1 #LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
74 \usepackage[samesize]{cancel}
76 % enables calculation of values,
79 % for multiple table row and column cells
86 % center multirows (e.g. in sec. 13.3)
87 \renewcommand{\multirowsetup}{\centering}
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
113 % redefine the greyed out note
114 \renewenvironment{lyxgreyedout}
115 {\textcolor{blue}\bgroup}{\egroup}
117 % ------------------------------------
118 % used to check for needed LaTeX packages
121 % check for package eurosym
122 % used for the Euro symbol
124 \IfFileExists{eurosym.sty}
125 {\usepackage[gennarrow]{eurosym}
126 \setboolean{eurosym}{true}}
127 {\setboolean{eurosym}{false}}
129 % needed in sec. 22.4
130 % check for package braket
132 \IfFileExists{braket.sty}
134 \setboolean{braket}{true}}
135 {\setboolean{braket}{false}}
137 % needed in sec. 22.10
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pagebackref false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
182 \paperorientation portrait
185 \paragraph_separation skip
187 \quotes_language english
190 \paperpagestyle plain
194 \tracking_changes false
195 \output_changes false
203 LyX's detailed Math manual
211 \begin_layout Plain Layout
213 If you have comments or error corrections, please send them to the LyX Documenta
217 \begin_inset CommandInset href
219 name "lyx-docs@lists.lyx.org"
220 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
231 \begin_inset Note Note
234 \begin_layout Plain Layout
241 \begin_inset Newline newline
245 \begin_inset Newline newline
253 \begin_layout Standard
254 \begin_inset CommandInset toc
255 LatexCommand tableofcontents
262 \begin_layout Standard
263 \begin_inset Note Note
266 \begin_layout Plain Layout
267 To export this document to PDF, PS, or DVI the LaTeX-packages
280 If they are not installed you can export the document anyway but the sections
281 where the packages are required won't appear in the output.
284 \begin_layout Plain Layout
285 The latest PDF-version of this document can be found here:
286 \begin_inset Newline newline
291 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
299 \begin_layout Standard
300 \begin_inset Newpage newpage
306 \begin_layout Section
308 \begin_inset CommandInset label
310 name "sec:Introduction"
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
460 \begin_inset CommandInset label
462 name "sec:General-Instructions"
469 \begin_layout Standard
470 To create an inline formula
474 \begin_layout Plain Layout
480 that is embedded into a text line, press
484 or the toolbar button
485 \begin_inset Graphics
486 filename ../images/math-mode.png
492 \begin_inset Newline newline
495 To create a display style formula
499 \begin_layout Plain Layout
500 Formula ! display style
505 that will appear bigger and in an own paragraph, press
512 \begin_layout Standard
513 To change a display style formula to an inline formula, set the cursor into
514 the formula and press
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
660 \begin_inset Note Note
663 \begin_layout Plain Layout
664 In LyX there are three
665 \begin_inset Quotes eld
669 \begin_inset Quotes erd
672 that appear in the output with sub- and superscript letters: TeX, LaTeX,
676 \begin_layout Plain Layout
677 To avoid that these names are recognized as proper names, a TeX-brace pair
686 \begin_layout Standard
687 To change the LaTeX-preamble
691 \begin_layout Plain Layout
699 Document\SpecialChar \menuseparator
700 Settings\SpecialChar \menuseparator
705 \begin_layout Plain Layout
721 \begin_layout Standard
722 To edit matrices, case differentiations, and multiline formulas subsequently,
725 Edit\SpecialChar \menuseparator
730 Edit\SpecialChar \menuseparator
732 \begin_inset space \thinspace{}
736 \begin_inset space \thinspace{}
746 When lines and columns are swapped via the menu, the column or line where
747 the cursor is in is exchanged with the column to the right or the line
749 Is the cursor in the last column or row, the exchange is done with the
750 column to the left or the line above.
753 \begin_layout Standard
754 To write text in formulas
758 \begin_layout Plain Layout
759 For multiline formulas the command
766 \begin_inset CommandInset ref
768 reference "sub:Text-in-multiline"
785 \begin_layout Plain Layout
795 \begin_layout Plain Layout
802 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
924 \begin_layout Subsection*
925 \begin_inset Newpage newpage
931 \begin_layout Itemize
936 \begin_layout Plain Layout
937 This visible space character can be created with the command
947 \begin_layout Plain Layout
955 , inserted in TeX-mode.
964 \begin_layout Plain Layout
977 denotes a space character to be input.
980 \begin_layout Itemize
982 \begin_inset Formula $\to$
985 denotes the usage of the corresponding arrow key on the keyboard.
988 \begin_layout Subsection*
992 \begin_layout Standard
994 \begin_inset Float table
1000 \begin_layout Plain Layout
1002 \begin_inset Caption
1004 \begin_layout Plain Layout
1005 \begin_inset CommandInset label
1007 name "tab:Available-units"
1019 \begin_layout Plain Layout
1021 \begin_inset Tabular
1022 <lyxtabular version="3" rows="13" columns="2">
1024 <column alignment="center" valignment="top" width="0">
1025 <column alignment="center" valignment="top" width="0">
1027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1030 \begin_layout Plain Layout
1036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1039 \begin_layout Plain Layout
1047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1050 \begin_layout Plain Layout
1056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1059 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset space \thinspace{}
1227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1230 \begin_layout Plain Layout
1236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1239 \begin_layout Plain Layout
1241 \begin_inset space \thinspace{}
1245 \begin_inset Formula $\approx$
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1273 \begin_inset space \thinspace{}
1277 \begin_inset space \thinspace{}
1287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1290 \begin_layout Plain Layout
1296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1299 \begin_layout Plain Layout
1303 \begin_inset Quotes eld
1309 \begin_inset Quotes erd
1319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1322 \begin_layout Plain Layout
1328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1331 \begin_layout Plain Layout
1333 \begin_inset Quotes eld
1341 \begin_inset Quotes erd
1351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1354 \begin_layout Plain Layout
1360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1363 \begin_layout Plain Layout
1365 \begin_inset space \thinspace{}
1369 \begin_inset Formula $\nicefrac{1}{18}$
1373 \begin_inset space \thinspace{}
1394 \begin_layout Standard
1395 \begin_inset Newpage newpage
1401 \begin_layout Section
1405 \begin_layout Subsection
1410 \begin_layout Plain Layout
1420 \begin_layout Plain Layout
1430 \begin_layout Plain Layout
1435 \begin_layout Plain Layout
1446 \begin_layout Plain Layout
1462 \begin_layout Plain Layout
1467 \begin_layout Plain Layout
1478 \begin_layout Plain Layout
1493 \begin_layout Standard
1494 Indices are created with an underscore
1495 \begin_inset Quotes eld
1499 \begin_inset Quotes erd
1502 or via the math toolbar button
1503 \begin_inset Graphics
1504 filename ../images/math-subscript.png
1509 , exponents with a caret
1510 \begin_inset Quotes eld
1514 \begin_inset Quotes erd
1517 or via the math toolbar button
1518 \begin_inset Graphics
1519 filename ../images/math-superscript.png
1527 \begin_layout Standard
1529 \begin_inset Tabular
1530 <lyxtabular version="3" rows="4" columns="2">
1532 <column alignment="center" valignment="top" width="0pt">
1533 <column alignment="center" valignment="top" width="0pt">
1535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1538 \begin_layout Plain Layout
1544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1547 \begin_layout Plain Layout
1549 \begin_inset Note Note
1552 \begin_layout Plain Layout
1559 is only used as spacer.
1571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1574 \begin_layout Plain Layout
1580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1583 \begin_layout Plain Layout
1584 \begin_inset Formula $B_{V}$
1594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1597 \begin_layout Plain Layout
1603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1620 \begin_layout Plain Layout
1625 \begin_layout Plain Layout
1639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1642 \begin_layout Plain Layout
1643 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1659 \begin_layout Standard
1660 As the caret is in some languages an accent, vowels will be accentuated
1661 in this case and not set as exponents
1665 \begin_layout Plain Layout
1666 Depending on the used keyboard settings this can also happen for other character
1673 To get in this case exponents, press
1677 after the caret as in the last example.
1680 \begin_layout Subsection
1682 \begin_inset CommandInset label
1684 name "sub:Fractions"
1692 \begin_layout Plain Layout
1701 \begin_layout Standard
1702 Fractions are generated with the command
1712 \begin_layout Plain Layout
1720 or via the math toolbar button
1721 \begin_inset Graphics
1722 filename ../images/math/frac.png
1728 The font size is adjusted automatically, depending on whether the fraction
1729 is in an inline or display style formula.
1730 With the math toolbar button
1731 \begin_inset Graphics
1732 filename ../images/math/frac-square.png
1737 you can select different fraction types.
1740 \begin_layout Standard
1749 \begin_layout Plain Layout
1759 a fraction can be created that has in any case the size of a display style
1769 \begin_layout Plain Layout
1779 the fraction appears always with the size of an inline formula.
1783 \begin_layout Standard
1784 A line with the fraction
1785 \begin_inset Formula $\frac{1}{2}$
1788 that was created with the command
1797 \begin_layout Standard
1798 A line with the fraction
1799 \begin_inset Formula $\dfrac{1}{2}$
1802 that was created with the command
1811 \begin_layout Standard
1813 \begin_inset Tabular
1814 <lyxtabular version="3" rows="4" columns="2">
1816 <column alignment="center" valignment="top" width="0pt">
1817 <column alignment="center" valignment="top" width="0pt">
1819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1822 \begin_layout Plain Layout
1828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1831 \begin_layout Plain Layout
1833 \begin_inset Note Note
1836 \begin_layout Plain Layout
1843 is only used as spacer.
1855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1858 \begin_layout Plain Layout
1865 \begin_layout Plain Layout
1875 \begin_inset Formula $\downarrow$
1883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1886 \begin_layout Plain Layout
1887 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1900 \begin_layout Plain Layout
1907 \begin_layout Plain Layout
1917 \begin_inset Formula $\downarrow$
1925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1928 \begin_layout Plain Layout
1929 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1942 \begin_layout Plain Layout
1949 \begin_layout Plain Layout
1962 \begin_layout Plain Layout
1977 \begin_layout Plain Layout
1987 \begin_inset Formula $\downarrow$
1991 \begin_inset Formula $\downarrow\downarrow$
1999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2002 \begin_layout Plain Layout
2003 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2019 \begin_layout Standard
2020 \begin_inset VSpace bigskip
2024 \begin_inset Newpage newpage
2027 For nested fractions the command
2037 \begin_layout Plain Layout
2047 \begin_inset VSpace -3mm
2053 \begin_layout Standard
2054 \begin_inset Formula \begin{align*}
2055 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2056 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2063 \begin_layout Standard
2064 The command for the example above is:
2067 \begin_layout Standard
2073 \begin_inset Formula $\to$
2083 \begin_inset Formula $\to$
2089 \begin_inset Formula $\to\to$
2097 \begin_layout Standard
2098 \begin_inset VSpace medskip
2104 \begin_layout Standard
2111 sets the fraction always in the size of a displayed formula, also when
2112 it is part of another fraction.
2119 has the following command scheme:
2122 \begin_layout Standard
2127 cfrac[numerator position]{numerator}{denominator}
2130 \begin_layout Standard
2131 The numerator position can be
2144 l or r aligns the numerator to the left or right, resp.
2145 \begin_inset space ~
2148 with the fraction stroke.
2153 or no position is given, the numerator appears centered.
2154 These fractions demonstrate the different alignments:
2155 \begin_inset Newline newline
2161 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2165 \begin_inset Formula $\cfrac{A}{B+C}$
2169 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2175 \begin_layout Standard
2176 \begin_inset VSpace medskip
2179 It is often advantageous to combine
2192 \begin_inset Formula \[
2193 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2200 \begin_layout Standard
2201 For inline fractions with a sloped fraction stroke you can use the command
2212 \begin_layout Plain Layout
2221 \begin_inset Formula $\nicefrac{5}{31}$
2234 \begin_layout Plain Layout
2243 \begin_inset Formula $\unitfrac{5}{31}$
2246 There is furthermore the command
2252 that offers to write a fraction in combination with a number:
2253 \begin_inset Formula $\unitfrac[2]{1}{3}$
2257 \begin_inset Newline newline
2266 is not a real LaTeX command but the command
2267 \begin_inset Newline newline
2274 unitfrac[number]{numerator}{denominator}
2276 , therefore you cannot use it in TeX code.
2279 \begin_layout Standard
2280 How to define own fractions where the fraction stroke can be changed, is
2282 \begin_inset CommandInset ref
2284 reference "sub:Self-defined-Fractions"
2291 \begin_layout Subsection
2296 \begin_layout Plain Layout
2305 \begin_layout Standard
2306 Square roots are created with
2316 \begin_layout Plain Layout
2324 or the math toolbar button
2325 \begin_inset Graphics
2326 filename ../images/math/sqrt.png
2331 , all other roots with the command
2341 \begin_layout Plain Layout
2349 or with the math toolbar button
2350 \begin_inset Graphics
2351 filename ../images/math/root.png
2359 \begin_layout Standard
2361 \begin_inset Tabular
2362 <lyxtabular version="3" rows="3" columns="2">
2364 <column alignment="center" valignment="top" width="0pt">
2365 <column alignment="center" valignment="top" width="0pt">
2367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2370 \begin_layout Plain Layout
2376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2379 \begin_layout Plain Layout
2381 \begin_inset Note Note
2384 \begin_layout Plain Layout
2391 is only used as spacer.
2403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2406 \begin_layout Plain Layout
2413 \begin_layout Plain Layout
2427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2430 \begin_layout Plain Layout
2431 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2441 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2444 \begin_layout Plain Layout
2451 \begin_layout Plain Layout
2461 \begin_inset Formula $\downarrow$
2469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2472 \begin_layout Plain Layout
2473 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2489 \begin_layout Standard
2490 A square root can also be created with
2496 when the root index field is left empty.
2499 \begin_layout Standard
2500 With certain indices the distance to the root is too small, like in this
2502 \begin_inset Formula $\sqrt[\beta]{B}$
2506 \begin_inset Newline newline
2510 \begin_inset Formula $\beta$
2514 To avoid this, the commands
2524 \begin_layout Plain Layout
2542 \begin_layout Plain Layout
2550 are used with the following scheme:
2553 \begin_layout Standard
2567 \begin_layout Standard
2568 Distance is the number of Big Points (unit bp;
2569 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2572 ), that the index should be moved to the left or top, resp..
2573 The commands are written to the index.
2574 This way the command
2575 \begin_inset Newline newline
2585 \begin_inset Formula $\to$
2591 \begin_inset Formula $\to$
2600 \begin_layout Plain Layout
2610 \begin_inset Formula $\to$
2614 \begin_inset Newline newline
2619 produces a correct typeset formula:
2620 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2626 \begin_layout Subsection
2627 Binomial Coefficients
2631 \begin_layout Plain Layout
2632 Binomial coefficients
2640 \begin_layout Standard
2641 Binomial coefficients are inserted with the command
2651 \begin_layout Plain Layout
2659 or with the submenu of the math toolbar button
2660 \begin_inset Graphics
2661 filename ../images/math/frac-square.png
2667 Analog to fractions (
2687 \begin_layout Plain Layout
2707 \begin_layout Plain Layout
2716 For other brackets around binomial coeficients there are the commands
2726 \begin_layout Plain Layout
2744 \begin_layout Plain Layout
2755 \begin_layout Standard
2757 \begin_inset Tabular
2758 <lyxtabular version="3" rows="6" columns="2">
2760 <column alignment="center" valignment="top" width="0pt">
2761 <column alignment="center" valignment="top" width="0pt">
2763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2766 \begin_layout Plain Layout
2772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2775 \begin_layout Plain Layout
2777 \begin_inset Note Note
2780 \begin_layout Plain Layout
2787 is only used as spacer.
2799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2802 \begin_layout Plain Layout
2809 \begin_layout Plain Layout
2819 \begin_inset Formula $\downarrow$
2827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2830 \begin_layout Plain Layout
2831 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2844 \begin_layout Plain Layout
2851 \begin_layout Plain Layout
2861 \begin_inset Formula $\downarrow$
2869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2872 \begin_layout Plain Layout
2873 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2886 \begin_layout Plain Layout
2893 \begin_layout Plain Layout
2903 \begin_inset Formula $\downarrow$
2911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2914 \begin_layout Plain Layout
2915 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2928 \begin_layout Plain Layout
2935 \begin_layout Plain Layout
2945 \begin_inset Formula $\downarrow$
2953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2956 \begin_layout Plain Layout
2957 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2970 \begin_layout Plain Layout
2977 \begin_layout Plain Layout
2987 \begin_inset Formula $\downarrow$
2995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2998 \begin_layout Plain Layout
2999 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3015 \begin_layout Subsection
3016 Case Differentiations
3020 \begin_layout Plain Layout
3021 Case differentiations
3029 \begin_layout Standard
3031 \begin_inset Tabular
3032 <lyxtabular version="3" rows="3" columns="2">
3034 <column alignment="center" valignment="top" width="0pt">
3035 <column alignment="center" valignment="top" width="0pt">
3037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3040 \begin_layout Plain Layout
3046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3049 \begin_layout Plain Layout
3057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3060 \begin_layout Plain Layout
3067 \begin_layout Plain Layout
3077 \begin_inset Formula $\to$
3084 \begin_layout Plain Layout
3097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3100 \begin_layout Plain Layout
3101 \begin_inset Formula $\begin{cases}
3112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3115 \begin_layout Plain Layout
3122 \begin_layout Plain Layout
3136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3139 \begin_layout Plain Layout
3140 \begin_inset Formula $\begin{cases}
3141 A & \textrm{for }x>0\\
3142 B & \textrm{for }x=0\end{cases}$
3158 \begin_layout Standard
3165 or the usage of the math toolbar button
3166 \begin_inset Graphics
3167 filename ../images/math/cases.png
3172 you can create new lines with the shortcut
3176 or the table toolbar button
3177 \begin_inset Graphics
3178 filename ../images/tabular-feature_append-row.png
3186 \begin_layout Standard
3193 is also available via the menu
3195 Insert\SpecialChar \menuseparator
3196 Math\SpecialChar \menuseparator
3202 \begin_layout Subsection
3207 \begin_layout Plain Layout
3216 \begin_layout Standard
3227 \begin_layout Plain Layout
3235 every character can be displayed canceled.
3236 The characters are quasi accentuated by a slash.
3239 \begin_layout Standard
3241 \begin_inset Tabular
3242 <lyxtabular version="3" rows="4" columns="2">
3244 <column alignment="center" valignment="top" width="0pt">
3245 <column alignment="center" valignment="top" width="0pt">
3247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3250 \begin_layout Plain Layout
3256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3259 \begin_layout Plain Layout
3267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3270 \begin_layout Plain Layout
3278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3281 \begin_layout Plain Layout
3282 \begin_inset Formula $\not=$
3292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3295 \begin_layout Plain Layout
3305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3308 \begin_layout Plain Layout
3309 \begin_inset Formula $\not\le$
3319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3322 \begin_layout Plain Layout
3332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3335 \begin_layout Plain Layout
3336 \begin_inset Formula $\not\parallel$
3352 \begin_layout Standard
3353 The last example shows, that not all negations look good.
3354 Therefore there are for some negations special commands (see
3355 \begin_inset CommandInset ref
3357 reference "sub:Mathematical-Symbols"
3362 \begin_inset CommandInset ref
3364 reference "sec:Relations"
3371 \begin_layout Subsection
3373 \begin_inset CommandInset label
3375 name "sub:Placeholders"
3383 \begin_layout Plain Layout
3393 \begin_layout Plain Layout
3394 Chemical characters ! Isotopes
3403 \begin_layout Plain Layout
3408 \begin_layout Plain Layout
3419 \begin_layout Plain Layout
3434 \begin_layout Standard
3436 \begin_inset space \thinspace{}
3440 \begin_inset space ~
3447 \begin_layout Plain Layout
3448 More about chemical symbols is written in
3449 \begin_inset CommandInset ref
3451 reference "sub:Chemical-Symbols-and"
3460 the following problem occurs:
3463 \begin_layout Standard
3465 \begin_inset Tabular
3466 <lyxtabular version="3" rows="2" columns="2">
3468 <column alignment="center" valignment="top" width="0pt">
3469 <column alignment="center" valignment="top" width="0pt">
3471 <cell alignment="center" valignment="top" usebox="none">
3474 \begin_layout Plain Layout
3475 Indices created with sub- and superscripts:
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3484 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3494 <cell alignment="center" valignment="top" usebox="none">
3497 \begin_layout Plain Layout
3503 <cell alignment="center" valignment="top" usebox="none">
3506 \begin_layout Plain Layout
3507 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3521 \begin_inset Note Note
3524 \begin_layout Plain Layout
3531 is only used as spacer.
3539 \begin_layout Standard
3540 The shorter index is by default placed below or above the first character
3541 of the longer index.
3542 To avoid this there is the command
3552 \begin_layout Plain Layout
3560 or the math toolbar button
3561 \begin_inset space \thinspace{}
3568 \begin_layout Plain Layout
3569 can be found in the submenu of the toolbar button
3570 \begin_inset Graphics
3571 filename ../images/math/space.png
3582 \begin_inset Graphics
3583 filename ../images/math/phantom.png
3588 that creates one or more phantom characters.
3595 a small blue box appears that is superposed with two red arrows.
3596 The arrows indicate that the complete width and height of the box content
3597 will be created as placeholder.
3598 Phantom characters are accordingly placeholders with the size of the characters.
3601 \begin_layout Standard
3603 \begin_inset Tabular
3604 <lyxtabular version="3" rows="4" columns="2">
3606 <column alignment="center" valignment="top" width="0">
3607 <column alignment="center" valignment="top" width="0">
3609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3612 \begin_layout Plain Layout
3618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3621 \begin_layout Plain Layout
3623 \begin_inset Note Note
3626 \begin_layout Plain Layout
3633 is only used as spacer.
3645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3648 \begin_layout Plain Layout
3653 \begin_layout Plain Layout
3668 \begin_layout Plain Layout
3678 \begin_inset Formula $\to$
3685 \begin_layout Plain Layout
3699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3702 \begin_layout Plain Layout
3703 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3716 \begin_layout Plain Layout
3721 \begin_layout Plain Layout
3736 \begin_layout Plain Layout
3746 \begin_inset Formula $\to$
3753 \begin_layout Plain Layout
3767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3770 \begin_layout Plain Layout
3771 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3784 \begin_layout Plain Layout
3791 \begin_layout Plain Layout
3806 \begin_layout Plain Layout
3816 \begin_inset Formula $\to$
3823 \begin_layout Plain Layout
3837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3840 \begin_layout Plain Layout
3841 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3857 \begin_layout Standard
3858 Furthermore there are the commands
3868 \begin_layout Plain Layout
3877 \begin_inset space ~
3881 \begin_inset Graphics
3882 filename ../images/math/vphantom.png
3897 \begin_layout Plain Layout
3906 \begin_inset space ~
3910 \begin_inset Graphics
3911 filename ../images/math/hphantom.png
3923 creates only space for the maximal height of the characters in the box
3924 but not for its width.
3931 creates only space for the width of the box content.
3932 Therefore the boxes of both commands have only one red arrow.
3935 \begin_layout Standard
3946 \begin_layout Plain Layout
3961 space for the height of the integral sign,
3965 \begin_layout Plain Layout
3972 creates an integral sign, see
3973 \begin_inset CommandInset ref
3975 reference "sub:Big-Operators"
3984 because this is the larger character.
3985 An example application is in
3986 \begin_inset CommandInset ref
3988 reference "sub:Multiline-Brackets"
3995 \begin_layout Subsection
4000 \begin_layout Plain Layout
4010 \begin_layout Plain Layout
4011 Formula ! underlined
4019 \begin_layout Standard
4021 \begin_inset Tabular
4022 <lyxtabular version="3" rows="4" columns="2">
4024 <column alignment="center" valignment="top" width="0pt">
4025 <column alignment="center" valignment="top" width="0pt">
4027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4030 \begin_layout Plain Layout
4036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4039 \begin_layout Plain Layout
4041 \begin_inset Note Note
4044 \begin_layout Plain Layout
4051 is only used as spacer.
4063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4066 \begin_layout Plain Layout
4073 \begin_layout Plain Layout
4086 \begin_layout Plain Layout
4099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4102 \begin_layout Plain Layout
4103 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4116 \begin_layout Plain Layout
4123 \begin_layout Plain Layout
4136 \begin_layout Plain Layout
4149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4152 \begin_layout Plain Layout
4153 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4166 \begin_layout Plain Layout
4173 \begin_layout Plain Layout
4188 \begin_layout Plain Layout
4202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4205 \begin_layout Plain Layout
4206 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4222 \begin_layout Standard
4223 In the last example it doesn't matter if first
4238 \begin_layout Standard
4239 To double underline e.
4240 \begin_inset space \thinspace{}
4253 \begin_layout Standard
4254 It is possible to place up to 6 lines above or below characters.
4257 \begin_layout Standard
4258 \begin_inset VSpace bigskip
4261 Custom lines can be created using the command
4271 \begin_layout Plain Layout
4279 which has the following scheme:
4282 \begin_layout Standard
4287 rule[vertical offset]{length}{thickness}
4290 \begin_layout Standard
4291 The optional vertical offset shifts the line upwards (or downwards, when
4292 the value is negative).
4294 \begin_inset CommandInset ref
4296 reference "tab:Available-units"
4300 can be used for the values.
4301 Here are two example lines created with the commands
4302 \begin_inset Newline newline
4309 rule[-2ex]{3cm}{2pt}
4320 \begin_layout Standard
4322 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4328 \begin_layout Standard
4335 can also be used for text when it is inserted in TeX-mode.
4338 \begin_layout Subsection
4340 \begin_inset CommandInset label
4350 \begin_layout Plain Layout
4359 \begin_layout Standard
4360 There are different types of ellipses available.
4364 \begin_layout Plain Layout
4365 In the math toolbar in the submenu of the button
4366 \begin_inset Graphics
4367 filename ../images/math/ldots.png
4377 For listings dots at the baseline are used (
4387 \begin_layout Plain Layout
4395 ), while for operations dots are needed that are on the same height as the
4406 \begin_layout Plain Layout
4415 When using the command
4425 \begin_layout Plain Layout
4433 , LaTeX decides on the basis of the next character what type is used.
4436 \begin_layout Standard
4438 \begin_inset Tabular
4439 <lyxtabular version="3" rows="8" columns="2">
4441 <column alignment="center" valignment="top" width="0pt">
4442 <column alignment="center" valignment="top" width="0pt">
4444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4447 \begin_layout Plain Layout
4453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4456 \begin_layout Plain Layout
4464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4467 \begin_layout Plain Layout
4472 \begin_layout Plain Layout
4487 \begin_layout Plain Layout
4501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4504 \begin_layout Plain Layout
4505 \begin_inset Formula $A_{1},\dots,A_{n}$
4515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4518 \begin_layout Plain Layout
4523 \begin_layout Plain Layout
4538 \begin_layout Plain Layout
4552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4555 \begin_layout Plain Layout
4556 \begin_inset Formula $A_{1}+\dots+A_{n}$
4566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4569 \begin_layout Plain Layout
4574 \begin_layout Plain Layout
4589 \begin_layout Plain Layout
4603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4606 \begin_layout Plain Layout
4607 \begin_inset Formula $A_{1},\ldots,A_{n}$
4617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4620 \begin_layout Plain Layout
4625 \begin_layout Plain Layout
4640 \begin_layout Plain Layout
4654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4657 \begin_layout Plain Layout
4658 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4671 \begin_layout Plain Layout
4679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4682 \begin_layout Plain Layout
4683 \begin_inset Formula $\vdots$
4693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4696 \begin_layout Plain Layout
4704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4707 \begin_layout Plain Layout
4708 \begin_inset Formula $\ddots$
4718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4721 \begin_layout Plain Layout
4723 \begin_inset space \thinspace{}
4726 matrix with the different dots
4731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4734 \begin_layout Plain Layout
4735 \begin_inset Formula $\begin{array}{ccc}
4736 A_{11} & \cdots & A_{1m}\\
4737 \vdots & \ddots & \vdots\\
4738 A_{n1} & \cdots & A_{nm}\end{array}$
4754 \begin_layout Standard
4755 The ellipses available in menu
4757 Insert\SpecialChar \menuseparator
4759 \begin_inset space ~
4773 \begin_layout Standard
4774 \begin_inset VSpace medskip
4777 Specially for matrices there are ellipses that span over several columns.
4778 They are created with the command
4788 \begin_layout Plain Layout
4796 , that has the following scheme:
4799 \begin_layout Standard
4804 hdotsfor[distance]{number of columns}
4807 \begin_layout Standard
4808 The number of columns specifies how many columns should be spanned.
4809 Distance is a factor for the distance between the dots.
4812 \begin_layout Standard
4813 In the following matrix the command
4819 was inserted in the first box of the second line, to get an ellipsis with
4820 a dot distance twice as long as with the command
4827 \begin_inset Formula \[
4828 \left(\begin{array}{cccc}
4831 q & w & e & r\end{array}\right)\]
4835 Note that the matrix fields that should be spanned must be empty, otherwise
4836 you get LaTeX-errors.
4839 \begin_layout Standard
4840 \begin_inset VSpace bigskip
4843 Furthermore you can fill with the command
4853 \begin_layout Plain Layout
4861 the rest of a line with dots.
4862 The effect of these commands is the same like with
4869 \begin_inset CommandInset ref
4871 reference "sub:Variable-Space"
4878 \begin_layout Standard
4879 For example the command
4887 \begin_layout Plain Layout
4901 \begin_layout Standard
4902 \begin_inset Formula $A\dotfill B$
4908 \begin_layout Standard
4915 there is for a line the command
4925 \begin_layout Plain Layout
4936 \begin_layout Standard
4937 \begin_inset Formula $A\hrulefill B$
4943 \begin_layout Standard
4944 To use the commands for text, they have to be inserted in TeX-mode.
4947 \begin_layout Section
4949 \begin_inset CommandInset label
4959 \begin_layout Plain Layout
4968 \begin_layout Standard
4969 Matrices can be inserted via the math toolbar button
4970 \begin_inset Graphics
4971 filename ../images/dialog-show_mathmatrix.png
4978 Insert\SpecialChar \menuseparator
4979 Math\SpecialChar \menuseparator
4983 You will be asked for the number of matrix columns and rows, and the alignment.
4984 The vertical alignment is hereby only of importance for matrices in inline
4988 \begin_layout Standard
4989 The first matrix is top
4990 \begin_inset Formula $\begin{array}[t]{cccc}
4993 C & F & I & L\end{array}$
4997 \begin_inset Formula $\begin{array}{cccc}
5000 C & F & I & L\end{array}$
5003 , and the third bottom
5004 \begin_inset Formula $\begin{array}[b]{cccc}
5007 C & F & I & L\end{array}$
5013 \begin_layout Standard
5014 The horizontal alignment specifies how the column entries should be aligned.
5015 It is set by entering a letter for every column.
5020 denotes left aligned,
5029 To create for example a 4
5034 \begin_inset space ~
5037 matrix where the first column is left aligned, the second and third are
5038 centered, and the last one is right aligned, one enters for the horizontal
5044 Normally are in a matrix all columns centered, therefore the default is
5045 for every column is a
5052 \begin_layout Standard
5053 Horizontal alignment:
5056 \begin_layout Standard
5062 \begin_inset Formula $\begin{array}{lll}
5065 C & F & 10000\end{array}$
5073 \begin_inset Formula $\begin{array}{ccc}
5076 C & F & 10000\end{array}$
5084 \begin_inset Formula $\begin{array}{rrr}
5087 C & F & 10000\end{array}$
5093 \begin_layout Standard
5094 To add or delete rows and columns subsequently, the math toolbar buttons
5096 \begin_inset Graphics
5097 filename ../images/tabular-feature_append-row.png
5103 \begin_inset Graphics
5104 filename ../images/tabular-feature_delete-row.png
5110 \begin_inset space \thinspace{}
5115 Edit\SpecialChar \menuseparator
5119 New rows can also be created with
5126 \begin_layout Standard
5127 \begin_inset VSpace bigskip
5130 Parentheses around a matrix can can either be created with the commands
5141 \begin_layout Plain Layout
5159 \begin_layout Plain Layout
5170 \begin_inset space ~
5176 \begin_inset CommandInset ref
5178 reference "sub:Automatic-Bracket-Size"
5182 , or by using the following commands:
5183 \begin_inset VSpace medskip
5189 \begin_layout Standard
5190 \begin_inset space \hfill{}
5194 \begin_inset Tabular
5195 <lyxtabular version="3" rows="4" columns="2">
5197 <column alignment="center" valignment="top" width="0">
5198 <column alignment="center" valignment="top" width="0">
5200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5203 \begin_layout Plain Layout
5209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5212 \begin_layout Plain Layout
5214 \begin_inset Note Note
5217 \begin_layout Plain Layout
5224 is only used as spacer.
5236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5239 \begin_layout Plain Layout
5246 \begin_layout Plain Layout
5260 \begin_inset space \thinspace{}
5268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5271 \begin_layout Plain Layout
5272 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5273 0 & \textrm{-}\mathrm{i}\\
5274 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5287 \begin_layout Plain Layout
5294 \begin_layout Plain Layout
5308 \begin_inset space \thinspace{}
5316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5319 \begin_layout Plain Layout
5320 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5321 0 & \textrm{-}\mathrm{i}\\
5322 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5335 \begin_layout Plain Layout
5342 \begin_layout Plain Layout
5356 \begin_inset space \thinspace{}
5364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5367 \begin_layout Plain Layout
5368 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5369 0 & \textrm{-}\mathrm{i}\\
5370 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5384 \begin_inset space \hfill{}
5388 \begin_inset Tabular
5389 <lyxtabular version="3" rows="4" columns="2">
5391 <column alignment="center" valignment="top" width="0">
5392 <column alignment="center" valignment="top" width="0">
5394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5397 \begin_layout Plain Layout
5403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5406 \begin_layout Plain Layout
5414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5417 \begin_layout Plain Layout
5424 \begin_layout Plain Layout
5438 \begin_inset space \thinspace{}
5446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5449 \begin_layout Plain Layout
5450 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5451 0 & \textrm{-}\mathrm{i}\\
5452 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5465 \begin_layout Plain Layout
5472 \begin_layout Plain Layout
5486 \begin_inset space \thinspace{}
5494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5497 \begin_layout Plain Layout
5498 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5499 0 & \textrm{-}\mathrm{i}\\
5500 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5513 \begin_layout Plain Layout
5520 \begin_layout Plain Layout
5534 \begin_inset space \thinspace{}
5542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5545 \begin_layout Plain Layout
5546 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5547 0 & \textrm{-}\mathrm{i}\\
5548 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5562 \begin_inset space \hfill{}
5568 \begin_layout Standard
5569 \begin_inset VSpace medskip
5573 \begin_inset space \thinspace{}
5577 \begin_inset space ~
5586 is inserted, a blue box appears between two vertical lines where the matrix
5590 \begin_layout Standard
5591 \begin_inset VSpace bigskip
5594 As all multiline formulas are matrices, the length
5604 \begin_layout Plain Layout
5612 that is described in
5613 \begin_inset CommandInset ref
5615 reference "sub:Column-Separation"
5619 can also be used to change the column separation of matrices.
5622 \begin_layout Standard
5623 To change the row separation, the command
5633 \begin_layout Plain Layout
5642 It is used as follows:
5645 \begin_layout Standard
5652 arraystretch}{stretch factor}
5656 \begin_layout Plain Layout
5667 \begin_layout Standard
5674 assigns the stretch factor to the predefined command
5682 \begin_inset space \thinspace{}
5686 \begin_inset space ~
5689 the row separation, use the factor 2.
5690 This is then used for all following matrices.
5691 To go back to the original separation, assign the factor 1 to
5700 \begin_layout Standard
5701 To set matrices into a text line, the command
5711 \begin_layout Plain Layout
5720 When it is inserted a blue box with two dashed lines appears.
5721 In this box the matrix is inserted.
5724 \begin_layout Standard
5726 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5727 C & D\end{smallmatrix}\right)$
5733 \begin_layout Section
5734 Brackets and Delimiters
5738 \begin_layout Plain Layout
5748 \begin_layout Plain Layout
5757 \begin_layout Subsection
5758 Vertical Brackets and Delimiters
5762 \begin_layout Plain Layout
5771 \begin_layout Standard
5772 \begin_inset space \hfill{}
5776 \begin_inset Tabular
5777 <lyxtabular version="3" rows="9" columns="2">
5779 <column alignment="center" valignment="top" width="0pt">
5780 <column alignment="center" valignment="top" width="0pt">
5782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5785 \begin_layout Plain Layout
5791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5794 \begin_layout Plain Layout
5802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5805 \begin_layout Plain Layout
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5814 \begin_layout Plain Layout
5815 \begin_inset Formula $($
5825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5828 \begin_layout Plain Layout
5834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5837 \begin_layout Plain Layout
5838 \begin_inset Formula $\{$
5848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5851 \begin_layout Plain Layout
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5860 \begin_layout Plain Layout
5861 \begin_inset Formula $[$
5871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5874 \begin_layout Plain Layout
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5885 \begin_layout Plain Layout
5886 \begin_inset Formula $\langle$
5896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5899 \begin_layout Plain Layout
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5910 \begin_layout Plain Layout
5911 \begin_inset Formula $\lceil$
5921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5924 \begin_layout Plain Layout
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5935 \begin_layout Plain Layout
5936 \begin_inset Formula $\lfloor$
5946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5949 \begin_layout Plain Layout
5955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5958 \begin_layout Plain Layout
5959 \begin_inset Formula $/$
5969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5972 \begin_layout Plain Layout
5978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5981 \begin_layout Plain Layout
5982 \begin_inset Formula $|$
5996 \begin_inset space \hfill{}
6000 \begin_inset Tabular
6001 <lyxtabular version="3" rows="9" columns="2">
6003 <column alignment="center" valignment="top" width="0pt">
6004 <column alignment="center" valignment="top" width="0pt">
6006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6009 \begin_layout Plain Layout
6015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6018 \begin_layout Plain Layout
6026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6029 \begin_layout Plain Layout
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6038 \begin_layout Plain Layout
6039 \begin_inset Formula $)$
6049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6052 \begin_layout Plain Layout
6058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6061 \begin_layout Plain Layout
6062 \begin_inset Formula $\}$
6072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6075 \begin_layout Plain Layout
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6084 \begin_layout Plain Layout
6085 \begin_inset Formula $]$
6095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6098 \begin_layout Plain Layout
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6109 \begin_layout Plain Layout
6110 \begin_inset Formula $\rangle$
6120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6123 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $\rceil$
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6159 \begin_layout Plain Layout
6160 \begin_inset Formula $\rfloor$
6170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6173 \begin_layout Plain Layout
6183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6186 \begin_layout Plain Layout
6187 \begin_inset Formula $\backslash$
6197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6200 \begin_layout Plain Layout
6208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6211 \begin_layout Plain Layout
6212 \begin_inset Formula $\|$
6226 \begin_inset space \hfill{}
6232 \begin_layout Standard
6235 \begin_inset Note Greyedout
6238 \begin_layout Plain Layout
6243 In TeX-mode the command
6253 \begin_layout Plain Layout
6261 must be used for the backslash, because the command
6269 produces there a line break.
6277 \begin_layout Standard
6278 For all characters listed above the size can be adjusted with the commands
6279 described in the following two subsections.
6280 When using these commands, the characters < and > can directly be used
6281 instead of the commands
6296 \begin_layout Subsubsection
6298 \begin_inset CommandInset label
6300 name "sub:Manual-Bracket-Size"
6308 \begin_layout Plain Layout
6309 Bracket size ! manual
6317 \begin_layout Standard
6318 The bracket size can be specified manually by the LaTeX-commands
6328 \begin_layout Plain Layout
6361 denotes the smallest and
6367 the largest bracket size.
6370 \begin_layout Standard
6371 These commands are used to emphasize levels of brackets:
6374 \begin_layout Standard
6376 \begin_inset Tabular
6377 <lyxtabular version="3" rows="2" columns="2">
6379 <column alignment="center" valignment="top" width="0pt">
6380 <column alignment="center" valignment="top" width="0pt">
6382 <cell alignment="center" valignment="top" usebox="none">
6385 \begin_layout Plain Layout
6386 all brackets in the same size:
6391 <cell alignment="center" valignment="top" usebox="none">
6394 \begin_layout Plain Layout
6395 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6405 <cell alignment="center" valignment="top" usebox="none">
6408 \begin_layout Plain Layout
6414 <cell alignment="center" valignment="top" usebox="none">
6417 \begin_layout Plain Layout
6418 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6432 \begin_inset Note Note
6435 \begin_layout Plain Layout
6442 is only used as spacer.
6450 \begin_layout Standard
6451 For the second formula the command
6461 \begin_layout Plain Layout
6475 \begin_layout Standard
6476 Here is an overview about all bracket sizes:
6479 \begin_layout Standard
6499 \begin_layout Plain Layout
6516 \begin_layout Plain Layout
6529 \begin_layout Plain Layout
6545 \begin_layout Standard
6547 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6553 \begin_layout Standard
6560 -commands there is the variant
6570 \begin_layout Plain Layout
6578 that adds a bit more space between the bracket and its content, and the
6595 \begin_layout Plain Layout
6605 , that don't add additional space.
6610 at the end of the command
6616 is for a left bracket; for a right bracket this will be replaced by an
6622 A left or right bracket can each be an opening or closing bracket.
6625 \begin_layout Standard
6626 In the following table is a comparison of the variants:
6629 \begin_layout Standard
6631 \begin_inset Tabular
6632 <lyxtabular version="3" rows="5" columns="2">
6634 <column alignment="center" valignment="middle" width="0">
6635 <column alignment="center" valignment="middle" width="0">
6637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6640 \begin_layout Plain Layout
6646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6649 \begin_layout Plain Layout
6651 \begin_inset Note Note
6654 \begin_layout Plain Layout
6661 is only used as spacer.
6673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6676 \begin_layout Plain Layout
6691 \begin_layout Plain Layout
6709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6712 \begin_layout Plain Layout
6713 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6726 \begin_layout Plain Layout
6741 \begin_layout Plain Layout
6759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6762 \begin_layout Plain Layout
6763 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6776 \begin_layout Plain Layout
6791 \begin_layout Plain Layout
6809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6812 \begin_layout Plain Layout
6813 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6826 \begin_layout Plain Layout
6838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6841 \begin_layout Plain Layout
6842 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6858 \begin_layout Subsubsection
6859 Automatic Bracket Size
6860 \begin_inset CommandInset label
6862 name "sub:Automatic-Bracket-Size"
6870 \begin_layout Plain Layout
6871 Bracket size ! automatic
6879 \begin_layout Standard
6880 Brackets with variable size can be inserted with the commands
6890 \begin_layout Plain Layout
6908 \begin_layout Plain Layout
6916 or via the math toolbar button
6917 \begin_inset Graphics
6918 filename ../images/dialog-show_mathdelimiter.png
6936 the wanted bracket must be inserted.
6937 The bracket size will then automatically be calculated for the output.
6940 \begin_layout Standard
6942 normal bracket: The command
6952 \begin_layout Plain Layout
6962 \begin_inset Formula $\downarrow$
6969 \begin_layout Plain Layout
6981 \begin_inset Formula \[
6989 \begin_layout Standard
6991 multiline bracket: The command
7003 \begin_layout Plain Layout
7013 \begin_inset Formula $\downarrow$
7020 \begin_layout Plain Layout
7034 \begin_inset Formula \[
7035 \ln\left(\frac{A}{C}\right)\]
7042 \begin_layout Standard
7058 \begin_inset space ~
7064 This has the advantage that you can see in LyX immediately the real bracket
7065 size and that the matching right bracket will be created too.
7066 \begin_inset Newline newline
7069 The command for the last example would then be:
7083 \begin_layout Plain Layout
7093 \begin_inset Formula $\downarrow$
7099 \begin_layout Standard
7100 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7101 For example the command
7111 \begin_layout Plain Layout
7121 \begin_inset Formula $\downarrow$
7128 \begin_layout Plain Layout
7144 \begin_inset Formula \[
7145 \left.\frac{A}{B}\right\} \]
7163 will be converted by LyX to brackets in the right size when the document
7164 is reloaded and an omitted bracket will appear as dashed line.
7167 \begin_layout Standard
7168 \begin_inset VSpace bigskip
7171 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7182 \begin_layout Plain Layout
7190 is additionally available for all brackets and limits.
7191 With this command the height of the following character is adapted to the
7192 one of the surrounding brackets, what is e.
7193 \begin_inset space \thinspace{}
7197 \begin_inset space ~
7200 needed for physical vectors:
7201 \begin_inset Formula \[
7202 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7206 For physical vectors there is a special LaTeX-package, described in
7207 \begin_inset CommandInset ref
7209 reference "sub:Physical-Vectors"
7216 \begin_layout Subsection
7221 \begin_layout Plain Layout
7222 Brackets ! horizontal
7230 \begin_layout Standard
7232 \begin_inset Tabular
7233 <lyxtabular version="3" rows="4" columns="2">
7235 <column alignment="center" valignment="top" width="0pt">
7236 <column alignment="center" valignment="top" width="0pt">
7238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7241 \begin_layout Plain Layout
7243 \begin_inset Note Note
7246 \begin_layout Plain Layout
7253 is only used as spacer.
7263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7266 \begin_layout Plain Layout
7274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7277 \begin_layout Plain Layout
7281 \begin_layout Plain Layout
7296 \begin_layout Plain Layout
7309 \begin_layout Plain Layout
7322 \begin_layout Plain Layout
7335 \begin_layout Plain Layout
7346 \begin_layout Plain Layout
7359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7362 \begin_layout Plain Layout
7363 \begin_inset Formula $\overbrace{A+B}^{3}$
7373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7376 \begin_layout Plain Layout
7380 \begin_layout Plain Layout
7395 \begin_layout Plain Layout
7408 \begin_layout Plain Layout
7421 \begin_layout Plain Layout
7432 \begin_layout Plain Layout
7445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7448 \begin_layout Plain Layout
7449 \begin_inset Formula $\underbrace{A+B}_{5}$
7459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7462 \begin_layout Plain Layout
7469 \begin_layout Plain Layout
7484 \begin_layout Plain Layout
7497 \begin_layout Plain Layout
7510 \begin_layout Plain Layout
7523 \begin_layout Plain Layout
7536 \begin_layout Plain Layout
7549 \begin_layout Plain Layout
7563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7566 \begin_layout Plain Layout
7567 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7583 \begin_layout Standard
7584 In the last example it doesn't matter if
7596 is inserted at first.
7599 \begin_layout Standard
7600 \begin_inset VSpace bigskip
7603 When brackets are needed that overlap each other, multiline formulas, as
7605 \begin_inset CommandInset ref
7607 reference "sec:Multiline-Formulas"
7612 \begin_inset Formula \begin{eqnarray*}
7613 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7614 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7618 In the first row the formula is inserted together with the first brace.
7619 It is hereby important that the space command
7623 \begin_layout Plain Layout
7624 Space commands are explained in
7625 \begin_inset CommandInset ref
7627 reference "sub:Predefined-Space"
7642 is inserted before the first
7643 \begin_inset Formula $d$
7646 , because the brace that ends behind the
7647 \begin_inset Formula $q$
7650 prevents that the following
7651 \begin_inset Quotes eld
7655 \begin_inset Quotes erd
7658 is surrounded by space.
7662 \begin_layout Plain Layout
7663 because a bracket is not handled as character, see
7664 \begin_inset CommandInset ref
7666 reference "sub:Binary-Operators"
7675 In the second row the second brace is inserted.
7676 As it should begin before the
7677 \begin_inset Formula $b$
7692 \begin_layout Plain Layout
7700 \begin_inset CommandInset ref
7702 reference "sub:Placeholders"
7711 This space is needed because the
7712 \begin_inset Quotes eld
7716 \begin_inset Quotes erd
7719 is also surrounded by space in the formula.
7720 The brace is placed under the command
7729 \begin_layout Standard
7730 It gets more complicated when brackets overlap each other, like in the following
7735 \begin_layout Plain Layout
7747 \begin_inset Formula \begin{eqnarray*}
7748 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7749 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7757 \begin_layout Plain Layout
7768 The first formula row is the same as the second row of the previous example,
7769 with the difference that the brace is above.
7770 The second row contains the formula together with the second brace.
7771 To avoid that there is space between the upper brace in the first row and
7772 the formula, the row spacing need to be reduced.
7773 This is not easily possible due to a bug in LyX
7777 \begin_layout Plain Layout
7778 \begin_inset CommandInset href
7780 name "LyX-bug #1505"
7781 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7791 As solution for the problem, the global formula row separation
7801 \begin_layout Plain Layout
7809 must be changed to -6
7810 \begin_inset space \thinspace{}
7813 pt before the formula with the command
7828 is set back after the formula to the standard value of 3
7829 \begin_inset space \thinspace{}
7832 pt using the same command.
7833 More about the row separation in formulas is explained in
7834 \begin_inset CommandInset ref
7836 reference "sub:Line-Separation"
7843 \begin_layout Section
7848 \begin_layout Plain Layout
7857 \begin_layout Standard
7858 Arrows can be inserted via the math toolbar button
7859 \begin_inset Graphics
7860 filename ../images/math/leftarrow.png
7865 or the commands listed in the following subsections.
7868 \begin_layout Standard
7869 \begin_inset Newpage newpage
7875 \begin_layout Subsection
7880 \begin_layout Plain Layout
7889 \begin_layout Standard
7890 \begin_inset space \hfill{}
7894 \begin_inset Tabular
7895 <lyxtabular version="3" rows="8" columns="2">
7897 <column alignment="center" valignment="top" width="0pt">
7898 <column alignment="center" valignment="top" width="0pt">
7900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7903 \begin_layout Plain Layout
7909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7912 \begin_layout Plain Layout
7920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7923 \begin_layout Plain Layout
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7934 \begin_layout Plain Layout
7935 \begin_inset Formula $\gets$
7945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7948 \begin_layout Plain Layout
7956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7959 \begin_layout Plain Layout
7960 \begin_inset Formula $\Leftarrow$
7970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7984 \begin_layout Plain Layout
7985 \begin_inset Formula $\longleftarrow$
7995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7998 \begin_layout Plain Layout
8006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8009 \begin_layout Plain Layout
8010 \begin_inset Formula $\Longleftarrow$
8020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8023 \begin_layout Plain Layout
8031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8034 \begin_layout Plain Layout
8035 \begin_inset Formula $\leftharpoonup$
8045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8048 \begin_layout Plain Layout
8056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8059 \begin_layout Plain Layout
8060 \begin_inset Formula $\leftharpoondown$
8070 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8073 \begin_layout Plain Layout
8081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8084 \begin_layout Plain Layout
8085 \begin_inset Formula $\hookleftarrow$
8099 \begin_inset space \hfill{}
8103 \begin_inset Tabular
8104 <lyxtabular version="3" rows="8" columns="2">
8106 <column alignment="center" valignment="top" width="0pt">
8107 <column alignment="center" valignment="top" width="0pt">
8109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8112 \begin_layout Plain Layout
8118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8121 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8132 \begin_layout Plain Layout
8140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8143 \begin_layout Plain Layout
8144 \begin_inset Formula $\to$
8154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8168 \begin_layout Plain Layout
8169 \begin_inset Formula $\Rightarrow$
8179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8182 \begin_layout Plain Layout
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8193 \begin_layout Plain Layout
8194 \begin_inset Formula $\longrightarrow$
8204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\Longrightarrow$
8229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8244 \begin_inset Formula $\rightharpoonup$
8254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8257 \begin_layout Plain Layout
8265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8268 \begin_layout Plain Layout
8269 \begin_inset Formula $\rightharpoondown$
8279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8293 \begin_layout Plain Layout
8294 \begin_inset Formula $\hookrightarrow$
8308 \begin_inset space \hfill{}
8314 \begin_layout Standard
8315 \begin_inset space \hfill{}
8319 \begin_inset Tabular
8320 <lyxtabular version="3" rows="6" columns="2">
8322 <column alignment="center" valignment="top" width="0pt">
8323 <column alignment="center" valignment="top" width="0pt">
8325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8328 \begin_layout Plain Layout
8334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8337 \begin_layout Plain Layout
8345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8348 \begin_layout Plain Layout
8356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8359 \begin_layout Plain Layout
8360 \begin_inset Formula $\leftrightarrow$
8370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8373 \begin_layout Plain Layout
8381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8384 \begin_layout Plain Layout
8385 \begin_inset Formula $\Leftrightarrow$
8395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8398 \begin_layout Plain Layout
8406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8409 \begin_layout Plain Layout
8410 \begin_inset Formula $\longleftrightarrow$
8420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8423 \begin_layout Plain Layout
8431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8434 \begin_layout Plain Layout
8435 \begin_inset Formula $\Longleftrightarrow$
8445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8448 \begin_layout Plain Layout
8456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8459 \begin_layout Plain Layout
8460 \begin_inset Formula $\rightleftharpoons$
8474 \begin_inset space \hspace{}
8479 \begin_inset space \hfill{}
8483 \begin_inset Tabular
8484 <lyxtabular version="3" rows="5" columns="2">
8486 <column alignment="center" valignment="top" width="0pt">
8487 <column alignment="center" valignment="top" width="0pt">
8489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8492 \begin_layout Plain Layout
8498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8501 \begin_layout Plain Layout
8509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8512 \begin_layout Plain Layout
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $\mapsto$
8534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8537 \begin_layout Plain Layout
8545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Plain Layout
8549 \begin_inset Formula $\longmapsto$
8559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8573 \begin_layout Plain Layout
8574 \begin_inset Formula $\leadsto$
8584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8587 \begin_layout Plain Layout
8595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8598 \begin_layout Plain Layout
8599 \begin_inset Formula $\dasharrow$
8613 \begin_inset space \hfill{}
8619 \begin_layout Standard
8620 \begin_inset VSpace medskip
8623 Arrows used as accent like e.
8624 \begin_inset space \thinspace{}
8628 \begin_inset space ~
8631 vector arrows are listed in
8632 \begin_inset CommandInset ref
8634 reference "sec:Accents"
8641 \begin_layout Standard
8642 \begin_inset VSpace bigskip
8645 Furthermore there are the labeled arrows
8649 \begin_layout Plain Layout
8665 \begin_layout Plain Layout
8683 \begin_layout Plain Layout
8690 \begin_layout Plain Layout
8705 When inserting one of these commands in a formula, an arrow with two blue
8706 boxes appear where the label can be inserted.
8707 The length of the arrow adapts to the label width.
8710 \begin_layout Standard
8712 \begin_inset Tabular
8713 <lyxtabular version="3" rows="3" columns="2">
8715 <column alignment="center" valignment="top" width="0pt">
8716 <column alignment="center" valignment="top" width="0pt">
8718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8721 \begin_layout Plain Layout
8727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8730 \begin_layout Plain Layout
8732 \begin_inset Note Note
8735 \begin_layout Plain Layout
8742 is only used as spacer.
8754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8757 \begin_layout Plain Layout
8764 \begin_layout Plain Layout
8774 \begin_inset Formula $\downarrow$
8778 \begin_inset Formula $\to$
8786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8789 \begin_layout Plain Layout
8790 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8803 \begin_layout Plain Layout
8810 \begin_layout Plain Layout
8820 \begin_inset Formula $\downarrow$
8824 \begin_inset Formula $\to$
8832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8835 \begin_layout Plain Layout
8836 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8852 \begin_layout Subsection
8853 Vertical and diagonal Arrows
8857 \begin_layout Plain Layout
8867 \begin_layout Plain Layout
8876 \begin_layout Standard
8877 \begin_inset space \hfill{}
8881 \begin_inset Tabular
8882 <lyxtabular version="3" rows="7" columns="2">
8884 <column alignment="center" valignment="top" width="0pt">
8885 <column alignment="center" valignment="top" width="0pt">
8887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8890 \begin_layout Plain Layout
8896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8899 \begin_layout Plain Layout
8907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8910 \begin_layout Plain Layout
8918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8921 \begin_layout Plain Layout
8922 \begin_inset Formula $\uparrow$
8932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8935 \begin_layout Plain Layout
8943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8946 \begin_layout Plain Layout
8947 \begin_inset Formula $\Uparrow$
8957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8960 \begin_layout Plain Layout
8968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8971 \begin_layout Plain Layout
8972 \begin_inset Formula $\updownarrow$
8982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8985 \begin_layout Plain Layout
8993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8996 \begin_layout Plain Layout
8997 \begin_inset Formula $\Updownarrow$
9007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9010 \begin_layout Plain Layout
9018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9021 \begin_layout Plain Layout
9022 \begin_inset Formula $\Downarrow$
9032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9035 \begin_layout Plain Layout
9043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9046 \begin_layout Plain Layout
9047 \begin_inset Formula $\downarrow$
9061 \begin_inset space \hfill{}
9065 \begin_inset Tabular
9066 <lyxtabular version="3" rows="5" columns="2">
9068 <column alignment="center" valignment="top" width="0pt">
9069 <column alignment="center" valignment="top" width="0pt">
9071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9074 \begin_layout Plain Layout
9080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9083 \begin_layout Plain Layout
9091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9094 \begin_layout Plain Layout
9102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9105 \begin_layout Plain Layout
9106 \begin_inset Formula $\nearrow$
9116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9119 \begin_layout Plain Layout
9127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9130 \begin_layout Plain Layout
9131 \begin_inset Formula $\searrow$
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9155 \begin_layout Plain Layout
9156 \begin_inset Formula $\swarrow$
9166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9169 \begin_layout Plain Layout
9177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9180 \begin_layout Plain Layout
9181 \begin_inset Formula $\nwarrow$
9195 \begin_inset space \hfill{}
9201 \begin_layout Standard
9202 \begin_inset VSpace medskip
9205 Vertical arrows can be used also as delimiter together with the commands
9207 \begin_inset CommandInset ref
9209 reference "sub:Manual-Bracket-Size"
9214 \begin_inset CommandInset ref
9216 reference "sub:Automatic-Bracket-Size"
9223 \begin_layout Standard
9224 \begin_inset Newpage newpage
9230 \begin_layout Section
9232 \begin_inset CommandInset label
9242 \begin_layout Plain Layout
9251 \begin_layout Standard
9252 Accents can be inserted via the math toolbar button
9253 \begin_inset Graphics
9254 filename ../images/math/hat.png
9259 or the commands listed in the following subsections.
9262 \begin_layout Subsection
9263 Accents for one Character
9267 \begin_layout Plain Layout
9280 \begin_layout Plain Layout
9282 \begin_inset CommandInset ref
9284 reference "sub:Accents-in-Text"
9297 \begin_layout Plain Layout
9305 \begin_inset Note Note
9308 \begin_layout Plain Layout
9311 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9314 \begin_layout Plain Layout
9317 texorpdfstring is in section
9318 \begin_inset CommandInset ref
9320 reference "sub:Formulas-in-Section"
9330 \begin_inset CommandInset label
9332 name "sub:Accents-for-one"
9340 \begin_layout Plain Layout
9341 Accents ! for one character
9349 \begin_layout Standard
9350 \begin_inset space \hfill{}
9354 \begin_inset Tabular
9355 <lyxtabular version="3" rows="8" columns="2">
9357 <column alignment="center" valignment="top" width="0pt">
9358 <column alignment="center" valignment="top" width="0pt">
9360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9363 \begin_layout Plain Layout
9369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9372 \begin_layout Plain Layout
9374 \begin_inset Note Note
9377 \begin_layout Plain Layout
9384 is only used as spacer.
9396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9399 \begin_layout Plain Layout
9406 \begin_layout Plain Layout
9420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9423 \begin_layout Plain Layout
9424 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9437 \begin_layout Plain Layout
9444 \begin_layout Plain Layout
9458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9461 \begin_layout Plain Layout
9462 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9475 \begin_layout Plain Layout
9482 \begin_layout Plain Layout
9496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9499 \begin_layout Plain Layout
9500 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9513 \begin_layout Plain Layout
9521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9524 \begin_layout Plain Layout
9525 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9538 \begin_layout Plain Layout
9545 \begin_layout Plain Layout
9558 \begin_layout Plain Layout
9569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9572 \begin_layout Plain Layout
9573 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9586 \begin_layout Plain Layout
9593 \begin_layout Plain Layout
9607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9610 \begin_layout Plain Layout
9611 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9624 \begin_layout Plain Layout
9631 \begin_layout Plain Layout
9645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9648 \begin_layout Plain Layout
9649 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9663 \begin_inset space \hfill{}
9667 \begin_inset Tabular
9668 <lyxtabular version="3" rows="7" columns="2">
9670 <column alignment="center" valignment="top" width="0pt">
9671 <column alignment="center" valignment="top" width="0pt">
9673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9676 \begin_layout Plain Layout
9682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9685 \begin_layout Plain Layout
9693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9696 \begin_layout Plain Layout
9703 \begin_layout Plain Layout
9717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9720 \begin_layout Plain Layout
9721 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9734 \begin_layout Plain Layout
9741 \begin_layout Plain Layout
9755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9758 \begin_layout Plain Layout
9759 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9772 \begin_layout Plain Layout
9779 \begin_layout Plain Layout
9793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9796 \begin_layout Plain Layout
9797 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9810 \begin_layout Plain Layout
9817 \begin_layout Plain Layout
9831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9834 \begin_layout Plain Layout
9835 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9848 \begin_layout Plain Layout
9855 \begin_layout Plain Layout
9869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9872 \begin_layout Plain Layout
9873 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9886 \begin_layout Plain Layout
9893 \begin_layout Plain Layout
9907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9910 \begin_layout Plain Layout
9911 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9925 \begin_inset space \hfill{}
9931 \begin_layout Standard
9932 \begin_inset VSpace bigskip
9939 \begin_layout Plain Layout
9945 in formulas, a quotation mark is inserted before the vowel.
9946 These two characters are then treated by LaTeX as
9950 character when the formula part with the umlaut is marked as German.
9958 \begin_inset Quotes eld
9962 \begin_inset Quotes erd
9965 umlauts are created as demonstrated in the following example:
9968 \begin_layout Standard
9969 \begin_inset VSpace -2mm
9975 \begin_layout Standard
9977 \begin_inset Tabular
9978 <lyxtabular version="3" rows="3" columns="2">
9980 <column alignment="center" valignment="top" width="0">
9981 <column alignment="center" valignment="top" width="0">
9983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9986 \begin_layout Plain Layout
9992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9995 \begin_layout Plain Layout
9997 \begin_inset Note Note
10000 \begin_layout Plain Layout
10008 \begin_inset space \thinspace{}
10011 pt space are only used as spacer.
10023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10026 \begin_layout Plain Layout
10029 \begin_inset Quotes grd
10037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10040 \begin_layout Plain Layout
10041 \begin_inset space \hspace{}
10048 \begin_inset Formula $"i$
10058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10061 \begin_layout Plain Layout
10068 \begin_layout Plain Layout
10082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10085 \begin_layout Plain Layout
10086 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10102 \begin_layout Standard
10103 Another advantage to
10109 is that umlauts can directly be converted to mathematical text because
10110 the accent commands above are
10116 in mathematical text
10119 To convert an accented character to mathematical text, only the character
10120 under the accent may be converted.
10121 This applies also for all other conversions, e.
10122 \begin_inset space \thinspace{}
10126 \begin_inset space ~
10132 \begin_layout Standard
10133 In mathematical text, umlauts and other accented characters can directly
10137 \begin_layout Subsection
10138 Accents for Operators
10142 \begin_layout Plain Layout
10143 Accents ! for operators
10151 \begin_layout Standard
10162 \begin_layout Plain Layout
10180 \begin_layout Plain Layout
10188 characters can be placed above or below an operator, respectively, to accent
10200 \begin_layout Plain Layout
10208 characters can be set before and behind an operator.
10209 The command scheme is:
10212 \begin_layout Standard
10228 \begin_layout Standard
10235 must always be before the operator that should be accented.
10236 You can accent with several characters and even with other operators and
10244 for example only characters behind an operator, write nothing between the
10245 first braces but don't omit the braces.
10248 \begin_layout Standard
10249 For example the command
10254 \begin_inset Formula $\to$
10264 \begin_inset Formula $\to$
10273 \begin_layout Plain Layout
10289 \begin_inset Formula \[
10290 \sideset{}{'}\sum_{k=1}^{n}\]
10297 \begin_layout Standard
10306 \begin_layout Plain Layout
10321 \begin_layout Plain Layout
10333 \begin_inset Formula $\uparrow$
10341 \begin_inset Formula \[
10342 \overset{a}{\maltese}\]
10346 As seen in the last example, with
10358 also symbols and characters can be accented; with
10364 this is not possible.
10367 \begin_layout Subsection
10368 Accents for several Characters
10369 \begin_inset CommandInset label
10371 name "sub:Accents-for-several"
10379 \begin_layout Plain Layout
10380 Accents ! for several characters
10388 \begin_layout Standard
10389 \begin_inset space \hfill{}
10393 \begin_inset Tabular
10394 <lyxtabular version="3" rows="5" columns="2">
10396 <column alignment="center" valignment="top" width="0pt">
10397 <column alignment="center" valignment="top" width="0pt">
10399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10402 \begin_layout Plain Layout
10408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10411 \begin_layout Plain Layout
10413 \begin_inset Note Note
10416 \begin_layout Plain Layout
10423 is only used as spacer.
10435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10438 \begin_layout Plain Layout
10445 \begin_layout Plain Layout
10459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10462 \begin_layout Plain Layout
10463 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10476 \begin_layout Plain Layout
10483 \begin_layout Plain Layout
10497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10500 \begin_layout Plain Layout
10501 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10514 \begin_layout Plain Layout
10521 \begin_layout Plain Layout
10535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10538 \begin_layout Plain Layout
10539 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10552 \begin_layout Plain Layout
10555 underleftrightarrow
10559 \begin_layout Plain Layout
10573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10576 \begin_layout Plain Layout
10577 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10591 \begin_inset space \hfill{}
10595 \begin_inset Tabular
10596 <lyxtabular version="3" rows="5" columns="2">
10598 <column alignment="center" valignment="top" width="0pt">
10599 <column alignment="center" valignment="top" width="0pt">
10601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10604 \begin_layout Plain Layout
10610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10613 \begin_layout Plain Layout
10621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10624 \begin_layout Plain Layout
10631 \begin_layout Plain Layout
10645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10648 \begin_layout Plain Layout
10649 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10662 \begin_layout Plain Layout
10669 \begin_layout Plain Layout
10683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10686 \begin_layout Plain Layout
10687 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10700 \begin_layout Plain Layout
10707 \begin_layout Plain Layout
10721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10724 \begin_layout Plain Layout
10725 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10738 \begin_layout Plain Layout
10745 \begin_layout Plain Layout
10759 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10762 \begin_layout Plain Layout
10763 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10777 \begin_inset space \hfill{}
10783 \begin_layout Standard
10784 \begin_inset VSpace medskip
10787 With these commands as many characters as you like can be accented.
10800 will only be set in the output with a length of three characters, as shown
10801 in the following example:
10802 \begin_inset Formula \[
10803 \widetilde{A+B=C-D}\]
10810 \begin_layout Standard
10821 \begin_layout Plain Layout
10839 \begin_layout Plain Layout
10847 described in the previous subsection it is also possible to accent several
10857 \begin_layout Plain Layout
10867 \begin_inset Formula $\downarrow$
10873 \begin_inset Formula \[
10874 \underset{***}{A=B}\]
10881 \begin_layout Section
10883 \begin_inset CommandInset label
10893 \begin_layout Plain Layout
10902 \begin_layout Subsection
10904 \begin_inset CommandInset label
10906 name "sub:Predefined-Space"
10914 \begin_layout Plain Layout
10915 Space ! horizontal ! predefined
10923 \begin_layout Standard
10924 Sometimes it is necessary to insert horizontal space to a formula.
10925 This is done by inserting a protected space (shortcut
10931 \begin_inset Quotes eld
10941 \begin_layout Plain Layout
10954 \begin_inset Quotes erd
10957 appears and by pressing
10961 several times one can select one of eight different space sizes.
10962 The spaces can also be inserted using the math toolbar button
10963 \begin_inset Graphics
10964 filename ../images/math/space.png
10969 or special commands.
10970 Independent from the inserted command, one can select the size again by
10978 \begin_layout Standard
10981 \begin_inset VSpace -5mm
10985 \begin_inset Tabular
10986 <lyxtabular version="3" rows="3" columns="7">
10988 <column alignment="center" valignment="middle" width="6.8cm">
10989 <column alignment="center" valignment="top" width="0">
10990 <column alignment="center" valignment="top" width="0">
10991 <column alignment="center" valignment="top" width="0">
10992 <column alignment="center" valignment="top" width="0">
10993 <column alignment="center" valignment="top" width="0">
10994 <column alignment="center" valignment="top" width="0">
10996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10999 \begin_layout Plain Layout
11005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11008 \begin_layout Plain Layout
11016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11019 \begin_layout Plain Layout
11027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11030 \begin_layout Plain Layout
11038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11041 \begin_layout Plain Layout
11049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11052 \begin_layout Plain Layout
11060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11063 \begin_layout Plain Layout
11073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11076 \begin_layout Plain Layout
11081 keystrokes after inserting the protected space
11086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11089 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11116 \begin_layout Plain Layout
11122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11125 \begin_layout Plain Layout
11131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11134 \begin_layout Plain Layout
11142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11154 \begin_layout Plain Layout
11155 \begin_inset Formula $A\, B$
11163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11166 \begin_layout Plain Layout
11167 \begin_inset Formula $A\: B$
11175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11178 \begin_layout Plain Layout
11179 \begin_inset Formula $A\; B$
11187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11190 \begin_layout Plain Layout
11191 \begin_inset Formula $A\quad B$
11199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11202 \begin_layout Plain Layout
11203 \begin_inset Formula $A\qquad B$
11211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11214 \begin_layout Plain Layout
11215 \begin_inset Formula $A\! B$
11231 \begin_layout Standard
11232 The last size seem to produce no space.
11233 It is displayed red in LyX contrary to the other sizes, because it is a
11235 There are two more negative spaces:
11238 \begin_layout Standard
11240 \begin_inset Tabular
11241 <lyxtabular version="3" rows="3" columns="3">
11243 <column alignment="center" valignment="middle" width="6.8cm">
11244 <column alignment="center" valignment="top" width="0pt">
11245 <column alignment="center" valignment="top" width="0pt">
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11250 \begin_layout Plain Layout
11256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11259 \begin_layout Plain Layout
11267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11270 \begin_layout Plain Layout
11280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11283 \begin_layout Plain Layout
11288 keystrokes after inserting the protected space
11293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11296 \begin_layout Plain Layout
11302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11305 \begin_layout Plain Layout
11313 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11316 \begin_layout Plain Layout
11322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11325 \begin_layout Plain Layout
11326 \begin_inset Formula $A\negmedspace B$
11334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11337 \begin_layout Plain Layout
11338 \begin_inset Formula $A\negthickspace B$
11354 \begin_layout Standard
11355 Negative spaces can lead to characters overlapping each other.
11356 Thus they can be used to enforce ligatures, what is e.
11357 \begin_inset space \thinspace{}
11361 \begin_inset space ~
11364 useful for summation operators:
11367 \begin_layout Standard
11369 \begin_inset Tabular
11370 <lyxtabular version="3" rows="3" columns="2">
11372 <column alignment="center" valignment="top" width="0">
11373 <column alignment="center" valignment="top" width="0">
11375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11378 \begin_layout Plain Layout
11384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11387 \begin_layout Plain Layout
11389 \begin_inset Note Note
11392 \begin_layout Plain Layout
11399 is only used as spacer.
11411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11414 \begin_layout Plain Layout
11423 \begin_layout Plain Layout
11437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11440 \begin_layout Plain Layout
11441 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11465 \begin_layout Plain Layout
11479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11482 \begin_layout Plain Layout
11483 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11499 \begin_layout Standard
11500 Relations like for example equal signs, are always surrounded by space.
11501 To suppress this, the equal sign is placed into a TeX-brace.
11502 The following example demonstrates this:
11505 \begin_layout Standard
11507 \begin_inset Tabular
11508 <lyxtabular version="3" rows="2" columns="2">
11510 <column alignment="center" valignment="top" width="0pt">
11511 <column alignment="center" valignment="top" width="0pt">
11513 <cell alignment="center" valignment="top" usebox="none">
11516 \begin_layout Plain Layout
11522 <cell alignment="center" valignment="top" usebox="none">
11525 \begin_layout Plain Layout
11526 \begin_inset Formula $A=B$
11536 <cell alignment="center" valignment="top" usebox="none">
11539 \begin_layout Plain Layout
11540 \begin_inset Note Note
11543 \begin_layout Plain Layout
11550 is only used as spacer.
11556 \begin_inset Formula $\raisebox{5mm}{}$
11559 equation without space
11564 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11567 \begin_layout Plain Layout
11568 \begin_inset Formula $A{=}B$
11584 \begin_layout Standard
11586 The command for the last formula is:
11591 \begin_inset Formula $\to$
11597 \begin_layout Standard
11598 \begin_inset VSpace bigskip
11601 Spaces are needed for physical units, because the space between the value
11602 and the unit is the smallest one and not a normal space.
11603 For units in text, the smallest space is inserted via the menu
11605 Insert\SpecialChar \menuseparator
11606 Formatting\SpecialChar \menuseparator
11608 \begin_inset space ~
11620 \begin_layout Standard
11621 An example to visualize the difference:
11624 \begin_layout Standard
11625 \begin_inset Tabular
11626 <lyxtabular version="3" rows="2" columns="2">
11628 <column alignment="left" valignment="top" width="0">
11629 <column alignment="left" valignment="top" width="0">
11631 <cell alignment="center" valignment="top" usebox="none">
11634 \begin_layout Plain Layout
11636 \begin_inset Formula $\cdot$
11644 <cell alignment="center" valignment="top" usebox="none">
11647 \begin_layout Plain Layout
11648 space between value and unit
11655 <cell alignment="center" valignment="top" usebox="none">
11658 \begin_layout Plain Layout
11660 \begin_inset space \thinspace{}
11664 \begin_inset Formula $\cdot$
11672 <cell alignment="center" valignment="top" usebox="none">
11675 \begin_layout Plain Layout
11676 smallest space between value and unit
11689 \begin_layout Subsection
11694 \begin_layout Plain Layout
11707 \begin_layout Plain Layout
11708 for vertical space in formulas see
11709 \begin_inset CommandInset ref
11711 reference "sub:Line-Separation"
11724 \begin_layout Plain Layout
11732 \begin_inset Note Note
11735 \begin_layout Plain Layout
11738 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11741 \begin_layout Plain Layout
11744 texorpdfstring is in section
11745 \begin_inset CommandInset ref
11747 reference "sub:Formulas-in-Section"
11757 \begin_inset CommandInset label
11759 name "sub:Variable-Space"
11767 \begin_layout Plain Layout
11768 Space ! horizontal ! variable
11776 \begin_layout Standard
11777 Space with a defined length can be inserted in LyX with the command
11778 \begin_inset Newline newline
11791 \begin_layout Plain Layout
11800 For the length all units listed in
11801 \begin_inset CommandInset ref
11803 reference "tab:Available-units"
11807 are allowed, except of the unit
11808 \begin_inset Quotes eld
11812 \begin_inset Quotes erd
11816 The length may also be negative.
11817 To insert so many space that the formula uses all available space, the
11828 \begin_layout Plain Layout
11839 \begin_layout Standard
11840 \begin_inset VSpace -1mm
11846 \begin_layout Standard
11848 \begin_inset Tabular
11849 <lyxtabular version="3" rows="4" columns="2">
11851 <column alignment="center" valignment="top" width="0">
11852 <column alignment="center" valignment="top" width="0">
11854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11857 \begin_layout Plain Layout
11863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11866 \begin_layout Plain Layout
11874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11877 \begin_layout Plain Layout
11881 \begin_inset Formula $\to$
11891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11894 \begin_layout Plain Layout
11895 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11908 \begin_layout Plain Layout
11912 \begin_inset Formula $\to$
11922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11925 \begin_layout Plain Layout
11926 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11939 \begin_layout Plain Layout
11946 \begin_layout Plain Layout
11960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11963 \begin_layout Plain Layout
11964 \begin_inset Formula $A=A\hfill B=B$
11980 \begin_layout Standard
11981 In the last example the available space is given by the longest column entry
11983 In an inline formula the space depends on the length of the line in which
11991 Thus, when the line uses the full width, no space will be created.
11998 only has an effect on displayed formulas when the formula style
12003 (Formula styles are explained in
12004 \begin_inset CommandInset ref
12006 reference "sec:Formula-Styles"
12013 \begin_layout Standard
12020 , there are the commands
12032 that fill the space with a pattern, see
12033 \begin_inset CommandInset ref
12035 reference "sub:Ellipses"
12042 \begin_layout Standard
12043 For text, variable space can be inserted via the menu
12045 Insert\SpecialChar \menuseparator
12046 Formatting\SpecialChar \menuseparator
12048 \begin_inset space ~
12053 , what is not possible in formulas:
12056 \begin_layout Standard
12057 This is a line with
12058 \begin_inset space \hspace{}
12063 \begin_inset space \thinspace{}
12069 \begin_layout Standard
12070 This is a line with
12071 \begin_inset space \hfill{}
12077 \begin_layout Subsection
12078 Space besides inline Formulas
12082 \begin_layout Plain Layout
12083 Space ! besides inline formulas
12091 \begin_layout Standard
12092 The space that surrounds inline formulas can be adjusted with the length
12101 \begin_layout Plain Layout
12112 The value of a length is set with the command
12120 \begin_layout Plain Layout
12130 that has the following scheme:
12133 \begin_layout Standard
12138 setlength{length name}{value}
12141 \begin_layout Standard
12149 \begin_inset space \thinspace{}
12155 \begin_layout Standard
12165 \begin_layout Standard
12166 is inserted in TeX-mode.
12168 \begin_inset space \thinspace{}
12171 mm space will now be set around all inline formulas:
12175 \begin_layout Plain Layout
12189 \begin_layout Standard
12190 This is a line with an inline formula
12191 \begin_inset Formula $A=B$
12195 \begin_inset space \thinspace{}
12198 mm surrounding space.
12202 \begin_layout Plain Layout
12216 \begin_layout Standard
12217 To return to the predefined value,
12223 is set to the value 0
12224 \begin_inset space \thinspace{}
12230 \begin_layout Section
12235 \begin_layout Plain Layout
12245 \begin_layout Plain Layout
12250 \begin_layout Plain Layout
12261 \begin_layout Plain Layout
12276 \begin_layout Standard
12277 Boxes for text are described in chapter
12284 \begin_inset space ~
12292 \begin_layout Subsection
12294 \begin_inset CommandInset label
12296 name "sub:Boxes-with-Frame"
12304 \begin_layout Plain Layout
12313 \begin_layout Standard
12314 It is possible to frame formulas or parts of it with the commands
12324 \begin_layout Plain Layout
12342 \begin_layout Plain Layout
12353 \begin_layout Standard
12354 When one of these commands is inserted to a formula, a blue box appears
12355 within a frame to enter formula parts.
12362 an additional formula has to be created by
12370 \begin_layout Plain Layout
12371 Due to a bug in LyX it is not possible to create a new formula with
12376 \begin_inset CommandInset href
12378 name "LyX-bug #1435"
12379 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12388 , because the box content will otherwise be treated as mathematical text.
12395 is used, a new formula is automatically created inside the frame.
12398 \begin_layout Standard
12405 is not suitable to frame displayed formulas, because the formula will always
12406 be set in the size of the text.
12413 is in contrary not suitable to frame inline formulas, because the formula
12414 will always be set in the size of a displayed formula.
12417 \begin_layout Standard
12424 there is the command
12434 \begin_layout Plain Layout
12442 where additionally the frame width and the alignment can be specified.
12449 is used in the following scheme:
12452 \begin_layout Standard
12457 framebox[frame width][position]{box content}
12460 \begin_layout Standard
12461 The position can either be
12478 right aligns the formula in the box.
12479 When no position is given, the formula will be centered.
12480 \begin_inset Newline newline
12483 Is no width given, also no position can be given.
12484 In this case the frame width is adjusted to the box content like for
12493 \begin_layout Standard
12500 is inserted, a box appears containing three blue boxes.
12501 The first two boxes are surrounded by brackets and denote the two optional
12503 The third box is for formula parts like for
12512 \begin_layout Standard
12514 \begin_inset Note Note
12517 \begin_layout Plain Layout
12518 The table has been set into a minipage to make the footnote appearing.
12519 Otherwise the footnote text would not be displayed.
12525 \begin_inset Box Frameless
12534 height_special "totalheight"
12537 \begin_layout Plain Layout
12539 \begin_inset Tabular
12540 <lyxtabular version="3" rows="5" columns="2">
12542 <column alignment="center" valignment="top" width="0">
12543 <column alignment="center" valignment="top" width="0">
12545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12548 \begin_layout Plain Layout
12553 \begin_layout Plain Layout
12554 Due to a bug in LyX it is not possible to create a new formula with
12559 \begin_inset CommandInset href
12561 name "LyX-bug #1435"
12562 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12579 \begin_layout Plain Layout
12581 \begin_inset Note Note
12584 \begin_layout Plain Layout
12591 is only used as spacer.
12603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12606 \begin_layout Plain Layout
12613 \begin_layout Plain Layout
12632 \begin_layout Plain Layout
12646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12649 \begin_layout Plain Layout
12650 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12663 \begin_layout Plain Layout
12670 \begin_layout Plain Layout
12685 \begin_layout Plain Layout
12699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12702 \begin_layout Plain Layout
12703 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12716 \begin_layout Plain Layout
12723 \begin_layout Plain Layout
12737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12740 \begin_layout Plain Layout
12741 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12754 \begin_layout Plain Layout
12761 \begin_layout Plain Layout
12771 \begin_inset Formula $\to$
12775 \begin_inset Formula $\to$
12788 \begin_layout Plain Layout
12798 \begin_inset Formula $\downarrow$
12806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12809 \begin_layout Plain Layout
12810 \begin_inset Formula $\raisebox{6mm}{}$
12814 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12818 \begin_inset Formula $\raisebox{-4mm}{}$
12839 \begin_layout Standard
12840 The frame thickness can also be adjusted.
12841 To do this the following commands have to be inserted in TeX-mode before
12845 \begin_layout Standard
12855 \begin_inset Quotes eld
12859 \begin_inset Quotes erd
12873 \begin_inset Quotes eld
12877 \begin_inset Quotes erd
12883 \begin_layout Standard
12884 \begin_inset Quotes eld
12888 \begin_inset Quotes erd
12891 specifies the minimal distance between the frame and the first character
12893 An example for this is the following framed formula:
12897 \begin_layout Plain Layout
12909 \begin_inset Formula \[
12914 Before this formula the commands
12917 \begin_layout Standard
12939 \begin_layout Standard
12940 were inserted in TeX-mode.
12941 The given values are used for all following boxes.
12944 \begin_layout Standard
12945 To return to the standard frame size, the command
12948 \begin_layout Standard
12973 \begin_layout Plain Layout
12987 \begin_layout Standard
12988 is inserted in TeX-mode before the next formula.
12991 \begin_layout Subsection
12992 Boxes without Frame
12993 \begin_inset CommandInset label
12995 name "sub:Boxes-without-Frame"
13003 \begin_layout Plain Layout
13004 Boxes ! without frame
13012 \begin_layout Standard
13013 For boxes without a frame there are the following box commands:
13023 \begin_layout Plain Layout
13041 \begin_layout Plain Layout
13059 \begin_layout Plain Layout
13070 \begin_layout Standard
13077 a box can be super- or subscripted.
13078 But in contrary to normal super- and subscripting, the characters in the
13079 box keep their font size.
13086 is used in the following scheme:
13089 \begin_layout Standard
13094 raisebox{height}{box content}
13097 \begin_layout Standard
13098 When the box should contain a formula, an extra formula is needed like for
13108 \begin_layout Standard
13110 \begin_inset Tabular
13111 <lyxtabular version="3" rows="4" columns="2">
13113 <column alignment="center" valignment="top" width="0">
13114 <column alignment="center" valignment="top" width="0">
13116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13119 \begin_layout Plain Layout
13125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13128 \begin_layout Plain Layout
13136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13139 \begin_layout Plain Layout
13143 \begin_inset Formula $\to$
13149 \begin_inset Formula $\to$
13157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13160 \begin_layout Plain Layout
13161 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13174 \begin_layout Plain Layout
13178 \begin_inset Formula $\to$
13184 \begin_inset Formula $\to$
13192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13195 \begin_layout Plain Layout
13196 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13209 \begin_layout Plain Layout
13213 \begin_inset Formula $\to$
13228 \begin_layout Plain Layout
13242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13245 \begin_layout Plain Layout
13249 \begin_layout Plain Layout
13273 \begin_layout Standard
13274 The last formula can currently only be created using TeX-mode because LyX
13275 inserts a box instead of the needed extra formula.
13279 \begin_layout Plain Layout
13281 \begin_inset CommandInset href
13283 name "LyX-bug #1435"
13284 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13296 \begin_layout Standard
13321 , with the difference that there is no frame.
13324 \begin_layout Subsection
13326 \begin_inset CommandInset label
13328 name "sub:Colored-Boxes"
13336 \begin_layout Plain Layout
13345 \begin_layout Standard
13346 To be able to use all commands explained in this section, the LaTeX-package
13355 \begin_layout Plain Layout
13360 is part of every LaTeX standard installation.
13369 \begin_layout Plain Layout
13375 has to be loaded in the LaTeX-preamble with the line
13379 \begin_layout Plain Layout
13380 When text is colored somewhere in the document with a predefined color,
13381 LyX loads the LaTeX-package
13386 Thus it is possible that the package is loaded twice, but this doesn't
13393 \begin_inset Note Note
13396 \begin_layout Plain Layout
13397 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13406 \begin_layout Standard
13414 \begin_layout Standard
13415 \begin_inset VSpace medskip
13418 To color boxes, the command
13428 \begin_layout Plain Layout
13436 is used in the following scheme:
13439 \begin_layout Standard
13444 colorbox{color}{box content}
13447 \begin_layout Standard
13448 The box content can also be a box and a
13454 can also be part of another box (see the 2nd and 3rd example).
13455 When the box should contain a formula, an extra formula has to be created,
13466 \begin_layout Plain Layout
13467 This also applies for the command
13475 \begin_inset CommandInset href
13477 name "LyX-bug #1435"
13478 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13490 \begin_layout Standard
13491 One of the following predefined colors can be chosen:
13494 \begin_layout Standard
13528 \begin_layout Standard
13530 \begin_inset Tabular
13531 <lyxtabular version="3" rows="4" columns="2">
13533 <column alignment="center" valignment="top" width="0">
13534 <column alignment="center" valignment="top" width="0">
13536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13539 \begin_layout Plain Layout
13545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13548 \begin_layout Plain Layout
13550 \begin_inset Note Note
13553 \begin_layout Plain Layout
13560 is only used as spacer.
13572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13575 \begin_layout Plain Layout
13579 \begin_inset Formula $\to$
13589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13592 \begin_layout Plain Layout
13593 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13606 \begin_layout Plain Layout
13610 \begin_inset Formula $\to$
13621 \begin_layout Plain Layout
13635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13638 \begin_layout Plain Layout
13639 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13652 \begin_layout Plain Layout
13659 \begin_layout Plain Layout
13671 \begin_inset Formula $\to$
13681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13684 \begin_layout Plain Layout
13685 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13701 \begin_layout Standard
13708 only colors the box but not the characters in the box.
13709 To color all characters, the whole formula is highlighted and the wanted
13710 color is chosen in the
13713 \begin_inset space ~
13719 The dialog can be called with the toolbar button
13720 \begin_inset Graphics
13721 filename ../images/dialog-show_character.png
13728 Edit\SpecialChar \menuseparator
13730 \begin_inset space ~
13733 Style\SpecialChar \menuseparator
13737 The formula number has then the same color as the formula.
13738 When the formula number should get another color than the formula characters,
13739 the color must be changed within the formula.
13742 \begin_layout Standard
13746 \begin_layout Standard
13749 \begin_inset Formula \begin{equation}
13750 \int A=B\label{eq:red}\end{equation}
13757 \begin_inset Formula \begin{equation}
13758 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13765 \begin_layout Standard
13767 \begin_inset CommandInset ref
13773 is completely colored red.
13774 \begin_inset Newline newline
13778 \begin_inset CommandInset ref
13780 reference "eq:redgreen"
13784 was first completely colored green to set the color for the formula number.
13785 Subsequently the formula characters were colored red.
13788 \begin_layout Standard
13789 \begin_inset VSpace bigskip
13792 To color the frame different than the rest of the box, the command
13802 \begin_layout Plain Layout
13810 is used in the following scheme:
13813 \begin_layout Standard
13818 fcolorbox{frame color}{color}{box content}
13821 \begin_layout Standard
13828 is an extension of the command
13835 The frame width is set, like for
13858 \begin_layout Plain Layout
13870 \begin_inset Formula \[
13871 \fcolorbox{cyan}{magenta}{A=B}\]
13879 \begin_layout Plain Layout
13893 \begin_layout Standard
13894 This formula was created with the command
13895 \begin_inset Newline newline
13903 \begin_inset Formula $\to$
13909 \begin_inset Formula $\to$
13919 \begin_layout Standard
13920 \begin_inset VSpace bigskip
13923 To use other colors than the predefined ones, they have to be defined first.
13926 \begin_layout Standard
13927 One can for example define the color
13928 \begin_inset Quotes eld
13936 \begin_inset Quotes erd
13939 with the LaTeX-preamble line:
13942 \begin_layout Standard
13947 definecolor{darkgreen}{cmyk}{0.5,
13965 \begin_layout Plain Layout
13976 \begin_layout Standard
13981 is the color space that denotes the colors
13998 The four comma separated numbers are the portion factor for the corresponding
13999 colors of the color space.
14000 The factors can be in the range of 0
14001 \begin_inset space \thinspace{}
14005 \begin_inset space \thinspace{}
14013 also the color space
14017 can be used for definitions.
14034 , so that there are in this case three portion factors for the corresponding
14036 Furthermore there is the color space
14040 with one portion factor for the gray value.
14043 \begin_layout Standard
14044 As example a framed box with the new defined color
14048 where the characters have been colored
14053 \begin_inset Formula \begin{equation}
14054 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14061 \begin_layout Standard
14062 Self-defined colors can also be used for text with the help of the command
14073 \begin_layout Plain Layout
14082 \begin_layout Standard
14086 \begin_layout Plain Layout
14090 textcolor{darkgreen}{
14096 \begin_inset Quotes eld
14100 \begin_inset Quotes erd
14107 \begin_layout Plain Layout
14117 \begin_layout Standard
14128 \begin_layout Plain Layout
14136 is used in the scheme
14140 textcolor{color}{characters to color}
14145 \begin_layout Subsection
14147 \begin_inset CommandInset label
14149 name "sub:Paragraph-Boxes"
14157 \begin_layout Plain Layout
14158 Boxes ! as paragraph
14166 \begin_layout Standard
14167 A box that can contain several lines and paragraphs, a so called paragraph
14168 box (parbox), can be created with the menu
14170 Insert\SpecialChar \menuseparator
14173 or the toolbar button
14174 \begin_inset Graphics
14175 filename ../images/box-insert.png
14183 \begin_layout Standard
14184 The following example shows a framed parbox in a line:
14187 \begin_layout Standard
14188 \begin_inset VSpace medskip
14192 \begin_inset Box Boxed
14201 height_special "totalheight"
14204 \begin_layout Plain Layout
14205 This is a paragraph box.
14207 \begin_inset space \thinspace{}
14210 cm long and can also contain formulas:
14211 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14222 \begin_layout Standard
14223 \begin_inset VSpace medskip
14229 \begin_layout Standard
14230 Such a box is created by right-clicking on the gray box inset.
14231 A dialog pops up showing the box properties.
14245 \begin_inset space \thinspace{}
14250 Vertical Box Alignment
14255 \begin_layout Standard
14256 \begin_inset VSpace medskip
14259 In LaTeX a parbox is created with the command
14269 \begin_layout Plain Layout
14277 that has the following scheme:
14280 \begin_layout Standard
14285 parbox[position]{width}{box content}
14288 \begin_layout Standard
14302 for bottom means that the box is aligned within the surrounding text with
14308 for top this is done with the first line.
14309 When no position is given, the box will be vertically centered, see section
14317 \begin_inset space ~
14322 manual for examples.
14325 \begin_layout Standard
14326 \begin_inset VSpace bigskip
14329 To frame formulas completely, including the formula number, the formula
14330 must be set into a parbox.
14331 To do this, the command
14345 is inserted in TeX-mode before the formula.
14354 \begin_layout Plain Layout
14364 is hereby the line width set for the document.
14365 Because the frame is outside the parbox, 2
14366 \begin_inset space \thinspace{}
14369 times the frame separation and the frame thickness must be subtracted from
14371 As this is not automatically done by LyX due to a bug
14375 \begin_layout Plain Layout
14376 \begin_inset CommandInset href
14378 name "LyX-bug #4483"
14379 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14388 , TeX-mode has to be used.
14389 To be able to multiply and subtract in arguments, the LaTeX-package
14397 \begin_layout Plain Layout
14402 is part of every LaTeX standard installation.
14411 \begin_layout Plain Layout
14417 must be loaded in the LaTeX-preamble with the line
14420 \begin_layout Standard
14428 \begin_layout Standard
14429 Behind the formula both boxes are closed by entering
14434 Here is an example:
14438 \begin_layout Plain Layout
14452 \begin_layout Standard
14456 \begin_layout Plain Layout
14474 \begin_inset Formula \begin{equation}
14475 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14483 \begin_layout Plain Layout
14494 \begin_layout Plain Layout
14508 \begin_layout Standard
14509 \begin_inset VSpace medskip
14512 As a parbox is used as argument of
14518 , there is in this case no difference between
14533 \begin_layout Standard
14534 \begin_inset VSpace bigskip
14537 Paragraph boxes are very useful to comment formulas directly.
14544 is used in combination with the command
14558 \begin_inset CommandInset ref
14560 reference "sub:User-defined-Numbering"
14567 \begin_layout Standard
14568 An example of a formula commented with
14577 \begin_layout Standard
14581 \begin_layout Plain Layout
14594 This is a description.
14595 It is distinctly separated from the formula and multiline.
14599 \begin_layout Plain Layout
14611 \begin_layout Standard
14612 Such a formula must be inserted completely in TeX-mode because LyX does
14613 not yet support the command
14620 The formula is created with the following command sequence:
14623 \begin_layout Standard
14636 is inserted in TeX-mode.
14640 \begin_layout Plain Layout
14641 When the formula style
14653 can also be replaced by
14660 (formula styles see
14661 \begin_inset CommandInset ref
14663 reference "sec:Formula-Styles"
14672 Then the description follows as normal text, and finally
14678 is inserted in TeX-mode.
14691 hereby create a displayed formula.
14694 \begin_layout Standard
14701 can be seen in this example that was
14702 \begin_inset Quotes eld
14706 \begin_inset Quotes erd
14709 using the mathematical textmode:
14710 \begin_inset Formula \[
14711 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14718 \begin_layout Section
14723 \begin_layout Plain Layout
14732 \begin_layout Subsection
14734 \begin_inset CommandInset label
14736 name "sub:Big-Operators"
14744 \begin_layout Plain Layout
14754 \begin_layout Plain Layout
14764 \begin_layout Plain Layout
14773 \begin_layout Standard
14774 To be able to use all integral operators listed here, the option
14776 Use esint package automatically
14778 must be set in the document settings under
14781 \begin_inset space ~
14789 \begin_layout Standard
14790 \begin_inset space \hfill{}
14794 \begin_inset Tabular
14795 <lyxtabular version="3" rows="11" columns="2">
14797 <column alignment="center" valignment="top" width="0pt">
14798 <column alignment="center" valignment="top" width="0pt">
14800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14803 \begin_layout Plain Layout
14809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14812 \begin_layout Plain Layout
14820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14823 \begin_layout Plain Layout
14830 \begin_layout Plain Layout
14843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14846 \begin_layout Plain Layout
14847 \begin_inset Formula $\sum$
14857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14860 \begin_layout Plain Layout
14867 \begin_layout Plain Layout
14880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14883 \begin_layout Plain Layout
14884 \begin_inset Formula $\int$
14894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14908 \begin_layout Plain Layout
14909 \begin_inset Formula $\intop$
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14922 \begin_layout Plain Layout
14930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14933 \begin_layout Plain Layout
14934 \begin_inset Formula $\oint$
14944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14947 \begin_layout Plain Layout
14955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14958 \begin_layout Plain Layout
14959 \begin_inset Formula $\ointop$
14969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14972 \begin_layout Plain Layout
14980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14983 \begin_layout Plain Layout
14984 \begin_inset Formula $\ointctrclockwise$
14994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14997 \begin_layout Plain Layout
15005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15008 \begin_layout Plain Layout
15009 \begin_inset Formula $\ointclockwise$
15019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15022 \begin_layout Plain Layout
15030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15033 \begin_layout Plain Layout
15034 \begin_inset Formula $\sqint$
15044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15047 \begin_layout Plain Layout
15055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15058 \begin_layout Plain Layout
15059 \begin_inset Formula $\bigcap$
15069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15072 \begin_layout Plain Layout
15080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15083 \begin_layout Plain Layout
15084 \begin_inset Formula $\bigcup$
15098 \begin_inset space \hfill{}
15102 \begin_inset Tabular
15103 <lyxtabular version="3" rows="10" columns="2">
15105 <column alignment="center" valignment="top" width="0pt">
15106 <column alignment="center" valignment="top" width="0pt">
15108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15111 \begin_layout Plain Layout
15117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15120 \begin_layout Plain Layout
15128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15131 \begin_layout Plain Layout
15138 \begin_layout Plain Layout
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15154 \begin_layout Plain Layout
15155 \begin_inset Formula $\prod$
15165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15168 \begin_layout Plain Layout
15176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15179 \begin_layout Plain Layout
15180 \begin_inset Formula $\coprod$
15190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15193 \begin_layout Plain Layout
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15204 \begin_layout Plain Layout
15205 \begin_inset Formula $\bigodot$
15215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15218 \begin_layout Plain Layout
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15229 \begin_layout Plain Layout
15230 \begin_inset Formula $\bigotimes$
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15254 \begin_layout Plain Layout
15255 \begin_inset Formula $\bigoplus$
15265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15268 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\bigwedge$
15290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15304 \begin_layout Plain Layout
15305 \begin_inset Formula $\bigvee$
15315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15318 \begin_layout Plain Layout
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15329 \begin_layout Plain Layout
15330 \begin_inset Formula $\bigsqcup$
15340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15343 \begin_layout Plain Layout
15351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15354 \begin_layout Plain Layout
15355 \begin_inset Formula $\biguplus$
15369 \begin_inset space \hfill{}
15375 \begin_layout Standard
15376 All big operators can also be inserted via the math toolbar button
15377 \begin_inset Graphics
15378 filename ../images/math/intop.png
15386 \begin_layout Standard
15387 The operators are called big because they are bigger than the sometimes
15388 equal looking binary operators.
15389 All big operators can have limits as described in the next subsection.
15392 \begin_layout Standard
15418 \begin_inset space ~
15421 in the style the operator limits are displayed, see
15422 \begin_inset CommandInset ref
15424 reference "sub:Operator-Limits"
15432 \begin_layout Subsubsection*
15433 Advices for Integrals
15436 \begin_layout Standard
15441 in an integral is an operator, that therefore has to be set upright.
15442 This is done by highlighting the
15446 and using the keyboard shortcut
15449 \begin_inset space ~
15458 \begin_layout Plain Layout
15464 \begin_inset CommandInset ref
15466 reference "sub:Font-Styles"
15476 Finally the smallest space is inserted before the
15480 , as this is usual for operators.
15484 \begin_layout Standard
15486 \begin_inset Formula $\int A(x)dx$
15490 \begin_inset Newline newline
15497 \begin_layout Plain Layout
15507 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15513 \begin_layout Standard
15514 For multiple integrals there are the following commands:
15515 \begin_inset VSpace medskip
15521 \begin_layout Standard
15522 \begin_inset space \hfill{}
15526 \begin_inset Tabular
15527 <lyxtabular version="3" rows="4" columns="2">
15529 <column alignment="center" valignment="top" width="0">
15530 <column alignment="center" valignment="top" width="0">
15532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15535 \begin_layout Plain Layout
15541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15544 \begin_layout Plain Layout
15546 \begin_inset Note Note
15549 \begin_layout Plain Layout
15556 is only used as spacer.
15568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15571 \begin_layout Plain Layout
15579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15582 \begin_layout Plain Layout
15583 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15596 \begin_layout Plain Layout
15604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15607 \begin_layout Plain Layout
15608 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15621 \begin_layout Plain Layout
15629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15632 \begin_layout Plain Layout
15633 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15647 \begin_inset space \hfill{}
15651 \begin_inset Tabular
15652 <lyxtabular version="3" rows="4" columns="2">
15654 <column alignment="center" valignment="top" width="0">
15655 <column alignment="center" valignment="top" width="0">
15657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15660 \begin_layout Plain Layout
15666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15669 \begin_layout Plain Layout
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15680 \begin_layout Plain Layout
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15691 \begin_layout Plain Layout
15692 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15705 \begin_layout Plain Layout
15713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15716 \begin_layout Plain Layout
15717 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15730 \begin_layout Plain Layout
15738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15741 \begin_layout Plain Layout
15742 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15756 \begin_inset space \hfill{}
15762 \begin_layout Subsection
15764 \begin_inset CommandInset label
15766 name "sub:Operator-Limits"
15774 \begin_layout Plain Layout
15783 \begin_layout Standard
15784 Limits are created by super- and subscripts:
15787 \begin_layout Standard
15789 \begin_inset Tabular
15790 <lyxtabular version="3" rows="2" columns="2">
15792 <column alignment="center" valignment="top" width="0pt">
15793 <column alignment="center" valignment="top" width="0pt">
15795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15798 \begin_layout Plain Layout
15804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15807 \begin_layout Plain Layout
15809 \begin_inset Note Note
15812 \begin_layout Plain Layout
15819 is only used as spacer.
15831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15834 \begin_layout Plain Layout
15843 \begin_layout Plain Layout
15853 \begin_inset Formula $\to$
15857 \begin_inset Formula $\to$
15865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15868 \begin_layout Plain Layout
15869 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15885 \begin_layout Standard
15886 Limits of inline formulas are set right beside the operator.
15887 Limits in displayed formulas are set above or below the operator, except
15888 of integral limits.
15891 \begin_layout Standard
15892 To force that the limits are set beside the operator, the cursor is set
15893 directly behind the operator and the limits type is changed with the menu
15896 Edit\SpecialChar \menuseparator
15897 Math\SpecialChar \menuseparator
15909 \begin_inset space ~
15918 \begin_layout Standard
15919 The default limits type is this:
15920 \begin_inset Formula \[
15921 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15925 This is how it looks when the limits type was changed to
15932 \begin_inset Formula \[
15933 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15937 For integrals, except of
15949 , the limits are by default set beside the operator.
15950 But for multiple integrals the limits are often set below the operator.
15951 In the following example the limits type was therefore set to
15955 and so set below the integrals:
15956 \begin_inset Formula \begin{equation}
15957 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15964 \begin_layout Standard
15965 \begin_inset VSpace medskip
15968 To specify conditions for limits, the commands
15978 \begin_layout Plain Layout
15996 \begin_layout Plain Layout
16005 To create for example this expression
16006 \begin_inset Formula \begin{equation}
16007 \sum_{\begin{subarray}{c}
16009 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16016 \begin_layout Standard
16017 the following has to be done:
16018 \begin_inset Newline newline
16033 \begin_layout Plain Layout
16045 One is now in a blue box under the summation operator and insert there
16054 \begin_layout Plain Layout
16066 The blue box is now within a purple box and now several lines can be written
16068 A new line is created by inserting a line break (
16074 \begin_inset Newline newline
16079 0<k<1000 Ctrl-Return
16080 \begin_inset Newline newline
16085 is typed in, a new box appears below for the new line.
16088 \begin_layout Standard
16089 The alignment of the lines can be changed to left aligned with the
16099 Edit\SpecialChar \menuseparator
16103 To get right alignment,
16111 \begin_layout Plain Layout
16122 is inserted at the beginning of the line.
16125 \begin_layout Standard
16138 with the difference that the lines are always centered.
16141 \begin_layout Standard
16142 \begin_inset VSpace bigskip
16146 \begin_inset CommandInset ref
16148 reference "eq:substack"
16152 there can be too much space beside an operator, because the characters
16153 following the operator are set beside the limits.
16156 \begin_layout Standard
16157 To avoid this, the following macro can be used in the LaTeX-preamble:
16160 \begin_layout Standard
16174 \begin_inset Newline newline
16186 \begin_inset Newline newline
16193 mathclapinternal #1#2{
16197 mathsurround =0pt #1{#2}$}}
16200 \begin_layout Standard
16201 This defines the command
16211 \begin_layout Plain Layout
16219 that sets the width of the limit to 0
16220 \begin_inset space \thinspace{}
16224 The command scheme is
16227 \begin_layout Standard
16235 \begin_layout Standard
16236 where the limit can consist of several conditions.
16239 \begin_layout Standard
16241 \begin_inset CommandInset ref
16243 reference "eq:substack"
16247 , one uses the command
16250 \begin_layout Standard
16263 \begin_layout Plain Layout
16272 0<k<1000 Ctrl-Enter
16275 \begin_layout Standard
16276 to create the lower limit.
16277 The summand is now directly behind the summation operator:
16278 \begin_inset Formula \[
16279 \sum_{\mathclap{\substack{0<k<1000\\
16280 \\k\,\in\,\mathbb{N}}
16288 \begin_layout Standard
16289 \begin_inset VSpace bigskip
16292 How to use one limit for several operators is described in
16293 \begin_inset CommandInset ref
16295 reference "sub:Self-defined-Operators"
16302 \begin_layout Standard
16303 \begin_inset Newpage newpage
16309 \begin_layout Subsection
16311 \begin_inset CommandInset label
16313 name "sub:Binary-Operators"
16321 \begin_layout Plain Layout
16330 \begin_layout Standard
16331 Binary operators are surrounded by space when there is a character before
16333 \begin_inset VSpace medskip
16339 \begin_layout Standard
16340 \begin_inset space \hfill{}
16344 \begin_inset Tabular
16345 <lyxtabular version="3" rows="13" columns="2">
16347 <column alignment="center" valignment="top" width="0pt">
16348 <column alignment="center" valignment="top" width="0pt">
16350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16353 \begin_layout Plain Layout
16355 \begin_inset Note Note
16358 \begin_layout Plain Layout
16365 is only used as spacer.
16375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16378 \begin_layout Plain Layout
16386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16389 \begin_layout Plain Layout
16395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16398 \begin_layout Plain Layout
16399 \begin_inset Formula $+$
16409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16412 \begin_layout Plain Layout
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16421 \begin_layout Plain Layout
16422 \begin_inset Formula $-$
16432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16435 \begin_layout Plain Layout
16443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16446 \begin_layout Plain Layout
16447 \begin_inset Formula $\pm$
16457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16460 \begin_layout Plain Layout
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16471 \begin_layout Plain Layout
16472 \begin_inset Formula $\mp$
16482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16485 \begin_layout Plain Layout
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16496 \begin_layout Plain Layout
16497 \begin_inset Formula $\cdot$
16507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16510 \begin_layout Plain Layout
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16521 \begin_layout Plain Layout
16522 \begin_inset Formula $\times$
16532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16535 \begin_layout Plain Layout
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16546 \begin_layout Plain Layout
16547 \begin_inset Formula $\div$
16557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16560 \begin_layout Plain Layout
16564 \begin_layout Plain Layout
16577 \begin_layout Plain Layout
16589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16592 \begin_layout Plain Layout
16593 \begin_inset Formula $*$
16603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16606 \begin_layout Plain Layout
16614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16617 \begin_layout Plain Layout
16618 \begin_inset Formula $\star$
16628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16631 \begin_layout Plain Layout
16639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16642 \begin_layout Plain Layout
16643 \begin_inset Formula $\circ$
16653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16656 \begin_layout Plain Layout
16664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16667 \begin_layout Plain Layout
16668 \begin_inset Formula $\diamond$
16678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16681 \begin_layout Plain Layout
16689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16692 \begin_layout Plain Layout
16693 \begin_inset Formula $\bullet$
16707 \begin_inset space \hfill{}
16711 \begin_inset Tabular
16712 <lyxtabular version="3" rows="13" columns="2">
16714 <column alignment="center" valignment="top" width="0pt">
16715 <column alignment="center" valignment="top" width="0pt">
16717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16720 \begin_layout Plain Layout
16726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16729 \begin_layout Plain Layout
16737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16740 \begin_layout Plain Layout
16748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16751 \begin_layout Plain Layout
16752 \begin_inset Formula $\nabla$
16762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16765 \begin_layout Plain Layout
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16776 \begin_layout Plain Layout
16777 \begin_inset Formula $\bigtriangledown$
16787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16790 \begin_layout Plain Layout
16798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16801 \begin_layout Plain Layout
16802 \begin_inset Formula $\bigtriangleup$
16812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16815 \begin_layout Plain Layout
16823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16826 \begin_layout Plain Layout
16827 \begin_inset Formula $\Box$
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16840 \begin_layout Plain Layout
16848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16851 \begin_layout Plain Layout
16852 \begin_inset Formula $\cap$
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16865 \begin_layout Plain Layout
16873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16876 \begin_layout Plain Layout
16877 \begin_inset Formula $\cup$
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16890 \begin_layout Plain Layout
16898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16901 \begin_layout Plain Layout
16902 \begin_inset Formula $\dagger$
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16915 \begin_layout Plain Layout
16923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16926 \begin_layout Plain Layout
16927 \begin_inset Formula $\ddagger$
16937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16940 \begin_layout Plain Layout
16948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16951 \begin_layout Plain Layout
16952 \begin_inset Formula $\wr$
16962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16965 \begin_layout Plain Layout
16973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16976 \begin_layout Plain Layout
16977 \begin_inset Formula $\bigcirc$
16987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16990 \begin_layout Plain Layout
16998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17001 \begin_layout Plain Layout
17002 \begin_inset Formula $\wedge$
17012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17015 \begin_layout Plain Layout
17023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17026 \begin_layout Plain Layout
17027 \begin_inset Formula $\vee$
17041 \begin_inset space \hfill{}
17045 \begin_inset Tabular
17046 <lyxtabular version="3" rows="13" columns="2">
17048 <column alignment="center" valignment="top" width="0pt">
17049 <column alignment="center" valignment="top" width="0pt">
17051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17054 \begin_layout Plain Layout
17060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17063 \begin_layout Plain Layout
17071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17074 \begin_layout Plain Layout
17082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17085 \begin_layout Plain Layout
17086 \begin_inset Formula $\oplus$
17096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17099 \begin_layout Plain Layout
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17110 \begin_layout Plain Layout
17111 \begin_inset Formula $\ominus$
17121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17124 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17135 \begin_layout Plain Layout
17136 \begin_inset Formula $\otimes$
17146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17149 \begin_layout Plain Layout
17157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17160 \begin_layout Plain Layout
17161 \begin_inset Formula $\oslash$
17171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17174 \begin_layout Plain Layout
17182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17185 \begin_layout Plain Layout
17186 \begin_inset Formula $\odot$
17196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17199 \begin_layout Plain Layout
17207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17210 \begin_layout Plain Layout
17211 \begin_inset Formula $\amalg$
17221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17224 \begin_layout Plain Layout
17232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17235 \begin_layout Plain Layout
17236 \begin_inset Formula $\uplus$
17246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17249 \begin_layout Plain Layout
17257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17260 \begin_layout Plain Layout
17261 \begin_inset Formula $\setminus$
17271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17274 \begin_layout Plain Layout
17282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17285 \begin_layout Plain Layout
17286 \begin_inset Formula $\sqcap$
17296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17299 \begin_layout Plain Layout
17307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17310 \begin_layout Plain Layout
17311 \begin_inset Formula $\sqcup$
17321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17324 \begin_layout Plain Layout
17332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17335 \begin_layout Plain Layout
17336 \begin_inset Formula $\triangleleft$
17346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17349 \begin_layout Plain Layout
17357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17360 \begin_layout Plain Layout
17361 \begin_inset Formula $\triangleright$
17375 \begin_inset space \hfill{}
17381 \begin_layout Standard
17382 All binary operators can also be inserted via the math toolbar button
17383 \begin_inset Graphics
17384 filename ../images/math/pm.png
17392 \begin_layout Standard
17393 To typeset the Laplace operator also
17410 \begin_inset Formula $\nabla^{2}$
17413 ) can be used instead of
17422 \begin_layout Standard
17429 Insert\SpecialChar \menuseparator
17441 \begin_layout Subsection
17442 Self-defined Operators
17443 \begin_inset CommandInset label
17445 name "sub:Self-defined-Operators"
17453 \begin_layout Plain Layout
17454 Operators ! self-defined
17462 \begin_layout Standard
17463 With the help of the command
17467 DeclareMathOperator
17473 \begin_layout Plain Layout
17478 DeclareMathOperator
17483 custom operators can be defined in the LaTeX-preamble.
17484 Its command scheme is:
17487 \begin_layout Standard
17492 DeclareMathOperator{new command}{display}
17495 \begin_layout Standard
17496 Display can be characters or symbols that define how the operator looks
17498 To define a big operator a * is set behind the command.
17499 All self-defined big operators can have limits as described in
17500 \begin_inset CommandInset ref
17502 reference "sub:Operator-Limits"
17509 \begin_layout Standard
17510 For example the LaTeX-preamble line
17513 \begin_layout Standard
17518 DeclareMathOperator*{
17525 \begin_layout Standard
17526 defines the command
17532 , that inserts a big operator consisting of the lozenge symbol from
17533 \begin_inset CommandInset ref
17535 reference "sub:Miscellaneous-Symbols"
17540 \begin_inset Formula \[
17541 \Lozenge_{n=1}^{\infty}\]
17545 The command for this formula is:
17556 \begin_inset Formula $\to$
17562 \begin_layout Standard
17563 \begin_inset VSpace bigskip
17566 When self-defined operators are not used several times in the document,
17567 they can also be defined with the commands
17577 \begin_layout Plain Layout
17595 \begin_layout Plain Layout
17603 , which have the following scheme:
17606 \begin_layout Standard
17620 \begin_layout Standard
17627 defines big operators,
17636 \begin_layout Standard
17644 \begin_inset space \thinspace{}
17648 \begin_inset space ~
17651 be used to use one limit for several operators:
17654 \begin_layout Standard
17655 \begin_inset Formula \[
17656 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17663 \begin_layout Standard
17664 The command for the formula above is:
17665 \begin_inset Newline newline
17684 \begin_layout Plain Layout
17696 \begin_inset Formula $\to$
17705 \begin_layout Plain Layout
17719 \begin_layout Section
17724 \begin_layout Plain Layout
17733 \begin_layout Subsection
17735 \begin_inset CommandInset label
17737 name "sub:Font-Styles"
17745 \begin_layout Plain Layout
17754 \begin_layout Standard
17755 Latin letters in formulas can be set in one of the following font styles:
17756 \begin_inset VSpace -2mm
17762 \begin_layout Standard
17764 \begin_inset Tabular
17765 <lyxtabular version="3" rows="6" columns="3">
17767 <column alignment="center" valignment="top" width="0">
17768 <column alignment="center" valignment="top" width="0">
17769 <column alignment="center" valignment="top" width="0">
17771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17774 \begin_layout Plain Layout
17780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17783 \begin_layout Plain Layout
17789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17792 \begin_layout Plain Layout
17800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17803 \begin_layout Plain Layout
17812 \begin_layout Plain Layout
17828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17831 \begin_layout Plain Layout
17832 \begin_inset Formula $\mathbb{ABC}$
17840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17843 \begin_layout Plain Layout
17851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17854 \begin_layout Plain Layout
17863 \begin_layout Plain Layout
17879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17882 \begin_layout Plain Layout
17883 \begin_inset Formula $\mathbf{AbC}$
17891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17894 \begin_layout Plain Layout
17902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17905 \begin_layout Plain Layout
17914 \begin_layout Plain Layout
17930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17933 \begin_layout Plain Layout
17934 \begin_inset Formula $\boldsymbol{AbC}$
17942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17945 \begin_layout Plain Layout
17946 Alt-c b or Ctrl-Alt-b
17953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17956 \begin_layout Plain Layout
17965 \begin_layout Plain Layout
17981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17984 \begin_layout Plain Layout
17985 \begin_inset Formula $\mathcal{ABC}$
17993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17996 \begin_layout Plain Layout
18004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18007 \begin_layout Plain Layout
18016 \begin_layout Plain Layout
18032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18035 \begin_layout Plain Layout
18036 \begin_inset Formula $\mathfrak{AbC}$
18044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18047 \begin_layout Plain Layout
18061 \begin_layout Standard
18063 \begin_inset Tabular
18064 <lyxtabular version="3" rows="5" columns="3">
18066 <column alignment="center" valignment="top" width="0">
18067 <column alignment="center" valignment="top" width="0">
18068 <column alignment="center" valignment="top" width="0">
18070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18073 \begin_layout Plain Layout
18079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18082 \begin_layout Plain Layout
18088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18091 \begin_layout Plain Layout
18099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18102 \begin_layout Plain Layout
18111 \begin_layout Plain Layout
18127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18130 \begin_layout Plain Layout
18131 \begin_inset Formula $\mathit{AbC}$
18139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18142 \begin_layout Plain Layout
18150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18153 \begin_layout Plain Layout
18162 \begin_layout Plain Layout
18178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18181 \begin_layout Plain Layout
18182 \begin_inset Formula $\mathrm{AbC}$
18190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18193 \begin_layout Plain Layout
18201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18204 \begin_layout Plain Layout
18213 \begin_layout Plain Layout
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18232 \begin_layout Plain Layout
18233 \begin_inset Formula $\mathsf{AbC}$
18241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18244 \begin_layout Plain Layout
18252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18255 \begin_layout Plain Layout
18264 \begin_layout Plain Layout
18280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18283 \begin_layout Plain Layout
18284 \begin_inset Formula $\mathtt{AbC}$
18292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18295 \begin_layout Plain Layout
18309 \begin_layout Standard
18310 \begin_inset Note Greyedout
18313 \begin_layout Plain Layout
18330 can only be used for big letters.
18338 \begin_layout Standard
18339 Predefined is the style
18348 \begin_layout Standard
18349 The style commands work also for letters in mathematical constructs:
18350 \begin_inset Formula \[
18351 \mathfrak{A=\frac{b}{C}}\]
18358 \begin_layout Standard
18359 Characters in mathematical text don't appear in a math font style but in
18360 the text font style
18367 That their style can't be set correctly via the text style dialog is a
18372 \begin_layout Plain Layout
18373 \begin_inset CommandInset href
18375 name "LyX-bug #4091"
18376 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18388 \begin_layout Standard
18389 Instead of the style commands the dialog
18391 Edit\SpecialChar \menuseparator
18392 Math\SpecialChar \menuseparator
18395 or the toolbar button
18396 \begin_inset Graphics
18397 filename ../images/math/font.png
18405 \begin_layout Subsection
18407 \begin_inset CommandInset label
18409 name "sub:Bold-Formulas"
18417 \begin_layout Plain Layout
18426 \begin_layout Standard
18427 To make a complete formula bold, the command
18433 from the previous subsection cannot be used, because it doesn't work for
18434 small Greek letters.
18435 Furthermore it prints Latin letters always upright, like in the following
18439 \begin_layout Standard
18440 \begin_inset Formula \[
18441 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18448 \begin_layout Standard
18449 To display the formula correctly, the command
18456 \begin_inset Formula \[
18457 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18461 It is also possible to set the formula in a
18463 boldmath environment
18466 This environment is created by inserting the command
18474 \begin_layout Plain Layout
18485 To end the environment, the command
18493 \begin_layout Plain Layout
18503 is inserted in TeX-mode.
18507 \begin_layout Plain Layout
18517 \begin_inset Formula \[
18518 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18526 \begin_layout Plain Layout
18538 \begin_layout Subsection
18543 \begin_layout Plain Layout
18552 \begin_layout Standard
18553 Formulas can be colored like normal text: Highlight a formula or a formula
18559 Here is a formula in magenta:
18560 \begin_inset Formula \[
18561 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18568 \begin_layout Standard
18569 You can also define your own colors as described in
18570 \begin_inset CommandInset ref
18572 reference "sub:Colored-Boxes"
18577 They can be used with the TeX code command
18587 \begin_layout Plain Layout
18598 \begin_layout Standard
18603 textcolor{color}{characters or formula}
18606 \begin_layout Standard
18607 The following example was colored completely dark green and partly red:
18610 \begin_layout Standard
18614 \begin_layout Plain Layout
18618 textcolor{darkgreen}{
18624 \begin_inset Formula \[
18625 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18633 \begin_layout Plain Layout
18643 \begin_layout Standard
18644 Due to a bug in LyX only complete formulas can be colored with self-defined
18649 \begin_layout Plain Layout
18650 \begin_inset CommandInset href
18652 name "LyX-bug #5269"
18653 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18665 \begin_layout Subsection
18667 \begin_inset CommandInset label
18669 name "sub:Font-Sizes"
18677 \begin_layout Plain Layout
18686 \begin_layout Standard
18687 For characters in formulas there are, analog to characters in text, the
18688 following size commands:
18691 \begin_layout Standard
18735 \begin_inset Newline newline
18757 \begin_layout Standard
18758 The size produced by the commands depends on the document font size, that
18759 corresponds with the command
18766 The other commands produce smaller or larger sizes than
18773 The font size can however not exceed a certain value.
18774 Is for example the document font size 12
18775 \begin_inset space \thinspace{}
18784 switches to the same size as
18794 \begin_layout Standard
18795 A size command is inserted in TeX-mode before the formula and sets the size
18796 for all following formula and text characters.
18797 To switch back to the initial size, the command
18803 is inserted behind the formula in TeX-mode.
18806 \begin_layout Standard
18807 Within a formula the size can only be changed for symbols or letters in
18809 To do this, the size command is inserted in mathematical text.
18810 All following characters until the end of the mathematical text or until
18811 another size command will have the selected size.
18813 \begin_inset VSpace -2mm
18819 \begin_layout Standard
18823 \begin_layout Plain Layout
18833 \begin_inset Formula \[
18834 A=\frac{B}{c}\cdot\maltese\]
18839 \begin_inset Formula \[
18840 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18848 \begin_layout Plain Layout
18860 \begin_layout Standard
18861 \begin_inset VSpace medskip
18864 Before both formulas the command
18871 The command for the second formula is:
18872 \begin_inset Newline newline
18883 \begin_layout Plain Layout
18898 \begin_layout Plain Layout
18913 \begin_layout Plain Layout
18928 \begin_layout Plain Layout
18938 \begin_inset Formula $\to$
18942 \begin_inset Formula $\to$
18946 \begin_inset Newline newline
18950 \begin_inset space \hspace*{}
18964 \begin_layout Plain Layout
18979 \begin_layout Plain Layout
18994 \begin_layout Plain Layout
19006 \begin_layout Standard
19007 If a symbol cannot be displayed in different sizes, it will always be displayed
19008 in the default size.
19011 \begin_layout Section
19016 \begin_layout Plain Layout
19025 \begin_layout Standard
19026 All Greek letters can also be inserted via the toolbar button
19027 \begin_inset Graphics
19028 filename ../images/math/alpha.png
19036 \begin_layout Subsection
19038 \begin_inset CommandInset label
19040 name "sub:Small-Letters"
19048 \begin_layout Plain Layout
19049 Greek letters ! small
19057 \begin_layout Standard
19058 \begin_inset space \hfill{}
19062 \begin_inset Tabular
19063 <lyxtabular version="3" rows="11" columns="2">
19065 <column alignment="center" valignment="top" width="0pt">
19066 <column alignment="center" valignment="top" width="0pt">
19068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19071 \begin_layout Plain Layout
19077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19080 \begin_layout Plain Layout
19088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19091 \begin_layout Plain Layout
19099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19102 \begin_layout Plain Layout
19103 \begin_inset Formula $\alpha$
19113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19116 \begin_layout Plain Layout
19124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19127 \begin_layout Plain Layout
19128 \begin_inset Formula $\beta$
19138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19141 \begin_layout Plain Layout
19149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19152 \begin_layout Plain Layout
19153 \begin_inset Formula $\gamma$
19163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19166 \begin_layout Plain Layout
19174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19177 \begin_layout Plain Layout
19178 \begin_inset Formula $\delta$
19188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19191 \begin_layout Plain Layout
19199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19202 \begin_layout Plain Layout
19203 \begin_inset Formula $\epsilon$
19213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19216 \begin_layout Plain Layout
19224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19227 \begin_layout Plain Layout
19228 \begin_inset Formula $\varepsilon$
19238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19241 \begin_layout Plain Layout
19249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19252 \begin_layout Plain Layout
19253 \begin_inset Formula $\zeta$
19263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19266 \begin_layout Plain Layout
19274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19277 \begin_layout Plain Layout
19278 \begin_inset Formula $\eta$
19288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19291 \begin_layout Plain Layout
19299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19302 \begin_layout Plain Layout
19303 \begin_inset Formula $\theta$
19313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19316 \begin_layout Plain Layout
19324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19327 \begin_layout Plain Layout
19328 \begin_inset Formula $\vartheta$
19342 \begin_inset space \hfill{}
19346 \begin_inset Tabular
19347 <lyxtabular version="3" rows="12" columns="2">
19349 <column alignment="center" valignment="top" width="0pt">
19350 <column alignment="center" valignment="top" width="0pt">
19352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19355 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19364 \begin_layout Plain Layout
19372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19375 \begin_layout Plain Layout
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19386 \begin_layout Plain Layout
19387 \begin_inset Formula $\iota$
19397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19400 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19411 \begin_layout Plain Layout
19412 \begin_inset Formula $\kappa$
19422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19425 \begin_layout Plain Layout
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19436 \begin_layout Plain Layout
19437 \begin_inset Formula $\varkappa$
19447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19461 \begin_layout Plain Layout
19462 \begin_inset Formula $\lambda$
19472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19475 \begin_layout Plain Layout
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19486 \begin_layout Plain Layout
19487 \begin_inset Formula $\mu$
19497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19500 \begin_layout Plain Layout
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19511 \begin_layout Plain Layout
19512 \begin_inset Formula $\nu$
19522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19525 \begin_layout Plain Layout
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19536 \begin_layout Plain Layout
19537 \begin_inset Formula $\xi$
19547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19550 \begin_layout Plain Layout
19556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19559 \begin_layout Plain Layout
19560 \begin_inset Formula $o$
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19573 \begin_layout Plain Layout
19581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19584 \begin_layout Plain Layout
19585 \begin_inset Formula $\pi$
19595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19598 \begin_layout Plain Layout
19606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19609 \begin_layout Plain Layout
19610 \begin_inset Formula $\varpi$
19620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19623 \begin_layout Plain Layout
19631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19634 \begin_layout Plain Layout
19635 \begin_inset Formula $\rho$
19649 \begin_inset space \hfill{}
19653 \begin_inset Tabular
19654 <lyxtabular version="3" rows="11" columns="2">
19656 <column alignment="center" valignment="top" width="0pt">
19657 <column alignment="center" valignment="top" width="0pt">
19659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19662 \begin_layout Plain Layout
19668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19671 \begin_layout Plain Layout
19679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19682 \begin_layout Plain Layout
19690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19693 \begin_layout Plain Layout
19694 \begin_inset Formula $\varrho$
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19707 \begin_layout Plain Layout
19715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19718 \begin_layout Plain Layout
19719 \begin_inset Formula $\sigma$
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19732 \begin_layout Plain Layout
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19743 \begin_layout Plain Layout
19744 \begin_inset Formula $\varsigma$
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19757 \begin_layout Plain Layout
19765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Plain Layout
19769 \begin_inset Formula $\tau$
19779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19782 \begin_layout Plain Layout
19790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19793 \begin_layout Plain Layout
19794 \begin_inset Formula $\upsilon$
19804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19807 \begin_layout Plain Layout
19815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19818 \begin_layout Plain Layout
19819 \begin_inset Formula $\phi$
19829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19832 \begin_layout Plain Layout
19840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19843 \begin_layout Plain Layout
19844 \begin_inset Formula $\varphi$
19854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19869 \begin_inset Formula $\chi$
19879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19882 \begin_layout Plain Layout
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19893 \begin_layout Plain Layout
19894 \begin_inset Formula $\psi$
19904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19907 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19918 \begin_layout Plain Layout
19919 \begin_inset Formula $\omega$
19933 \begin_inset space \hfill{}
19939 \begin_layout Standard
19940 \begin_inset VSpace medskip
19946 \begin_layout Standard
19947 How to create upright Greek letters is explained in
19948 \begin_inset CommandInset ref
19950 reference "sub:Upright-small-Greek"
19957 \begin_layout Subsection
19962 \begin_layout Plain Layout
19963 Greek letters ! big
19971 \begin_layout Standard
19972 \begin_inset space \hfill{}
19976 \begin_inset Tabular
19977 <lyxtabular version="3" rows="7" columns="2">
19979 <column alignment="center" valignment="top" width="0pt">
19980 <column alignment="center" valignment="top" width="0pt">
19982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19985 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
20002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20005 \begin_layout Plain Layout
20013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20016 \begin_layout Plain Layout
20017 \begin_inset Formula $\Gamma$
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20030 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20041 \begin_layout Plain Layout
20042 \begin_inset Formula $\Delta$
20052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20055 \begin_layout Plain Layout
20063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20066 \begin_layout Plain Layout
20067 \begin_inset Formula $\Theta$
20077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20080 \begin_layout Plain Layout
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20091 \begin_layout Plain Layout
20092 \begin_inset Formula $\Lambda$
20102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20105 \begin_layout Plain Layout
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20116 \begin_layout Plain Layout
20117 \begin_inset Formula $\Xi$
20127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20130 \begin_layout Plain Layout
20138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20141 \begin_layout Plain Layout
20142 \begin_inset Formula $\Pi$
20156 \begin_inset space \hfill{}
20160 \begin_inset Tabular
20161 <lyxtabular version="3" rows="6" columns="2">
20163 <column alignment="center" valignment="top" width="0pt">
20164 <column alignment="center" valignment="top" width="0pt">
20166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20169 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20178 \begin_layout Plain Layout
20186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20189 \begin_layout Plain Layout
20197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20200 \begin_layout Plain Layout
20201 \begin_inset Formula $\Sigma$
20211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $\Upsilon$
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\Phi$
20261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20264 \begin_layout Plain Layout
20272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20275 \begin_layout Plain Layout
20276 \begin_inset Formula $\Psi$
20286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20289 \begin_layout Plain Layout
20297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20300 \begin_layout Plain Layout
20301 \begin_inset Formula $\Omega$
20315 \begin_inset space \hfill{}
20321 \begin_layout Standard
20322 \begin_inset VSpace medskip
20325 That the big Greek letters appear upright is caused by a design bug when
20327 To get correct italic big letters, begin every command with
20332 For example the command
20339 \begin_inset Formula $\varGamma$
20345 \begin_layout Subsection
20350 \begin_layout Plain Layout
20351 Greek letters ! bold
20359 \begin_layout Standard
20360 Greek letters cannot be set with different font styles like Latin letters.
20361 They can only be made bold with the command
20371 \begin_layout Plain Layout
20382 \begin_layout Standard
20384 \begin_inset Tabular
20385 <lyxtabular version="3" rows="3" columns="2">
20387 <column alignment="center" valignment="top" width="0">
20388 <column alignment="center" valignment="top" width="0">
20390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20413 \begin_layout Plain Layout
20425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20428 \begin_layout Plain Layout
20429 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20442 \begin_layout Plain Layout
20454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20457 \begin_layout Plain Layout
20458 \begin_inset Formula $\theta\boldsymbol{\theta}$
20474 \begin_layout Section
20479 \begin_layout Plain Layout
20492 \begin_layout Plain Layout
20493 A list with all symbols of most of the LaTeX-packages can be found in
20494 \begin_inset CommandInset citation
20509 \begin_layout Plain Layout
20517 \begin_inset Note Note
20520 \begin_layout Plain Layout
20523 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20526 \begin_layout Plain Layout
20529 texorpdfstring is in section
20530 \begin_inset CommandInset ref
20532 reference "sub:Formulas-in-Section"
20545 \begin_layout Plain Layout
20554 \begin_layout Standard
20555 Many of the symbols listed in this section can also be inserted via the
20557 \begin_inset Graphics
20558 filename ../images/math/nabla.png
20564 \begin_inset Graphics
20565 filename ../images/math/digamma.png
20573 \begin_layout Subsection
20574 Mathematical Symbols
20575 \begin_inset CommandInset label
20577 name "sub:Mathematical-Symbols"
20585 \begin_layout Plain Layout
20586 Symbols ! mathematical
20594 \begin_layout Standard
20595 \begin_inset space \hfill{}
20599 \begin_inset Tabular
20600 <lyxtabular version="3" rows="10" columns="2">
20602 <column alignment="center" valignment="top" width="0pt">
20603 <column alignment="center" valignment="top" width="0pt">
20605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20608 \begin_layout Plain Layout
20614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20617 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20628 \begin_layout Plain Layout
20636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20639 \begin_layout Plain Layout
20640 \begin_inset Formula $\neg$
20650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20653 \begin_layout Plain Layout
20661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20664 \begin_layout Plain Layout
20665 \begin_inset Formula $\Im$
20675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20678 \begin_layout Plain Layout
20686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20689 \begin_layout Plain Layout
20690 \begin_inset Formula $\Re$
20700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20703 \begin_layout Plain Layout
20711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20714 \begin_layout Plain Layout
20715 \begin_inset Formula $\aleph$
20725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20728 \begin_layout Plain Layout
20736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20739 \begin_layout Plain Layout
20740 \begin_inset Formula $\partial$
20750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20753 \begin_layout Plain Layout
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20764 \begin_layout Plain Layout
20765 \begin_inset Formula $\infty$
20775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20778 \begin_layout Plain Layout
20786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20789 \begin_layout Plain Layout
20790 \begin_inset Formula $\wp$
20800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20803 \begin_layout Plain Layout
20811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20814 \begin_layout Plain Layout
20815 \begin_inset Formula $\imath$
20825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20828 \begin_layout Plain Layout
20836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20839 \begin_layout Plain Layout
20840 \begin_inset Formula $\jmath$
20854 \begin_inset space \hfill{}
20858 \begin_inset Tabular
20859 <lyxtabular version="3" rows="10" columns="2">
20861 <column alignment="center" valignment="top" width="0pt">
20862 <column alignment="center" valignment="top" width="0pt">
20864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20867 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20876 \begin_layout Plain Layout
20878 \begin_inset Note Note
20881 \begin_layout Plain Layout
20888 is only used as spacer.
20900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20903 \begin_layout Plain Layout
20911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20914 \begin_layout Plain Layout
20915 \begin_inset Formula $\forall$
20925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20928 \begin_layout Plain Layout
20936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20939 \begin_layout Plain Layout
20940 \begin_inset Formula $\exists$
20950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20953 \begin_layout Plain Layout
20961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20964 \begin_layout Plain Layout
20965 \begin_inset Formula $\nexists$
20975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20978 \begin_layout Plain Layout
20986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20989 \begin_layout Plain Layout
20990 \begin_inset Formula $\emptyset$
21000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21003 \begin_layout Plain Layout
21011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21014 \begin_layout Plain Layout
21015 \begin_inset Formula $\varnothing$
21025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21028 \begin_layout Plain Layout
21036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21039 \begin_layout Plain Layout
21040 \begin_inset Formula $\dag$
21050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21053 \begin_layout Plain Layout
21061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21064 \begin_layout Plain Layout
21065 \begin_inset Formula $\ddag$
21075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21078 \begin_layout Plain Layout
21086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21089 \begin_layout Plain Layout
21093 \begin_layout Plain Layout
21103 \begin_inset Formula $\complement$
21110 \begin_layout Plain Layout
21124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21127 \begin_layout Plain Layout
21135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21138 \begin_layout Plain Layout
21139 \begin_inset Formula $\Bbbk$
21153 \begin_inset space \hfill{}
21157 \begin_inset Tabular
21158 <lyxtabular version="3" rows="10" columns="2">
21160 <column alignment="center" valignment="top" width="0pt">
21161 <column alignment="center" valignment="top" width="0pt">
21163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21166 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21175 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21186 \begin_layout Plain Layout
21194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21197 \begin_layout Plain Layout
21198 \begin_inset Formula $\prime$
21208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21211 \begin_layout Plain Layout
21219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21222 \begin_layout Plain Layout
21223 \begin_inset Formula $\backprime$
21233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21236 \begin_layout Plain Layout
21244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21247 \begin_layout Plain Layout
21248 \begin_inset Formula $\mho$
21258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21261 \begin_layout Plain Layout
21269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21272 \begin_layout Plain Layout
21273 \begin_inset Formula $\triangle$
21283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21286 \begin_layout Plain Layout
21294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21297 \begin_layout Plain Layout
21298 \begin_inset Formula $\angle$
21308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21311 \begin_layout Plain Layout
21319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21322 \begin_layout Plain Layout
21323 \begin_inset Formula $\measuredangle$
21333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21336 \begin_layout Plain Layout
21344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21347 \begin_layout Plain Layout
21348 \begin_inset Formula $\sphericalangle$
21358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21361 \begin_layout Plain Layout
21369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21372 \begin_layout Plain Layout
21373 \begin_inset Formula $\top$
21383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21386 \begin_layout Plain Layout
21394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21397 \begin_layout Plain Layout
21398 \begin_inset Formula $\bot$
21412 \begin_inset space \hfill{}
21418 \begin_layout Subsection
21419 Miscellaneous Symbols
21420 \begin_inset CommandInset label
21422 name "sub:Miscellaneous-Symbols"
21430 \begin_layout Plain Layout
21431 Symbols ! miscellaneous
21439 \begin_layout Standard
21442 \begin_inset Tabular
21443 <lyxtabular version="3" rows="10" columns="2">
21445 <column alignment="center" valignment="top" width="0pt">
21446 <column alignment="center" valignment="top" width="0pt">
21448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21460 \begin_layout Plain Layout
21468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21471 \begin_layout Plain Layout
21479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21482 \begin_layout Plain Layout
21483 \begin_inset Formula $\flat$
21493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21496 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21507 \begin_layout Plain Layout
21508 \begin_inset Formula $\natural$
21518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21532 \begin_layout Plain Layout
21533 \begin_inset Formula $\sharp$
21543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\surd$
21568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\checkmark$
21593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\yen$
21618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\pounds$
21643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21655 \begin_layout Plain Layout
21656 \begin_inset Formula $\$$
21666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21669 \begin_layout Plain Layout
21675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21678 \begin_layout Plain Layout
21679 \begin_inset Formula $§$
21693 \begin_inset Tabular
21694 <lyxtabular version="3" rows="10" columns="2">
21696 <column alignment="center" valignment="top" width="0">
21697 <column alignment="center" valignment="top" width="0">
21699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21702 \begin_layout Plain Layout
21708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Plain Layout
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21722 \begin_layout Plain Layout
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21733 \begin_layout Plain Layout
21734 \begin_inset Formula $\hbar$
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21747 \begin_layout Plain Layout
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21758 \begin_layout Plain Layout
21759 \begin_inset Formula $\hslash$
21769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21772 \begin_layout Plain Layout
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21783 \begin_layout Plain Layout
21784 \begin_inset Formula $\clubsuit$
21794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21797 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21809 \begin_inset Formula $\spadesuit$
21819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21822 \begin_layout Plain Layout
21830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21833 \begin_layout Plain Layout
21834 \begin_inset Formula $\bigstar$
21844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21847 \begin_layout Plain Layout
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21858 \begin_layout Plain Layout
21859 \begin_inset Formula $\blacklozenge$
21869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21872 \begin_layout Plain Layout
21880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21883 \begin_layout Plain Layout
21884 \begin_inset Formula $\blacktriangle$
21894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21897 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21909 \begin_inset Formula $\blacktriangledown$
21919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21922 \begin_layout Plain Layout
21930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21933 \begin_layout Plain Layout
21934 \begin_inset Formula $\bullet$
21948 \begin_inset Tabular
21949 <lyxtabular version="3" rows="10" columns="2">
21951 <column alignment="center" valignment="top" width="0pt">
21952 <column alignment="center" valignment="top" width="0pt">
21954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21957 \begin_layout Plain Layout
21963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21966 \begin_layout Plain Layout
21974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21977 \begin_layout Plain Layout
21985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21988 \begin_layout Plain Layout
21989 \begin_inset Formula $\diamondsuit$
21999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22002 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22013 \begin_layout Plain Layout
22014 \begin_inset Formula $\Diamond$
22024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22027 \begin_layout Plain Layout
22035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22038 \begin_layout Plain Layout
22039 \begin_inset Formula $\heartsuit$
22049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22052 \begin_layout Plain Layout
22060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22063 \begin_layout Plain Layout
22064 \begin_inset Formula $\P$
22074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22077 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22089 \begin_inset Formula $\copyright$
22099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22102 \begin_layout Plain Layout
22110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22113 \begin_layout Plain Layout
22114 \begin_inset Formula $\circledR$
22124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22127 \begin_layout Plain Layout
22135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22138 \begin_layout Plain Layout
22139 \begin_inset Formula $\maltese$
22149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22152 \begin_layout Plain Layout
22160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22163 \begin_layout Plain Layout
22164 \begin_inset Formula $\diagup$
22174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22177 \begin_layout Plain Layout
22185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22188 \begin_layout Plain Layout
22189 \begin_inset Formula $\diagdown$
22205 \begin_layout Standard
22206 \begin_inset VSpace medskip
22209 More symbols are listed in
22210 \begin_inset CommandInset ref
22212 reference "sub:Miscellaneous-special-Characters"
22219 \begin_layout Standard
22220 Some symbols can be displayed in different sizes, see
22221 \begin_inset CommandInset ref
22223 reference "sub:Font-Sizes"
22230 \begin_layout Subsection
22235 \begin_layout Plain Layout
22236 Symbols ! Euro-symbol
22245 \begin_layout Plain Layout
22252 \begin_layout Plain Layout
22269 \begin_layout Standard
22270 To use the Euro symbol in formulas, the LaTeX-package
22278 \begin_layout Plain Layout
22284 must be installed and loaded with the LaTeX-preamble line
22287 \begin_layout Standard
22292 usepackage[gennarrow]{eurosym}
22295 \begin_layout Standard
22296 The Euro symbol can now be inserted with the command
22306 \begin_layout Plain Layout
22317 \begin_layout Standard
22318 The Euro symbol can directly be inserted with the € key in mathematical
22319 text, without having
22334 can also be inserted in TeX-mode.
22335 The official currency symbol can then be inserted with the command
22345 \begin_layout Plain Layout
22353 , that is only available in TeX-mode.
22356 \begin_layout Standard
22360 \begin_layout Plain Layout
22370 \begin_inset Note Note
22373 \begin_layout Plain Layout
22374 The following table will only be displayed when the LaTeX-package
22386 \begin_layout Standard
22387 An overview about the different Euro symbols:
22390 \begin_layout Standard
22392 \begin_inset Tabular
22393 <lyxtabular version="3" rows="4" columns="3">
22395 <column alignment="center" valignment="top" width="0pt">
22396 <column alignment="center" valignment="top" width="0pt">
22397 <column alignment="center" valignment="top" width="0pt">
22399 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22402 \begin_layout Plain Layout
22408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22411 \begin_layout Plain Layout
22417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22420 \begin_layout Plain Layout
22428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22431 \begin_layout Plain Layout
22437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22440 \begin_layout Plain Layout
22448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22451 \begin_layout Plain Layout
22452 \begin_inset Formula $\euro$
22462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22465 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22474 \begin_layout Plain Layout
22480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22483 \begin_layout Plain Layout
22484 \begin_inset Formula $\mbox{€}$
22494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22497 \begin_layout Plain Layout
22503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22506 \begin_layout Plain Layout
22514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22517 \begin_layout Plain Layout
22521 \begin_layout Plain Layout
22543 \begin_layout Standard
22547 \begin_layout Plain Layout
22557 \begin_inset Note Note
22560 \begin_layout Plain Layout
22561 The following will be displayed when the LaTeX-package
22573 \begin_layout Standard
22574 You need to install the LaTeX-package
22578 to see the rest of this subsection in the output.
22581 \begin_layout Standard
22585 \begin_layout Plain Layout
22597 \begin_layout Section
22599 \begin_inset CommandInset label
22601 name "sec:Relations"
22609 \begin_layout Plain Layout
22619 \begin_layout Plain Layout
22624 \begin_layout Plain Layout
22635 \begin_layout Plain Layout
22650 \begin_layout Standard
22651 All relations can also be inserted via the toolbar button
22652 \begin_inset Graphics
22653 filename ../images/math/leq.png
22661 \begin_layout Standard
22662 \begin_inset space \hfill{}
22666 \begin_inset Tabular
22667 <lyxtabular version="3" rows="17" columns="2">
22669 <column alignment="center" valignment="top" width="0pt">
22670 <column alignment="center" valignment="top" width="0pt">
22672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22675 \begin_layout Plain Layout
22681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22684 \begin_layout Plain Layout
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22695 \begin_layout Plain Layout
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Plain Layout
22705 \begin_inset Formula $<$
22715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22718 \begin_layout Plain Layout
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22729 \begin_layout Plain Layout
22730 \begin_inset Formula $\le$
22740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22743 \begin_layout Plain Layout
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22754 \begin_layout Plain Layout
22755 \begin_inset Formula $\ll$
22765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22768 \begin_layout Plain Layout
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22779 \begin_layout Plain Layout
22780 \begin_inset Formula $\prec$
22790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22793 \begin_layout Plain Layout
22801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22804 \begin_layout Plain Layout
22805 \begin_inset Formula $\preceq$
22815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22818 \begin_layout Plain Layout
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22829 \begin_layout Plain Layout
22830 \begin_inset Formula $\subset$
22840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22843 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22854 \begin_layout Plain Layout
22855 \begin_inset Formula $\subseteq$
22865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22868 \begin_layout Plain Layout
22876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22879 \begin_layout Plain Layout
22880 \begin_inset Formula $\sqsubseteq$
22890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22893 \begin_layout Plain Layout
22901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22904 \begin_layout Plain Layout
22905 \begin_inset Formula $\in$
22915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22918 \begin_layout Plain Layout
22926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22929 \begin_layout Plain Layout
22930 \begin_inset Formula $\vdash$
22940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22943 \begin_layout Plain Layout
22951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22954 \begin_layout Plain Layout
22955 \begin_inset Formula $\smile$
22965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22968 \begin_layout Plain Layout
22976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22979 \begin_layout Plain Layout
22980 \begin_inset Formula $\lhd$
22990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22993 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23004 \begin_layout Plain Layout
23005 \begin_inset Formula $\unlhd$
23015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23018 \begin_layout Plain Layout
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23029 \begin_layout Plain Layout
23030 \begin_inset Formula $\gtrless$
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23054 \begin_layout Plain Layout
23055 \begin_inset Formula $\mid$
23065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23068 \begin_layout Plain Layout
23076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23079 \begin_layout Plain Layout
23080 \begin_inset Formula $\nmid$
23094 \begin_inset space \hfill{}
23098 \begin_inset Tabular
23099 <lyxtabular version="3" rows="17" columns="2">
23101 <column alignment="center" valignment="top" width="0pt">
23102 <column alignment="center" valignment="top" width="0pt">
23104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23107 \begin_layout Plain Layout
23113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23116 \begin_layout Plain Layout
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Plain Layout
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23136 \begin_layout Plain Layout
23137 \begin_inset Formula $=$
23147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23150 \begin_layout Plain Layout
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23161 \begin_layout Plain Layout
23162 \begin_inset Formula $\not=$
23172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23175 \begin_layout Plain Layout
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23186 \begin_layout Plain Layout
23187 \begin_inset Formula $\equiv$
23197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23200 \begin_layout Plain Layout
23208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23211 \begin_layout Plain Layout
23212 \begin_inset Formula $\sim$
23222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23225 \begin_layout Plain Layout
23233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23236 \begin_layout Plain Layout
23237 \begin_inset Formula $\simeq$
23247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23250 \begin_layout Plain Layout
23258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23261 \begin_layout Plain Layout
23262 \begin_inset Formula $\approx$
23272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23275 \begin_layout Plain Layout
23283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23286 \begin_layout Plain Layout
23287 \begin_inset Formula $\cong$
23297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23300 \begin_layout Plain Layout
23308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23311 \begin_layout Plain Layout
23312 \begin_inset Formula $\bowtie$
23322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23325 \begin_layout Plain Layout
23333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23336 \begin_layout Plain Layout
23337 \begin_inset Formula $\notin$
23347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23350 \begin_layout Plain Layout
23358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23361 \begin_layout Plain Layout
23362 \begin_inset Formula $\perp$
23372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23375 \begin_layout Plain Layout
23383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23386 \begin_layout Plain Layout
23387 \begin_inset Formula $\propto$
23397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23400 \begin_layout Plain Layout
23408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23411 \begin_layout Plain Layout
23412 \begin_inset Formula $\asymp$
23422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23425 \begin_layout Plain Layout
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23436 \begin_layout Plain Layout
23437 \begin_inset Formula $\doteq$
23447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23450 \begin_layout Plain Layout
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Plain Layout
23462 \begin_inset Formula $\circeq$
23472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23475 \begin_layout Plain Layout
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23486 \begin_layout Plain Layout
23487 \begin_inset Formula $\models$
23497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23500 \begin_layout Plain Layout
23508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23511 \begin_layout Plain Layout
23512 \begin_inset Formula $\widehat{=}$
23526 \begin_inset space \hfill{}
23530 \begin_inset Tabular
23531 <lyxtabular version="3" rows="17" columns="2">
23533 <column alignment="center" valignment="top" width="0pt">
23534 <column alignment="center" valignment="top" width="0pt">
23536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23539 \begin_layout Plain Layout
23545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23548 \begin_layout Plain Layout
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23568 \begin_layout Plain Layout
23569 \begin_inset Formula $>$
23579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23582 \begin_layout Plain Layout
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23593 \begin_layout Plain Layout
23594 \begin_inset Formula $\ge$
23604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23607 \begin_layout Plain Layout
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23618 \begin_layout Plain Layout
23619 \begin_inset Formula $\gg$
23629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23632 \begin_layout Plain Layout
23640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23643 \begin_layout Plain Layout
23644 \begin_inset Formula $\succ$
23654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23657 \begin_layout Plain Layout
23665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23668 \begin_layout Plain Layout
23669 \begin_inset Formula $\succeq$
23679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23682 \begin_layout Plain Layout
23690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23693 \begin_layout Plain Layout
23694 \begin_inset Formula $\supset$
23704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23707 \begin_layout Plain Layout
23715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23718 \begin_layout Plain Layout
23719 \begin_inset Formula $\supseteq$
23729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23732 \begin_layout Plain Layout
23740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23743 \begin_layout Plain Layout
23744 \begin_inset Formula $\sqsupseteq$
23754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23757 \begin_layout Plain Layout
23765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23768 \begin_layout Plain Layout
23769 \begin_inset Formula $\ni$
23779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23782 \begin_layout Plain Layout
23790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23793 \begin_layout Plain Layout
23794 \begin_inset Formula $\dashv$
23804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23807 \begin_layout Plain Layout
23815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23818 \begin_layout Plain Layout
23819 \begin_inset Formula $\frown$
23829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23832 \begin_layout Plain Layout
23840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23843 \begin_layout Plain Layout
23844 \begin_inset Formula $\rhd$
23854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23857 \begin_layout Plain Layout
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23868 \begin_layout Plain Layout
23869 \begin_inset Formula $\unrhd$
23879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23882 \begin_layout Plain Layout
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23893 \begin_layout Plain Layout
23894 \begin_inset Formula $\lessgtr$
23904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23907 \begin_layout Plain Layout
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23918 \begin_layout Plain Layout
23919 \begin_inset Formula $\parallel$
23929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23932 \begin_layout Plain Layout
23940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23943 \begin_layout Plain Layout
23944 \begin_inset Formula $\nparallel$
23958 \begin_inset space \hfill{}
23964 \begin_layout Standard
23965 \begin_inset VSpace medskip
23980 are bigger than the equal looking operators
23995 \begin_layout Standard
23996 Relations are, in contrary to symbols, always surrounded by space.
23999 \begin_layout Standard
24000 Relations with labels can be created with the command
24010 \begin_layout Plain Layout
24021 \begin_layout Standard
24023 \begin_inset Tabular
24024 <lyxtabular version="3" rows="2" columns="2">
24026 <column alignment="center" valignment="top" width="0">
24027 <column alignment="center" valignment="top" width="0">
24029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24032 \begin_layout Plain Layout
24038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24041 \begin_layout Plain Layout
24043 \begin_inset Note Note
24046 \begin_layout Plain Layout
24053 is only used as spacer.
24065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24075 \begin_layout Plain Layout
24092 \begin_layout Plain Layout
24102 \begin_inset Formula $\downarrow$
24111 \begin_layout Plain Layout
24124 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24141 \begin_layout Plain Layout
24142 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24158 \begin_layout Section
24162 \begin_layout Subsection
24163 Predefined Functions
24164 \begin_inset CommandInset label
24166 name "sub:Predefined-Functions"
24174 \begin_layout Plain Layout
24175 Functions ! predefined
24183 \begin_layout Standard
24184 In general, variables are set
24188 in mathematical expressions, but not function names, because
24189 \begin_inset Formula $sin$
24192 could be misunderstood as
24193 \begin_inset Formula $s\cdot i\cdot n$
24197 Therefore there are predefined functions, that are additionally a bit separated
24199 They are inserted as commands starting with a backslash before their name.
24202 \begin_layout Standard
24204 \begin_inset Tabular
24205 <lyxtabular version="3" rows="2" columns="4">
24207 <column alignment="center" valignment="top" width="0pt">
24208 <column alignment="center" valignment="top" width="0pt">
24209 <column alignment="center" valignment="top" width="0pt">
24210 <column alignment="center" valignment="top" width="0pt">
24212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24215 \begin_layout Plain Layout
24221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24224 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24233 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24253 \begin_layout Plain Layout
24259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24262 \begin_layout Plain Layout
24263 \begin_inset Formula $Asin(x)+B$
24271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24274 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24285 \begin_layout Plain Layout
24286 \begin_inset Formula $A\sin(x)+B$
24302 \begin_layout Standard
24303 The following functions are predefined:
24306 \begin_layout Standard
24307 \begin_inset VSpace -2mm
24313 \begin_layout Standard
24315 \begin_inset Tabular
24316 <lyxtabular version="3" rows="9" columns="4">
24318 <column alignment="center" valignment="top" width="0pt">
24319 <column alignment="center" valignment="top" width="0pt">
24320 <column alignment="center" valignment="top" width="0pt">
24321 <column alignment="center" valignment="top" width="0pt">
24323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24335 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24344 \begin_layout Plain Layout
24350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24353 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24364 \begin_layout Plain Layout
24372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24410 \begin_layout Plain Layout
24418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24421 \begin_layout Plain Layout
24429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24432 \begin_layout Plain Layout
24440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24443 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24456 \begin_layout Plain Layout
24464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24467 \begin_layout Plain Layout
24475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24478 \begin_layout Plain Layout
24486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24489 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24502 \begin_layout Plain Layout
24510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24513 \begin_layout Plain Layout
24521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24524 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24535 \begin_layout Plain Layout
24545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24548 \begin_layout Plain Layout
24556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24559 \begin_layout Plain Layout
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24581 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24594 \begin_layout Plain Layout
24602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24605 \begin_layout Plain Layout
24613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24616 \begin_layout Plain Layout
24624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24627 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24640 \begin_layout Plain Layout
24648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24651 \begin_layout Plain Layout
24659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24662 \begin_layout Plain Layout
24670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24673 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24686 \begin_layout Plain Layout
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24697 \begin_layout Plain Layout
24705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24735 \begin_layout Standard
24736 They can also be inserted with the math toolbar button
24737 \begin_inset Graphics
24738 filename ../images/math/functions.png
24746 \begin_layout Subsection
24747 Self-defined Functions
24751 \begin_layout Plain Layout
24752 Functions ! self-defined
24760 \begin_layout Standard
24761 To use a function that is not predefined, like for example the sign function
24762 sgn(x), there are two possibilities:
24765 \begin_layout Itemize
24766 Define the function by inserting the following line to the LaTeX-preamble
24770 \begin_layout Plain Layout
24775 DeclareMathOperator
24778 \begin_inset CommandInset ref
24780 reference "sub:Self-defined-Operators"
24790 \begin_inset Newline newline
24794 \begin_inset VSpace -3mm
24798 \begin_inset Newline newline
24805 DeclareMathOperator{
24813 \begin_layout Plain Layout
24818 DeclareMathOperator
24824 \begin_inset Newline newline
24828 \begin_inset VSpace -2mm
24832 \begin_inset Newline newline
24835 Now the new defined function can be called with the command
24844 \begin_layout Itemize
24845 Write the the formula as usual, mark the formula name, in our example the
24850 , and change it to mathematical text.
24851 At last a space is inserted between prefactor and function.
24854 \begin_layout Standard
24855 The result is the same with both methods as with a predefined function
24859 \begin_layout Plain Layout
24860 In LyX self-defined functions are displayed red, predefined ones black.
24868 \begin_layout Standard
24870 \begin_inset Tabular
24871 <lyxtabular version="3" rows="3" columns="2">
24873 <column alignment="center" valignment="top" width="0pt">
24874 <column alignment="center" valignment="top" width="0pt">
24876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24879 \begin_layout Plain Layout
24885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24888 \begin_layout Plain Layout
24896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24899 \begin_layout Plain Layout
24907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24910 \begin_layout Plain Layout
24911 \begin_inset Formula $A\sgn(x)+B$
24921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24924 \begin_layout Plain Layout
24928 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24939 \begin_layout Plain Layout
24940 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24956 \begin_layout Standard
24957 The first method is more suitable when the self-defined function should
24958 be used several times.
24961 \begin_layout Subsection
24966 \begin_layout Plain Layout
24975 \begin_layout Standard
24976 For limits there are defined besides
24986 \begin_layout Plain Layout
25006 furthermore the following functions:
25009 \begin_layout Standard
25011 \begin_inset Tabular
25012 <lyxtabular version="3" rows="5" columns="2">
25014 <column alignment="center" valignment="top" width="0">
25015 <column alignment="center" valignment="top" width="0">
25017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25020 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25029 \begin_layout Plain Layout
25031 \begin_inset Note Note
25034 \begin_layout Plain Layout
25041 is only used as spacer.
25053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25068 \begin_inset Formula $\varliminf$
25078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25081 \begin_layout Plain Layout
25089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25092 \begin_layout Plain Layout
25093 \begin_inset Formula $\varlimsup$
25103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25106 \begin_layout Plain Layout
25114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25117 \begin_layout Plain Layout
25118 \begin_inset Formula $\varprojlim$
25128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25131 \begin_layout Plain Layout
25139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25142 \begin_layout Plain Layout
25143 \begin_inset Formula $\varinjlim$
25147 \begin_inset Formula $\raisebox{-2.5mm}{}$
25163 \begin_layout Standard
25164 \begin_inset VSpace medskip
25167 The limit is created by inserting a subscript.
25168 It is set right beside the function in an inline formula:
25171 \begin_layout Standard
25173 \begin_inset Tabular
25174 <lyxtabular version="3" rows="2" columns="2">
25176 <column alignment="center" valignment="top" width="0pt">
25177 <column alignment="center" valignment="top" width="0pt">
25179 <cell alignment="center" valignment="top" usebox="none">
25182 \begin_layout Plain Layout
25188 <cell alignment="center" valignment="top" usebox="none">
25191 \begin_layout Plain Layout
25192 \begin_inset space \hspace{}
25197 \begin_inset Note Note
25200 \begin_layout Plain Layout
25213 are used here as spacer.
25225 <cell alignment="center" valignment="top" usebox="none">
25228 \begin_layout Plain Layout
25237 \begin_layout Plain Layout
25250 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" usebox="none">
25267 \begin_layout Plain Layout
25268 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25284 \begin_layout Standard
25285 In a displayed formula the limit is set below the formula, as usual:
25286 \begin_inset Formula \[
25294 \begin_layout Subsection
25299 \begin_layout Plain Layout
25300 Functions ! modulo-
25308 \begin_layout Standard
25309 The modulo-function is special, because it exists in four variants.
25312 \begin_layout Standard
25313 The variants in a displayed formula:
25314 \begin_inset Formula \begin{align*}
25315 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25316 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25317 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25318 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25319 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25326 \begin_layout Standard
25327 In an inline formula less space is set before the function names for all
25331 \begin_layout Section
25336 \begin_layout Plain Layout
25345 \begin_layout Subsection
25346 Special Characters in Mathematical Text
25349 \begin_layout Standard
25350 The following commands can only be used in mathematical text or in TeX-mode:
25353 \begin_layout Standard
25354 \begin_inset space \hfill{}
25358 \begin_inset Tabular
25359 <lyxtabular version="3" rows="8" columns="2">
25361 <column alignment="block" valignment="top" width="0">
25362 <column alignment="block" valignment="top" width="0">
25364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25367 \begin_layout Plain Layout
25373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25376 \begin_layout Plain Layout
25384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25387 \begin_layout Plain Layout
25395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25398 \begin_layout Plain Layout
25399 \begin_inset Formula $\textrm{œ}$
25409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25412 \begin_layout Plain Layout
25420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25423 \begin_layout Plain Layout
25424 \begin_inset Formula $\textrm{Œ}$
25434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25437 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25448 \begin_layout Plain Layout
25449 \begin_inset Formula $\textrm{æ}$
25459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25462 \begin_layout Plain Layout
25470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25473 \begin_layout Plain Layout
25474 \begin_inset Formula $\textrm{Æ}$
25484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25487 \begin_layout Plain Layout
25495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25498 \begin_layout Plain Layout
25499 \begin_inset Formula $\textrm{\aa}$
25509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25519 \begin_layout Plain Layout
25526 \begin_layout Plain Layout
25547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25550 \begin_layout Plain Layout
25551 \begin_inset Formula $\textrm{Å}$
25561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25564 \begin_layout Plain Layout
25572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25575 \begin_layout Plain Layout
25576 \begin_inset Formula $\textrm{ı}$
25590 \begin_inset space \hfill{}
25594 \begin_inset Tabular
25595 <lyxtabular version="3" rows="8" columns="2">
25597 <column alignment="block" valignment="top" width="0">
25598 <column alignment="center" valignment="top" width="0">
25600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25603 \begin_layout Plain Layout
25605 \begin_inset Note Note
25608 \begin_layout Plain Layout
25615 is used for separation, because otherwise the output will be ¡ and ¿ respective
25626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25629 \begin_layout Plain Layout
25637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25640 \begin_layout Plain Layout
25648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25651 \begin_layout Plain Layout
25652 \begin_inset Formula $\textrm{ø}$
25662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25665 \begin_layout Plain Layout
25673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25676 \begin_layout Plain Layout
25677 \begin_inset Formula $\textrm{Ø}$
25687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25690 \begin_layout Plain Layout
25698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25701 \begin_layout Plain Layout
25702 \begin_inset Formula $\textrm{ł}$
25712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25715 \begin_layout Plain Layout
25723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25726 \begin_layout Plain Layout
25727 \begin_inset Formula $\textrm{Ł}$
25737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25740 \begin_layout Plain Layout
25742 \begin_inset space \hspace{}
25750 \begin_layout Plain Layout
25764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25767 \begin_layout Plain Layout
25768 \begin_inset Formula $\textrm{!`}$
25778 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25781 \begin_layout Plain Layout
25783 \begin_inset space \hspace{}
25791 \begin_layout Plain Layout
25805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25808 \begin_layout Plain Layout
25809 \begin_inset Formula $\textrm{?`}$
25819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25822 \begin_layout Plain Layout
25830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25833 \begin_layout Plain Layout
25834 \begin_inset Formula $\textrm{ȷ}$
25848 \begin_inset space \hfill{}
25854 \begin_layout Standard
25856 \begin_inset Formula $\textrm{\textrm{Å}}$
25860 \begin_inset Formula $\textrm{\textrm{Ø}}$
25863 can also be inserted via the math toolbar button
25864 \begin_inset Graphics
25865 filename ../images/math/digamma.png
25873 \begin_layout Standard
25874 An exception are the commands
25877 \begin_inset space \hspace{}
25886 \begin_inset space \hspace{}
25892 , because they can be inserted in LyX directly to text.
25895 \begin_layout Subsection
25897 \begin_inset CommandInset label
25899 name "sub:Accents-in-Text"
25907 \begin_layout Plain Layout
25916 \begin_layout Standard
25917 With the following commands all letters can be accented.
25918 The commands must be inserted in TeX-mode.
25921 \begin_layout Standard
25922 \begin_inset space \hfill{}
25926 \begin_inset Tabular
25927 <lyxtabular version="3" rows="8" columns="2">
25929 <column alignment="block" valignment="top" width="0">
25930 <column alignment="block" valignment="top" width="0">
25932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25935 \begin_layout Plain Layout
25941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25944 \begin_layout Plain Layout
25952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25955 \begin_layout Plain Layout
25959 \begin_inset Quotes grd
25967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25970 \begin_layout Plain Layout
25974 \begin_layout Plain Layout
25990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25993 \begin_layout Plain Layout
26001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26004 \begin_layout Plain Layout
26008 \begin_layout Plain Layout
26024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26027 \begin_layout Plain Layout
26034 \begin_layout Plain Layout
26048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26051 \begin_layout Plain Layout
26055 \begin_layout Plain Layout
26071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26074 \begin_layout Plain Layout
26082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26085 \begin_layout Plain Layout
26089 \begin_layout Plain Layout
26105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26108 \begin_layout Plain Layout
26115 \begin_layout Plain Layout
26129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26132 \begin_layout Plain Layout
26136 \begin_layout Plain Layout
26152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26155 \begin_layout Plain Layout
26162 \begin_layout Plain Layout
26176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26179 \begin_layout Plain Layout
26183 \begin_layout Plain Layout
26199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26202 \begin_layout Plain Layout
26209 \begin_layout Plain Layout
26223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26226 \begin_layout Plain Layout
26230 \begin_layout Plain Layout
26250 \begin_inset space \hfill{}
26254 \begin_inset Tabular
26255 <lyxtabular version="3" rows="8" columns="2">
26257 <column alignment="block" valignment="top" width="0">
26258 <column alignment="center" valignment="top" width="0">
26260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26263 \begin_layout Plain Layout
26269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26272 \begin_layout Plain Layout
26280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26283 \begin_layout Plain Layout
26290 \begin_layout Plain Layout
26304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26307 \begin_layout Plain Layout
26311 \begin_layout Plain Layout
26327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26330 \begin_layout Plain Layout
26338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26341 \begin_layout Plain Layout
26345 \begin_layout Plain Layout
26361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26364 \begin_layout Plain Layout
26371 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26385 \begin_layout Plain Layout
26389 \begin_layout Plain Layout
26405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26408 \begin_layout Plain Layout
26416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26419 \begin_layout Plain Layout
26423 \begin_layout Plain Layout
26439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26442 \begin_layout Plain Layout
26449 \begin_layout Plain Layout
26463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26466 \begin_layout Plain Layout
26470 \begin_layout Plain Layout
26486 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26489 \begin_layout Plain Layout
26496 \begin_layout Plain Layout
26510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26513 \begin_layout Plain Layout
26517 \begin_layout Plain Layout
26533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26536 \begin_layout Plain Layout
26543 \begin_layout Plain Layout
26557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26564 \begin_layout Plain Layout
26584 \begin_inset space \hfill{}
26590 \begin_layout Standard
26591 \begin_inset VSpace medskip
26600 also two different characters can be accented.
26609 \begin_layout Plain Layout
26624 \begin_layout Plain Layout
26636 \begin_layout Standard
26649 can in combination with vowels directly be inserted with the keyboard without
26651 The same applies for the tilde
26655 \begin_layout Plain Layout
26656 This only applies for keyboards where the tilde is defined as accent.
26665 in combination with
26680 \begin_layout Standard
26723 , and accents inserted directly with the keyboard are also available in
26725 For the other accents there are special math commands to be used in formulas,
26727 \begin_inset CommandInset ref
26729 reference "sub:Accents-for-one"
26736 \begin_layout Standard
26737 \begin_inset VSpace bigskip
26740 Furthermore, with the command
26750 \begin_layout Plain Layout
26758 all numbers and letters can be set into a circle, quasi accented with a
26759 circle, similar to the the copyright symbol.
26762 \begin_layout Standard
26764 \begin_inset Tabular
26765 <lyxtabular version="3" rows="3" columns="2">
26767 <column alignment="center" valignment="top" width="0">
26768 <column alignment="center" valignment="top" width="0">
26770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26773 \begin_layout Plain Layout
26779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26782 \begin_layout Plain Layout
26784 \begin_inset Note Note
26787 \begin_layout Plain Layout
26794 is only used as spacer.
26806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26809 \begin_layout Plain Layout
26817 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26820 \begin_layout Plain Layout
26824 \begin_layout Plain Layout
26840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26843 \begin_layout Plain Layout
26854 raisebox{-1.5pt}{W}}
26859 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26862 \begin_layout Plain Layout
26863 \begin_inset Formula $\raisebox{4.5mm}{}$
26870 \begin_layout Plain Layout
26888 \begin_inset Formula $\raisebox{-2mm}{}$
26904 \begin_layout Standard
26905 One has to take care that the character fits in the circle.
26916 \begin_layout Plain Layout
26918 \begin_inset CommandInset ref
26920 reference "sub:Font-Sizes"
26929 specifies thereby the size of the circle.
26940 \begin_layout Plain Layout
26942 \begin_inset CommandInset ref
26944 reference "sub:Boxes-without-Frame"
26953 the character can be centered.
26956 \begin_layout Subsection
26961 \begin_layout Plain Layout
26970 \begin_layout Standard
26971 Minuscule numbers are created with the command
26981 \begin_layout Plain Layout
26990 The command can be used in formulas and in TeX-mode.
26991 The command scheme is:
26994 \begin_layout Standard
26999 oldstylenums{number}
27002 \begin_layout Standard
27007 oldstylenums{0123456789
27010 \begin_inset Formula $\oldstylenums{0123456789}$
27016 \begin_layout Subsection
27017 Miscellaneous special Characters
27018 \begin_inset CommandInset label
27020 name "sub:Miscellaneous-special-Characters"
27028 \begin_layout Plain Layout
27029 Special characters ! miscellaneous
27037 \begin_layout Standard
27038 The following characters can only be inserted to formulas by using commands:
27041 \begin_layout Standard
27043 \begin_inset Tabular
27044 <lyxtabular version="3" rows="4" columns="2">
27046 <column alignment="center" valignment="top" width="0">
27047 <column alignment="center" valignment="top" width="0">
27049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27052 \begin_layout Plain Layout
27058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27061 \begin_layout Plain Layout
27069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27072 \begin_layout Plain Layout
27079 \begin_layout Plain Layout
27093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27096 \begin_layout Plain Layout
27097 \begin_inset Formula $\mathcircumflex$
27107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27110 \begin_layout Plain Layout
27118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27121 \begin_layout Plain Layout
27122 \begin_inset Formula $\_$
27132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27135 \begin_layout Plain Layout
27140 \begin_layout Plain Layout
27155 \begin_layout Plain Layout
27168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27171 \begin_layout Plain Layout
27172 \begin_inset Formula $^{\circ}$
27188 \begin_layout Standard
27189 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27190 contains the following line
27194 \begin_layout Plain Layout
27195 More about this is described in
27196 \begin_inset CommandInset ref
27198 reference "sub:Text-Characters-in"
27210 \begin_layout Standard
27215 DeclareInputtext{176}{
27228 \begin_layout Section
27230 \begin_inset CommandInset label
27232 name "sec:Formula-Styles"
27240 \begin_layout Plain Layout
27249 \begin_layout Itemize
27250 There are two different alignment styles:
27254 \begin_layout Description
27255 Centered is the predefined standard
27258 \begin_layout Description
27259 Indented for this the option
27263 must be inserted in the menu
27265 Document\SpecialChar \menuseparator
27271 \begin_inset space ~
27277 \begin_layout Standard
27282 is used, the indentation can be adjusted with the length
27292 \begin_layout Plain Layout
27301 Should the distance be 15
27302 \begin_inset space \thinspace{}
27305 mm, the following command line is inserted in the LaTeX-preamble
27308 \begin_layout Standard
27318 \begin_layout Standard
27319 When no length is specified, the predefined value of 30
27320 \begin_inset space \thinspace{}
27327 \begin_layout Itemize
27328 And two different numbering styles:
27332 \begin_layout Description
27333 Right is the predefined standard
27336 \begin_layout Description
27337 Left for this the option
27341 must be inserted in the menu
27343 Document\SpecialChar \menuseparator
27349 \begin_inset space ~
27356 \begin_layout Standard
27365 can also be used together.
27366 In this case both options are inserted, separated by a comma.
27369 \begin_layout Standard
27370 The chosen styles are used for all displayed formulas of the document.
27371 When both, centered and indented formulas should be created in a document,
27377 The indented formulas are then set in a flalign environment, see
27378 \begin_inset CommandInset ref
27380 reference "sub:Flalign-Environment"
27387 \begin_layout Section
27389 \begin_inset CommandInset label
27391 name "sec:Multiline-Formulas"
27399 \begin_layout Plain Layout
27400 Formula ! multiline
27408 \begin_layout Subsection
27412 \begin_layout Standard
27413 In LyX multiline formulas are created by pressing
27420 This creates either an
27422 eqnarray environment
27424 that is described in
27425 \begin_inset CommandInset ref
27427 reference "sub:Eqnarray-Environment"
27431 or, when the option
27433 Use AMS math package
27435 in the document settings is selected, an
27439 that is described in
27440 \begin_inset CommandInset ref
27442 reference "sub:Standard-align-Environment"
27449 \begin_layout Standard
27450 There are other multiline formula environments that can be created via the
27453 Insert\SpecialChar \menuseparator
27457 These environments are described in the following sections.
27460 \begin_layout Standard
27461 In all multiline formula environments a new line is created by pressing
27467 To add or delete lines, the math toolbar buttons
27468 \begin_inset Graphics
27469 filename ../images/tabular-feature_append-row.png
27475 \begin_inset Graphics
27476 filename ../images/tabular-feature_delete-row.png
27481 , respectively, or the menu
27483 Edit\SpecialChar \menuseparator
27489 \begin_layout Subsubsection
27491 \begin_inset CommandInset label
27493 name "sub:Line-Separation"
27501 \begin_layout Plain Layout
27502 Formula ! multiline ! Line separation
27510 \begin_layout Standard
27511 There is sometimes not enough space in multiline formulas between the lines:
27512 \begin_inset Formula \begin{eqnarray*}
27513 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}\\
27514 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*}
27521 \begin_layout Standard
27522 In LaTeX additional line space is specified as optional argument of the
27524 This is not yet possible in LyX
27528 \begin_layout Plain Layout
27530 \begin_inset CommandInset href
27532 name "LyX-bug #1505"
27533 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27542 , therefore the whole formula must be inserted in TeX-mode.
27543 To add in our example space, the command
27551 is inserted at the end of the first line.
27556 \begin_layout Plain Layout
27563 \begin_layout Plain Layout
27565 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27568 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27575 \begin_layout Plain Layout
27579 left(B^{2}+x_{0}^{2}
27587 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27592 \begin_layout Plain Layout
27604 \begin_layout Standard
27605 \begin_inset VSpace bigskip
27608 To set the the line separation for all lines in a formula, the length
27618 \begin_layout Plain Layout
27628 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27639 \begin_inset space \thinspace{}
27644 \begin_inset space \thinspace{}
27647 mm additional line separation as in the previous example, the command
27650 \begin_layout Standard
27660 \begin_layout Standard
27661 is inserted in TeX-mode before the formula.
27662 This requires that the LaTeX-package
27670 \begin_layout Plain Layout
27675 is part of every LaTeX standard installation.
27684 \begin_layout Plain Layout
27690 was loaded in LaTeX-preamble with the line
27693 \begin_layout Standard
27701 \begin_layout Standard
27706 \begin_layout Plain Layout
27718 \begin_inset Formula \begin{eqnarray*}
27719 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}\\
27720 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*}
27727 \begin_layout Standard
27731 \begin_layout Plain Layout
27742 To get back to the predefined distance,
27748 is set to the value 3
27749 \begin_inset space \thinspace{}
27755 \begin_layout Subsubsection
27757 \begin_inset CommandInset label
27759 name "sub:Column-Separation"
27767 \begin_layout Plain Layout
27768 Formula ! multiline ! Column separation
27776 \begin_layout Standard
27777 Multiline formulas form a matrix.
27778 A formula in the eqnarray environment is for example a matrix with three
27780 By changing the column separation in this environment, the space beside
27781 the relation sign can be changed.
27784 \begin_layout Standard
27785 The column separation is specified with the length
27795 \begin_layout Plain Layout
27804 \begin_inset Newline newline
27807 column separation = 2
27808 \begin_inset space \thinspace{}
27818 \begin_inset Newline newline
27824 \begin_layout Standard
27834 \begin_layout Standard
27835 inserted in TeX-mode, sets for all following formulas a column separation
27837 \begin_inset space \thinspace{}
27841 To get back to the predefined distance,
27848 \begin_inset space \thinspace{}
27854 \begin_layout Standard
27856 \begin_inset space \thinspace{}
27859 cm column separation:
27863 \begin_layout Plain Layout
27875 \begin_inset Formula \begin{eqnarray*}
27877 C & \ne & A\end{eqnarray*}
27881 A formula with the predefined column separation for matrices of 10
27882 \begin_inset space \thinspace{}
27889 \begin_layout Plain Layout
27901 \begin_inset Formula \begin{eqnarray*}
27903 C & \ne & A\end{eqnarray*}
27910 \begin_layout Subsubsection
27915 \begin_layout Plain Layout
27924 \begin_layout Standard
27925 Long formulas can be typeset using these methods:
27928 \begin_layout Itemize
27929 When one side of the equation is much shorther than the line width, this
27930 one is chosen for the left side and the right side is typeset over two
27935 \begin_layout Plain Layout
27945 \begin_inset Formula \begin{eqnarray}
27946 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 \\
27947 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
27955 \begin_layout Plain Layout
27965 \begin_inset Newline newline
27968 The minus sign at the beginning of the second line does normally not appear
27969 as operator because it is the first character of the line.
27970 Thus it would not be surrounded by space and could not be distinguished
27971 from the fraction bar.
27972 To avoid this, space was inserted behind the minus sign with the command
27983 \begin_layout Plain Layout
27991 \begin_inset CommandInset ref
27993 reference "sub:Variable-Space"
28006 \begin_layout Plain Layout
28017 \begin_layout Itemize
28018 When both sides of the equation are too long, the command
28028 \begin_layout Plain Layout
28037 It is inserted to the first column of the first line and effects that all
28038 further insertions overwrite the following columns:
28042 \begin_layout Plain Layout
28052 \begin_inset Formula \begin{eqnarray}
28053 \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 \\
28054 & & -\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 \\
28055 & & =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}
28063 \begin_layout Plain Layout
28073 \begin_inset Newline newline
28076 After the insertion of
28082 , the cursor is in a purple box that is a bit shifted to the left from the
28084 In this the formula is inserted.
28088 \begin_layout Plain Layout
28098 \begin_inset Newline newline
28101 The content of the further lines is inserted to the second or another formula
28103 The greater the column number where it was inserted, the larger the indentation.
28107 \begin_layout Plain Layout
28117 \begin_inset Newline newline
28121 \begin_inset Note Greyedout
28124 \begin_layout Plain Layout
28125 Note the following when using
28134 \begin_layout Itemize
28135 The formula doesn't use the full page width.
28137 \begin_inset space \thinspace{}
28141 \begin_inset space ~
28145 \begin_inset Formula $-B^{2}$
28148 is added to the first line in the above example, it would have been outside
28150 To better use the width, negative space can be inserted at the beginning
28154 \begin_layout Itemize
28155 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28160 \begin_layout Plain Layout
28161 \begin_inset CommandInset href
28163 name "LyX-bug #1429"
28164 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28173 One can only set the cursor at the beginning of the line and move it with
28182 \begin_layout Itemize
28183 Other methods to set long formulas are offered by the environments described
28185 \begin_inset CommandInset ref
28187 reference "sub:Multline-Environment"
28192 \begin_inset CommandInset ref
28194 reference "sub:Multiline-Formula-Parts"
28201 \begin_layout Subsubsection
28203 \begin_inset CommandInset label
28205 name "sub:Multiline-Brackets"
28213 \begin_layout Plain Layout
28214 Brackets ! for multiline expressions
28222 \begin_layout Standard
28223 For brackets spanning multiple lines the following problem occurs:
28224 \begin_inset Formula \begin{eqnarray*}
28225 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28226 & & \left.\cdots+B-D\right]\end{eqnarray*}
28233 \begin_layout Standard
28234 The closing bracket is smaller than the opening bracket because brackets
28235 with variable size may not span multiple lines.
28238 \begin_layout Standard
28239 To set the bracket size for the second line correctly, the first line is
28250 \begin_layout Plain Layout
28258 and the second line with
28266 \begin_layout Plain Layout
28280 \begin_inset CommandInset ref
28282 reference "sub:Automatic-Bracket-Size"
28297 \begin_layout Plain Layout
28323 \begin_layout Plain Layout
28342 \begin_layout Plain Layout
28361 \begin_layout Plain Layout
28373 \begin_inset Formula $\downarrow$
28382 \begin_layout Plain Layout
28390 is inserted, because the multiplication operator with its limits is the
28391 largest symbol in the first line and this should be the size for the bracket
28392 in the second line.
28395 \begin_layout Standard
28396 The result is this:
28397 \begin_inset Formula \begin{eqnarray*}
28398 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28399 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28406 \begin_layout Subsection
28410 \begin_layout Standard
28411 Align environments can be used for every kind of multiline formulas.
28412 They are specially useful to set several formulas side by side.
28415 \begin_layout Standard
28416 Align environments consist of columns.
28417 The odd columns are right aligned, the even ones left aligned.
28418 Every line in an Align environment can be numbered.
28421 \begin_layout Standard
28422 Align environments are created via the menu
28424 Insert\SpecialChar \menuseparator
28430 Edit\SpecialChar \menuseparator
28431 Math\SpecialChar \menuseparator
28432 Change Formula Type
28434 already existing formulas can be converted to Align environments.
28437 \begin_layout Standard
28438 To add or delete columns, the math toolbar buttons
28439 \begin_inset Graphics
28440 filename ../images/tabular-feature_append-column.png
28446 \begin_inset Graphics
28447 filename ../images/tabular-feature_delete-column.png
28452 , respectively, or the menu
28454 Edit\SpecialChar \menuseparator
28460 \begin_layout Subsubsection
28461 Standard align Environment
28462 \begin_inset CommandInset label
28464 name "sub:Standard-align-Environment"
28472 \begin_layout Plain Layout
28473 Formula ! multiline ! align environment
28481 \begin_layout Standard
28482 This Align environment is created by presssing
28486 in a formula or by the menu
28488 Insert\SpecialChar \menuseparator
28489 Math\SpecialChar \menuseparator
28490 AMS align Environment
28495 \begin_layout Standard
28496 An example for two formulas set side by side, that are created with a four
28497 column align environment:
28498 \begin_inset Formula \begin{align*}
28499 A & =\sin(B) & C & =D\\
28500 C & \ne A & B & \ne D\end{align*}
28504 As it can be seen, the formulas in this environment are placed so as if
28513 \begin_layout Plain Layout
28521 \begin_inset CommandInset ref
28523 reference "sub:Variable-Space"
28534 before the first and after every even column.
28535 When the formula style
28541 \begin_layout Plain Layout
28543 \begin_inset CommandInset ref
28545 reference "sec:Formula-Styles"
28556 is used, the formula is set without the
28562 before the first column.
28565 \begin_layout Subsubsection
28566 Alignat Environment
28570 \begin_layout Plain Layout
28571 Formula ! multiline ! alignat environment
28579 \begin_layout Standard
28580 The alignat environment has no predefined column separation.
28581 It can be inserted manually with the spaces that are described
28582 \begin_inset CommandInset ref
28584 reference "sub:Space"
28591 \begin_layout Standard
28592 The above example in the alignat environment where 1
28593 \begin_inset space \thinspace{}
28596 cm space was inserted at the beginning of the second formula:
28597 \begin_inset Formula \begin{alignat*}{2}
28598 A & =\sin(B) & \hspace{1cm}C & =D\\
28599 C & \ne A & B & \ne D\end{alignat*}
28603 Because the column separation can be set separately for every column, this
28604 environment is especially suitable to set three and more formulas side
28608 \begin_layout Subsubsection
28609 Flalign Environment
28610 \begin_inset CommandInset label
28612 name "sub:Flalign-Environment"
28620 \begin_layout Plain Layout
28621 Formula ! multiline ! flalign environment
28629 \begin_layout Standard
28630 In this environment the first two columns are always set as much as possible
28631 to the left and the last two ones to the right.
28633 \begin_inset Formula \begin{flalign*}
28634 A & =1 & B & =2 & C & =3\\
28635 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28642 \begin_layout Standard
28643 By creating a flalign environment with an odd number of columns where an
28644 empty TeX-brace is inserted to the last column, several formulas in a document
28645 can be set to the left, although the formula style
28650 As example the indented formula
28651 \begin_inset CommandInset ref
28653 reference "eq:VolInt"
28658 \begin_inset Formula \begin{flalign}
28659 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28663 The first two columns contain the formula.
28664 To indent it as with the formula style
28669 \begin_inset space \thinspace{}
28672 pt space was inserted at the beginning of the first column.
28675 \begin_layout Subsection
28676 Eqnarray Environment
28677 \begin_inset CommandInset label
28679 name "sub:Eqnarray-Environment"
28687 \begin_layout Plain Layout
28688 Formula ! multiline ! eqnarray environment
28696 \begin_layout Standard
28697 When this environment has been created, three blue boxes appear.
28698 The content of the first box is right aligned, the content of the last
28700 The content of the middle box appears centered and a bit smaller, because
28701 it is designed to insert there only relation characters.
28702 \begin_inset Formula \begin{eqnarray*}
28703 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28705 A & = & A\end{eqnarray*}
28712 \begin_layout Subsection
28717 \begin_layout Plain Layout
28718 Formula ! multiline ! gather environment
28726 \begin_layout Standard
28727 This environment consists of only one centered column.
28728 Every line can be numbered.
28729 \begin_inset Formula \begin{gather}
28731 X=\textrm{-}1\end{gather}
28738 \begin_layout Subsection
28739 Multline Environment
28740 \begin_inset CommandInset label
28742 name "sub:Multline-Environment"
28750 \begin_layout Plain Layout
28751 Formula ! multiline ! multline environment
28759 \begin_layout Standard
28760 The multline environment consists, like the gather environment, of only
28762 But the first line is left aligned, the last one right aligned.
28763 All other lines are centered.
28764 Therefore this environment is suitable for long formulas.
28766 \begin_inset CommandInset ref
28768 reference "eq:lefteqn"
28772 in the multline environment:
28773 \begin_inset Formula \begin{multline}
28774 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}\\
28775 -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}\\
28776 =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}
28783 \begin_layout Standard
28784 In the output only the last (first) line of a multline environment appears
28785 numbered when the document numbering is right (left).
28789 \begin_layout Plain Layout
28790 numbering styles see
28791 \begin_inset CommandInset ref
28793 reference "sec:Formula-Styles"
28805 \begin_layout Standard
28814 \begin_layout Plain Layout
28832 \begin_layout Plain Layout
28842 a centered line can be right or left aligned, respectively.
28843 The commands are used as follows:
28846 \begin_layout Standard
28851 shoveright{line content}
28857 shoveleft{line content}
28860 \begin_layout Standard
28861 \begin_inset VSpace medskip
28872 \begin_layout Plain Layout
28882 specifies the distance of the first line from the left page margin.
28883 Predefined is the length 0
28884 \begin_inset space \thinspace{}
28890 \begin_layout Standard
28891 As example the above formula where the command
28894 \begin_layout Standard
28904 \begin_layout Standard
28905 was inserted in TeX-mode before:
28909 \begin_layout Plain Layout
28921 \begin_inset Formula \begin{multline}
28922 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}\\
28923 \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}}\\
28924 =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}
28932 \begin_layout Plain Layout
28943 The second line was left aligned using
28952 \begin_layout Subsection
28953 Multiline Formula Parts
28954 \begin_inset CommandInset label
28956 name "sub:Multiline-Formula-Parts"
28964 \begin_layout Plain Layout
28965 Formula ! multiline ! formula parts
28973 \begin_layout Standard
28974 To display only parts of a formula with multiple lines, one of the following
28975 environments are used:
28992 They can be inserted via the menu
28994 Insert\SpecialChar \menuseparator
28997 or by using the commands described in this section.
29000 \begin_layout Standard
29001 The first three have the same properties as the corresponding multiline
29002 formula environments, but it is possible to set further formula parts beside
29005 \begin_inset Formula \[
29006 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29007 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29008 \right\} \textrm{Uncertainty relations}\]
29015 \begin_layout Standard
29016 To get this formula, a displayed formula is created where the command
29024 \begin_layout Plain Layout
29035 A purple box appears around the blue formula box where now columns and
29036 lines can be added.
29037 Outside the multiline environment other formula parts can be set, like
29041 \begin_layout Standard
29042 The aligned environment is also suitable for long formulas whose lines are
29043 horizontally aligned.
29044 Using aligned in a displayed formula has the advantage that the formula
29045 number is vertically centered behind the lines.
29047 \begin_inset CommandInset ref
29049 reference "eq:kurzlang"
29053 in the aligned environment:
29054 \begin_inset Formula \begin{equation}
29055 \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}|}\\
29056 & -\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}
29064 \begin_layout Standard
29065 To use the environments
29087 \begin_layout Plain Layout
29105 \begin_layout Plain Layout
29123 \begin_layout Plain Layout
29131 are inserted, respectively.
29132 The split environment has the same properties as the aligned environment
29133 but it can only have two columns.
29136 \begin_layout Subsection
29137 Text in multiline Formulas
29138 \begin_inset CommandInset label
29140 name "sub:Text-in-multiline"
29148 \begin_layout Plain Layout
29158 \begin_layout Plain Layout
29159 Formula ! multiline ! text
29167 \begin_layout Standard
29168 In the Align environments, and the multline and gather environment, text
29169 can be inserted that will appear in a separate line and doesn't affect
29170 the column alignment.
29171 To do this, the command
29179 \begin_layout Plain Layout
29189 is used in the following scheme:
29192 \begin_layout Standard
29200 \begin_layout Standard
29201 The text should not be longer than a line because it cannot be hyphenated.
29202 As LyX doesn't yet support
29208 directly, the text is written as mathematical text.
29215 must hereby be at the beginning of a line and appears in the output above
29217 An example where the text was inserted at the beginning of the second line:
29218 \begin_inset Formula \begin{align}
29219 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29220 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29227 \begin_layout Section
29232 \begin_layout Plain Layout
29242 \begin_layout Plain Layout
29243 Formula ! numbering|see
29247 \begin_layout Plain Layout
29258 \begin_layout Plain Layout
29273 \begin_layout Subsection
29277 \begin_layout Standard
29278 Numbered formulas can be created with the menu
29280 Insert\SpecialChar \menuseparator
29281 Math\SpecialChar \menuseparator
29283 \begin_inset space ~
29291 \begin_inset space ~
29297 Existing formulas can be numbered with the menu
29299 Edit\SpecialChar \menuseparator
29300 Math\SpecialChar \menuseparator
29302 \begin_inset space ~
29310 \begin_inset space ~
29316 The formula number is displayed in LyX behind the formula as number sign
29318 The number sign is replaced in the output by the formula number.
29321 \begin_layout Standard
29322 When numbering is turned on in multiline formulas, all lines will be numbered.
29323 But the numbering can be controlled with the menu
29325 Edit\SpecialChar \menuseparator
29326 Math\SpecialChar \menuseparator
29328 \begin_inset space ~
29332 \begin_inset space ~
29336 \begin_inset space ~
29344 \begin_inset space ~
29352 \begin_layout Standard
29353 Except of inline formulas, all formulas can be numbered with two different
29355 \begin_inset CommandInset ref
29357 reference "sec:Formula-Styles"
29364 \begin_layout Subsection
29366 \begin_inset CommandInset label
29368 name "sub:Cross-References"
29376 \begin_layout Plain Layout
29377 Cross-references ! to formulas
29385 \begin_layout Standard
29386 All labeled formulas can be cross-referenced.
29387 A label is added by the menu
29389 Insert\SpecialChar \menuseparator
29392 or the toolbar button
29393 \begin_inset Graphics
29394 filename ../images/label-insert.png
29400 The cursor must hereby be inside a displayed formula.
29401 A dialog pops up displaying the prefix
29406 The label is inserted there behind the prefix.
29407 The predefined prefix means
29408 \begin_inset Quotes eld
29412 \begin_inset Quotes erd
29415 and makes it easier to find labels in large documents because it marks
29416 it as formula label to divide it from e.
29417 \begin_inset space \thinspace{}
29421 \begin_inset space ~
29425 To change a label, the menu
29427 Insert\SpecialChar \menuseparator
29433 \begin_layout Standard
29434 The name of the label is displayed in LyX within two parentheses behind
29436 A formula with a label is always numbered.
29439 \begin_layout Standard
29440 Cross-references are inserted via the menu
29442 Insert\SpecialChar \menuseparator
29445 or with the toolbar button
29446 \begin_inset Graphics
29447 filename ../images/dialog-show-new-inset_ref.png
29453 A formula cross-reference appears in the output as formula number.
29454 When in the cross-reference dialog window the format
29458 is chosen, the cross-reference appears in the output as formula number
29460 \begin_inset Newline newline
29463 By right-clicking on a cross-reference in LyX, one jumps to the formula
29464 that is referenced.
29467 \begin_layout Standard
29468 Here are as examples cross-references to formulas of the following subsections:
29469 \begin_inset Note Note
29472 \begin_layout Plain Layout
29473 Note the different cross-reference types.
29481 \begin_layout Standard
29483 \begin_inset CommandInset ref
29490 \begin_inset CommandInset ref
29498 \begin_inset CommandInset ref
29504 ) big Latin letters are used for the numbering in contrary to (
29505 \begin_inset CommandInset ref
29514 \begin_layout Standard
29515 \begin_inset VSpace medskip
29518 When the argument of
29526 \begin_layout Plain Layout
29534 \begin_inset CommandInset ref
29536 reference "sub:User-defined-Numbering"
29547 contains a box like in
29548 \begin_inset CommandInset ref
29550 reference "sub:Paragraph-Boxes"
29554 , the formula cannot be referenced.
29557 \begin_layout Subsection
29562 \begin_layout Plain Layout
29563 Formula numbering ! subnumbering
29571 \begin_layout Standard
29572 With the help of the commands
29576 begin{subequations}
29584 formulas can be subnumbered.
29585 Both commands are inserted in TeX-mode.
29588 \begin_layout Standard
29590 \begin_inset Formula \begin{equation}
29591 A=C-B\label{eq:a}\end{equation}
29599 \begin_layout Plain Layout
29603 addtocounter{equation}{-1}
29612 \begin_layout Plain Layout
29616 begin{subequations}
29622 \begin_inset VSpace -5mm
29626 \begin_inset Formula \begin{equation}
29627 B=C-A\label{eq:b}\end{equation}
29632 \begin_inset Formula \begin{equation}
29633 C=A+B\label{eq:c}\end{equation}
29640 \begin_layout Standard
29644 \begin_layout Plain Layout
29656 \begin_layout Standard
29657 To create the example, the following is done:
29660 \begin_layout Enumerate
29661 first formula is inserted
29664 \begin_layout Enumerate
29669 addtocounter{equation}{-1}
29671 begin{subequations}
29675 \begin_layout Plain Layout
29684 \begin_inset Newline newline
29689 is inserted after the first formula
29692 \begin_layout Enumerate
29693 second formula is inserted
29696 \begin_layout Enumerate
29697 third formula is inserted
29700 \begin_layout Enumerate
29707 is inserted after the third formula
29710 \begin_layout Standard
29711 Every formula between the commands
29723 is subnumbered as a, b,
29724 \begin_inset Newline linebreak
29727 c, \SpecialChar \ldots{}
29728 For multiline formulas every line will be subnumbered.
29729 All subnumbered formulas are treated as
29734 But as every numbered formula increases the counter
29738 by one, the command
29744 is needed to decrease it.
29745 Otherwise the formulas
29746 \begin_inset CommandInset ref
29753 \begin_inset CommandInset ref
29760 \begin_inset CommandInset ref
29766 would be numbered as
29767 \begin_inset CommandInset ref
29774 \begin_inset CommandInset ref
29781 \begin_inset CommandInset ref
29790 \begin_layout Standard
29791 By inserting the commands in TeX-mode, a space is created between the first
29794 \begin_inset space \thinspace{}
29797 mm vertical space is inserted after the command
29801 begin{subequations}
29804 When the formula style
29810 \begin_layout Plain Layout
29812 \begin_inset CommandInset ref
29814 reference "sec:Formula-Styles"
29826 \begin_inset space \thinspace{}
29829 mm space is inserted instead.
29832 \begin_layout Standard
29833 Here is an example for a multiline formula where the numbering was turned
29834 off for the second line:
29838 \begin_layout Plain Layout
29842 begin{subequations}
29848 \begin_inset Formula \begin{eqnarray}
29849 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29850 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29851 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29859 \begin_layout Plain Layout
29871 \begin_layout Subsection
29872 User-defined Numbering
29873 \begin_inset CommandInset label
29875 name "sub:User-defined-Numbering"
29883 \begin_layout Plain Layout
29884 Formula numbering ! user-defined
29892 \begin_layout Standard
29896 \begin_layout Plain Layout
29897 Formula numbering ! self-defined delimiters
29902 With the standard numbering parentheses are set around the formula number.
29903 To replace the parentheses for example by vertical bars, the following
29904 line is added to the LaTeX-preamble:
29907 \begin_layout Standard
29919 \begin_inset Note Note
29922 \begin_layout Plain Layout
29923 This macro is already declared in the LaTeX-preamble for testing.
29924 To activate it, remove the percent sign at the beginning.
29932 \begin_layout Standard
29933 To use other characters, the vertical bars besides the
29937 are replaced by one ore more characters.
29938 To get only the formula number the vertical bars are omitted.
29941 \begin_layout Standard
29942 \begin_inset VSpace bigskip
29945 When there should be an expression of your choice instead of the consecutive
29946 formula number in parentheses behind the formula, the command
29956 \begin_layout Plain Layout
29965 \begin_inset Formula \begin{equation}
29966 A+B=C\tag{something}\label{eq:tag}\end{equation}
29970 In this example the command
29978 \begin_layout Plain Layout
29989 was inserted to the formula.
29992 \begin_layout Standard
30001 \begin_layout Plain Layout
30012 is inserted instead, the star prevents the parentheses around the expression:
30013 \begin_inset Formula \[
30014 A+B=C\tag*{something}\]
30021 \begin_layout Standard
30022 \begin_inset VSpace bigskip
30025 To restart the formula numbering with new document parts or sections, the
30026 following command is used:
30029 \begin_layout Standard
30034 @addtoreset{equation}{part}
30040 \begin_layout Plain Layout
30045 \begin_layout Plain Layout
30056 \begin_layout Plain Layout
30069 \begin_layout Plain Layout
30080 \begin_layout Plain Layout
30093 \begin_inset Newline newline
30097 \begin_inset Newline newline
30104 @addtoreset{equation}{section}
30107 \begin_layout Standard
30108 To be able to use these commands in TeX-mode, the
30109 \begin_inset Quotes eld
30113 \begin_inset Quotes erd
30116 character has to be made
30117 \begin_inset Quotes eld
30121 \begin_inset Quotes erd
30124 for LaTeX using the command
30138 So the command sequence in TeX-mode is:
30141 \begin_layout Standard
30147 \begin_inset Newline newline
30152 @addtoreset{equation}{section}
30153 \begin_inset Newline newline
30161 \begin_layout Standard
30162 In the LaTeX-preamble
30174 can be omitted as they are automatically internally inserted by LyX.
30177 \begin_layout Standard
30192 \begin_layout Plain Layout
30197 is part of the LaTeX-package
30205 \begin_layout Plain Layout
30206 Packages ! carlisle
30211 that is part of every LaTeX standard installation.
30220 \begin_layout Plain Layout
30221 Packages ! remreset
30226 has to be loaded in the LaTeX-preamble with the line
30229 \begin_layout Standard
30234 usepackage{remreset}
30237 \begin_layout Standard
30248 \begin_layout Plain Layout
30253 \begin_layout Plain Layout
30264 \begin_layout Plain Layout
30277 \begin_layout Plain Layout
30288 \begin_layout Plain Layout
30300 can be used with the same scheme as
30309 \begin_layout Standard
30310 \begin_inset VSpace bigskip
30313 Sometimes formulas should be numbered in the following form:
30316 \begin_layout Standard
30319 (section number.formula number)
30322 \begin_layout Standard
30323 The formula number should start with every section with
30324 \begin_inset Quotes eld
30328 \begin_inset Quotes erd
30334 \begin_layout Standard
30335 For this case there is the command
30345 \begin_layout Plain Layout
30353 , which is used with the following scheme:
30356 \begin_layout Standard
30361 numberwithin{counter}{sectioning}
30364 \begin_layout Standard
30365 Counter denotes what kind of numbering is affected, sectioning denotes what
30366 number is before the dot.
30369 \begin_layout Standard
30370 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30373 \begin_layout Standard
30378 numberwithin{equation}{section}
30381 \begin_layout Standard
30382 This is the result:
30386 \begin_layout Plain Layout
30390 numberwithin{equation}{section}
30396 \begin_inset Formula \begin{equation}
30397 A+B=C\end{equation}
30404 \begin_layout Standard
30406 \begin_inset space \thinspace{}
30410 \begin_inset space ~
30413 tables so that the number of the part is the sectioning,
30414 \begin_inset Newline newline
30421 numberwithin{table}{part}
30426 \begin_layout Standard
30427 To go back to the standard numbering or to prevent this kind of numbering
30428 when it is defined by the document class, the following command is inserted
30429 as TeX-Code or to the LaTeX-preamble:
30432 \begin_layout Standard
30445 \begin_layout Plain Layout
30459 \begin_layout Plain Layout
30475 \begin_inset Newline newline
30483 \begin_inset Newline newline
30495 \begin_layout Standard
30502 uses internally the command
30508 , described above, that also needs to be reverted.
30512 \begin_layout Plain Layout
30519 \begin_layout Plain Layout
30523 @removefromreset{equation}{section}
30526 \begin_layout Plain Layout
30538 \begin_layout Subsection
30539 Numbering with Roman Numbers and Letters
30540 \begin_inset CommandInset label
30542 name "sub:Numbering-with-Roman"
30550 \begin_layout Plain Layout
30551 Formula numbering ! with letters
30560 \begin_layout Plain Layout
30561 Formula numbering ! with Roman numbers
30569 \begin_layout Standard
30570 Formulas can also be numbered with Roman numbers and Latin letters.
30571 To number for example with small Roman numbers, the command
30574 \begin_layout Standard
30586 \begin_layout Standard
30587 is inserted before the formula in TeX-mode.
30598 \begin_layout Plain Layout
30606 redefines the predefined command
30622 \begin_layout Plain Layout
30629 has the same scheme like the command
30635 that is described in
30636 \begin_inset CommandInset ref
30638 reference "sec:User-defined-Commands"
30652 is the formula counter.
30659 is used as prefix for a counter, the value of the counter is output as
30661 When a formula is numbered, LaTeX sets internally the command
30667 behind the formula.
30676 \begin_layout Plain Layout
30686 outputs the counter as small Roman number.
30689 \begin_layout Standard
30690 All formulas behind the command
30700 are now numbered Roman.
30701 To switch to numbering with big Roman numbers, the command is inserted
30718 \begin_layout Plain Layout
30730 \begin_inset Quotes eld
30734 \begin_inset Quotes erd
30737 with small Latin letters there is the command
30747 \begin_layout Plain Layout
30755 , for big ones there is the command
30765 \begin_layout Plain Layout
30778 \begin_layout Standard
30779 \begin_inset Note Greyedout
30782 \begin_layout Plain Layout
30787 Only maximal 26 formulas can be numbered with Latin letters in one document.
30795 \begin_layout Standard
30799 \begin_layout Plain Layout
30815 \begin_layout Standard
30816 \begin_inset Formula \begin{equation}
30817 A=\textrm{small roman}\label{eq:rom}\end{equation}
30825 \begin_layout Plain Layout
30839 \begin_inset Formula \begin{equation}
30840 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30848 \begin_layout Plain Layout
30862 \begin_inset Formula \begin{equation}
30863 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30871 \begin_layout Plain Layout
30885 \begin_inset Formula \begin{equation}
30886 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30893 \begin_layout Standard
30894 To switch back to the default numbering, insert the command:
30897 \begin_layout Standard
30910 \begin_layout Plain Layout
30921 \begin_layout Standard
30925 \begin_layout Plain Layout
30939 \begin_inset Formula \begin{equation}
30940 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30947 \begin_layout Standard
30948 \begin_inset VSpace medskip
30951 As you see, formulas are numbered serially independent from the numbering
30953 When then numbering should start with
30954 \begin_inset Quotes eld
30958 \begin_inset Quotes erd
30961 when the style is changed, new equation counters have to be defined.
30962 A description about this can be found in the file
30963 \begin_inset CommandInset href
30965 target "Formula-numbering.lyx"
30972 \begin_layout Section
30973 User-defined Commands
30974 \begin_inset CommandInset label
30976 name "sec:User-defined-Commands"
30984 \begin_layout Plain Layout
30985 User-defined commands
30993 \begin_layout Standard
30994 Many LaTeX-commands are too long to be used frequently.
30995 But it is possible to define with the command
31005 \begin_layout Plain Layout
31013 new shorter commands.
31016 \begin_layout Standard
31017 The command scheme of
31026 \begin_layout Standard
31031 newcommand{new command name}[number of arguments][optional
31036 \begin_inset Newline newline
31043 \begin_layout Plain Layout
31058 \begin_layout Plain Layout
31065 {command definition}
31068 \begin_layout Standard
31069 \begin_inset Note Greyedout
31072 \begin_layout Plain Layout
31077 Assure that the name of the new command is not already used in your document
31078 or by LaTeX-packages that you use.
31079 When you for example define the command
31091 , you get an error message because
31097 is already defined as command for
31098 \begin_inset Quotes eld
31102 \begin_inset Formula $\le$
31106 \begin_inset Quotes erd
31117 \begin_layout Standard
31118 \begin_inset Note Greyedout
31121 \begin_layout Plain Layout
31126 The names of user-defined commands may only consist of Latin letters.
31134 \begin_layout Standard
31135 The number of arguments is an integer in the range 0
31136 \begin_inset space \thinspace{}
31140 \begin_inset space \thinspace{}
31143 9 and specifies how many arguments the new command should have.
31144 With the optional value a value for an optional argument can be predefined.
31145 When this is done, the
31153 rgument of the new command is automatically an optional one.
31156 \begin_layout Standard
31157 Here are some examples:
31160 \begin_layout Itemize
31161 To define the command
31173 , the LaTeX-preamble line is:
31177 \begin_layout Plain Layout
31189 \begin_inset Newline newline
31201 \begin_layout Itemize
31202 To define the command
31214 , the argument (that should be underlined) must be taken into account.
31215 For this the preamble line is:
31219 \begin_layout Plain Layout
31231 \begin_inset Newline newline
31246 \begin_layout Plain Layout
31258 \begin_inset Newline newline
31267 acts as argument placeholder, the
31271 behind it denotes that it is the placeholder for the first argument.
31274 \begin_layout Itemize
31282 \begin_inset space \thinspace{}
31286 \begin_inset space ~
31299 \begin_layout Plain Layout
31311 \begin_inset Newline newline
31320 framebox#1#2{$#3$}}
31326 \begin_layout Plain Layout
31338 \begin_inset Newline newline
31343 The two Dollar signs creates the extra formula needed for
31350 \begin_inset CommandInset ref
31352 reference "sub:Boxes-with-Frame"
31359 \begin_layout Itemize
31360 To create a new command for
31366 where the color for the box needn't to be specified, the argument for the
31367 color is defined optional:
31371 \begin_layout Plain Layout
31383 \begin_inset Newline newline
31392 fcolorbox{#2}{#1}{$#3$}}
31398 \begin_layout Plain Layout
31408 \begin_inset Newline newline
31411 When the color is not specified when using
31417 , the predefined color
31424 \begin_layout Standard
31425 A test of the new defined commands:
31428 \begin_layout Standard
31430 \begin_inset Tabular
31431 <lyxtabular version="3" rows="6" columns="2">
31433 <column alignment="center" valignment="top" width="0">
31434 <column alignment="center" valignment="top" width="0">
31436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31439 \begin_layout Plain Layout
31445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31448 \begin_layout Plain Layout
31450 \begin_inset Note Note
31453 \begin_layout Plain Layout
31460 is only used as spacer.
31472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31475 \begin_layout Plain Layout
31482 \begin_layout Plain Layout
31496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31499 \begin_layout Plain Layout
31500 \begin_inset Formula $A\gr B$
31510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31513 \begin_layout Plain Layout
31521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31524 \begin_layout Plain Layout
31525 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31538 \begin_layout Plain Layout
31542 \begin_inset Formula $\to$
31548 \begin_inset Formula $\to$
31559 \begin_layout Plain Layout
31573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31576 \begin_layout Plain Layout
31577 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31590 \begin_layout Plain Layout
31594 \begin_inset Formula $\to$
31605 \begin_layout Plain Layout
31619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31622 \begin_layout Plain Layout
31623 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31636 \begin_layout Plain Layout
31642 \begin_inset Formula $\to$
31653 \begin_layout Plain Layout
31667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31670 \begin_layout Plain Layout
31671 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31687 \begin_layout Section
31691 \begin_layout Standard
31692 LyX supports two types of commutative diagrams:
31700 that are explained in the following.
31703 \begin_layout Subsection
31708 \begin_layout Plain Layout
31717 \begin_layout Standard
31718 Diagrams of this type visualize relations by vertical and horizontal lines
31720 \begin_inset Formula \[
31721 \begin{CD}A@>>>B@>>>C\\
31723 F@<<<E@<<<D\end{CD}\]
31730 \begin_layout Standard
31731 To get them, the command
31739 \begin_layout Plain Layout
31749 is inserted to a formula.
31750 A blue box appears with two dashed lines where further commands can be
31756 a new line is created.
31757 Horizontal relations are inserted in odd, vertical in even formula lines.
31760 \begin_layout Standard
31761 To create the relations there are the following commands:
31764 \begin_layout Itemize
31769 creates a left arrow,
31780 \begin_layout Itemize
31785 creates an up arrow,
31793 a vertical equal sign
31796 \begin_layout Itemize
31802 is a placeholder for non-existent relations
31805 \begin_layout Standard
31806 All arrows can be labeled as follows:
31809 \begin_layout Itemize
31810 Is text inserted between the first and second < or >, resp., it is placed
31812 When it is inserted between the second and third one, it appears under
31816 \begin_layout Itemize
31817 When text for vertical arrows is inserted between the first and second A
31818 or V, resp., it is placed left beside the arrow.
31819 When it is inserted between the second and third one, it appears right
31821 If the text contains an A or V, these letters must be set into a TeX-brace.
31824 \begin_layout Standard
31825 As example a diagram with all possible relations:
31828 \begin_layout Standard
31829 \begin_inset Formula \[
31830 \begin{CD}A@>j>>B@>>k>C@=F\\
31832 D@<<j<E@>k>>F@=C\end{CD}\]
31839 \begin_layout Standard
31840 The command for this is:
31841 \begin_inset Newline newline
31852 \begin_layout Plain Layout
31861 A@>j>>B@>>k>C@=F Ctrl-Enter
31862 \begin_inset Newline newline
31869 \begin_layout Plain Layout
31884 \begin_layout Plain Layout
31897 \begin_layout Plain Layout
31909 \begin_inset Formula $\to$
31915 \begin_inset Newline newline
31922 \begin_layout Plain Layout
31937 \begin_layout Plain Layout
31950 \begin_layout Plain Layout
31960 \begin_layout Subsection
31965 \begin_layout Plain Layout
31966 Diagrams ! xymatrix
31974 \begin_layout Standard
31975 To be able to use xymatrices, the LaTeX-package
31980 A xymatrix is created by inserting the command
31987 Then you are able to add new matrix columns and rows like for normal matrices,
31989 \begin_inset CommandInset ref
31991 reference "sec:Matrices"
31998 \begin_layout Standard
31999 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32001 All possibilities to create commutative diagrams and decorations are explained
32002 in detail in this manual:
32003 \begin_inset CommandInset href
32005 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
32012 \begin_layout Standard
32013 \begin_inset Newpage newpage
32019 \begin_layout Section
32024 \begin_layout Plain Layout
32037 \begin_layout Plain Layout
32038 Other useful math tips can be found in
32039 \begin_inset CommandInset citation
32054 \begin_layout Plain Layout
32062 \begin_inset Note Note
32065 \begin_layout Plain Layout
32068 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32071 \begin_layout Plain Layout
32074 texorpdfstring is in section
32075 \begin_inset CommandInset ref
32077 reference "sub:Formulas-in-Section"
32090 \begin_layout Plain Layout
32100 \begin_layout Plain Layout
32105 \begin_layout Plain Layout
32112 Chemical characters
32116 \begin_layout Plain Layout
32131 \begin_layout Subsection
32132 Chemical Symbols and Equations
32133 \begin_inset CommandInset label
32135 name "sub:Chemical-Symbols-and"
32143 \begin_layout Plain Layout
32144 Chemical characters ! Symbols
32153 \begin_layout Plain Layout
32163 \begin_layout Plain Layout
32172 \begin_layout Standard
32173 An example text from chemistry:
32176 \begin_layout Quote
32178 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32181 -ion reacts with two
32182 \begin_inset Formula $\mathrm{Na^{+}}$
32185 -ions to sodium sulfate
32186 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32190 The chemical equation for this is:
32191 \begin_inset Formula \[
32192 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32199 \begin_layout Standard
32200 This chemical equation can directly be created as formula.
32201 To avoid that the symbols appear italic, everything is highlighted and
32202 changed by the shortcut
32205 \begin_inset space ~
32210 to the upright font style.
32214 \begin_layout Plain Layout
32220 \begin_inset CommandInset ref
32222 reference "sub:Font-Styles"
32234 \begin_layout Subsection
32239 \begin_layout Plain Layout
32248 \begin_layout Standard
32249 Negative numbers often look ugly in formulas because the minus sign before
32250 the number is set with the same length as the minus operator sign.
32251 When writing the negative number in normal text, the minus sign appears
32255 \begin_layout Standard
32256 Thus, the problem disappears when converting the minus sign to mathematical
32260 \begin_layout Standard
32261 An example to visualize the problem:
32264 \begin_layout Standard
32266 \begin_inset Tabular
32267 <lyxtabular version="3" rows="3" columns="2">
32269 <column alignment="right" valignment="top" width="0">
32270 <column alignment="left" valignment="top" width="0">
32272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32275 \begin_layout Plain Layout
32281 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32284 \begin_layout Plain Layout
32292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32295 \begin_layout Plain Layout
32301 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32304 \begin_layout Plain Layout
32305 \begin_inset Formula $x=-2$
32315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32318 \begin_layout Plain Layout
32324 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32327 \begin_layout Plain Layout
32328 \begin_inset Formula $x=\textrm{-}2$
32344 \begin_layout Subsection
32345 Comma as decimal Separator
32349 \begin_layout Plain Layout
32358 \begin_layout Standard
32359 In LaTeX a comma inside a formula is used, according to the English convention,
32360 as number group separator.
32361 So there will be space added behind all commas in formulas.
32364 \begin_layout Standard
32365 To avoid this, the comma is highlighted and changed to mathematical text
32369 \begin_inset space ~
32377 \begin_layout Standard
32378 To use all formula commas in the document as decimal separator, the file
32387 \begin_layout Plain Layout
32392 is part of the LaTeX-package
32400 \begin_layout Plain Layout
32405 \begin_layout Plain Layout
32428 \begin_layout Plain Layout
32434 is loaded with the LaTeX-preamble line
32437 \begin_layout Standard
32445 \begin_layout Subsection
32447 \begin_inset CommandInset label
32449 name "sub:Physical-Vectors"
32457 \begin_layout Plain Layout
32466 \begin_layout Standard
32467 Predefined vectors are offered by the LaTeX-package
32475 \begin_layout Plain Layout
32480 should be part of every LaTeX standard installation.
32489 \begin_layout Plain Layout
32495 that is loaded with the LaTeX-preamble line
32498 \begin_layout Standard
32506 \begin_layout Standard
32510 \begin_layout Plain Layout
32520 \begin_inset Note Note
32523 \begin_layout Plain Layout
32524 The following table will only be displayed when the LaTeX-package
32533 The following commands are defined:
32536 \begin_layout Standard
32538 \begin_inset Tabular
32539 <lyxtabular version="3" rows="4" columns="2">
32541 <column alignment="center" valignment="top" width="0">
32542 <column alignment="center" valignment="top" width="0">
32544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32547 \begin_layout Plain Layout
32553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32556 \begin_layout Plain Layout
32564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32567 \begin_layout Plain Layout
32577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32580 \begin_layout Plain Layout
32581 \begin_inset Formula $\Bra{\psi}$
32591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32594 \begin_layout Plain Layout
32604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32607 \begin_layout Plain Layout
32608 \begin_inset Formula $\Ket{\psi}$
32618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32621 \begin_layout Plain Layout
32633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32636 \begin_layout Plain Layout
32637 \begin_inset Formula $\Braket{\psi|\phi}$
32653 \begin_layout Standard
32660 assures that all vertical bars are set in the size of the surrounding brackets:
32661 \begin_inset Formula \[
32662 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32670 \begin_layout Plain Layout
32680 \begin_inset Note Note
32683 \begin_layout Plain Layout
32684 The following will be displayed when the LaTeX-package
32696 \begin_layout Standard
32697 You need to install the LaTeX-package
32701 to see the rest of this subsection in the output.
32704 \begin_layout Standard
32708 \begin_layout Plain Layout
32720 \begin_layout Standard
32727 can also be achieved using the command
32733 , that is described in
32734 \begin_inset CommandInset ref
32736 reference "sub:Automatic-Bracket-Size"
32743 \begin_layout Subsection
32744 Self-defined Fractions
32745 \begin_inset CommandInset label
32747 name "sub:Self-defined-Fractions"
32755 \begin_layout Plain Layout
32756 Fractions ! self-defined
32764 \begin_layout Standard
32765 To define custom commands for fractions, the command
32775 \begin_layout Plain Layout
32783 is used in the following scheme:
32786 \begin_layout Standard
32799 bracket}{fraction bar thickness}{style}
32800 \begin_inset Newline newline
32807 \begin_layout Plain Layout
32822 \begin_layout Plain Layout
32829 {numerator}{denominator}
32832 \begin_layout Standard
32833 The style is a number in the range of 0
32834 \begin_inset space \thinspace{}
32838 \begin_inset space \thinspace{}
32844 \begin_layout Standard
32846 \begin_inset Tabular
32847 <lyxtabular version="3" rows="5" columns="2">
32849 <column alignment="center" valignment="top" width="0">
32850 <column alignment="center" valignment="top" width="0">
32852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32855 \begin_layout Plain Layout
32861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32864 \begin_layout Plain Layout
32872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32875 \begin_layout Plain Layout
32881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32884 \begin_layout Plain Layout
32885 display style formula
32892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32895 \begin_layout Plain Layout
32901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32904 \begin_layout Plain Layout
32912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32915 \begin_layout Plain Layout
32921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32924 \begin_layout Plain Layout
32932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32935 \begin_layout Plain Layout
32941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32944 \begin_layout Plain Layout
32958 \begin_layout Standard
32959 When no style is given, the size is adjusted to the surrounding environment
32960 like for the command
32969 \begin_layout Standard
32970 When no fraction bar thickness is given, the predefined value of 0.4
32971 \begin_inset space \thinspace{}
32977 \begin_layout Standard
32978 \begin_inset VSpace medskip
32981 For example, the commands
32994 \begin_inset CommandInset ref
32996 reference "sub:Fractions"
33000 are defined with the commands
33003 \begin_layout Standard
33012 genfrac{}{}{}{0}{#1}{#2}}
33015 \begin_layout Standard
33019 \begin_layout Standard
33028 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33031 \begin_layout Standard
33032 \begin_inset VSpace medskip
33035 To define a fraction where the fraction bar thickness can be given as optional
33036 argument, the following line is inserted to the LaTeX-preamble:
33039 \begin_layout Standard
33048 genfrac{}{}{#1}{}{#2}{#3}}
33051 \begin_layout Standard
33053 \begin_inset Formula \begin{align*}
33054 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33055 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33059 As one can see, the distance of the numerator and the denominator to the
33060 fraction bar is round about three times the bar thickness.
33063 \begin_layout Subsection
33065 \begin_inset CommandInset label
33067 name "sub:Canceled-Formulas"
33075 \begin_layout Plain Layout
33084 \begin_layout Standard
33085 To cancel formulas or formula parts, the LaTeX-package
33093 \begin_layout Plain Layout
33098 is part of every LaTeX standard installation.
33107 \begin_layout Plain Layout
33113 has to be loaded with the LaTeX-preamble line
33116 \begin_layout Standard
33121 usepackage[samesize]{cancel}
33124 \begin_layout Standard
33125 There are four ways to cancel formulas:
33128 \begin_layout Standard
33130 \begin_inset Tabular
33131 <lyxtabular version="3" rows="5" columns="2">
33133 <column alignment="center" valignment="top" width="0">
33134 <column alignment="center" valignment="top" width="0">
33136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33139 \begin_layout Plain Layout
33145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33148 \begin_layout Plain Layout
33150 \begin_inset Note Note
33153 \begin_layout Plain Layout
33166 are used here as spacer.
33178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33181 \begin_layout Plain Layout
33190 \begin_layout Plain Layout
33204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33207 \begin_layout Plain Layout
33208 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33221 \begin_layout Plain Layout
33230 \begin_layout Plain Layout
33244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33247 \begin_layout Plain Layout
33248 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33261 \begin_layout Plain Layout
33270 \begin_layout Plain Layout
33284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33287 \begin_layout Plain Layout
33288 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33301 \begin_layout Plain Layout
33305 \begin_inset Formula $\to$
33316 \begin_layout Plain Layout
33330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33333 \begin_layout Plain Layout
33334 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33350 \begin_layout Standard
33357 is especially suitable to visualize the reduction of fractions within formulas:
33358 \begin_inset Formula \[
33359 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33366 \begin_layout Subsection
33367 Formulas in Section Headings
33368 \begin_inset CommandInset label
33370 name "sub:Formulas-in-Section"
33378 \begin_layout Plain Layout
33379 Formula ! in section headings
33387 \begin_layout Standard
33388 When formulas are used in section headings, the following has to be taken
33392 \begin_layout Standard
33393 \begin_inset Note Greyedout
33396 \begin_layout Plain Layout
33405 \begin_layout Plain Layout
33406 Packages ! hyperref
33411 support is enabled in the document settings dialog under
33414 \begin_inset space ~
33419 , PDF-bookmarks are created for every section heading in the table of contents.
33420 If a section heading contains formulas, they are incorrectly displayed
33421 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33430 \begin_layout Standard
33431 Both problems can be solved by inserting at the end of the section heading
33432 a short title with the menu
33434 Insert\SpecialChar \menuseparator
33436 \begin_inset space ~
33442 Short titles are used as alternative for multiline section headings to
33443 keep the table of contents clearly arranged.
33444 Only the short title appears in the table of contents and therefore also
33445 in the PDF-bookmark.
33448 \begin_layout Standard
33449 When formulas should be used in the table of contents but
33453 is used, one can use the following command in TeX-mode:
33456 \begin_layout Standard
33461 texorpdfstring{part}{alternative}
33465 \begin_layout Plain Layout
33476 \begin_layout Standard
33477 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33478 This can be characters, formulas, footnotes, but also cross-references.
33479 The alternative is used instead of the part for the bookmark.
33482 \begin_layout Standard
33483 Here are two example headings:
33484 \begin_inset VSpace -3mm
33491 \begin_layout Plain Layout
33503 \begin_layout Subsubsection
33504 Heading without formula in table of contents
33505 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33509 \begin_inset OptArg
33512 \begin_layout Plain Layout
33513 Heading without formula in table of contents
33521 \begin_layout Subsubsection
33522 Heading with formula in table of contents
33526 \begin_layout Plain Layout
33536 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33543 \begin_layout Plain Layout
33553 \begin_layout Standard
33557 \begin_layout Plain Layout
33566 In the first heading a short title was used, in the second one
33575 \begin_layout Standard
33576 To get the same formatting as for the other headings, the complete heading
33585 \begin_layout Plain Layout
33587 \begin_inset CommandInset ref
33589 reference "sub:Bold-Formulas"
33601 \begin_layout Subsection
33602 Formulas in multi-column Text
33606 \begin_layout Plain Layout
33607 Formula ! in multi-column text
33615 \begin_layout Standard
33616 Formulas in multi-column text are often too wide to fit into a column and
33617 thus need to be set over the whole page width.
33618 This is done by using the LaTeX-package
33626 \begin_layout Plain Layout
33631 is part of every LaTeX standard installation.
33640 \begin_layout Plain Layout
33641 Packages ! multicol
33646 , that is loaded with the LaTeX-preamble line
33649 \begin_layout Standard
33654 usepackage{multicol}
33657 \begin_layout Standard
33658 \begin_inset Note Greyedout
33661 \begin_layout Plain Layout
33662 Note herby that the setting
33665 \begin_inset space ~
33672 Document\SpecialChar \menuseparator
33678 \begin_inset space ~
33698 \begin_layout Standard
33699 Before the multi-column text the command
33702 \begin_layout Standard
33707 begin{multicols}{column number}
33710 \begin_layout Standard
33711 is written in TeX-mode.
33712 The column number is a number in the range of 2
33713 \begin_inset space \thinspace{}
33717 \begin_inset space \thinspace{}
33721 Before the formula the multi-column text is ended by inserting the command
33724 \begin_layout Standard
33732 \begin_layout Standard
33736 \begin_layout Standard
33737 Due to the command some space is automatically added before the formula.
33739 \begin_inset space \thinspace{}
33742 mm vertical space is inserted before the formula.
33743 When the formula style
33749 \begin_layout Plain Layout
33751 \begin_inset CommandInset ref
33753 reference "sec:Formula-Styles"
33765 \begin_inset space \thinspace{}
33768 mm space is inserted instead.
33771 \begin_layout Standard
33772 As example a multi-column text with a displayed formula:
33775 \begin_layout Standard
33779 \begin_layout Plain Layout
33783 begin{multicols}{2}
33788 Das Spektrum wird fouriertransformiert.
33789 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33790 , Lösungsmittel) zu trennen.
33791 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33792 nun das Aussehen des Ausgangssignals.
33793 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33794 über alle Phasen integrieren muss.
33796 \begin_inset Formula $S$
33799 unser normiertes Ausgangssignal and
33800 \begin_inset Formula $P$
33803 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33807 \begin_layout Plain Layout
33817 \begin_inset VSpace -6mm
33821 \begin_inset Formula \begin{equation}
33822 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33830 \begin_layout Plain Layout
33834 begin{multicols}{2}
33840 \begin_inset Formula $S_{0}$
33843 das Signal ohne Gradient ist and the Normierungsbedingung
33844 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33848 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33850 \begin_inset Formula $\nicefrac{\pi}{2}$
33854 \begin_inset space \thinspace{}
33857 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33858 das Signal zusätzlich abschwächt.
33859 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33861 \begin_inset Formula $T_{2}$
33867 \begin_layout Standard
33871 \begin_layout Plain Layout
33883 \begin_layout Subsection
33884 Formulas with Description of Variables
33888 \begin_layout Plain Layout
33889 Formula ! with description of variables
33897 \begin_layout Standard
33898 To describe variables within a formula, like in formula
33899 \begin_inset CommandInset ref
33901 reference "eq:within"
33910 \begin_inset Formula $n$
33914 \begin_inset space ~
33917 matrix is used with left aligned columns for the
33918 \begin_inset Formula $n$
33925 \begin_layout Plain Layout
33927 \begin_inset CommandInset ref
33929 reference "sec:Matrices"
33938 To set the description in a smaller size, before the matrix e.
33939 \begin_inset space \thinspace{}
33943 \begin_inset space ~
33956 \begin_layout Plain Layout
33958 \begin_inset CommandInset ref
33960 reference "sub:Font-Sizes"
33972 \begin_layout Standard
33973 When the formula style
33979 \begin_layout Plain Layout
33981 \begin_inset CommandInset ref
33983 reference "sec:Formula-Styles"
34004 \begin_layout Plain Layout
34011 only works in formulas with the style
34016 \begin_inset CommandInset ref
34018 reference "sub:Variable-Space"
34027 is inserted before and after the matrix to have the same separation of
34028 the matrix from the equation and the side margin.
34031 \begin_layout Standard
34032 When the formula style
34036 is used, the method described in
34037 \begin_inset CommandInset ref
34039 reference "sub:Flalign-Environment"
34043 is used to indent formulas.
34045 \begin_inset CommandInset ref
34047 reference "eq:within"
34051 consists of five columns whereas in the first two columns contain the equation,
34052 the third the matrix, and the last one an empty TeX-brace.
34053 \begin_inset Formula \begin{flalign}
34054 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34055 \rho & \textrm{density}\\
34056 V & \textrm{volume}\\
34057 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34064 \begin_layout Subsection
34065 Upright small Greek Letters
34066 \begin_inset CommandInset label
34068 name "sub:Upright-small-Greek"
34076 \begin_layout Plain Layout
34077 Greek letters ! upright
34085 \begin_layout Standard
34086 Most of the math fonts only provide italic small Greek letters.
34087 But for symbols of elementary particles like pions and neutrinos, upright
34088 Greek letters are needed.
34097 \begin_layout Plain Layout
34102 is part of the LaTeX-package
34110 \begin_layout Plain Layout
34115 \begin_layout Plain Layout
34138 \begin_layout Plain Layout
34144 that is loaded with the LaTeX-preamble line
34147 \begin_layout Standard
34152 usepackage{upgreek}
34155 \begin_layout Standard
34161 \begin_layout Plain Layout
34171 \begin_inset Note Note
34174 \begin_layout Plain Layout
34175 The following table will only be displayed when the LaTeX-package
34184 They are created when the command for a small Greek letters is started
34190 For example the command
34197 \begin_inset Formula $\uptau$
34203 \begin_layout Standard
34204 With these commands reactions of elementary particles can be typeset:
34205 \begin_inset Formula \[
34206 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34213 \begin_layout Standard
34214 The upright letters are more bold and wider than the italic ones.
34215 They should therefore not be used for units like
34216 \begin_inset Quotes eld
34220 \begin_inset Quotes erd
34226 \begin_layout Standard
34230 \begin_layout Plain Layout
34240 \begin_inset Note Note
34243 \begin_layout Plain Layout
34244 The following will be displayed when the LaTeX-package
34256 \begin_layout Standard
34257 You need to install the LaTeX-package
34261 to see the rest of this subsection in the output.
34264 \begin_layout Standard
34268 \begin_layout Plain Layout
34280 \begin_layout Subsection
34281 Text Characters in Formulas
34282 \begin_inset CommandInset label
34284 name "sub:Text-Characters-in"
34292 \begin_layout Plain Layout
34301 \begin_layout Standard
34302 In some cases you might want to insert text characters directly into formulas.
34303 When for example the centered dot · is often used in formulas like
34304 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34307 , one would have to insert the command
34317 \begin_layout Plain Layout
34319 \begin_inset CommandInset ref
34321 reference "sub:Binary-Operators"
34330 all the time, because this character is defined in all encodings as text
34332 But the encoding can be changed by this LaTeX-preamble line:
34335 \begin_layout Standard
34340 Declare Inputtext{183}{
34350 f\SpecialChar \textcompwordmark{}
34354 \begin_layout Standard
34355 The character encoding (menu
34357 Document\SpecialChar \menuseparator
34358 Settings\SpecialChar \menuseparator
34361 ) specifies what character appears when a keyboard key is pressed.
34362 When the key for the character '·' is pressed, internally the command
34369 But this command is not available in a formula so that you would get LaTeX-erro
34371 With the changed encoding the right command is chosen automatically, depending
34372 on if the character was inserted into a formula or not.
34375 \begin_layout Standard
34376 The encoding of several characters is saved in definition files.
34377 Fore example the encoding
34381 is defined in the file
34385 that is in the installation folder of LaTeX.
34386 Encodings should only be changed via the LaTeX-preamble and not in the
34388 Otherwise own documents could not be edited by other LyX users working
34389 on other computers.
34392 \begin_layout Standard
34393 \begin_inset VSpace medskip
34396 Besides the centered dot, in this document the degree sign ° is defined
34397 with the following LaTeX-preamble line so that it can directly be inserted
34401 \begin_layout Standard
34406 DeclareInputtext{176}{
34416 f\SpecialChar \textcompwordmark{}
34420 \begin_layout Standard
34421 \begin_inset Newpage newpage
34427 \begin_layout Section
34433 \begin_layout Plain Layout
34442 \begin_layout Standard
34443 This section is a summary of the most important typographic rules, listed
34448 \begin_layout Plain Layout
34449 This collection was partly taken from the German semi-official dictionary
34451 \begin_inset Quotes eld
34455 \begin_inset Quotes erd
34459 \begin_inset CommandInset citation
34465 that lists some of the ISO rules.
34473 \begin_layout Itemize
34482 \begin_layout Plain Layout
34483 done with font styles, see
34484 \begin_inset CommandInset ref
34486 reference "sub:Font-Styles"
34496 \begin_inset space \thinspace{}
34500 \begin_inset Newline newline
34503 Between the value and the unit is the smallest space, see
34504 \begin_inset CommandInset ref
34506 reference "sub:Predefined-Space"
34511 \begin_inset Newline newline
34514 This convention is automatically fulfilled when the command
34521 When it is entered to a formula, two boxes appear.
34522 In the first one the value is inserted, in the second one the unit, and
34524 \begin_inset Formula $\unit[30]{km/h}$
34528 \begin_inset space \thinspace{}
34538 is not a real LaTeX command but the command
34544 , therefore you cannot use it in TeX code.
34547 \begin_layout Itemize
34548 Percent and perthousand signs are set like physical units:
34549 \begin_inset Newline newline
34553 \begin_inset space \thinspace{}
34559 \begin_layout Itemize
34560 The degree sign follows directly on the value: 15°, but not when it is used
34562 \begin_inset space \thinspace{}
34568 \begin_layout Itemize
34569 In numbers with more than four digits the smallest space is inserted before
34570 every third digit to group them:
34580 \begin_inset space \thinspace{}
34584 \begin_inset space \thinspace{}
34590 \begin_layout Itemize
34591 For dimensions like 120×90×40
34592 \begin_inset space \thinspace{}
34595 cm the multiplication sign
34596 \begin_inset Quotes eld
34600 \begin_inset Quotes erd
34604 It is available with the LaTeX-command
34610 , but can also directly be inserted with some keyboard definitions.
34613 \begin_layout Itemize
34614 Functions with names consisting of several letters are set upright to avoid
34616 \begin_inset CommandInset ref
34618 reference "sub:Predefined-Functions"
34625 \begin_layout Itemize
34626 Indices consisting of several letters, are set upright:
34627 \begin_inset Formula $E_{\mathrm{kin}}$
34631 \begin_inset Newline newline
34634 Components of matrices are set italic:
34635 \begin_inset Formula $\hat{H}_{kl}$
34641 \begin_layout Itemize
34642 The differentiation/integration operator 'd', the Euler's number 'e', and
34643 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34647 \begin_layout Standard
34648 \begin_inset Newpage newpage
34654 \begin_layout Section
34659 \begin_layout Plain Layout
34668 \begin_layout Standard
34669 Some characters and symbols can be created with several commands.
34670 Here is a list of the synonym commands:
34673 \begin_layout Standard
34674 \begin_inset VSpace bigskip
34678 \begin_inset space \hfill{}
34682 \begin_inset Tabular
34683 <lyxtabular version="3" rows="12" columns="2">
34685 <column alignment="center" valignment="top" width="0pt">
34686 <column alignment="center" valignment="top" width="0pt">
34688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34691 \begin_layout Plain Layout
34697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34700 \begin_layout Plain Layout
34702 \begin_inset Note Note
34705 \begin_layout Plain Layout
34712 is only used as spacer.
34724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34727 \begin_layout Plain Layout
34735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34738 \begin_layout Plain Layout
34742 \begin_layout Plain Layout
34755 \begin_layout Plain Layout
34769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34772 \begin_layout Plain Layout
34780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34783 \begin_layout Plain Layout
34793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34796 \begin_layout Plain Layout
34804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34807 \begin_layout Plain Layout
34817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34820 \begin_layout Plain Layout
34828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34831 \begin_layout Plain Layout
34839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34842 \begin_layout Plain Layout
34850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34853 \begin_layout Plain Layout
34861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34864 \begin_layout Plain Layout
34872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34875 \begin_layout Plain Layout
34885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34888 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34899 \begin_layout Plain Layout
34909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34912 \begin_layout Plain Layout
34920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34923 \begin_layout Plain Layout
34933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34936 \begin_layout Plain Layout
34944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34947 \begin_layout Plain Layout
34957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34960 \begin_layout Plain Layout
34968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34971 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34982 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34993 \begin_layout Plain Layout
35005 \begin_inset space \hfill{}
35009 \begin_inset Tabular
35010 <lyxtabular version="3" rows="12" columns="2">
35012 <column alignment="center" valignment="top" width="0pt">
35013 <column alignment="center" valignment="top" width="0pt">
35015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35018 \begin_layout Plain Layout
35024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35027 \begin_layout Plain Layout
35035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35038 \begin_layout Plain Layout
35046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35049 \begin_layout Plain Layout
35061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35064 \begin_layout Plain Layout
35072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35075 \begin_layout Plain Layout
35085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35088 \begin_layout Plain Layout
35096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35099 \begin_layout Plain Layout
35109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35112 \begin_layout Plain Layout
35120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35123 \begin_layout Plain Layout
35131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35134 \begin_layout Plain Layout
35142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35145 \begin_layout Plain Layout
35153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35156 \begin_layout Plain Layout
35164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35167 \begin_layout Plain Layout
35177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35180 \begin_layout Plain Layout
35188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35191 \begin_layout Plain Layout
35201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35204 \begin_layout Plain Layout
35212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35215 \begin_layout Plain Layout
35225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35228 \begin_layout Plain Layout
35236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35239 \begin_layout Plain Layout
35249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35252 \begin_layout Plain Layout
35260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35263 \begin_layout Plain Layout
35273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35276 \begin_layout Plain Layout
35284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35287 \begin_layout Plain Layout
35301 \begin_inset space \hfill{}
35307 \begin_layout Standard
35308 \begin_inset Newpage newpage
35314 \begin_layout Bibliography
35315 \begin_inset CommandInset bibitem
35316 LatexCommand bibitem
35328 The LaTeX Companion
35331 Addison Wesley, 2004
35334 \begin_layout Bibliography
35335 \begin_inset CommandInset bibitem
35336 LatexCommand bibitem
35342 \begin_inset CommandInset href
35345 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35349 of LaTeX's math abilities
35352 \begin_layout Bibliography
35353 \begin_inset CommandInset bibitem
35354 LatexCommand bibitem
35359 LaTeX tips and tricks-
35360 \begin_inset CommandInset href
35363 target "http://tug.org/TeXnik/"
35370 \begin_layout Bibliography
35371 \begin_inset CommandInset bibitem
35372 LatexCommand bibitem
35378 \begin_inset CommandInset href
35381 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35389 \begin_layout Plain Layout
35401 \begin_layout Bibliography
35402 \begin_inset CommandInset bibitem
35403 LatexCommand bibitem
35409 \begin_inset CommandInset href
35412 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35416 of all symbols available with LaTeX-packages
35419 \begin_layout Bibliography
35420 \begin_inset CommandInset bibitem
35421 LatexCommand bibitem
35427 \begin_inset CommandInset href
35429 name "Documentation"
35430 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35434 of the LaTeX-package
35442 \begin_layout Plain Layout
35443 Packages ! hyperref
35451 \begin_layout Bibliography
35452 \begin_inset CommandInset bibitem
35453 LatexCommand bibitem
35459 \begin_inset CommandInset href
35462 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35473 \begin_inset CommandInset ref
35475 reference "sub:Operator-Limits"
35483 \begin_layout Plain Layout
35494 \begin_layout Bibliography
35495 \begin_inset CommandInset bibitem
35496 LatexCommand bibitem
35507 Auflage, Duden 2001
35510 \begin_layout Subsubsection*
35511 \begin_inset CommandInset index_print
35512 LatexCommand printindex