spacer.
25361 <cell alignment="center" valignment="top" usebox="none">
25364 \begin_layout Plain Layout
25373 \begin_layout Plain Layout
25386 \begin_layout Plain Layout
25400 <cell alignment="center" valignment="top" usebox="none">
25403 \begin_layout Plain Layout
25404 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25420 \begin_layout Standard
25421 In a displayed formula the limit is set below the formula, as usual:
25422 \begin_inset Formula \[
25430 \begin_layout Subsection
25435 \begin_layout Plain Layout
25436 Functions ! modulo-
25444 \begin_layout Standard
25445 The modulo-function is special, because it exists in four variants.
25448 \begin_layout Standard
25449 The variants in a displayed formula:
25450 \begin_inset Formula \begin{align*}
25451 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25452 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25453 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25454 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25455 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25462 \begin_layout Standard
25463 In an inline formula less space is set before the function names for all
25467 \begin_layout Section
25472 \begin_layout Plain Layout
25481 \begin_layout Subsection
25482 Special Characters in Mathematical Text
25485 \begin_layout Standard
25486 The following commands can only be used in mathematical text or in TeX-mode:
25489 \begin_layout Standard
25490 \begin_inset space \hfill{}
25494 \begin_inset Tabular
25495 <lyxtabular version="3" rows="8" columns="2">
25497 <column alignment="block" valignment="top" width="0">
25498 <column alignment="block" valignment="top" width="0">
25500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25503 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25523 \begin_layout Plain Layout
25531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25534 \begin_layout Plain Layout
25535 \begin_inset Formula $\textrm{œ}$
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25548 \begin_layout Plain Layout
25556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25559 \begin_layout Plain Layout
25560 \begin_inset Formula $\textrm{Œ}$
25570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25573 \begin_layout Plain Layout
25581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25584 \begin_layout Plain Layout
25585 \begin_inset Formula $\textrm{æ}$
25595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25598 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25609 \begin_layout Plain Layout
25610 \begin_inset Formula $\textrm{Æ}$
25620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25623 \begin_layout Plain Layout
25631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25634 \begin_layout Plain Layout
25635 \begin_inset Formula $\textrm{\aa}$
25645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25648 \begin_layout Plain Layout
25655 \begin_layout Plain Layout
25662 \begin_layout Plain Layout
25683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25686 \begin_layout Plain Layout
25687 \begin_inset Formula $\textrm{Å}$
25697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25700 \begin_layout Plain Layout
25708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25711 \begin_layout Plain Layout
25712 \begin_inset Formula $\textrm{ı}$
25726 \begin_inset space \hfill{}
25730 \begin_inset Tabular
25731 <lyxtabular version="3" rows="8" columns="2">
25733 <column alignment="block" valignment="top" width="0">
25734 <column alignment="center" valignment="top" width="0">
25736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25739 \begin_layout Plain Layout
25741 \begin_inset Note Note
25744 \begin_layout Plain Layout
25746 \begin_inset space \thinspace{}
25749 mm is used for separation, because otherwise the output will be ¡ and ¿
25760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25763 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25785 \begin_layout Plain Layout
25786 \begin_inset Formula $\textrm{ø}$
25796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25799 \begin_layout Plain Layout
25807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25810 \begin_layout Plain Layout
25811 \begin_inset Formula $\textrm{Ø}$
25821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25824 \begin_layout Plain Layout
25832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25835 \begin_layout Plain Layout
25836 \begin_inset Formula $\textrm{ł}$
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25860 \begin_layout Plain Layout
25861 \begin_inset Formula $\textrm{Ł}$
25871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25876 \begin_inset space \hspace{}
25884 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25901 \begin_layout Plain Layout
25902 \begin_inset Formula $\textrm{!`}$
25912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25915 \begin_layout Plain Layout
25917 \begin_inset space \hspace{}
25925 \begin_layout Plain Layout
25939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25942 \begin_layout Plain Layout
25943 \begin_inset Formula $\textrm{?`}$
25953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25956 \begin_layout Plain Layout
25964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25968 \begin_inset Formula $\textrm{ȷ}$
25982 \begin_inset space \hfill{}
25988 \begin_layout Standard
25990 \begin_inset Formula $\textrm{\textrm{Å}}$
25994 \begin_inset Formula $\textrm{\textrm{Ø}}$
25997 can also be inserted via the math toolbar button
25998 \begin_inset Graphics
25999 filename ../images/math/digamma.png
26007 \begin_layout Standard
26008 An exception are the commands
26011 \begin_inset space \hspace{}
26020 \begin_inset space \hspace{}
26026 , because they can be inserted in LyX directly to text.
26029 \begin_layout Subsection
26031 \begin_inset CommandInset label
26033 name "sub:Accents-in-Text"
26041 \begin_layout Plain Layout
26050 \begin_layout Standard
26051 With the following commands all letters can be accented.
26052 The commands must be inserted in TeX-mode.
26055 \begin_layout Standard
26056 \begin_inset space \hfill{}
26060 \begin_inset Tabular
26061 <lyxtabular version="3" rows="8" columns="2">
26063 <column alignment="block" valignment="top" width="0">
26064 <column alignment="block" valignment="top" width="0">
26066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26078 \begin_layout Plain Layout
26086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26089 \begin_layout Plain Layout
26093 \begin_inset Quotes grd
26101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26108 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26127 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26142 \begin_layout Plain Layout
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26168 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26189 \begin_layout Plain Layout
26205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26219 \begin_layout Plain Layout
26223 \begin_layout Plain Layout
26239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26249 \begin_layout Plain Layout
26263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26266 \begin_layout Plain Layout
26270 \begin_layout Plain Layout
26286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26289 \begin_layout Plain Layout
26296 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26317 \begin_layout Plain Layout
26333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26336 \begin_layout Plain Layout
26343 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26364 \begin_layout Plain Layout
26384 \begin_inset space \hfill{}
26388 \begin_inset Tabular
26389 <lyxtabular version="3" rows="8" columns="2">
26391 <column alignment="block" valignment="top" width="0">
26392 <column alignment="center" valignment="top" width="0">
26394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26406 \begin_layout Plain Layout
26414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26417 \begin_layout Plain Layout
26424 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26441 \begin_layout Plain Layout
26445 \begin_layout Plain Layout
26461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26464 \begin_layout Plain Layout
26472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26475 \begin_layout Plain Layout
26479 \begin_layout Plain Layout
26495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26498 \begin_layout Plain Layout
26505 \begin_layout Plain Layout
26516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26519 \begin_layout Plain Layout
26523 \begin_layout Plain Layout
26539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26542 \begin_layout Plain Layout
26550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26553 \begin_layout Plain Layout
26557 \begin_layout Plain Layout
26573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26576 \begin_layout Plain Layout
26583 \begin_layout Plain Layout
26597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26600 \begin_layout Plain Layout
26604 \begin_layout Plain Layout
26620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26623 \begin_layout Plain Layout
26630 \begin_layout Plain Layout
26644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26647 \begin_layout Plain Layout
26651 \begin_layout Plain Layout
26667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26670 \begin_layout Plain Layout
26677 \begin_layout Plain Layout
26691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26694 \begin_layout Plain Layout
26698 \begin_layout Plain Layout
26718 \begin_inset space \hfill{}
26724 \begin_layout Standard
26725 \begin_inset VSpace medskip
26734 also two different characters can be accented.
26743 \begin_layout Plain Layout
26758 \begin_layout Plain Layout
26770 \begin_layout Standard
26783 can in combination with vowels directly be inserted with the keyboard without
26785 The same applies for the tilde
26789 \begin_layout Plain Layout
26790 This only applies for keyboards where the tilde is defined as accent.
26799 in combination with
26814 \begin_layout Standard
26857 , and accents inserted directly with the keyboard are also available in
26859 For the other accents there are special math commands to be used in formulas,
26861 \begin_inset CommandInset ref
26863 reference "sub:Accents-for-one"
26870 \begin_layout Standard
26871 \begin_inset VSpace bigskip
26874 Furthermore, with the command
26884 \begin_layout Plain Layout
26892 all numbers and letters can be set into a circle, quasi accented with a
26893 circle, similar to the the copyright symbol.
26896 \begin_layout Standard
26898 \begin_inset Tabular
26899 <lyxtabular version="3" rows="3" columns="2">
26901 <column alignment="center" valignment="top" width="0">
26902 <column alignment="center" valignment="top" width="0">
26904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26907 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26916 \begin_layout Plain Layout
26918 \begin_inset Note Note
26921 \begin_layout Plain Layout
26928 is only used as spacer.
26940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26943 \begin_layout Plain Layout
26951 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26954 \begin_layout Plain Layout
26958 \begin_layout Plain Layout
26974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26977 \begin_layout Plain Layout
26988 raisebox{-1.5pt}{W}}
26993 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26996 \begin_layout Plain Layout
26997 \begin_inset Formula $\raisebox{4.5mm}{}$
27004 \begin_layout Plain Layout
27022 \begin_inset Formula $\raisebox{-2mm}{}$
27038 \begin_layout Standard
27039 One has to take care that the character fits in the circle.
27050 \begin_layout Plain Layout
27052 \begin_inset CommandInset ref
27054 reference "sub:Font-Sizes"
27063 specifies thereby the size of the circle.
27074 \begin_layout Plain Layout
27076 \begin_inset CommandInset ref
27078 reference "sub:Boxes-without-Frame"
27087 the character can be centered.
27090 \begin_layout Subsection
27095 \begin_layout Plain Layout
27104 \begin_layout Standard
27105 Minuscule numbers are created with the command
27115 \begin_layout Plain Layout
27124 The command can be used in formulas and in TeX-mode.
27125 The command scheme is:
27128 \begin_layout Standard
27133 oldstylenums{number}
27136 \begin_layout Standard
27141 oldstylenums{0123456789
27144 \begin_inset Formula $\oldstylenums{0123456789}$
27150 \begin_layout Subsection
27151 Miscellaneous special Characters
27152 \begin_inset CommandInset label
27154 name "sub:Miscellaneous-special-Characters"
27162 \begin_layout Plain Layout
27163 Special characters ! miscellaneous
27171 \begin_layout Standard
27172 The following characters can only be inserted to formulas by using commands:
27175 \begin_layout Standard
27177 \begin_inset Tabular
27178 <lyxtabular version="3" rows="4" columns="2">
27180 <column alignment="center" valignment="top" width="0">
27181 <column alignment="center" valignment="top" width="0">
27183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27186 \begin_layout Plain Layout
27192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27195 \begin_layout Plain Layout
27203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27206 \begin_layout Plain Layout
27213 \begin_layout Plain Layout
27227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27230 \begin_layout Plain Layout
27231 \begin_inset Formula $\mathcircumflex$
27241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27244 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27255 \begin_layout Plain Layout
27256 \begin_inset Formula $\_$
27266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27269 \begin_layout Plain Layout
27274 \begin_layout Plain Layout
27289 \begin_layout Plain Layout
27302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27305 \begin_layout Plain Layout
27306 \begin_inset Formula $^{\circ}$
27322 \begin_layout Standard
27323 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27324 contains the following line
27328 \begin_layout Plain Layout
27329 More about this is described in
27330 \begin_inset CommandInset ref
27332 reference "sub:Text-Characters-in"
27344 \begin_layout Standard
27349 DeclareInputtext{176}{
27362 \begin_layout Section
27364 \begin_inset CommandInset label
27366 name "sec:Formula-Styles"
27374 \begin_layout Plain Layout
27383 \begin_layout Itemize
27384 There are two different alignment styles:
27388 \begin_layout Description
27389 Centered is the predefined standard
27392 \begin_layout Description
27393 Indented for this the option
27397 must be inserted in the menu
27399 Document\SpecialChar \menuseparator
27405 \begin_inset space ~
27411 \begin_layout Standard
27416 is used, the indentation can be adjusted with the length
27426 \begin_layout Plain Layout
27435 Should the distance be 15
27436 \begin_inset space \thinspace{}
27439 mm, the following command line is inserted in the LaTeX-preamble
27442 \begin_layout Standard
27452 \begin_layout Standard
27453 When no length is specified, the predefined value of 30
27454 \begin_inset space \thinspace{}
27461 \begin_layout Itemize
27462 And two different numbering styles:
27466 \begin_layout Description
27467 Right is the predefined standard
27470 \begin_layout Description
27471 Left for this the option
27475 must be inserted in the menu
27477 Document\SpecialChar \menuseparator
27483 \begin_inset space ~
27490 \begin_layout Standard
27499 can also be used together.
27500 In this case both options are inserted, separated by a comma.
27503 \begin_layout Standard
27504 The chosen styles are used for all displayed formulas of the document.
27505 When both, centered and indented formulas should be created in a document,
27511 The indented formulas are then set in a flalign environment, see
27512 \begin_inset CommandInset ref
27514 reference "sub:Flalign-Environment"
27521 \begin_layout Section
27523 \begin_inset CommandInset label
27525 name "sec:Multiline-Formulas"
27533 \begin_layout Plain Layout
27534 Formula ! multiline
27542 \begin_layout Subsection
27546 \begin_layout Standard
27547 In LyX multiline formulas are created by pressing
27552 arg "newline-insert newline"
27558 This creates either an
27560 eqnarray environment
27562 that is described in
27563 \begin_inset CommandInset ref
27565 reference "sub:Eqnarray-Environment"
27569 or, when the option
27571 Use AMS math package
27573 in the document settings is selected, an
27577 that is described in
27578 \begin_inset CommandInset ref
27580 reference "sub:Standard-align-Environment"
27587 \begin_layout Standard
27588 There are other multiline formula environments that can be created via the
27591 Insert\SpecialChar \menuseparator
27595 These environments are described in the following sections.
27598 \begin_layout Standard
27599 In all multiline formula environments a new line is created by pressing
27603 arg "newline-insert newline"
27607 To add or delete lines, the math toolbar buttons
27608 \begin_inset Graphics
27609 filename ../images/tabular-feature_append-row.png
27615 \begin_inset Graphics
27616 filename ../images/tabular-feature_delete-row.png
27621 , respectively, or the menu
27623 Edit\SpecialChar \menuseparator
27629 \begin_layout Subsubsection
27631 \begin_inset CommandInset label
27633 name "sub:Line-Separation"
27641 \begin_layout Plain Layout
27642 Formula ! multiline ! Line separation
27650 \begin_layout Standard
27651 There is sometimes not enough space in multiline formulas between the lines:
27652 \begin_inset Formula \begin{eqnarray*}
27653 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}\\
27654 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*}
27661 \begin_layout Standard
27662 In LaTeX additional line space is specified as optional argument of the
27664 This is not yet possible in LyX
27668 \begin_layout Plain Layout
27670 \begin_inset CommandInset href
27672 name "LyX-bug #1505"
27673 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27682 , therefore the whole formula must be inserted in TeX-mode.
27683 To add in our example space, the command
27691 is inserted at the end of the first line.
27696 \begin_layout Plain Layout
27703 \begin_layout Plain Layout
27705 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27708 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27715 \begin_layout Plain Layout
27719 left(B^{2}+x_{0}^{2}
27727 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27732 \begin_layout Plain Layout
27744 \begin_layout Standard
27745 \begin_inset VSpace bigskip
27748 To set the the line separation for all lines in a formula, the length
27758 \begin_layout Plain Layout
27768 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27779 \begin_inset space \thinspace{}
27784 \begin_inset space \thinspace{}
27787 mm additional line separation as in the previous example, the command
27790 \begin_layout Standard
27800 \begin_layout Standard
27801 is inserted in TeX-mode before the formula.
27802 This requires that the LaTeX-package
27810 \begin_layout Plain Layout
27815 is part of every LaTeX standard installation.
27824 \begin_layout Plain Layout
27830 was loaded in LaTeX-preamble with the line
27833 \begin_layout Standard
27841 \begin_layout Standard
27846 \begin_layout Plain Layout
27858 \begin_inset Formula \begin{eqnarray*}
27859 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}\\
27860 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*}
27867 \begin_layout Standard
27871 \begin_layout Plain Layout
27882 To get back to the predefined distance,
27888 is set to the value 3
27889 \begin_inset space \thinspace{}
27895 \begin_layout Subsubsection
27897 \begin_inset CommandInset label
27899 name "sub:Column-Separation"
27907 \begin_layout Plain Layout
27908 Formula ! multiline ! Column separation
27916 \begin_layout Standard
27917 Multiline formulas form a matrix.
27918 A formula in the eqnarray environment is for example a matrix with three
27920 By changing the column separation in this environment, the space beside
27921 the relation sign can be changed.
27924 \begin_layout Standard
27925 The column separation is specified with the length
27935 \begin_layout Plain Layout
27944 \begin_inset Newline newline
27947 column separation = 2
27948 \begin_inset space \thinspace{}
27958 \begin_inset Newline newline
27964 \begin_layout Standard
27974 \begin_layout Standard
27975 inserted in TeX-mode, sets for all following formulas a column separation
27977 \begin_inset space \thinspace{}
27981 To get back to the predefined distance,
27988 \begin_inset space \thinspace{}
27994 \begin_layout Standard
27996 \begin_inset space \thinspace{}
27999 cm column separation:
28003 \begin_layout Plain Layout
28015 \begin_inset Formula \begin{eqnarray*}
28017 C & \ne & A\end{eqnarray*}
28021 A formula with the predefined column separation for matrices of 10
28022 \begin_inset space \thinspace{}
28029 \begin_layout Plain Layout
28041 \begin_inset Formula \begin{eqnarray*}
28043 C & \ne & A\end{eqnarray*}
28050 \begin_layout Subsubsection
28055 \begin_layout Plain Layout
28064 \begin_layout Standard
28065 Long formulas can be typeset using these methods:
28068 \begin_layout Itemize
28069 When one side of the equation is much shorther than the line width, this
28070 one is chosen for the left side and the right side is typeset over two
28072 \begin_inset Formula \begin{eqnarray}
28073 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 \\
28074 & & -\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}
28078 The minus sign at the beginning of the second line does normally not appear
28079 as operator because it is the first character of the line.
28080 Thus it would not be surrounded by space and could not be distinguished
28081 from the fraction bar.
28083 \begin_inset space \thinspace{}
28086 pt space was inserted behind the minus sign with the command
28096 \begin_layout Plain Layout
28104 \begin_inset CommandInset ref
28106 reference "sub:Variable-Space"
28119 \begin_layout Plain Layout
28130 \begin_layout Itemize
28131 When both sides of the equation are too long, the command
28141 \begin_layout Plain Layout
28150 It is inserted to the first column of the first line and effects that all
28151 further insertions overwrite the following columns:
28152 \begin_inset Formula \begin{eqnarray}
28153 \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 \\
28154 & & -\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 \\
28155 & & =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}
28159 After the insertion of
28165 , the cursor is in a purple box that is a bit shifted to the left from the
28167 In this the formula is inserted.
28168 \begin_inset Newline newline
28171 The content of the further lines is inserted to the second or another formula
28173 The greater the column number where it was inserted, the larger the indentation.
28174 \begin_inset VSpace medskip
28178 \begin_inset Newline newline
28182 \begin_inset Note Greyedout
28185 \begin_layout Plain Layout
28186 Note the following when using
28195 \begin_layout Itemize
28196 The formula doesn't use the full page width.
28198 \begin_inset space \thinspace{}
28202 \begin_inset space \space{}
28206 \begin_inset Formula $-B^{2}$
28209 is added to the first line in the above example, it would have been outside
28211 To better use the width, negative space can be inserted at the beginning
28215 \begin_layout Itemize
28216 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28221 \begin_layout Plain Layout
28222 \begin_inset CommandInset href
28224 name "LyX-bug #1429"
28225 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28234 One can only set the cursor at the beginning of the line and move it with
28243 \begin_layout Itemize
28244 Other methods to set long formulas are offered by the environments described
28246 \begin_inset CommandInset ref
28248 reference "sub:Multline-Environment"
28253 \begin_inset CommandInset ref
28255 reference "sub:Multiline-Formula-Parts"
28262 \begin_layout Subsubsection
28264 \begin_inset CommandInset label
28266 name "sub:Multiline-Brackets"
28274 \begin_layout Plain Layout
28275 Brackets ! for multiline expressions
28283 \begin_layout Standard
28284 For brackets spanning multiple lines the following problem occurs:
28285 \begin_inset Formula \begin{eqnarray*}
28286 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28287 & & \left.\cdots+B-D\right]\end{eqnarray*}
28294 \begin_layout Standard
28295 The closing bracket is smaller than the opening bracket because brackets
28296 with variable size may not span multiple lines.
28299 \begin_layout Standard
28300 To set the bracket size for the second line correctly, the first line is
28311 \begin_layout Plain Layout
28319 and the second line with
28327 \begin_layout Plain Layout
28341 \begin_inset CommandInset ref
28343 reference "sub:Automatic-Bracket-Size"
28358 \begin_layout Plain Layout
28384 \begin_layout Plain Layout
28403 \begin_layout Plain Layout
28422 \begin_layout Plain Layout
28434 \begin_inset Formula $\downarrow$
28443 \begin_layout Plain Layout
28451 is inserted, because the multiplication operator with its limits is the
28452 largest symbol in the first line and this should be the size for the bracket
28453 in the second line.
28456 \begin_layout Standard
28457 The result is this:
28458 \begin_inset Formula \begin{eqnarray*}
28459 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28460 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28467 \begin_layout Subsection
28471 \begin_layout Standard
28472 Align environments can be used for every kind of multiline formulas.
28473 They are specially useful to set several formulas side by side.
28476 \begin_layout Standard
28477 Align environments consist of columns.
28478 The odd columns are right aligned, the even ones left aligned.
28479 Every line in an Align environment can be numbered.
28482 \begin_layout Standard
28483 Align environments are created via the menu
28485 Insert\SpecialChar \menuseparator
28491 Edit\SpecialChar \menuseparator
28492 Math\SpecialChar \menuseparator
28493 Change Formula Type
28495 already existing formulas can be converted to Align environments.
28498 \begin_layout Standard
28499 To add or delete columns, the math toolbar buttons
28500 \begin_inset Graphics
28501 filename ../images/tabular-feature_append-column.png
28507 \begin_inset Graphics
28508 filename ../images/tabular-feature_delete-column.png
28513 , respectively, or the menu
28515 Edit\SpecialChar \menuseparator
28521 \begin_layout Subsubsection
28522 Standard align Environment
28523 \begin_inset CommandInset label
28525 name "sub:Standard-align-Environment"
28533 \begin_layout Plain Layout
28534 Formula ! multiline ! align environment
28542 \begin_layout Standard
28543 This Align environment is created by presssing
28546 arg "newline-insert newline"
28549 in a formula or by the menu
28551 Insert\SpecialChar \menuseparator
28552 Math\SpecialChar \menuseparator
28553 AMS align Environment
28558 \begin_layout Standard
28559 An example for two formulas set side by side, that are created with a four
28560 column align environment:
28561 \begin_inset Formula \begin{align*}
28562 A & =\sin(B) & C & =D\\
28563 C & \ne A & B & \ne D\end{align*}
28567 As it can be seen, the formulas in this environment are placed so as if
28576 \begin_layout Plain Layout
28584 \begin_inset CommandInset ref
28586 reference "sub:Variable-Space"
28597 before the first and after every even column.
28598 When the formula style
28604 \begin_layout Plain Layout
28606 \begin_inset CommandInset ref
28608 reference "sec:Formula-Styles"
28619 is used, the formula is set without the
28625 before the first column.
28628 \begin_layout Subsubsection
28629 Alignat Environment
28633 \begin_layout Plain Layout
28634 Formula ! multiline ! alignat environment
28642 \begin_layout Standard
28643 The alignat environment has no predefined column separation.
28644 It can be inserted manually with the spaces that are described
28645 \begin_inset CommandInset ref
28647 reference "sub:Space"
28654 \begin_layout Standard
28655 The above example in the alignat environment where 1
28656 \begin_inset space \thinspace{}
28659 cm space was inserted at the beginning of the second formula:
28660 \begin_inset Formula \begin{alignat*}{2}
28661 A & =\sin(B) & \hspace{1cm}C & =D\\
28662 C & \ne A & B & \ne D\end{alignat*}
28666 Because the column separation can be set separately for every column, this
28667 environment is especially suitable to set three and more formulas side
28671 \begin_layout Subsubsection
28672 Flalign Environment
28673 \begin_inset CommandInset label
28675 name "sub:Flalign-Environment"
28683 \begin_layout Plain Layout
28684 Formula ! multiline ! flalign environment
28692 \begin_layout Standard
28693 In this environment the first two columns are always set as much as possible
28694 to the left and the last two ones to the right.
28696 \begin_inset Formula \begin{flalign*}
28697 A & =1 & B & =2 & C & =3\\
28698 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28705 \begin_layout Standard
28706 By creating a flalign environment with an odd number of columns where an
28707 empty TeX-brace is inserted to the last column, several formulas in a document
28708 can be set to the left, although the formula style
28713 As example the indented formula
28714 \begin_inset CommandInset ref
28716 reference "eq:VolInt"
28721 \begin_inset Formula \begin{flalign}
28722 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28726 The first two columns contain the formula.
28727 To indent it as with the formula style
28732 \begin_inset space \thinspace{}
28735 pt space was inserted at the beginning of the first column.
28738 \begin_layout Subsection
28739 Eqnarray Environment
28740 \begin_inset CommandInset label
28742 name "sub:Eqnarray-Environment"
28750 \begin_layout Plain Layout
28751 Formula ! multiline ! eqnarray environment
28759 \begin_layout Standard
28760 When this environment has been created, three blue boxes appear.
28761 The content of the first box is right aligned, the content of the last
28763 The content of the middle box appears centered and a bit smaller, because
28764 it is designed to insert there only relation characters.
28765 \begin_inset Formula \begin{eqnarray*}
28766 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28768 A & = & A\end{eqnarray*}
28775 \begin_layout Subsection
28780 \begin_layout Plain Layout
28781 Formula ! multiline ! gather environment
28789 \begin_layout Standard
28790 This environment consists of only one centered column.
28791 Every line can be numbered.
28792 \begin_inset Formula \begin{gather}
28794 X=\textrm{-}1\end{gather}
28801 \begin_layout Subsection
28802 Multline Environment
28803 \begin_inset CommandInset label
28805 name "sub:Multline-Environment"
28813 \begin_layout Plain Layout
28814 Formula ! multiline ! multline environment
28822 \begin_layout Standard
28823 The multline environment consists, like the gather environment, of only
28825 But the first line is left aligned, the last one right aligned.
28826 All other lines are centered.
28827 Therefore this environment is suitable for long formulas.
28829 \begin_inset CommandInset ref
28831 reference "eq:lefteqn"
28835 in the multline environment:
28836 \begin_inset Formula \begin{multline}
28837 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}\\
28838 -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}\\
28839 =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}
28846 \begin_layout Standard
28847 In the output only the last (first) line of a multline environment appears
28848 numbered when the document numbering is right (left).
28852 \begin_layout Plain Layout
28853 numbering styles see
28854 \begin_inset CommandInset ref
28856 reference "sec:Formula-Styles"
28868 \begin_layout Standard
28877 \begin_layout Plain Layout
28895 \begin_layout Plain Layout
28905 a centered line can be right or left aligned, respectively.
28906 The commands are used as follows:
28909 \begin_layout Standard
28914 shoveright{line content}
28920 shoveleft{line content}
28923 \begin_layout Standard
28924 \begin_inset VSpace medskip
28935 \begin_layout Plain Layout
28945 specifies the distance of the first line from the left page margin.
28946 Predefined is the length 0
28947 \begin_inset space \thinspace{}
28953 \begin_layout Standard
28954 As example the above formula where the command
28957 \begin_layout Standard
28967 \begin_layout Standard
28968 was inserted in TeX-mode before:
28972 \begin_layout Plain Layout
28984 \begin_inset Formula \begin{multline}
28985 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}\\
28986 \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}}\\
28987 =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}
28995 \begin_layout Plain Layout
29006 The second line was left aligned using
29015 \begin_layout Subsection
29016 Multiline Formula Parts
29017 \begin_inset CommandInset label
29019 name "sub:Multiline-Formula-Parts"
29027 \begin_layout Plain Layout
29028 Formula ! multiline ! formula parts
29036 \begin_layout Standard
29037 To display only parts of a formula with multiple lines, one of the following
29038 environments are used:
29055 They can be inserted via the menu
29057 Insert\SpecialChar \menuseparator
29060 or by using the commands described in this section.
29063 \begin_layout Standard
29064 The first three have the same properties as the corresponding multiline
29065 formula environments, but it is possible to set further formula parts beside
29068 \begin_inset Formula \[
29069 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29070 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29071 \right\} \textrm{Uncertainty relations}\]
29078 \begin_layout Standard
29079 To get this formula, a displayed formula is created where the command
29087 \begin_layout Plain Layout
29098 A purple box appears around the blue formula box where now columns and
29099 lines can be added.
29100 Outside the multiline environment other formula parts can be set, like
29104 \begin_layout Standard
29105 The aligned environment is also suitable for long formulas whose lines are
29106 horizontally aligned.
29107 Using aligned in a displayed formula has the advantage that the formula
29108 number is vertically centered behind the lines.
29110 \begin_inset CommandInset ref
29112 reference "eq:shortlong"
29116 in the aligned environment:
29117 \begin_inset Formula \begin{equation}
29118 \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}|}\\
29119 & -\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}
29127 \begin_layout Standard
29128 To use the environments
29150 \begin_layout Plain Layout
29168 \begin_layout Plain Layout
29186 \begin_layout Plain Layout
29194 are inserted, respectively.
29195 The split environment has the same properties as the aligned environment
29196 but it can only have two columns.
29199 \begin_layout Subsection
29200 Text in multiline Formulas
29201 \begin_inset CommandInset label
29203 name "sub:Text-in-multiline"
29211 \begin_layout Plain Layout
29221 \begin_layout Plain Layout
29222 Formula ! multiline ! text
29230 \begin_layout Standard
29231 In the Align environments, and the multline and gather environment, text
29232 can be inserted that will appear in a separate line and doesn't affect
29233 the column alignment.
29234 To do this, the command
29242 \begin_layout Plain Layout
29252 is used in the following scheme:
29255 \begin_layout Standard
29263 \begin_layout Standard
29264 The text should not be longer than a line because it cannot be hyphenated.
29265 As LyX doesn't yet support
29271 directly, the text is written as mathematical text.
29278 must hereby be at the beginning of a line and appears in the output above
29280 An example where the text was inserted at the beginning of the second line:
29281 \begin_inset Formula \begin{align}
29282 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29283 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29290 \begin_layout Section
29295 \begin_layout Plain Layout
29305 \begin_layout Plain Layout
29306 Formula ! numbering|see
29310 \begin_layout Plain Layout
29321 \begin_layout Plain Layout
29336 \begin_layout Subsection
29340 \begin_layout Standard
29341 Numbered formulas can be created with the menu
29343 Insert\SpecialChar \menuseparator
29344 Math\SpecialChar \menuseparator
29346 \begin_inset space ~
29354 \begin_inset space ~
29360 Existing formulas can be numbered with the menu
29362 Edit\SpecialChar \menuseparator
29363 Math\SpecialChar \menuseparator
29365 \begin_inset space ~
29373 arg "math-number-toggle"
29377 The formula number is displayed in LyX behind the formula as number sign
29379 The number sign is replaced in the output by the formula number.
29382 \begin_layout Standard
29383 When numbering is turned on in multiline formulas, all lines will be numbered.
29384 But the numbering can be controlled with the menu
29386 Edit\SpecialChar \menuseparator
29387 Math\SpecialChar \menuseparator
29389 \begin_inset space ~
29393 \begin_inset space ~
29397 \begin_inset space ~
29405 arg "math-number-line-toggle"
29411 \begin_layout Standard
29412 Except for inline formulas, all formulas can be numbered with two different
29414 \begin_inset CommandInset ref
29416 reference "sec:Formula-Styles"
29423 \begin_layout Subsection
29428 \begin_layout Plain Layout
29429 Cross-references ! to formulas
29437 \begin_layout Standard
29438 All labeled formulas can be cross-referenced.
29439 A label is added by the menu
29441 Insert\SpecialChar \menuseparator
29444 or the toolbar button
29445 \begin_inset Graphics
29446 filename ../images/label-insert.png
29452 The cursor must hereby be inside a displayed formula.
29453 A dialog pops up displaying the prefix
29458 The label is inserted there behind the prefix.
29459 The predefined prefix means
29460 \begin_inset Quotes eld
29464 \begin_inset Quotes erd
29467 and makes it easier to find labels in large documents because it marks
29468 it as formula label to divide it from e.
29469 \begin_inset space \thinspace{}
29473 \begin_inset space \space{}
29477 To change a label, the menu
29479 Insert\SpecialChar \menuseparator
29485 \begin_layout Standard
29486 The name of the label is displayed in LyX within two parentheses behind
29488 A formula with a label is always numbered.
29491 \begin_layout Standard
29492 Cross-references are inserted via the menu
29494 Insert\SpecialChar \menuseparator
29497 or with the toolbar button
29498 \begin_inset Graphics
29499 filename ../images/dialog-show-new-inset_ref.png
29505 A formula cross-reference appears in the output as formula number.
29506 When in the cross-reference dialog window the format
29510 is chosen, the cross-reference appears in the output as formula number
29512 \begin_inset Newline newline
29515 By right-clicking on a cross-reference in LyX, one jumps to the formula
29516 that is referenced.
29519 \begin_layout Standard
29520 Here are as examples cross-references to formulas of the following subsections:
29521 \begin_inset Note Note
29524 \begin_layout Plain Layout
29525 Note the different cross-reference types.
29533 \begin_layout Standard
29535 \begin_inset CommandInset ref
29542 \begin_inset CommandInset ref
29550 \begin_inset CommandInset ref
29556 ) big Latin letters are used for the numbering in contrary to (
29557 \begin_inset CommandInset ref
29566 \begin_layout Standard
29567 \begin_inset VSpace medskip
29570 When the argument of
29578 \begin_layout Plain Layout
29586 \begin_inset CommandInset ref
29588 reference "sub:User-defined-Numbering"
29599 contains a box like in
29600 \begin_inset CommandInset ref
29602 reference "sub:Paragraph-Boxes"
29606 , the formula cannot be referenced.
29609 \begin_layout Subsection
29614 \begin_layout Plain Layout
29615 Formula numbering ! subnumbering
29623 \begin_layout Standard
29624 With the help of the commands
29628 begin{subequations}
29636 formulas can be subnumbered.
29637 Both commands are inserted in TeX-mode.
29640 \begin_layout Standard
29642 \begin_inset Formula \begin{equation}
29643 A=C-B\label{eq:a}\end{equation}
29651 \begin_layout Plain Layout
29655 addtocounter{equation}{-1}
29664 \begin_layout Plain Layout
29668 begin{subequations}
29674 \begin_inset VSpace -5mm
29678 \begin_inset Formula \begin{equation}
29679 B=C-A\label{eq:b}\end{equation}
29684 \begin_inset Formula \begin{equation}
29685 C=A+B\label{eq:c}\end{equation}
29692 \begin_layout Standard
29696 \begin_layout Plain Layout
29708 \begin_layout Standard
29709 To create the example, the following is done:
29712 \begin_layout Enumerate
29713 first formula is inserted
29716 \begin_layout Enumerate
29721 addtocounter{equation}{-1}
29723 begin{subequations}
29727 \begin_layout Plain Layout
29736 \begin_inset Newline newline
29741 is inserted after the first formula
29744 \begin_layout Enumerate
29745 second formula is inserted
29748 \begin_layout Enumerate
29749 third formula is inserted
29752 \begin_layout Enumerate
29759 is inserted after the third formula
29762 \begin_layout Standard
29763 Every formula between the commands
29775 is subnumbered as a, b,
29776 \begin_inset Newline linebreak
29779 c, \SpecialChar \ldots{}
29780 For multiline formulas every line will be subnumbered.
29781 All subnumbered formulas are treated as
29786 But as every numbered formula increases the counter
29790 by one, the command
29796 is needed to decrease it.
29797 Otherwise the formulas
29798 \begin_inset CommandInset ref
29805 \begin_inset CommandInset ref
29812 \begin_inset CommandInset ref
29818 would be numbered as
29819 \begin_inset CommandInset ref
29826 \begin_inset CommandInset ref
29833 \begin_inset CommandInset ref
29842 \begin_layout Standard
29843 By inserting the commands in TeX-mode, a space is created between the first
29846 \begin_inset space \thinspace{}
29849 mm vertical space is inserted after the command
29853 begin{subequations}
29856 When the formula style
29862 \begin_layout Plain Layout
29864 \begin_inset CommandInset ref
29866 reference "sec:Formula-Styles"
29878 \begin_inset space \thinspace{}
29881 mm space is inserted instead.
29884 \begin_layout Standard
29885 Here is an example for a multiline formula where the numbering was turned
29886 off for the second line:
29890 \begin_layout Plain Layout
29894 begin{subequations}
29900 \begin_inset Formula \begin{eqnarray}
29901 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29902 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29903 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29911 \begin_layout Plain Layout
29923 \begin_layout Subsection
29924 User-defined Numbering
29925 \begin_inset CommandInset label
29927 name "sub:User-defined-Numbering"
29935 \begin_layout Plain Layout
29936 Formula numbering ! user-defined
29944 \begin_layout Standard
29948 \begin_layout Plain Layout
29949 Formula numbering ! self-defined delimiters
29954 With the standard numbering parentheses are set around the formula number.
29955 To replace the parentheses for example by vertical bars, the following
29956 line is added to the LaTeX-preamble:
29959 \begin_layout Standard
29971 \begin_inset Note Note
29974 \begin_layout Plain Layout
29975 This macro is already declared in the LaTeX-preamble for testing.
29976 To activate it, remove the percent sign at the beginning.
29984 \begin_layout Standard
29985 To use other characters, the vertical bars besides the
29989 are replaced by one ore more characters.
29990 To get only the formula number the vertical bars are omitted.
29993 \begin_layout Standard
29994 \begin_inset VSpace bigskip
29997 When there should be an expression of your choice instead of the consecutive
29998 formula number in parentheses behind the formula, the command
30008 \begin_layout Plain Layout
30017 \begin_inset Formula \begin{equation}
30018 A+B=C\tag{something}\label{eq:tag}\end{equation}
30022 In this example the command
30030 \begin_layout Plain Layout
30041 was inserted to the formula.
30044 \begin_layout Standard
30053 \begin_layout Plain Layout
30064 is inserted instead, the star prevents the parentheses around the expression:
30065 \begin_inset Formula \[
30066 A+B=C\tag*{something}\]
30073 \begin_layout Standard
30074 \begin_inset VSpace bigskip
30077 To restart the formula numbering with new document parts or sections, the
30078 following command is used:
30081 \begin_layout Standard
30086 @addtoreset{equation}{part}
30092 \begin_layout Plain Layout
30097 \begin_layout Plain Layout
30108 \begin_layout Plain Layout
30121 \begin_layout Plain Layout
30132 \begin_layout Plain Layout
30145 \begin_inset Newline newline
30149 \begin_inset Newline newline
30156 @addtoreset{equation}{section}
30159 \begin_layout Standard
30160 To be able to use these commands in TeX-mode, the
30161 \begin_inset Quotes eld
30165 \begin_inset Quotes erd
30168 character has to be made
30169 \begin_inset Quotes eld
30173 \begin_inset Quotes erd
30176 for LaTeX using the command
30190 So the command sequence in TeX-mode is:
30193 \begin_layout Standard
30199 \begin_inset Newline newline
30204 @addtoreset{equation}{section}
30205 \begin_inset Newline newline
30213 \begin_layout Standard
30214 In the LaTeX-preamble
30226 can be omitted as they are automatically internally inserted by LyX.
30229 \begin_layout Standard
30244 \begin_layout Plain Layout
30249 is part of the LaTeX-package
30257 \begin_layout Plain Layout
30258 Packages ! carlisle
30263 that is part of every LaTeX standard installation.
30272 \begin_layout Plain Layout
30273 Packages ! remreset
30278 has to be loaded in the LaTeX-preamble with the line
30281 \begin_layout Standard
30286 usepackage{remreset}
30289 \begin_layout Standard
30300 \begin_layout Plain Layout
30305 \begin_layout Plain Layout
30316 \begin_layout Plain Layout
30329 \begin_layout Plain Layout
30340 \begin_layout Plain Layout
30352 can be used with the same scheme as
30361 \begin_layout Standard
30362 \begin_inset VSpace bigskip
30365 Sometimes formulas should be numbered in the following form:
30368 \begin_layout Standard
30371 (section number.formula number)
30374 \begin_layout Standard
30375 The formula number should start with every section with
30376 \begin_inset Quotes eld
30380 \begin_inset Quotes erd
30386 \begin_layout Standard
30387 For this case there is the command
30397 \begin_layout Plain Layout
30405 , which is used with the following scheme:
30408 \begin_layout Standard
30413 numberwithin{counter}{sectioning}
30416 \begin_layout Standard
30417 Counter denotes what kind of numbering is affected, sectioning denotes what
30418 number is before the dot.
30421 \begin_layout Standard
30422 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30425 \begin_layout Standard
30430 numberwithin{equation}{section}
30433 \begin_layout Standard
30434 This is the result:
30438 \begin_layout Plain Layout
30442 numberwithin{equation}{section}
30448 \begin_inset Formula \begin{equation}
30449 A+B=C\end{equation}
30456 \begin_layout Standard
30458 \begin_inset space \thinspace{}
30462 \begin_inset space \space{}
30465 tables so that the number of the part is the sectioning,
30466 \begin_inset Newline newline
30473 numberwithin{table}{part}
30478 \begin_layout Standard
30479 To go back to the standard numbering or to prevent this kind of numbering
30480 when it is defined by the document class, the following command is inserted
30481 as TeX-Code or to the LaTeX-preamble:
30484 \begin_layout Standard
30497 \begin_layout Plain Layout
30511 \begin_layout Plain Layout
30527 \begin_inset Newline newline
30535 \begin_inset Newline newline
30547 \begin_layout Standard
30554 uses internally the command
30560 , described above, that also needs to be reverted.
30564 \begin_layout Plain Layout
30571 \begin_layout Plain Layout
30575 @removefromreset{equation}{section}
30578 \begin_layout Plain Layout
30590 \begin_layout Subsection
30591 Numbering with Roman Numbers and Letters
30595 \begin_layout Plain Layout
30596 Formula numbering ! with letters
30605 \begin_layout Plain Layout
30606 Formula numbering ! with Roman numbers
30614 \begin_layout Standard
30615 Formulas can also be numbered with Roman numbers and Latin letters.
30616 To number for example with small Roman numbers, the command
30619 \begin_layout Standard
30631 \begin_layout Standard
30632 is inserted before the formula in TeX-mode.
30643 \begin_layout Plain Layout
30651 redefines the predefined command
30667 \begin_layout Plain Layout
30674 has the same scheme like the command
30680 that is described in
30681 \begin_inset CommandInset ref
30683 reference "sub:The-Command-newcommand"
30696 is the formula counter.
30703 is used as prefix for a counter, the value of the counter is output as
30705 When a formula is numbered, LaTeX sets internally the command
30711 behind the formula.
30720 \begin_layout Plain Layout
30730 outputs the counter as small Roman number.
30733 \begin_layout Standard
30734 All formulas behind the command
30744 are now numbered Roman.
30745 To switch to numbering with big Roman numbers, the command is inserted
30762 \begin_layout Plain Layout
30774 \begin_inset Quotes eld
30778 \begin_inset Quotes erd
30781 with small Latin letters there is the command
30791 \begin_layout Plain Layout
30799 , for big ones there is the command
30809 \begin_layout Plain Layout
30822 \begin_layout Standard
30823 \begin_inset Note Greyedout
30826 \begin_layout Plain Layout
30831 Only maximal 26 formulas can be numbered with Latin letters in one document.
30839 \begin_layout Standard
30843 \begin_layout Plain Layout
30859 \begin_layout Standard
30860 \begin_inset Formula \begin{equation}
30861 A=\textrm{small roman}\label{eq:rom}\end{equation}
30869 \begin_layout Plain Layout
30883 \begin_inset Formula \begin{equation}
30884 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30892 \begin_layout Plain Layout
30906 \begin_inset Formula \begin{equation}
30907 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30915 \begin_layout Plain Layout
30929 \begin_inset Formula \begin{equation}
30930 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30937 \begin_layout Standard
30938 To switch back to the default numbering, insert the command:
30941 \begin_layout Standard
30954 \begin_layout Plain Layout
30965 \begin_layout Standard
30969 \begin_layout Plain Layout
30983 \begin_inset Formula \begin{equation}
30984 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30991 \begin_layout Standard
30992 \begin_inset VSpace medskip
30995 As you see, formulas are numbered serially independent from the numbering
30997 When then numbering should start with
30998 \begin_inset Quotes eld
31002 \begin_inset Quotes erd
31005 when the style is changed, new equation counters have to be defined.
31006 A description about this can be found in the file
31007 \begin_inset CommandInset href
31009 target "Formula-numbering.lyx"
31016 \begin_layout Section
31017 User-defined Commands
31021 \begin_layout Plain Layout
31022 User-defined commands
31030 \begin_layout Standard
31031 \begin_inset Note Greyedout
31034 \begin_layout Plain Layout
31039 The names of user-defined commands and macros may only consist of Latin
31048 \begin_layout Subsection
31052 \begin_inset CommandInset label
31054 name "sub:The-Command-newcommand"
31062 \begin_layout Plain Layout
31063 User-defined commands !
31074 \begin_layout Plain Layout
31085 \begin_layout Standard
31086 Many LaTeX-commands are too long to be used frequently.
31087 But it is possible to define with the command
31093 new shorter commands.
31096 \begin_layout Standard
31097 The command scheme of
31106 \begin_layout Standard
31111 newcommand{new command name}[number of arguments][optional
31116 \begin_inset Newline newline
31123 \begin_layout Plain Layout
31138 \begin_layout Plain Layout
31145 {command definition}
31148 \begin_layout Standard
31149 \begin_inset Note Greyedout
31152 \begin_layout Plain Layout
31157 Assure that the name of the new command is not already used in your document
31158 or by LaTeX-packages that you use.
31159 When you for example define the command
31171 , you get an error message because
31177 is already defined as command for
31178 \begin_inset Quotes eld
31182 \begin_inset Formula $\le$
31186 \begin_inset Quotes erd
31197 \begin_layout Standard
31198 The number of arguments is an integer in the range 0
31199 \begin_inset space \thinspace{}
31203 \begin_inset space \thinspace{}
31206 9 and specifies how many arguments the new command should have.
31207 With the optional value a value for an optional argument can be predefined.
31208 When this is done, the
31216 rgument of the new command is automatically an optional one.
31219 \begin_layout Standard
31220 Here are some examples:
31223 \begin_layout Itemize
31224 To define the command
31236 , the LaTeX-preamble line is:
31237 \begin_inset VSpace medskip
31241 \begin_inset Newline newline
31255 \begin_layout Itemize
31256 To define the command
31268 , the argument (that should be underlined) must be taken into account.
31269 For this the preamble line is:
31270 \begin_inset VSpace medskip
31274 \begin_inset Newline newline
31288 \begin_inset VSpace medskip
31292 \begin_inset Newline newline
31299 acts as argument placeholder, the
31303 behind it denotes that it is the placeholder for the first argument.
31306 \begin_layout Itemize
31314 \begin_inset space \thinspace{}
31318 \begin_inset space \space{}
31328 \begin_inset VSpace medskip
31332 \begin_inset Newline newline
31343 framebox#1#2{$#3$}}
31346 \begin_inset VSpace medskip
31350 \begin_inset Newline newline
31353 The two Dollar signs creates the extra formula needed for
31360 \begin_inset CommandInset ref
31362 reference "sub:Boxes-with-Frame"
31369 \begin_layout Itemize
31370 To create a new command for
31376 where the color for the box needn't to be specified, the argument for the
31377 color is defined optional:
31378 \begin_inset VSpace medskip
31382 \begin_inset Newline newline
31393 fcolorbox{#2}{#1}{$#3$}}
31396 \begin_inset VSpace medskip
31400 \begin_inset Newline newline
31403 When the color is not specified when using
31409 , the predefined color
31416 \begin_layout Standard
31417 A test of the new defined commands:
31420 \begin_layout Standard
31422 \begin_inset Tabular
31423 <lyxtabular version="3" rows="6" columns="2">
31425 <column alignment="center" valignment="top" width="0">
31426 <column alignment="center" valignment="top" width="0">
31428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31431 \begin_layout Plain Layout
31437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31440 \begin_layout Plain Layout
31442 \begin_inset Note Note
31445 \begin_layout Plain Layout
31452 is only used as spacer.
31464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31467 \begin_layout Plain Layout
31474 \begin_layout Plain Layout
31488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31491 \begin_layout Plain Layout
31492 \begin_inset Formula $A\gr B$
31502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31505 \begin_layout Plain Layout
31513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31516 \begin_layout Plain Layout
31517 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31530 \begin_layout Plain Layout
31534 \begin_inset Formula $\to$
31540 \begin_inset Formula $\to$
31551 \begin_layout Plain Layout
31565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31568 \begin_layout Plain Layout
31569 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31582 \begin_layout Plain Layout
31586 \begin_inset Formula $\to$
31597 \begin_layout Plain Layout
31611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31614 \begin_layout Plain Layout
31615 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31628 \begin_layout Plain Layout
31634 \begin_inset Formula $\to$
31645 \begin_layout Plain Layout
31659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31662 \begin_layout Plain Layout
31663 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31679 \begin_layout Subsection
31684 \begin_layout Plain Layout
31685 User-defined commands! Math macros
31694 \begin_layout Plain Layout
31703 \begin_layout Standard
31704 User-defined commands are especially convenient for complex expressions.
31705 When you are for example dealing in a document with quadratic equations,
31706 the same solution type occurs several times.
31707 The general form of a quadratic equation is
31708 \begin_inset Formula \[
31709 0=\lambda^{2}+p\lambda+q\]
31713 The general form of the solution is
31714 \begin_inset Formula \[
31715 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31722 \begin_layout Standard
31723 To define a command for the solution formula where only the three parameters
31725 \begin_inset Formula $\lambda$
31729 \begin_inset Formula $p$
31733 \begin_inset Formula $q$
31736 need to be specified and the index of
31737 \begin_inset Formula $\lambda$
31740 can be given optionally, the LaTeX-preamble line is
31741 \begin_inset Newline newline
31757 \begin_inset Newline newline
31764 \begin_layout Plain Layout
31779 \begin_layout Plain Layout
31790 frac{#3^{2}}{4}-#4}}
31793 \begin_layout Standard
31794 To create with this the solution formula, the command
31795 \begin_inset Newline newline
31805 \begin_inset Formula $\to$
31811 \begin_inset Formula $\to$
31818 is inserted to a formula
31823 \begin_layout Standard
31824 The definition of the new command is unintuitive because one has to know
31825 the schemes of all used LaTeX commands, e.
31826 \begin_inset space \thinspace{}
31830 \begin_inset space \space{}
31833 that a fraction is inserted in LaTeX as
31837 frac{numerator}{denominator}
31840 Furthermore one can easily forget a brace in the definition and cannot
31841 see in LyX what the new command is doing.
31842 To avoid these problems LyX offers the possibility to use math macros instead
31852 \begin_layout Standard
31856 \begin_layout Plain Layout
31866 \begin_inset Note Note
31869 \begin_layout Plain Layout
31870 The following table will only be displayed when the LaTeX-package
31880 \begin_inset Note Note
31883 \begin_layout Plain Layout
31884 xargs is default since TeXLive 2008, so this construct here can be deleted
31885 when TeXLive 2009 is out.
31893 \begin_layout Standard
31894 A math macro is created by using the menu
31896 Insert\SpecialChar \menuseparator
31897 Math\SpecialChar \menuseparator
31900 or the toolbar button
31901 \begin_inset Graphics
31902 filename ../images/math-macro_newmacroname_newcommand.png
31908 The math macro toolbar appears together with the following box where the
31910 \begin_inset Newline newline
31914 \begin_inset space \hspace*{\fill}
31918 \begin_inset Graphics
31919 filename clipart/macrobox.png
31924 \begin_inset space \hspace*{\fill}
31928 \begin_inset Newline newline
31932 \begin_inset FormulaMacro
31933 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31938 newmacroname is the default name of the macro that should be changed to
31939 something sensible.
31940 The wanted formula is inserted in the first blue box.
31941 An argument placeholder is inserted with the command
31948 \begin_inset space \thinspace{}
31952 \begin_inset space \space{}
31961 or by using the macro toolbar button
31962 \begin_inset Graphics
31963 filename ../images/math-macro-add-param.png
31969 Argument placeholders are displayed red.
31970 Maximum 9 arguments are possible.
31971 Optional arguments are created with the toolbar button
31972 \begin_inset Graphics
31973 filename ../images/math-macro-add-optional-param.png
31979 The first non-optional argument can be transformed to an optional one with
31981 \begin_inset Graphics
31982 filename ../images/math-macro-make-optional.png
31988 In the second blue box the appearance of the macro in LyX can be defined.
31989 Normally you want to see it as it is defined, so the box is kept empty.
31990 But when you have created a macro that needs lot of space on the screen,
31991 you can insert in the box for example
31992 \begin_inset Newline newline
32022 \begin_inset Newline newline
32027 For the macro only the arguments with the macro name in front of them will
32028 then be displayed in LyX, leading to a better overview.
32029 The formula appears in the output as defined in the first box.
32030 \begin_inset Newline newline
32033 The appearance of macros in formulas can furthermore be changed for single
32034 macros by setting the cursor in the macro and using the menu
32036 View\SpecialChar \menuseparator
32038 \begin_inset space ~
32042 \begin_inset space ~
32050 \begin_layout Standard
32051 To use a macro, the macro name is inserted as command to a formula, in our
32059 Our macro looks in LyX like this:
32060 \begin_inset Newline newline
32064 \begin_inset space \hspace*{\fill}
32068 \begin_inset Graphics
32069 filename clipart/macrouse.png
32074 \begin_inset space \hspace*{\fill}
32078 \begin_inset Newline newline
32081 Here is our macro example with the arguments
32082 \begin_inset Formula $x$
32086 \begin_inset Formula $\ln(x)$
32090 \begin_inset Formula $B$
32096 \begin_layout Standard
32097 \begin_inset Formula \[
32105 \begin_layout Standard
32106 A math macro is transformed internally to a
32112 command when exporting the document.
32119 command is not placed in the LaTeX-preamble, therefore macros can only
32120 be used in formulas that are in the document below the macro definition
32124 \begin_layout Standard
32125 Math macros can also be directly be created from a
32132 When writing for example the command
32135 \begin_inset Newline newline
32144 xleftarrow[#2]{#1}}
32145 \begin_inset Newline newline
32150 in LyX as normal text, highlighting it completely and using then the shortcut
32155 , the command will be transformed to a math macro.
32156 Using this method you need to be careful that the
32162 command is typed correctly, otherwise you get a faulty macro leading to
32166 \begin_layout Standard
32167 Math macros currently yet have the problem that further formulas in macro
32168 definitions are handled wrongly.
32169 Therefore the example
32176 \begin_inset CommandInset ref
32178 reference "sub:The-Command-newcommand"
32182 cannot be created as macro.
32185 \begin_layout Standard
32186 When the cursor is in a macro definition box, you will see the macro toolbar
32190 \begin_layout Standard
32191 \begin_inset VSpace defskip
32197 \begin_layout Standard
32198 \begin_inset Graphics
32199 filename clipart/MacroToolbar.png
32207 \begin_layout Plain Layout
32216 \begin_layout Standard
32217 \begin_inset VSpace defskip
32223 \begin_layout Standard
32224 The macro toolbar contains from left to right the following buttons:
32227 \begin_layout Standard
32228 \begin_inset VSpace defskip
32234 \begin_layout Standard
32235 \begin_inset Tabular
32236 <lyxtabular version="3" rows="9" columns="2">
32237 <features islongtable="true">
32238 <column alignment="left" valignment="top" width="0">
32239 <column alignment="left" valignment="top" width="85col%">
32240 <row interlinespace="2.5mm">
32241 <cell alignment="center" valignment="top" usebox="none">
32244 \begin_layout Plain Layout
32245 \begin_inset Graphics
32246 filename ../images/math-macro-remove-param.png
32247 BoundingBox 0bp 5bp 20bp 25bp
32248 rotateOrigin center
32257 <cell alignment="center" valignment="top" usebox="none">
32260 \begin_layout Plain Layout
32263 Edit\SpecialChar \menuseparator
32264 Math\SpecialChar \menuseparator
32266 \begin_inset space ~
32269 Definition\SpecialChar \menuseparator
32270 Remove Last Argument
32276 <row interlinespace="2.5mm">
32277 <cell alignment="center" valignment="top" usebox="none">
32280 \begin_layout Plain Layout
32281 \begin_inset Graphics
32282 filename ../images/math-macro-add-param.png
32283 BoundingBox 0bp 5bp 20bp 25bp
32284 rotateOrigin center
32293 <cell alignment="center" valignment="top" usebox="none">
32296 \begin_layout Plain Layout
32299 Edit\SpecialChar \menuseparator
32300 Math\SpecialChar \menuseparator
32302 \begin_inset space ~
32305 Definition\SpecialChar \menuseparator
32312 <row interlinespace="2.5mm">
32313 <cell alignment="center" valignment="top" usebox="none">
32316 \begin_layout Plain Layout
32317 \begin_inset Graphics
32318 filename ../images/math-macro-make-optional.png
32319 BoundingBox 0bp 5bp 20bp 25bp
32320 rotateOrigin center
32329 <cell alignment="center" valignment="top" usebox="none">
32332 \begin_layout Plain Layout
32335 Edit\SpecialChar \menuseparator
32336 Math\SpecialChar \menuseparator
32338 \begin_inset space ~
32341 Definition\SpecialChar \menuseparator
32342 Make First Non-Optional into
32343 \begin_inset Newline newline
32350 \begin_layout Plain Layout
32359 Edit\SpecialChar \menuseparator
32360 Math\SpecialChar \menuseparator
32362 \begin_inset space ~
32365 Definition\SpecialChar \menuseparator
32370 \begin_layout Plain Layout
32383 <row interlinespace="2.5mm">
32384 <cell alignment="center" valignment="top" usebox="none">
32387 \begin_layout Plain Layout
32388 \begin_inset Graphics
32389 filename ../images/math-macro-make-nonoptional.png
32390 BoundingBox 0bp 5bp 20bp 25bp
32391 rotateOrigin center
32400 <cell alignment="center" valignment="top" usebox="none">
32403 \begin_layout Plain Layout
32406 Edit\SpecialChar \menuseparator
32407 Math\SpecialChar \menuseparator
32409 \begin_inset space ~
32412 Definition\SpecialChar \menuseparator
32413 Make Last Optional into
32414 \begin_inset Newline newline
32421 \begin_layout Plain Layout
32430 Edit\SpecialChar \menuseparator
32431 Math\SpecialChar \menuseparator
32433 \begin_inset space ~
32436 Definition\SpecialChar \menuseparator
32441 \begin_layout Plain Layout
32448 Non-Optional Argument
32454 <row interlinespace="2.5mm">
32455 <cell alignment="center" valignment="top" usebox="none">
32458 \begin_layout Plain Layout
32459 \begin_inset Graphics
32460 filename ../images/math-macro-remove-optional-param.png
32461 BoundingBox 0bp 5bp 20bp 25bp
32462 rotateOrigin center
32471 <cell alignment="center" valignment="top" usebox="none">
32474 \begin_layout Plain Layout
32477 Edit\SpecialChar \menuseparator
32478 Math\SpecialChar \menuseparator
32480 \begin_inset space ~
32483 Definition\SpecialChar \menuseparator
32484 Remove Optional Argument
32490 <row interlinespace="2.5mm">
32491 <cell alignment="center" valignment="top" usebox="none">
32494 \begin_layout Plain Layout
32495 \begin_inset Graphics
32496 filename ../images/math-macro-add-optional-param.png
32497 BoundingBox 0bp 5bp 20bp 25bp
32498 rotateOrigin center
32507 <cell alignment="center" valignment="top" usebox="none">
32510 \begin_layout Plain Layout
32513 Edit\SpecialChar \menuseparator
32514 Math\SpecialChar \menuseparator
32516 \begin_inset space ~
32519 Definition\SpecialChar \menuseparator
32520 Insert Optional Argument
32526 <row interlinespace="2.5mm">
32527 <cell alignment="center" valignment="top" usebox="none">
32530 \begin_layout Plain Layout
32531 \begin_inset Graphics
32532 filename ../images/math-macro-remove-greedy-param.png
32533 BoundingBox 0bp 5bp 20bp 25bp
32534 rotateOrigin center
32543 <cell alignment="center" valignment="top" usebox="none">
32546 \begin_layout Plain Layout
32549 Edit\SpecialChar \menuseparator
32550 Math\SpecialChar \menuseparator
32552 \begin_inset space ~
32555 Definition\SpecialChar \menuseparator
32556 Remove Last Argument
32557 \begin_inset Newline newline
32564 \begin_layout Plain Layout
32573 Edit\SpecialChar \menuseparator
32574 Math\SpecialChar \menuseparator
32576 \begin_inset space ~
32579 Definition\SpecialChar \menuseparator
32584 \begin_layout Plain Layout
32591 Spitting Out To The Right
32597 <row interlinespace="2.5mm">
32598 <cell alignment="center" valignment="top" usebox="none">
32601 \begin_layout Plain Layout
32602 \begin_inset Graphics
32603 filename ../images/math-macro-append-greedy-param.png
32604 BoundingBox 0bp 5bp 20bp 25bp
32605 rotateOrigin center
32614 <cell alignment="center" valignment="top" usebox="none">
32617 \begin_layout Plain Layout
32620 Edit\SpecialChar \menuseparator
32621 Math\SpecialChar \menuseparator
32623 \begin_inset space ~
32626 Definition\SpecialChar \menuseparator
32628 \begin_inset Newline newline
32635 \begin_layout Plain Layout
32644 Edit\SpecialChar \menuseparator
32645 Math\SpecialChar \menuseparator
32647 \begin_inset space ~
32650 Definition\SpecialChar \menuseparator
32655 \begin_layout Plain Layout
32662 Eating From The Right
32668 <row interlinespace="2.5mm">
32669 <cell alignment="center" valignment="top" usebox="none">
32672 \begin_layout Plain Layout
32673 \begin_inset Graphics
32674 filename ../images/math-macro-add-greedy-optional-param.png
32675 BoundingBox 0bp 5bp 20bp 25bp
32676 rotateOrigin center
32685 <cell alignment="center" valignment="top" usebox="none">
32688 \begin_layout Plain Layout
32691 Edit\SpecialChar \menuseparator
32692 Math\SpecialChar \menuseparator
32694 \begin_inset space ~
32697 Definition\SpecialChar \menuseparator
32698 Append Optional Argument
32699 \begin_inset Newline newline
32706 \begin_layout Plain Layout
32715 Edit\SpecialChar \menuseparator
32716 Math\SpecialChar \menuseparator
32718 \begin_inset space ~
32721 Definition\SpecialChar \menuseparator
32726 \begin_layout Plain Layout
32733 Eating From The Right
32746 \begin_layout Standard
32750 \begin_layout Plain Layout
32760 \begin_inset Note Note
32763 \begin_layout Plain Layout
32764 The following will be displayed when the LaTeX-package
32776 \begin_layout Standard
32777 You need to install the LaTeX-package
32781 to see the rest of this subsection in the output.
32784 \begin_layout Standard
32788 \begin_layout Plain Layout
32800 \begin_layout Standard
32801 \begin_inset Newpage newpage
32807 \begin_layout Section
32811 \begin_layout Standard
32812 LyX supports two types of commutative diagrams:
32820 that are explained in the following.
32823 \begin_layout Subsection
32828 \begin_layout Plain Layout
32837 \begin_layout Standard
32838 Diagrams of this type visualize relations by vertical and horizontal lines
32840 \begin_inset Formula \[
32841 \begin{CD}A@>>>B@>>>C\\
32843 F@<<<E@<<<D\end{CD}\]
32850 \begin_layout Standard
32851 To get them, the command
32859 \begin_layout Plain Layout
32869 is inserted to a formula.
32870 A blue box appears with two dashed lines where further commands can be
32875 arg "newline-insert newline"
32878 a new line is created.
32879 Horizontal relations are inserted in odd, vertical in even formula lines.
32882 \begin_layout Standard
32883 To create the relations there are the following commands:
32886 \begin_layout Itemize
32891 creates a left arrow,
32902 \begin_layout Itemize
32907 creates an up arrow,
32915 a vertical equal sign
32918 \begin_layout Itemize
32924 is a placeholder for non-existent relations
32927 \begin_layout Standard
32928 All arrows can be labeled as follows:
32931 \begin_layout Itemize
32932 Is text inserted between the first and second < or >, resp., it is placed
32934 When it is inserted between the second and third one, it appears under
32938 \begin_layout Itemize
32939 When text for vertical arrows is inserted between the first and second A
32940 or V, resp., it is placed left beside the arrow.
32941 When it is inserted between the second and third one, it appears right
32943 If the text contains an A or V, these letters must be set into a TeX-brace.
32946 \begin_layout Standard
32947 As example a diagram with all possible relations:
32950 \begin_layout Standard
32951 \begin_inset Formula \[
32952 \begin{CD}A@>j>>B@>>k>C@=F\\
32954 D@<<j<E@>k>>F@=C\end{CD}\]
32961 \begin_layout Standard
32962 The command for this is:
32963 \begin_inset Newline newline
32974 \begin_layout Plain Layout
32983 A@>j>>B@>>k>C@=F Ctrl+Return
32984 \begin_inset Newline newline
32991 \begin_layout Plain Layout
33006 \begin_layout Plain Layout
33019 \begin_layout Plain Layout
33031 \begin_inset Formula $\to$
33037 \begin_inset Newline newline
33044 \begin_layout Plain Layout
33059 \begin_layout Plain Layout
33072 \begin_layout Plain Layout
33082 \begin_layout Subsection
33087 \begin_layout Plain Layout
33088 Diagrams ! xymatrix
33096 \begin_layout Standard
33097 To be able to use xymatrices, the LaTeX-package
33102 A xymatrix is created by inserting the command
33109 Then you are able to add new matrix columns and rows like for normal matrices,
33111 \begin_inset CommandInset ref
33113 reference "sec:Matrices"
33120 \begin_layout Standard
33121 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33123 All possibilities to create commutative diagrams and decorations are explained
33128 that you find in the menu
33130 Help\SpecialChar \menuseparator
33132 \begin_inset space ~
33135 Manuals\SpecialChar \menuseparator
33137 \begin_inset space ~
33145 \begin_layout Standard
33146 \begin_inset Newpage newpage
33152 \begin_layout Section
33157 \begin_layout Plain Layout
33170 \begin_layout Plain Layout
33171 Other useful math tips can be found in
33172 \begin_inset CommandInset citation
33187 \begin_layout Plain Layout
33195 \begin_inset Note Note
33198 \begin_layout Plain Layout
33201 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33204 \begin_layout Plain Layout
33207 texorpdfstring is in section
33208 \begin_inset CommandInset ref
33210 reference "sub:Formulas-in-Section"
33223 \begin_layout Plain Layout
33233 \begin_layout Plain Layout
33238 \begin_layout Plain Layout
33245 Chemical characters
33249 \begin_layout Plain Layout
33264 \begin_layout Subsection
33265 Chemical Symbols and Equations
33266 \begin_inset CommandInset label
33268 name "sub:Chemical-Symbols-and"
33276 \begin_layout Plain Layout
33277 Chemical characters ! Symbols
33286 \begin_layout Plain Layout
33296 \begin_layout Plain Layout
33305 \begin_layout Standard
33306 An example text from chemistry:
33309 \begin_layout Quote
33311 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33314 -ion reacts with two
33315 \begin_inset Formula $\mathrm{Na^{+}}$
33318 -ions to sodium sulfate
33319 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33323 The chemical equation for this is:
33324 \begin_inset Formula \[
33325 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33332 \begin_layout Standard
33333 This chemical equation can directly be created as formula.
33334 To avoid that the symbols appear italic, everything is highlighted and
33335 changed by the shortcut
33341 to the upright font style.
33345 \begin_layout Plain Layout
33351 \begin_inset CommandInset ref
33353 reference "sub:Font-Styles"
33365 \begin_layout Subsection
33370 \begin_layout Plain Layout
33379 \begin_layout Standard
33380 Negative numbers often look ugly in formulas because the minus sign before
33381 the number is set with the same length as the minus operator sign.
33382 When writing the negative number in normal text, the minus sign appears
33386 \begin_layout Standard
33387 Thus, the problem disappears when converting the minus sign to mathematical
33391 \begin_layout Standard
33392 An example to visualize the problem:
33395 \begin_layout Standard
33397 \begin_inset Tabular
33398 <lyxtabular version="3" rows="3" columns="2">
33400 <column alignment="right" valignment="top" width="0">
33401 <column alignment="left" valignment="top" width="0">
33403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33406 \begin_layout Plain Layout
33412 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33415 \begin_layout Plain Layout
33423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33426 \begin_layout Plain Layout
33432 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33435 \begin_layout Plain Layout
33436 \begin_inset Formula $x=-2$
33446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33449 \begin_layout Plain Layout
33455 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33458 \begin_layout Plain Layout
33459 \begin_inset Formula $x=\textrm{-}2$
33475 \begin_layout Subsection
33476 Comma as decimal Separator
33480 \begin_layout Plain Layout
33489 \begin_layout Standard
33490 In LaTeX a comma inside a formula is used, according to the English convention,
33491 as number group separator.
33492 So there will be space added behind all commas in formulas.
33495 \begin_layout Standard
33496 To avoid this, the comma is highlighted and changed to mathematical text
33506 \begin_layout Standard
33507 To use all formula commas in the document as decimal separator, the file
33516 \begin_layout Plain Layout
33521 is part of the LaTeX-package
33529 \begin_layout Plain Layout
33534 \begin_layout Plain Layout
33557 \begin_layout Plain Layout
33563 is loaded with the LaTeX-preamble line
33566 \begin_layout Standard
33574 \begin_layout Subsection
33576 \begin_inset CommandInset label
33578 name "sub:Physical-Vectors"
33586 \begin_layout Plain Layout
33595 \begin_layout Standard
33596 Predefined vectors are offered by the LaTeX-package
33604 \begin_layout Plain Layout
33609 should be part of every LaTeX standard installation.
33618 \begin_layout Plain Layout
33624 that is loaded with the LaTeX-preamble line
33627 \begin_layout Standard
33635 \begin_layout Standard
33639 \begin_layout Plain Layout
33649 \begin_inset Note Note
33652 \begin_layout Plain Layout
33653 The following table will only be displayed when the LaTeX-package
33662 The following commands are defined:
33665 \begin_layout Standard
33667 \begin_inset Tabular
33668 <lyxtabular version="3" rows="4" columns="2">
33670 <column alignment="center" valignment="top" width="0">
33671 <column alignment="center" valignment="top" width="0">
33673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33676 \begin_layout Plain Layout
33682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33685 \begin_layout Plain Layout
33693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33696 \begin_layout Plain Layout
33706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33709 \begin_layout Plain Layout
33710 \begin_inset Formula $\Bra{\psi}$
33720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33723 \begin_layout Plain Layout
33733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33736 \begin_layout Plain Layout
33737 \begin_inset Formula $\Ket{\psi}$
33747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33750 \begin_layout Plain Layout
33762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33765 \begin_layout Plain Layout
33766 \begin_inset Formula $\Braket{\psi|\phi}$
33782 \begin_layout Standard
33789 assures that all vertical bars are set in the size of the surrounding brackets:
33790 \begin_inset Formula \[
33791 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33799 \begin_layout Plain Layout
33809 \begin_inset Note Note
33812 \begin_layout Plain Layout
33813 The following will be displayed when the LaTeX-package
33825 \begin_layout Standard
33826 You need to install the LaTeX-package
33830 to see the rest of this subsection in the output.
33833 \begin_layout Standard
33837 \begin_layout Plain Layout
33849 \begin_layout Standard
33856 can also be achieved using the command
33862 , that is described in
33863 \begin_inset CommandInset ref
33865 reference "sub:Automatic-Bracket-Size"
33872 \begin_layout Subsection
33873 Self-defined Fractions
33874 \begin_inset CommandInset label
33876 name "sub:Self-defined-Fractions"
33884 \begin_layout Plain Layout
33885 Fractions ! self-defined
33893 \begin_layout Standard
33894 To define custom commands for fractions, the command
33904 \begin_layout Plain Layout
33912 is used in the following scheme:
33915 \begin_layout Standard
33928 bracket}{fraction bar thickness}{style}
33929 \begin_inset Newline newline
33936 \begin_layout Plain Layout
33951 \begin_layout Plain Layout
33958 {numerator}{denominator}
33961 \begin_layout Standard
33962 The style is a number in the range of 0
33963 \begin_inset space \thinspace{}
33967 \begin_inset space \thinspace{}
33973 \begin_layout Standard
33975 \begin_inset Tabular
33976 <lyxtabular version="3" rows="5" columns="2">
33978 <column alignment="center" valignment="top" width="0">
33979 <column alignment="center" valignment="top" width="0">
33981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33984 \begin_layout Plain Layout
33990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33993 \begin_layout Plain Layout
34001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34004 \begin_layout Plain Layout
34010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34013 \begin_layout Plain Layout
34014 display style formula
34021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34024 \begin_layout Plain Layout
34030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34033 \begin_layout Plain Layout
34041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34044 \begin_layout Plain Layout
34050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34053 \begin_layout Plain Layout
34061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34064 \begin_layout Plain Layout
34070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34073 \begin_layout Plain Layout
34087 \begin_layout Standard
34088 When no style is given, the size is adjusted to the surrounding environment
34089 like for the command
34098 \begin_layout Standard
34099 When no fraction bar thickness is given, the predefined value of 0.4
34100 \begin_inset space \thinspace{}
34106 \begin_layout Standard
34107 \begin_inset VSpace medskip
34110 For example, the commands
34123 \begin_inset CommandInset ref
34125 reference "sub:Fractions"
34129 are defined with the commands
34132 \begin_layout Standard
34141 genfrac{}{}{}{0}{#1}{#2}}
34144 \begin_layout Standard
34148 \begin_layout Standard
34157 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34160 \begin_layout Standard
34161 \begin_inset VSpace medskip
34164 To define a fraction where the fraction bar thickness can be given as optional
34165 argument, the following line is inserted to the LaTeX-preamble:
34168 \begin_layout Standard
34177 genfrac{}{}{#1}{}{#2}{#3}}
34180 \begin_layout Standard
34182 \begin_inset Formula \begin{align*}
34183 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34184 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34188 As one can see, the distance of the numerator and the denominator to the
34189 fraction bar is round about three times the bar thickness.
34192 \begin_layout Subsection
34197 \begin_layout Plain Layout
34206 \begin_layout Standard
34207 To cancel formulas or formula parts, the LaTeX-package
34215 \begin_layout Plain Layout
34220 is part of every LaTeX standard installation.
34229 \begin_layout Plain Layout
34235 has to be loaded with the LaTeX-preamble line
34238 \begin_layout Standard
34243 usepackage[samesize]{cancel}
34246 \begin_layout Standard
34247 There are four ways to cancel formulas:
34250 \begin_layout Standard
34252 \begin_inset Tabular
34253 <lyxtabular version="3" rows="5" columns="2">
34255 <column alignment="center" valignment="top" width="0">
34256 <column alignment="center" valignment="top" width="0">
34258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34261 \begin_layout Plain Layout
34267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34270 \begin_layout Plain Layout
34272 \begin_inset Note Note
34275 \begin_layout Plain Layout
34282 are used here as spacer.
34294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34297 \begin_layout Plain Layout
34306 \begin_layout Plain Layout
34320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34323 \begin_layout Plain Layout
34324 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34337 \begin_layout Plain Layout
34346 \begin_layout Plain Layout
34360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34363 \begin_layout Plain Layout
34364 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34377 \begin_layout Plain Layout
34386 \begin_layout Plain Layout
34400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34403 \begin_layout Plain Layout
34404 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34417 \begin_layout Plain Layout
34421 \begin_inset Formula $\to$
34432 \begin_layout Plain Layout
34446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34449 \begin_layout Plain Layout
34450 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34466 \begin_layout Standard
34473 is especially suitable to visualize the reduction of fractions within formulas:
34474 \begin_inset Formula \[
34475 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34482 \begin_layout Subsection
34483 Formulas in Section Headings
34484 \begin_inset CommandInset label
34486 name "sub:Formulas-in-Section"
34494 \begin_layout Plain Layout
34495 Formula ! in section headings
34503 \begin_layout Standard
34504 When formulas are used in section headings, the following has to be taken
34508 \begin_layout Standard
34509 \begin_inset Note Greyedout
34512 \begin_layout Plain Layout
34521 \begin_layout Plain Layout
34522 Packages ! hyperref
34527 support is enabled in the document settings dialog under
34530 \begin_inset space ~
34535 , PDF-bookmarks are created for every section heading in the table of contents.
34536 If a section heading contains formulas, they are incorrectly displayed
34537 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34546 \begin_layout Standard
34547 Both problems can be solved by inserting at the end of the section heading
34548 a short title with the menu
34550 Insert\SpecialChar \menuseparator
34552 \begin_inset space ~
34558 Short titles are used as alternative for multiline section headings to
34559 keep the table of contents clearly arranged.
34560 Only the short title appears in the table of contents and therefore also
34561 in the PDF-bookmark.
34564 \begin_layout Standard
34565 When formulas should be used in the table of contents but
34569 is used, one can use the following command in TeX-mode:
34572 \begin_layout Standard
34577 texorpdfstring{part}{alternative}
34581 \begin_layout Plain Layout
34592 \begin_layout Standard
34593 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34594 This can be characters, formulas, footnotes, but also cross-references.
34595 The alternative is used instead of the part for the bookmark.
34598 \begin_layout Standard
34599 Here are two example headings:
34600 \begin_inset VSpace -3mm
34607 \begin_layout Plain Layout
34619 \begin_layout Subsubsection
34620 Heading without formula in table of contents
34621 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34625 \begin_inset OptArg
34628 \begin_layout Plain Layout
34629 Heading without formula in table of contents
34637 \begin_layout Subsubsection
34638 Heading with formula in table of contents
34642 \begin_layout Plain Layout
34652 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34659 \begin_layout Plain Layout
34669 \begin_layout Standard
34673 \begin_layout Plain Layout
34682 In the first heading a short title was used, in the second one
34691 \begin_layout Standard
34692 To get the same formatting as for the other headings, the complete heading
34701 \begin_layout Plain Layout
34703 \begin_inset CommandInset ref
34705 reference "sub:Bold-Formulas"
34717 \begin_layout Subsection
34718 Formulas in multi-column Text
34722 \begin_layout Plain Layout
34723 Formula ! in multi-column text
34731 \begin_layout Standard
34732 Formulas in multi-column text are often too wide to fit into a column and
34733 thus need to be set over the whole page width.
34734 This is done by using the LaTeX-package
34742 \begin_layout Plain Layout
34747 is part of every LaTeX standard installation.
34756 \begin_layout Plain Layout
34757 Packages ! multicol
34762 , that is loaded with the LaTeX-preamble line
34765 \begin_layout Standard
34770 usepackage{multicol}
34773 \begin_layout Standard
34774 \begin_inset Note Greyedout
34777 \begin_layout Plain Layout
34778 Note herby that the setting
34781 \begin_inset space ~
34788 Document\SpecialChar \menuseparator
34794 \begin_inset space ~
34814 \begin_layout Standard
34815 Before the multi-column text the command
34818 \begin_layout Standard
34823 begin{multicols}{column number}
34826 \begin_layout Standard
34827 is written in TeX-mode.
34828 The column number is a number in the range of 2
34829 \begin_inset space \thinspace{}
34833 \begin_inset space \thinspace{}
34837 Before the formula the multi-column text is ended by inserting the command
34840 \begin_layout Standard
34848 \begin_layout Standard
34852 \begin_layout Standard
34853 Due to the command some space is automatically added before the formula.
34855 \begin_inset space \thinspace{}
34858 mm vertical space is inserted before the formula.
34859 When the formula style
34865 \begin_layout Plain Layout
34867 \begin_inset CommandInset ref
34869 reference "sec:Formula-Styles"
34881 \begin_inset space \thinspace{}
34884 mm space is inserted instead.
34887 \begin_layout Standard
34888 As example a multi-column text with a displayed formula:
34891 \begin_layout Standard
34895 \begin_layout Plain Layout
34899 begin{multicols}{2}
34904 Das Spektrum wird fouriertransformiert.
34905 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34906 , Lösungsmittel) zu trennen.
34907 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34908 nun das Aussehen des Ausgangssignals.
34909 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34910 über alle Phasen integrieren muss.
34912 \begin_inset Formula $S$
34915 unser normiertes Ausgangssignal and
34916 \begin_inset Formula $P$
34919 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34923 \begin_layout Plain Layout
34933 \begin_inset VSpace -6mm
34937 \begin_inset Formula \begin{equation}
34938 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34946 \begin_layout Plain Layout
34950 begin{multicols}{2}
34956 \begin_inset Formula $S_{0}$
34959 das Signal ohne Gradient ist and the Normierungsbedingung
34960 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34964 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34966 \begin_inset Formula $\nicefrac{\pi}{2}$
34970 \begin_inset space \thinspace{}
34973 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34974 das Signal zusätzlich abschwächt.
34975 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34977 \begin_inset Formula $T_{2}$
34983 \begin_layout Standard
34987 \begin_layout Plain Layout
34999 \begin_layout Subsection
35000 Formulas with Description of Variables
35004 \begin_layout Plain Layout
35005 Formula ! with description of variables
35013 \begin_layout Standard
35014 To describe variables within a formula, like in formula
35015 \begin_inset CommandInset ref
35017 reference "eq:within"
35026 \begin_inset Formula $n$
35030 \begin_inset space ~
35033 matrix is used with left aligned columns for the
35034 \begin_inset Formula $n$
35041 \begin_layout Plain Layout
35043 \begin_inset CommandInset ref
35045 reference "sec:Matrices"
35054 To set the description in a smaller size, before the matrix e.
35055 \begin_inset space \thinspace{}
35059 \begin_inset space \space{}
35072 \begin_layout Plain Layout
35074 \begin_inset CommandInset ref
35076 reference "sub:Font-Sizes"
35088 \begin_layout Standard
35089 When the formula style
35095 \begin_layout Plain Layout
35097 \begin_inset CommandInset ref
35099 reference "sec:Formula-Styles"
35120 \begin_layout Plain Layout
35127 only works in formulas with the style
35132 \begin_inset CommandInset ref
35134 reference "sub:Variable-Space"
35143 is inserted before and after the matrix to have the same separation of
35144 the matrix from the equation and the side margin.
35147 \begin_layout Standard
35148 When the formula style
35152 is used, the method described in
35153 \begin_inset CommandInset ref
35155 reference "sub:Flalign-Environment"
35159 is used to indent formulas.
35161 \begin_inset CommandInset ref
35163 reference "eq:within"
35167 consists of five columns whereas in the first two columns contain the equation,
35168 the third the matrix, and the last one an empty TeX-brace.
35169 \begin_inset Formula \begin{flalign}
35170 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35171 \rho & \textrm{density}\\
35172 V & \textrm{volume}\\
35173 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35180 \begin_layout Subsection
35181 Upright small Greek Letters
35182 \begin_inset CommandInset label
35184 name "sub:Upright-small-Greek"
35192 \begin_layout Plain Layout
35193 Greek letters ! upright
35201 \begin_layout Standard
35202 Most of the math fonts only provide italic small Greek letters.
35203 But for symbols of elementary particles like pions and neutrinos, upright
35204 Greek letters are needed.
35213 \begin_layout Plain Layout
35218 is part of the LaTeX-package
35226 \begin_layout Plain Layout
35231 \begin_layout Plain Layout
35254 \begin_layout Plain Layout
35260 that is loaded with the LaTeX-preamble line
35263 \begin_layout Standard
35268 usepackage{upgreek}
35271 \begin_layout Standard
35277 \begin_layout Plain Layout
35287 \begin_inset Note Note
35290 \begin_layout Plain Layout
35291 The following table will only be displayed when the LaTeX-package
35300 They are created when the command for a small Greek letters is started
35306 For example the command
35313 \begin_inset Formula $\uptau$
35319 \begin_layout Standard
35320 With these commands reactions of elementary particles can be typeset:
35321 \begin_inset Formula \[
35322 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35329 \begin_layout Standard
35330 The upright letters are more bold and wider than the italic ones.
35331 They should therefore not be used for units like
35332 \begin_inset Quotes eld
35336 \begin_inset Quotes erd
35342 \begin_layout Standard
35346 \begin_layout Plain Layout
35356 \begin_inset Note Note
35359 \begin_layout Plain Layout
35360 The following will be displayed when the LaTeX-package
35372 \begin_layout Standard
35373 You need to install the LaTeX-package
35377 to see the rest of this subsection in the output.
35380 \begin_layout Standard
35384 \begin_layout Plain Layout
35396 \begin_layout Subsection
35397 Text Characters in Formulas
35398 \begin_inset CommandInset label
35400 name "sub:Text-Characters-in"
35408 \begin_layout Plain Layout
35417 \begin_layout Standard
35418 In some cases you might want to insert text characters directly into formulas.
35419 When for example the centered dot · is often used in formulas like
35420 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35423 , one would have to insert the command
35433 \begin_layout Plain Layout
35435 \begin_inset CommandInset ref
35437 reference "sub:Binary-Operators"
35446 all the time, because this character is defined in all encodings as text
35448 But the encoding can be changed by this LaTeX-preamble line:
35451 \begin_layout Standard
35456 Declare Inputtext{183}{
35466 f\SpecialChar \textcompwordmark{}
35470 \begin_layout Standard
35471 The character encoding (menu
35473 Document\SpecialChar \menuseparator
35474 Settings\SpecialChar \menuseparator
35477 ) specifies what character appears when a keyboard key is pressed.
35478 When the key for the character '·' is pressed, internally the command
35485 But this command is not available in a formula so that you would get LaTeX-erro
35487 With the changed encoding the right command is chosen automatically, depending
35488 on if the character was inserted into a formula or not.
35491 \begin_layout Standard
35492 The encoding of several characters is saved in definition files.
35493 Fore example the encoding
35497 is defined in the file
35501 that is in the installation folder of LaTeX.
35502 Encodings should only be changed via the LaTeX-preamble and not in the
35504 Otherwise own documents could not be edited by other LyX users working
35505 on other computers.
35508 \begin_layout Standard
35509 \begin_inset VSpace medskip
35512 Besides the centered dot, in this document the degree sign ° is defined
35513 with the following LaTeX-preamble line so that it can directly be inserted
35517 \begin_layout Standard
35522 DeclareInputtext{176}{
35532 f\SpecialChar \textcompwordmark{}
35536 \begin_layout Standard
35537 \begin_inset Newpage newpage
35543 \begin_layout Section
35549 \begin_layout Plain Layout
35558 \begin_layout Standard
35559 This section is a summary of the most important typographic rules, listed
35564 \begin_layout Plain Layout
35565 This collection was partly taken from the German semi-official dictionary
35567 \begin_inset Quotes eld
35571 \begin_inset Quotes erd
35575 \begin_inset CommandInset citation
35581 that lists some of the ISO rules.
35589 \begin_layout Itemize
35598 \begin_layout Plain Layout
35599 done with font styles, see
35600 \begin_inset CommandInset ref
35602 reference "sub:Font-Styles"
35612 \begin_inset space \thinspace{}
35616 \begin_inset Newline newline
35619 Between the value and the unit is the smallest space, see
35620 \begin_inset CommandInset ref
35622 reference "sub:Predefined-Space"
35627 \begin_inset Newline newline
35630 This convention is automatically fulfilled when the command
35637 When it is entered to a formula, two boxes appear.
35638 In the first one the value is inserted, in the second one the unit, and
35640 \begin_inset Formula $\unit[30]{km/h}$
35644 \begin_inset space \thinspace{}
35654 is not a real LaTeX command but the command
35660 , therefore you cannot use it in TeX code.
35663 \begin_layout Itemize
35664 Percent and perthousand signs are set like physical units:
35665 \begin_inset Newline newline
35669 \begin_inset space \thinspace{}
35675 \begin_layout Itemize
35676 The degree sign follows directly on the value: 15°, but not when it is used
35678 \begin_inset space \thinspace{}
35684 \begin_layout Itemize
35685 In numbers with more than four digits the smallest space is inserted before
35686 every third digit to group them:
35696 \begin_inset space \thinspace{}
35700 \begin_inset space \thinspace{}
35706 \begin_layout Itemize
35707 For dimensions like 120×90×40
35708 \begin_inset space \thinspace{}
35711 cm the multiplication sign
35712 \begin_inset Quotes eld
35716 \begin_inset Quotes erd
35720 It is available via the menu
35722 Insert\SpecialChar \menuseparator
35723 Special Character\SpecialChar \menuseparator
35727 With some keyboard definitions it can also be inserted directly.
35730 \begin_layout Itemize
35731 Functions with names consisting of several letters are set upright to avoid
35733 \begin_inset CommandInset ref
35735 reference "sub:Predefined-Functions"
35742 \begin_layout Itemize
35743 Indices consisting of several letters, are set upright:
35744 \begin_inset Formula $E_{\mathrm{kin}}$
35748 \begin_inset Newline newline
35751 Components of matrices are set italic:
35752 \begin_inset Formula $\hat{H}_{kl}$
35758 \begin_layout Itemize
35759 The differentiation/integration operator 'd', the Euler's number 'e', and
35760 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35764 \begin_layout Standard
35765 \begin_inset Newpage newpage
35771 \begin_layout Section
35776 \begin_layout Plain Layout
35785 \begin_layout Standard
35786 Some characters and symbols can be created with several commands.
35787 Here is a list of the synonym commands:
35790 \begin_layout Standard
35791 \begin_inset VSpace bigskip
35795 \begin_inset space \hfill{}
35799 \begin_inset Tabular
35800 <lyxtabular version="3" rows="12" columns="2">
35802 <column alignment="center" valignment="top" width="0pt">
35803 <column alignment="center" valignment="top" width="0pt">
35805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35808 \begin_layout Plain Layout
35814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35817 \begin_layout Plain Layout
35819 \begin_inset Note Note
35822 \begin_layout Plain Layout
35829 is only used as spacer.
35841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35844 \begin_layout Plain Layout
35852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35855 \begin_layout Plain Layout
35859 \begin_layout Plain Layout
35872 \begin_layout Plain Layout
35886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35889 \begin_layout Plain Layout
35897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35900 \begin_layout Plain Layout
35910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35913 \begin_layout Plain Layout
35921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35924 \begin_layout Plain Layout
35934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35937 \begin_layout Plain Layout
35945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35948 \begin_layout Plain Layout
35956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35959 \begin_layout Plain Layout
35967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35970 \begin_layout Plain Layout
35978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35981 \begin_layout Plain Layout
35989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35992 \begin_layout Plain Layout
36002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36005 \begin_layout Plain Layout
36013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36016 \begin_layout Plain Layout
36026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36029 \begin_layout Plain Layout
36037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36040 \begin_layout Plain Layout
36050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36053 \begin_layout Plain Layout
36061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36064 \begin_layout Plain Layout
36074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36077 \begin_layout Plain Layout
36085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36088 \begin_layout Plain Layout
36096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36099 \begin_layout Plain Layout
36107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36110 \begin_layout Plain Layout
36122 \begin_inset space \hfill{}
36126 \begin_inset Tabular
36127 <lyxtabular version="3" rows="12" columns="2">
36129 <column alignment="center" valignment="top" width="0pt">
36130 <column alignment="center" valignment="top" width="0pt">
36132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36135 \begin_layout Plain Layout
36141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36144 \begin_layout Plain Layout
36152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36155 \begin_layout Plain Layout
36163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36166 \begin_layout Plain Layout
36178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36181 \begin_layout Plain Layout
36189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36192 \begin_layout Plain Layout
36202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36205 \begin_layout Plain Layout
36213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36216 \begin_layout Plain Layout
36226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36229 \begin_layout Plain Layout
36237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36240 \begin_layout Plain Layout
36248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36251 \begin_layout Plain Layout
36259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36262 \begin_layout Plain Layout
36270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36273 \begin_layout Plain Layout
36281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36284 \begin_layout Plain Layout
36294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36297 \begin_layout Plain Layout
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36401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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36424 \begin_layout Standard
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36431 \begin_layout Bibliography
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36433 LatexCommand bibitem
36445 The LaTeX Companion
36448 Addison Wesley, 2004
36451 \begin_layout Bibliography
36452 \begin_inset CommandInset bibitem
36453 LatexCommand bibitem
36459 \begin_inset CommandInset href
36462 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36466 of LaTeX's math abilities
36469 \begin_layout Bibliography
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36471 LatexCommand bibitem
36476 LaTeX tips and tricks-
36477 \begin_inset CommandInset href
36480 target "http://tug.org/TeXnik/"
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36489 LatexCommand bibitem
36495 \begin_inset CommandInset href
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36520 LatexCommand bibitem
36526 \begin_inset CommandInset href
36529 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36533 of all symbols available with LaTeX-packages
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36538 LatexCommand bibitem
36544 \begin_inset CommandInset href
36546 name "Documentation"
36547 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36551 of the LaTeX-package
36559 \begin_layout Plain Layout
36560 Packages ! hyperref
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36570 LatexCommand bibitem
36576 \begin_inset CommandInset href
36579 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36590 \begin_inset CommandInset ref
36592 reference "sub:Operator-Limits"
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36613 LatexCommand bibitem
36624 Auflage, Duden 2001
36627 \begin_layout Subsubsection*
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36629 LatexCommand printindex