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
10007 is only used as spacer.
10019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10022 \begin_layout Plain Layout
10025 \begin_inset Quotes grd
10033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10036 \begin_layout Plain Layout
10039 \begin_inset Formula $"i$
10049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10052 \begin_layout Plain Layout
10059 \begin_layout Plain Layout
10073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10076 \begin_layout Plain Layout
10077 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10093 \begin_layout Standard
10094 Another advantage to
10100 is that umlauts can directly be converted to mathematical text because
10101 the accent commands above are
10107 in mathematical text
10110 To convert an accented character to mathematical text, only the character
10111 under the accent may be converted.
10112 This applies also for all other conversions, e.
10113 \begin_inset space \thinspace{}
10117 \begin_inset space ~
10123 \begin_layout Standard
10124 In mathematical text, umlauts and other accented characters can directly
10128 \begin_layout Subsection
10129 Accents for Operators
10133 \begin_layout Plain Layout
10134 Accents ! for operators
10142 \begin_layout Standard
10153 \begin_layout Plain Layout
10171 \begin_layout Plain Layout
10179 characters can be placed above or below an operator, respectively, to accent
10191 \begin_layout Plain Layout
10199 characters can be set before and behind an operator.
10200 The command scheme is:
10203 \begin_layout Standard
10219 \begin_layout Standard
10226 must always be before the operator that should be accented.
10227 You can accent with several characters and even with other operators and
10235 for example only characters behind an operator, write nothing between the
10236 first braces but don't omit the braces.
10239 \begin_layout Standard
10240 For example the command
10245 \begin_inset Formula $\to$
10255 \begin_inset Formula $\to$
10264 \begin_layout Plain Layout
10280 \begin_inset Formula \[
10281 \sideset{}{'}\sum_{k=1}^{n}\]
10288 \begin_layout Standard
10297 \begin_layout Plain Layout
10312 \begin_layout Plain Layout
10324 \begin_inset Formula $\uparrow$
10332 \begin_inset Formula \[
10333 \overset{a}{\maltese}\]
10337 As seen in the last example, with
10349 also symbols and characters can be accented; with
10355 this is not possible.
10358 \begin_layout Subsection
10359 Accents for several Characters
10360 \begin_inset CommandInset label
10362 name "sub:Accents-for-several"
10370 \begin_layout Plain Layout
10371 Accents ! for several characters
10379 \begin_layout Standard
10380 \begin_inset space \hfill{}
10384 \begin_inset Tabular
10385 <lyxtabular version="3" rows="5" columns="2">
10387 <column alignment="center" valignment="top" width="0pt">
10388 <column alignment="center" valignment="top" width="0pt">
10390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10393 \begin_layout Plain Layout
10399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10402 \begin_layout Plain Layout
10404 \begin_inset Note Note
10407 \begin_layout Plain Layout
10414 is only used as spacer.
10426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10429 \begin_layout Plain Layout
10436 \begin_layout Plain Layout
10450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10453 \begin_layout Plain Layout
10454 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10467 \begin_layout Plain Layout
10474 \begin_layout Plain Layout
10488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10491 \begin_layout Plain Layout
10492 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10505 \begin_layout Plain Layout
10512 \begin_layout Plain Layout
10526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10529 \begin_layout Plain Layout
10530 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10543 \begin_layout Plain Layout
10546 underleftrightarrow
10550 \begin_layout Plain Layout
10564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10567 \begin_layout Plain Layout
10568 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10582 \begin_inset space \hfill{}
10586 \begin_inset Tabular
10587 <lyxtabular version="3" rows="5" columns="2">
10589 <column alignment="center" valignment="top" width="0pt">
10590 <column alignment="center" valignment="top" width="0pt">
10592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10595 \begin_layout Plain Layout
10601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10604 \begin_layout Plain Layout
10612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10615 \begin_layout Plain Layout
10622 \begin_layout Plain Layout
10636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10639 \begin_layout Plain Layout
10640 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10653 \begin_layout Plain Layout
10660 \begin_layout Plain Layout
10674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10677 \begin_layout Plain Layout
10678 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10691 \begin_layout Plain Layout
10698 \begin_layout Plain Layout
10712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10715 \begin_layout Plain Layout
10716 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10729 \begin_layout Plain Layout
10736 \begin_layout Plain Layout
10750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10753 \begin_layout Plain Layout
10754 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10768 \begin_inset space \hfill{}
10774 \begin_layout Standard
10775 \begin_inset VSpace medskip
10778 With these commands as many characters as you like can be accented.
10791 will only be set in the output with a length of three characters, as shown
10792 in the following example:
10793 \begin_inset Formula \[
10794 \widetilde{A+B=C-D}\]
10801 \begin_layout Standard
10812 \begin_layout Plain Layout
10830 \begin_layout Plain Layout
10838 described in the previous subsection it is also possible to accent several
10848 \begin_layout Plain Layout
10858 \begin_inset Formula $\downarrow$
10864 \begin_inset Formula \[
10865 \underset{***}{A=B}\]
10872 \begin_layout Section
10874 \begin_inset CommandInset label
10884 \begin_layout Plain Layout
10893 \begin_layout Subsection
10895 \begin_inset CommandInset label
10897 name "sub:Predefined-Space"
10905 \begin_layout Plain Layout
10906 Space ! horizontal ! predefined
10914 \begin_layout Standard
10915 Sometimes it is necessary to insert horizontal space to a formula.
10916 This is done by inserting a protected space (shortcut
10922 \begin_inset Quotes eld
10932 \begin_layout Plain Layout
10945 \begin_inset Quotes erd
10948 appears and by pressing
10952 several times one can select one of eight different space sizes.
10953 The spaces can also be inserted using the math toolbar button
10954 \begin_inset Graphics
10955 filename ../images/math/space.png
10960 or special commands.
10961 Independent from the inserted command, one can select the size again by
10969 \begin_layout Standard
10972 \begin_inset VSpace -5mm
10976 \begin_inset Tabular
10977 <lyxtabular version="3" rows="3" columns="7">
10979 <column alignment="center" valignment="middle" width="6.8cm">
10980 <column alignment="center" valignment="top" width="0">
10981 <column alignment="center" valignment="top" width="0">
10982 <column alignment="center" valignment="top" width="0">
10983 <column alignment="center" valignment="top" width="0">
10984 <column alignment="center" valignment="top" width="0">
10985 <column alignment="center" valignment="top" width="0">
10987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10990 \begin_layout Plain Layout
10996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10999 \begin_layout Plain Layout
11007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11021 \begin_layout Plain Layout
11029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11032 \begin_layout Plain Layout
11040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11043 \begin_layout Plain Layout
11051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11054 \begin_layout Plain Layout
11064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11067 \begin_layout Plain Layout
11072 keystrokes after inserting the protected space
11077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11089 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11116 \begin_layout Plain Layout
11122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11125 \begin_layout Plain Layout
11133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11136 \begin_layout Plain Layout
11142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11146 \begin_inset Formula $A\, B$
11154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11157 \begin_layout Plain Layout
11158 \begin_inset Formula $A\: B$
11166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11170 \begin_inset Formula $A\; B$
11178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11182 \begin_inset Formula $A\quad B$
11190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11193 \begin_layout Plain Layout
11194 \begin_inset Formula $A\qquad B$
11202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11205 \begin_layout Plain Layout
11206 \begin_inset Formula $A\! B$
11222 \begin_layout Standard
11223 The last size seem to produce no space.
11224 It is displayed red in LyX contrary to the other sizes, because it is a
11226 There are two more negative spaces:
11229 \begin_layout Standard
11231 \begin_inset Tabular
11232 <lyxtabular version="3" rows="3" columns="3">
11234 <column alignment="center" valignment="middle" width="6.8cm">
11235 <column alignment="center" valignment="top" width="0pt">
11236 <column alignment="center" valignment="top" width="0pt">
11238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11241 \begin_layout Plain Layout
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11250 \begin_layout Plain Layout
11258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11261 \begin_layout Plain Layout
11271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11274 \begin_layout Plain Layout
11279 keystrokes after inserting the protected space
11284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11287 \begin_layout Plain Layout
11293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11296 \begin_layout Plain Layout
11304 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11316 \begin_layout Plain Layout
11317 \begin_inset Formula $A\negmedspace B$
11325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11328 \begin_layout Plain Layout
11329 \begin_inset Formula $A\negthickspace B$
11345 \begin_layout Standard
11346 Negative spaces can lead to characters overlapping each other.
11347 Thus they can be used to enforce ligatures, what is e.
11348 \begin_inset space \thinspace{}
11352 \begin_inset space ~
11355 useful for summation operators:
11358 \begin_layout Standard
11360 \begin_inset Tabular
11361 <lyxtabular version="3" rows="3" columns="2">
11363 <column alignment="center" valignment="top" width="0">
11364 <column alignment="center" valignment="top" width="0">
11366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11369 \begin_layout Plain Layout
11375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11378 \begin_layout Plain Layout
11380 \begin_inset Note Note
11383 \begin_layout Plain Layout
11390 is only used as spacer.
11402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11405 \begin_layout Plain Layout
11414 \begin_layout Plain Layout
11428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11431 \begin_layout Plain Layout
11432 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11445 \begin_layout Plain Layout
11456 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11473 \begin_layout Plain Layout
11474 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11490 \begin_layout Standard
11491 Relations like for example equal signs, are always surrounded by space.
11492 To suppress this, the equal sign is placed into a TeX-brace.
11493 The following example demonstrates this:
11496 \begin_layout Standard
11498 \begin_inset Tabular
11499 <lyxtabular version="3" rows="2" columns="2">
11501 <column alignment="center" valignment="top" width="0pt">
11502 <column alignment="center" valignment="top" width="0pt">
11504 <cell alignment="center" valignment="top" usebox="none">
11507 \begin_layout Plain Layout
11513 <cell alignment="center" valignment="top" usebox="none">
11516 \begin_layout Plain Layout
11517 \begin_inset Formula $A=B$
11527 <cell alignment="center" valignment="top" usebox="none">
11530 \begin_layout Plain Layout
11531 \begin_inset Note Note
11534 \begin_layout Plain Layout
11541 is only used as spacer.
11547 \begin_inset Formula $\raisebox{5mm}{}$
11550 equation without space
11555 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11558 \begin_layout Plain Layout
11559 \begin_inset Formula $A{=}B$
11575 \begin_layout Standard
11577 The command for the last formula is:
11582 \begin_inset Formula $\to$
11588 \begin_layout Standard
11589 \begin_inset VSpace bigskip
11592 Spaces are needed for physical units, because the space between the value
11593 and the unit is the smallest one and not a normal space.
11594 For units in text, the smallest space is inserted via the menu
11596 Insert\SpecialChar \menuseparator
11597 Formatting\SpecialChar \menuseparator
11599 \begin_inset space ~
11611 \begin_layout Standard
11612 An example to visualize the difference:
11615 \begin_layout Standard
11616 \begin_inset Tabular
11617 <lyxtabular version="3" rows="2" columns="2">
11619 <column alignment="left" valignment="top" width="0">
11620 <column alignment="left" valignment="top" width="0">
11622 <cell alignment="center" valignment="top" usebox="none">
11625 \begin_layout Plain Layout
11627 \begin_inset Formula $\cdot$
11635 <cell alignment="center" valignment="top" usebox="none">
11638 \begin_layout Plain Layout
11639 space between value and unit
11646 <cell alignment="center" valignment="top" usebox="none">
11649 \begin_layout Plain Layout
11651 \begin_inset space \thinspace{}
11655 \begin_inset Formula $\cdot$
11663 <cell alignment="center" valignment="top" usebox="none">
11666 \begin_layout Plain Layout
11667 smallest space between value and unit
11680 \begin_layout Subsection
11685 \begin_layout Plain Layout
11698 \begin_layout Plain Layout
11699 for vertical space in formulas see
11700 \begin_inset CommandInset ref
11702 reference "sub:Line-Separation"
11715 \begin_layout Plain Layout
11723 \begin_inset Note Note
11726 \begin_layout Plain Layout
11729 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11732 \begin_layout Plain Layout
11735 texorpdfstring is in section
11736 \begin_inset CommandInset ref
11738 reference "sub:Formulas-in-Section"
11748 \begin_inset CommandInset label
11750 name "sub:Variable-Space"
11758 \begin_layout Plain Layout
11759 Space ! horizontal ! variable
11767 \begin_layout Standard
11768 Space with a defined length can be inserted in LyX with the command
11769 \begin_inset Newline newline
11782 \begin_layout Plain Layout
11791 For the length all units listed in
11792 \begin_inset CommandInset ref
11794 reference "tab:Available-units"
11798 are allowed, except of the unit
11799 \begin_inset Quotes eld
11803 \begin_inset Quotes erd
11807 The length may also be negative.
11808 To insert so many space that the formula uses all available space, the
11819 \begin_layout Plain Layout
11830 \begin_layout Standard
11831 \begin_inset VSpace -1mm
11837 \begin_layout Standard
11839 \begin_inset Tabular
11840 <lyxtabular version="3" rows="4" columns="2">
11842 <column alignment="center" valignment="top" width="0">
11843 <column alignment="center" valignment="top" width="0">
11845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11848 \begin_layout Plain Layout
11854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11857 \begin_layout Plain Layout
11865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11868 \begin_layout Plain Layout
11872 \begin_inset Formula $\to$
11882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11885 \begin_layout Plain Layout
11886 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11899 \begin_layout Plain Layout
11903 \begin_inset Formula $\to$
11913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11916 \begin_layout Plain Layout
11917 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11930 \begin_layout Plain Layout
11937 \begin_layout Plain Layout
11951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11954 \begin_layout Plain Layout
11955 \begin_inset Formula $A=A\hfill B=B$
11971 \begin_layout Standard
11972 In the last example the available space is given by the longest column entry
11974 In an inline formula the space depends on the length of the line in which
11982 Thus, when the line uses the full width, no space will be created.
11989 only has an effect on displayed formulas when the formula style
11994 (Formula styles are explained in
11995 \begin_inset CommandInset ref
11997 reference "sec:Formula-Styles"
12004 \begin_layout Standard
12011 , there are the commands
12023 that fill the space with a pattern, see
12024 \begin_inset CommandInset ref
12026 reference "sub:Ellipses"
12033 \begin_layout Standard
12034 For text, variable space can be inserted via the menu
12036 Insert\SpecialChar \menuseparator
12037 Formatting\SpecialChar \menuseparator
12039 \begin_inset space ~
12044 , what is not possible in formulas:
12047 \begin_layout Standard
12048 This is a line with
12049 \begin_inset space \hspace{}
12054 \begin_inset space \thinspace{}
12060 \begin_layout Standard
12061 This is a line with
12062 \begin_inset space \hfill{}
12068 \begin_layout Subsection
12069 Space besides inline Formulas
12073 \begin_layout Plain Layout
12074 Space ! besides inline formulas
12082 \begin_layout Standard
12083 The space that surrounds inline formulas can be adjusted with the length
12092 \begin_layout Plain Layout
12103 The value of a length is set with the command
12111 \begin_layout Plain Layout
12121 that has the following scheme:
12124 \begin_layout Standard
12129 setlength{length name}{value}
12132 \begin_layout Standard
12140 \begin_inset space \thinspace{}
12146 \begin_layout Standard
12156 \begin_layout Standard
12157 is inserted in TeX-mode.
12159 \begin_inset space \thinspace{}
12162 mm space will now be set around all inline formulas:
12166 \begin_layout Plain Layout
12180 \begin_layout Standard
12181 This is a line with an inline formula
12182 \begin_inset Formula $A=B$
12186 \begin_inset space \thinspace{}
12189 mm surrounding space.
12193 \begin_layout Plain Layout
12207 \begin_layout Standard
12208 To return to the predefined value,
12214 is set to the value 0
12215 \begin_inset space \thinspace{}
12221 \begin_layout Section
12226 \begin_layout Plain Layout
12236 \begin_layout Plain Layout
12241 \begin_layout Plain Layout
12252 \begin_layout Plain Layout
12267 \begin_layout Standard
12268 Boxes for text are described in chapter
12275 \begin_inset space ~
12283 \begin_layout Subsection
12285 \begin_inset CommandInset label
12287 name "sub:Boxes-with-Frame"
12295 \begin_layout Plain Layout
12304 \begin_layout Standard
12305 It is possible to frame formulas or parts of it with the commands
12315 \begin_layout Plain Layout
12333 \begin_layout Plain Layout
12344 \begin_layout Standard
12345 When one of these commands is inserted to a formula, a blue box appears
12346 within a frame to enter formula parts.
12353 an additional formula has to be created by
12361 \begin_layout Plain Layout
12362 Due to a bug in LyX it is not possible to create a new formula with
12367 \begin_inset CommandInset href
12369 name "LyX-bug #1435"
12370 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12379 , because the box content will otherwise be treated as mathematical text.
12386 is used, a new formula is automatically created inside the frame.
12389 \begin_layout Standard
12396 is not suitable to frame displayed formulas, because the formula will always
12397 be set in the size of the text.
12404 is in contrary not suitable to frame inline formulas, because the formula
12405 will always be set in the size of a displayed formula.
12408 \begin_layout Standard
12415 there is the command
12425 \begin_layout Plain Layout
12433 where additionally the frame width and the alignment can be specified.
12440 is used in the following scheme:
12443 \begin_layout Standard
12448 framebox[frame width][position]{box content}
12451 \begin_layout Standard
12452 The position can either be
12469 right aligns the formula in the box.
12470 When no position is given, the formula will be centered.
12471 \begin_inset Newline newline
12474 Is no width given, also no position can be given.
12475 In this case the frame width is adjusted to the box content like for
12484 \begin_layout Standard
12491 is inserted, a box appears containing three blue boxes.
12492 The first two boxes are surrounded by brackets and denote the two optional
12494 The third box is for formula parts like for
12503 \begin_layout Standard
12505 \begin_inset Note Note
12508 \begin_layout Plain Layout
12509 The table has been set into a minipage to make the footnote appearing.
12510 Otherwise the footnote text would not be displayed.
12516 \begin_inset Box Frameless
12525 height_special "totalheight"
12528 \begin_layout Plain Layout
12530 \begin_inset Tabular
12531 <lyxtabular version="3" rows="5" columns="2">
12533 <column alignment="center" valignment="top" width="0">
12534 <column alignment="center" valignment="top" width="0">
12536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12539 \begin_layout Plain Layout
12544 \begin_layout Plain Layout
12545 Due to a bug in LyX it is not possible to create a new formula with
12550 \begin_inset CommandInset href
12552 name "LyX-bug #1435"
12553 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12570 \begin_layout Plain Layout
12572 \begin_inset Note Note
12575 \begin_layout Plain Layout
12582 is only used as spacer.
12594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12597 \begin_layout Plain Layout
12604 \begin_layout Plain Layout
12623 \begin_layout Plain Layout
12637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12640 \begin_layout Plain Layout
12641 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12654 \begin_layout Plain Layout
12661 \begin_layout Plain Layout
12676 \begin_layout Plain Layout
12690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12693 \begin_layout Plain Layout
12694 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12707 \begin_layout Plain Layout
12714 \begin_layout Plain Layout
12728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12731 \begin_layout Plain Layout
12732 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12745 \begin_layout Plain Layout
12752 \begin_layout Plain Layout
12762 \begin_inset Formula $\to$
12766 \begin_inset Formula $\to$
12779 \begin_layout Plain Layout
12789 \begin_inset Formula $\downarrow$
12797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12800 \begin_layout Plain Layout
12801 \begin_inset Formula $\raisebox{6mm}{}$
12805 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12809 \begin_inset Formula $\raisebox{-4mm}{}$
12830 \begin_layout Standard
12831 The frame thickness can also be adjusted.
12832 To do this the following commands have to be inserted in TeX-mode before
12836 \begin_layout Standard
12846 \begin_inset Quotes eld
12850 \begin_inset Quotes erd
12864 \begin_inset Quotes eld
12868 \begin_inset Quotes erd
12874 \begin_layout Standard
12875 \begin_inset Quotes eld
12879 \begin_inset Quotes erd
12882 specifies the minimal distance between the frame and the first character
12884 An example for this is the following framed formula:
12888 \begin_layout Plain Layout
12900 \begin_inset Formula \[
12905 Before this formula the commands
12908 \begin_layout Standard
12930 \begin_layout Standard
12931 were inserted in TeX-mode.
12932 The given values are used for all following boxes.
12935 \begin_layout Standard
12936 To return to the standard frame size, the command
12939 \begin_layout Standard
12964 \begin_layout Plain Layout
12978 \begin_layout Standard
12979 is inserted in TeX-mode before the next formula.
12982 \begin_layout Subsection
12983 Boxes without Frame
12984 \begin_inset CommandInset label
12986 name "sub:Boxes-without-Frame"
12994 \begin_layout Plain Layout
12995 Boxes ! without frame
13003 \begin_layout Standard
13004 For boxes without a frame there are the following box commands:
13014 \begin_layout Plain Layout
13032 \begin_layout Plain Layout
13050 \begin_layout Plain Layout
13061 \begin_layout Standard
13068 a box can be super- or subscripted.
13069 But in contrary to normal super- and subscripting, the characters in the
13070 box keep their font size.
13077 is used in the following scheme:
13080 \begin_layout Standard
13085 raisebox{height}{box content}
13088 \begin_layout Standard
13089 When the box should contain a formula, an extra formula is needed like for
13099 \begin_layout Standard
13101 \begin_inset Tabular
13102 <lyxtabular version="3" rows="4" columns="2">
13104 <column alignment="center" valignment="top" width="0">
13105 <column alignment="center" valignment="top" width="0">
13107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13110 \begin_layout Plain Layout
13116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13119 \begin_layout Plain Layout
13127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13130 \begin_layout Plain Layout
13134 \begin_inset Formula $\to$
13140 \begin_inset Formula $\to$
13148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13151 \begin_layout Plain Layout
13152 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13165 \begin_layout Plain Layout
13169 \begin_inset Formula $\to$
13175 \begin_inset Formula $\to$
13183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13186 \begin_layout Plain Layout
13187 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13200 \begin_layout Plain Layout
13204 \begin_inset Formula $\to$
13219 \begin_layout Plain Layout
13233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13236 \begin_layout Plain Layout
13240 \begin_layout Plain Layout
13264 \begin_layout Standard
13265 The last formula can currently only be created using TeX-mode because LyX
13266 inserts a box instead of the needed extra formula.
13270 \begin_layout Plain Layout
13272 \begin_inset CommandInset href
13274 name "LyX-bug #1435"
13275 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13287 \begin_layout Standard
13312 , with the difference that there is no frame.
13315 \begin_layout Subsection
13317 \begin_inset CommandInset label
13319 name "sub:Colored-Boxes"
13327 \begin_layout Plain Layout
13336 \begin_layout Standard
13337 To be able to use all commands explained in this section, the LaTeX-package
13346 \begin_layout Plain Layout
13351 is part of every LaTeX standard installation.
13360 \begin_layout Plain Layout
13366 has to be loaded in the LaTeX-preamble with the line
13370 \begin_layout Plain Layout
13371 When text is colored somewhere in the document with a predefined color,
13372 LyX loads the LaTeX-package
13377 Thus it is possible that the package is loaded twice, but this doesn't
13384 \begin_inset Note Note
13387 \begin_layout Plain Layout
13388 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13397 \begin_layout Standard
13405 \begin_layout Standard
13406 \begin_inset VSpace medskip
13409 To color boxes, the command
13419 \begin_layout Plain Layout
13427 is used in the following scheme:
13430 \begin_layout Standard
13435 colorbox{color}{box content}
13438 \begin_layout Standard
13439 The box content can also be a box and a
13445 can also be part of another box (see the 2nd and 3rd example).
13446 When the box should contain a formula, an extra formula has to be created,
13457 \begin_layout Plain Layout
13458 This also applies for the command
13466 \begin_inset CommandInset href
13468 name "LyX-bug #1435"
13469 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13481 \begin_layout Standard
13482 One of the following predefined colors can be chosen:
13485 \begin_layout Standard
13519 \begin_layout Standard
13521 \begin_inset Tabular
13522 <lyxtabular version="3" rows="4" columns="2">
13524 <column alignment="center" valignment="top" width="0">
13525 <column alignment="center" valignment="top" width="0">
13527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13530 \begin_layout Plain Layout
13536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13539 \begin_layout Plain Layout
13541 \begin_inset Note Note
13544 \begin_layout Plain Layout
13551 is only used as spacer.
13563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13566 \begin_layout Plain Layout
13570 \begin_inset Formula $\to$
13580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13583 \begin_layout Plain Layout
13584 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13597 \begin_layout Plain Layout
13601 \begin_inset Formula $\to$
13612 \begin_layout Plain Layout
13626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13629 \begin_layout Plain Layout
13630 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13643 \begin_layout Plain Layout
13650 \begin_layout Plain Layout
13662 \begin_inset Formula $\to$
13672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13675 \begin_layout Plain Layout
13676 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13692 \begin_layout Standard
13699 only colors the box but not the characters in the box.
13700 To color all characters, the whole formula is highlighted and the wanted
13701 color is chosen in the
13704 \begin_inset space ~
13710 The dialog can be called with the toolbar button
13711 \begin_inset Graphics
13712 filename ../images/dialog-show_character.png
13719 Edit\SpecialChar \menuseparator
13721 \begin_inset space ~
13724 Style\SpecialChar \menuseparator
13728 The formula number has then the same color as the formula.
13729 When the formula number should get another color than the formula characters,
13730 the color must be changed within the formula.
13733 \begin_layout Standard
13737 \begin_layout Standard
13740 \begin_inset Formula \begin{equation}
13741 \int A=B\label{eq:red}\end{equation}
13748 \begin_inset Formula \begin{equation}
13749 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13756 \begin_layout Standard
13758 \begin_inset CommandInset ref
13764 is completely colored red.
13765 \begin_inset Newline newline
13769 \begin_inset CommandInset ref
13771 reference "eq:redgreen"
13775 was first completely colored green to set the color for the formula number.
13776 Subsequently the formula characters were colored red.
13779 \begin_layout Standard
13780 \begin_inset VSpace bigskip
13783 To color the frame different than the rest of the box, the command
13793 \begin_layout Plain Layout
13801 is used in the following scheme:
13804 \begin_layout Standard
13809 fcolorbox{frame color}{color}{box content}
13812 \begin_layout Standard
13819 is an extension of the command
13826 The frame width is set, like for
13849 \begin_layout Plain Layout
13861 \begin_inset Formula \[
13862 \fcolorbox{cyan}{magenta}{A=B}\]
13870 \begin_layout Plain Layout
13884 \begin_layout Standard
13885 This formula was created with the command
13886 \begin_inset Newline newline
13894 \begin_inset Formula $\to$
13900 \begin_inset Formula $\to$
13910 \begin_layout Standard
13911 \begin_inset VSpace bigskip
13914 To use other colors than the predefined ones, they have to be defined first.
13917 \begin_layout Standard
13918 One can for example define the color
13919 \begin_inset Quotes eld
13927 \begin_inset Quotes erd
13930 with the LaTeX-preamble line:
13933 \begin_layout Standard
13938 definecolor{darkgreen}{cmyk}{0.5,
13956 \begin_layout Plain Layout
13967 \begin_layout Standard
13972 is the color space that denotes the colors
13989 The four comma separated numbers are the portion factor for the corresponding
13990 colors of the color space.
13991 The factors can be in the range of 0
13992 \begin_inset space \thinspace{}
13996 \begin_inset space \thinspace{}
14004 also the color space
14008 can be used for definitions.
14025 , so that there are in this case three portion factors for the corresponding
14027 Furthermore there is the color space
14031 with one portion factor for the gray value.
14034 \begin_layout Standard
14035 As example a framed box with the new defined color
14039 where the characters have been colored
14044 \begin_inset Formula \begin{equation}
14045 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14052 \begin_layout Standard
14053 Self-defined colors can also be used for text with the help of the command
14064 \begin_layout Plain Layout
14073 \begin_layout Standard
14077 \begin_layout Plain Layout
14081 textcolor{darkgreen}{
14087 \begin_inset Quotes eld
14091 \begin_inset Quotes erd
14098 \begin_layout Plain Layout
14108 \begin_layout Standard
14119 \begin_layout Plain Layout
14127 is used in the scheme
14131 textcolor{color}{characters to color}
14136 \begin_layout Subsection
14138 \begin_inset CommandInset label
14140 name "sub:Paragraph-Boxes"
14148 \begin_layout Plain Layout
14149 Boxes ! as paragraph
14157 \begin_layout Standard
14158 A box that can contain several lines and paragraphs, a so called paragraph
14159 box (parbox), can be created with the menu
14161 Insert\SpecialChar \menuseparator
14164 or the toolbar button
14165 \begin_inset Graphics
14166 filename ../images/box-insert.png
14174 \begin_layout Standard
14175 The following example shows a framed parbox in a line:
14178 \begin_layout Standard
14179 \begin_inset VSpace medskip
14183 \begin_inset Box Boxed
14192 height_special "totalheight"
14195 \begin_layout Plain Layout
14196 This is a paragraph box.
14198 \begin_inset space \thinspace{}
14201 cm long and can also contain formulas:
14202 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14213 \begin_layout Standard
14214 \begin_inset VSpace medskip
14220 \begin_layout Standard
14221 Such a box is created by right-clicking on the gray box inset.
14222 A dialog pops up showing the box properties.
14236 \begin_inset space \thinspace{}
14241 Vertical Box Alignment
14246 \begin_layout Standard
14247 \begin_inset VSpace medskip
14250 In LaTeX a parbox is created with the command
14260 \begin_layout Plain Layout
14268 that has the following scheme:
14271 \begin_layout Standard
14276 parbox[position]{width}{box content}
14279 \begin_layout Standard
14293 for bottom means that the box is aligned within the surrounding text with
14299 for top this is done with the first line.
14300 When no position is given, the box will be vertically centered, see section
14308 \begin_inset space ~
14313 manual for examples.
14316 \begin_layout Standard
14317 \begin_inset VSpace bigskip
14320 To frame formulas completely, including the formula number, the formula
14321 must be set into a parbox.
14322 To do this, the command
14336 is inserted in TeX-mode before the formula.
14345 \begin_layout Plain Layout
14355 is hereby the line width set for the document.
14356 Because the frame is outside the parbox, 2
14357 \begin_inset space \thinspace{}
14360 times the frame separation and the frame thickness must be subtracted from
14362 As this is not automatically done by LyX due to a bug
14366 \begin_layout Plain Layout
14367 \begin_inset CommandInset href
14369 name "LyX-bug #4483"
14370 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14379 , TeX-mode has to be used.
14380 To be able to multiply and subtract in arguments, the LaTeX-package
14388 \begin_layout Plain Layout
14393 is part of every LaTeX standard installation.
14402 \begin_layout Plain Layout
14408 must be loaded in the LaTeX-preamble with the line
14411 \begin_layout Standard
14419 \begin_layout Standard
14420 Behind the formula both boxes are closed by entering
14425 Here is an example:
14429 \begin_layout Plain Layout
14443 \begin_layout Standard
14447 \begin_layout Plain Layout
14465 \begin_inset Formula \begin{equation}
14466 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14474 \begin_layout Plain Layout
14485 \begin_layout Plain Layout
14499 \begin_layout Standard
14500 \begin_inset VSpace medskip
14503 As a parbox is used as argument of
14509 , there is in this case no difference between
14524 \begin_layout Standard
14525 \begin_inset VSpace bigskip
14528 Paragraph boxes are very useful to comment formulas directly.
14535 is used in combination with the command
14549 \begin_inset CommandInset ref
14551 reference "sub:User-defined-Numbering"
14558 \begin_layout Standard
14559 An example of a formula commented with
14568 \begin_layout Standard
14572 \begin_layout Plain Layout
14585 This is a description.
14586 It is distinctly separated from the formula and multiline.
14590 \begin_layout Plain Layout
14602 \begin_layout Standard
14603 Such a formula must be inserted completely in TeX-mode because LyX does
14604 not yet support the command
14611 The formula is created with the following command sequence:
14614 \begin_layout Standard
14627 is inserted in TeX-mode.
14631 \begin_layout Plain Layout
14632 When the formula style
14644 can also be replaced by
14651 (formula styles see
14652 \begin_inset CommandInset ref
14654 reference "sec:Formula-Styles"
14663 Then the description follows as normal text, and finally
14669 is inserted in TeX-mode.
14682 hereby create a displayed formula.
14685 \begin_layout Standard
14692 can be seen in this example that was
14693 \begin_inset Quotes eld
14697 \begin_inset Quotes erd
14700 using the mathematical textmode:
14701 \begin_inset Formula \[
14702 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14709 \begin_layout Section
14714 \begin_layout Plain Layout
14723 \begin_layout Subsection
14725 \begin_inset CommandInset label
14727 name "sub:Big-Operators"
14735 \begin_layout Plain Layout
14745 \begin_layout Plain Layout
14755 \begin_layout Plain Layout
14764 \begin_layout Standard
14765 To be able to use all integral operators listed here, the option
14767 Use esint package automatically
14769 must be set in the document settings under
14772 \begin_inset space ~
14780 \begin_layout Standard
14781 \begin_inset space \hfill{}
14785 \begin_inset Tabular
14786 <lyxtabular version="3" rows="11" columns="2">
14788 <column alignment="center" valignment="top" width="0pt">
14789 <column alignment="center" valignment="top" width="0pt">
14791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14794 \begin_layout Plain Layout
14800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14803 \begin_layout Plain Layout
14811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14814 \begin_layout Plain Layout
14821 \begin_layout Plain Layout
14834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14837 \begin_layout Plain Layout
14838 \begin_inset Formula $\sum$
14848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14851 \begin_layout Plain Layout
14858 \begin_layout Plain Layout
14871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14874 \begin_layout Plain Layout
14875 \begin_inset Formula $\int$
14885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14888 \begin_layout Plain Layout
14896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14899 \begin_layout Plain Layout
14900 \begin_inset Formula $\intop$
14910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14913 \begin_layout Plain Layout
14921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14924 \begin_layout Plain Layout
14925 \begin_inset Formula $\oint$
14935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14938 \begin_layout Plain Layout
14946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14949 \begin_layout Plain Layout
14950 \begin_inset Formula $\ointop$
14960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14963 \begin_layout Plain Layout
14971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14974 \begin_layout Plain Layout
14975 \begin_inset Formula $\ointctrclockwise$
14985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14988 \begin_layout Plain Layout
14996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14999 \begin_layout Plain Layout
15000 \begin_inset Formula $\ointclockwise$
15010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15013 \begin_layout Plain Layout
15021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15024 \begin_layout Plain Layout
15025 \begin_inset Formula $\sqint$
15035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15038 \begin_layout Plain Layout
15046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15049 \begin_layout Plain Layout
15050 \begin_inset Formula $\bigcap$
15060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15063 \begin_layout Plain Layout
15071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15074 \begin_layout Plain Layout
15075 \begin_inset Formula $\bigcup$
15089 \begin_inset space \hfill{}
15093 \begin_inset Tabular
15094 <lyxtabular version="3" rows="10" columns="2">
15096 <column alignment="center" valignment="top" width="0pt">
15097 <column alignment="center" valignment="top" width="0pt">
15099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15111 \begin_layout Plain Layout
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15129 \begin_layout Plain Layout
15142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15145 \begin_layout Plain Layout
15146 \begin_inset Formula $\prod$
15156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15159 \begin_layout Plain Layout
15167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15170 \begin_layout Plain Layout
15171 \begin_inset Formula $\coprod$
15181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15184 \begin_layout Plain Layout
15192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15195 \begin_layout Plain Layout
15196 \begin_inset Formula $\bigodot$
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15221 \begin_inset Formula $\bigotimes$
15231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15234 \begin_layout Plain Layout
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15245 \begin_layout Plain Layout
15246 \begin_inset Formula $\bigoplus$
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15259 \begin_layout Plain Layout
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15270 \begin_layout Plain Layout
15271 \begin_inset Formula $\bigwedge$
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15284 \begin_layout Plain Layout
15292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15295 \begin_layout Plain Layout
15296 \begin_inset Formula $\bigvee$
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15309 \begin_layout Plain Layout
15317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15320 \begin_layout Plain Layout
15321 \begin_inset Formula $\bigsqcup$
15331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15334 \begin_layout Plain Layout
15342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15345 \begin_layout Plain Layout
15346 \begin_inset Formula $\biguplus$
15360 \begin_inset space \hfill{}
15366 \begin_layout Standard
15367 All big operators can also be inserted via the math toolbar button
15368 \begin_inset Graphics
15369 filename ../images/math/intop.png
15377 \begin_layout Standard
15378 The operators are called big because they are bigger than the sometimes
15379 equal looking binary operators.
15380 All big operators can have limits as described in the next subsection.
15383 \begin_layout Standard
15409 \begin_inset space ~
15412 in the style the operator limits are displayed, see
15413 \begin_inset CommandInset ref
15415 reference "sub:Operator-Limits"
15423 \begin_layout Subsubsection*
15424 Advices for Integrals
15427 \begin_layout Standard
15432 in an integral is an operator, that therefore has to be set upright.
15433 This is done by highlighting the
15437 and using the keyboard shortcut
15440 \begin_inset space ~
15449 \begin_layout Plain Layout
15455 \begin_inset CommandInset ref
15457 reference "sub:Font-Styles"
15467 Finally the smallest space is inserted before the
15471 , as this is usual for operators.
15475 \begin_layout Standard
15477 \begin_inset Formula $\int A(x)dx$
15481 \begin_inset Newline newline
15488 \begin_layout Plain Layout
15498 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15504 \begin_layout Standard
15505 For multiple integrals there are the following commands:
15506 \begin_inset VSpace medskip
15512 \begin_layout Standard
15513 \begin_inset space \hfill{}
15517 \begin_inset Tabular
15518 <lyxtabular version="3" rows="4" columns="2">
15520 <column alignment="center" valignment="top" width="0">
15521 <column alignment="center" valignment="top" width="0">
15523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15526 \begin_layout Plain Layout
15532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15535 \begin_layout Plain Layout
15537 \begin_inset Note Note
15540 \begin_layout Plain Layout
15547 is only used as spacer.
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15562 \begin_layout Plain Layout
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15573 \begin_layout Plain Layout
15574 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15587 \begin_layout Plain Layout
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15598 \begin_layout Plain Layout
15599 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15612 \begin_layout Plain Layout
15620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15623 \begin_layout Plain Layout
15624 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15638 \begin_inset space \hfill{}
15642 \begin_inset Tabular
15643 <lyxtabular version="3" rows="4" columns="2">
15645 <column alignment="center" valignment="top" width="0">
15646 <column alignment="center" valignment="top" width="0">
15648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15651 \begin_layout Plain Layout
15657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15660 \begin_layout Plain Layout
15668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15671 \begin_layout Plain Layout
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15682 \begin_layout Plain Layout
15683 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15696 \begin_layout Plain Layout
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15707 \begin_layout Plain Layout
15708 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15721 \begin_layout Plain Layout
15729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15732 \begin_layout Plain Layout
15733 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15747 \begin_inset space \hfill{}
15753 \begin_layout Subsection
15755 \begin_inset CommandInset label
15757 name "sub:Operator-Limits"
15765 \begin_layout Plain Layout
15774 \begin_layout Standard
15775 Limits are created by super- and subscripts:
15778 \begin_layout Standard
15780 \begin_inset Tabular
15781 <lyxtabular version="3" rows="2" columns="2">
15783 <column alignment="center" valignment="top" width="0pt">
15784 <column alignment="center" valignment="top" width="0pt">
15786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15789 \begin_layout Plain Layout
15795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15798 \begin_layout Plain Layout
15800 \begin_inset Note Note
15803 \begin_layout Plain Layout
15810 is only used as spacer.
15822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15825 \begin_layout Plain Layout
15834 \begin_layout Plain Layout
15844 \begin_inset Formula $\to$
15848 \begin_inset Formula $\to$
15856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15859 \begin_layout Plain Layout
15860 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15876 \begin_layout Standard
15877 Limits of inline formulas are set right beside the operator.
15878 Limits in displayed formulas are set above or below the operator, except
15879 of integral limits.
15882 \begin_layout Standard
15883 To force that the limits are set beside the operator, the cursor is set
15884 directly behind the operator and the limits type is changed with the menu
15887 Edit\SpecialChar \menuseparator
15888 Math\SpecialChar \menuseparator
15900 \begin_inset space ~
15909 \begin_layout Standard
15910 The default limits type is this:
15911 \begin_inset Formula \[
15912 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15916 This is how it looks when the limits type was changed to
15923 \begin_inset Formula \[
15924 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15928 For integrals, except of
15940 , the limits are by default set beside the operator.
15941 But for multiple integrals the limits are often set below the operator.
15942 In the following example the limits type was therefore set to
15946 and so set below the integrals:
15947 \begin_inset Formula \begin{equation}
15948 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15955 \begin_layout Standard
15956 \begin_inset VSpace medskip
15959 To specify conditions for limits, the commands
15969 \begin_layout Plain Layout
15987 \begin_layout Plain Layout
15996 To create for example this expression
15997 \begin_inset Formula \begin{equation}
15998 \sum_{\begin{subarray}{c}
16000 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16007 \begin_layout Standard
16008 the following has to be done:
16009 \begin_inset Newline newline
16024 \begin_layout Plain Layout
16036 One is now in a blue box under the summation operator and insert there
16045 \begin_layout Plain Layout
16057 The blue box is now within a purple box and now several lines can be written
16059 A new line is created by inserting a line break (
16065 \begin_inset Newline newline
16070 0<k<1000 Ctrl-Return
16071 \begin_inset Newline newline
16076 is typed in, a new box appears below for the new line.
16079 \begin_layout Standard
16080 The alignment of the lines can be changed to left aligned with the
16090 Edit\SpecialChar \menuseparator
16094 To get right alignment,
16102 \begin_layout Plain Layout
16113 is inserted at the beginning of the line.
16116 \begin_layout Standard
16129 with the difference that the lines are always centered.
16132 \begin_layout Standard
16133 \begin_inset VSpace bigskip
16137 \begin_inset CommandInset ref
16139 reference "eq:substack"
16143 there can be too much space beside an operator, because the characters
16144 following the operator are set beside the limits.
16147 \begin_layout Standard
16148 To avoid this, the following macro can be used in the LaTeX-preamble:
16151 \begin_layout Standard
16165 \begin_inset Newline newline
16177 \begin_inset Newline newline
16184 mathclapinternal #1#2{
16188 mathsurround =0pt #1{#2}$}}
16191 \begin_layout Standard
16192 This defines the command
16202 \begin_layout Plain Layout
16210 that sets the width of the limit to 0
16211 \begin_inset space \thinspace{}
16215 The command scheme is
16218 \begin_layout Standard
16226 \begin_layout Standard
16227 where the limit can consist of several conditions.
16230 \begin_layout Standard
16232 \begin_inset CommandInset ref
16234 reference "eq:substack"
16238 , one uses the command
16241 \begin_layout Standard
16254 \begin_layout Plain Layout
16263 0<k<1000 Ctrl-Enter
16266 \begin_layout Standard
16267 to create the lower limit.
16268 The summand is now directly behind the summation operator:
16269 \begin_inset Formula \[
16270 \sum_{\mathclap{\substack{0<k<1000\\
16271 \\k\,\in\,\mathbb{N}}
16279 \begin_layout Standard
16280 \begin_inset VSpace bigskip
16283 How to use one limit for several operators is described in
16284 \begin_inset CommandInset ref
16286 reference "sub:Self-defined-Operators"
16293 \begin_layout Standard
16294 \begin_inset Newpage newpage
16300 \begin_layout Subsection
16302 \begin_inset CommandInset label
16304 name "sub:Binary-Operators"
16312 \begin_layout Plain Layout
16321 \begin_layout Standard
16322 Binary operators are surrounded by space when there is a character before
16324 \begin_inset VSpace medskip
16330 \begin_layout Standard
16331 \begin_inset space \hfill{}
16335 \begin_inset Tabular
16336 <lyxtabular version="3" rows="13" columns="2">
16338 <column alignment="center" valignment="top" width="0pt">
16339 <column alignment="center" valignment="top" width="0pt">
16341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16344 \begin_layout Plain Layout
16346 \begin_inset Note Note
16349 \begin_layout Plain Layout
16356 is only used as spacer.
16366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16369 \begin_layout Plain Layout
16377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16380 \begin_layout Plain Layout
16386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16389 \begin_layout Plain Layout
16390 \begin_inset Formula $+$
16400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16403 \begin_layout Plain Layout
16409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16412 \begin_layout Plain Layout
16413 \begin_inset Formula $-$
16423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16426 \begin_layout Plain Layout
16434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16437 \begin_layout Plain Layout
16438 \begin_inset Formula $\pm$
16448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16451 \begin_layout Plain Layout
16459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16462 \begin_layout Plain Layout
16463 \begin_inset Formula $\mp$
16473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16476 \begin_layout Plain Layout
16484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16487 \begin_layout Plain Layout
16488 \begin_inset Formula $\cdot$
16498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16501 \begin_layout Plain Layout
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16512 \begin_layout Plain Layout
16513 \begin_inset Formula $\times$
16523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16526 \begin_layout Plain Layout
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16537 \begin_layout Plain Layout
16538 \begin_inset Formula $\div$
16548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16551 \begin_layout Plain Layout
16555 \begin_layout Plain Layout
16568 \begin_layout Plain Layout
16580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16583 \begin_layout Plain Layout
16584 \begin_inset Formula $*$
16594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16597 \begin_layout Plain Layout
16605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16608 \begin_layout Plain Layout
16609 \begin_inset Formula $\star$
16619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16622 \begin_layout Plain Layout
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16633 \begin_layout Plain Layout
16634 \begin_inset Formula $\circ$
16644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16647 \begin_layout Plain Layout
16655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16658 \begin_layout Plain Layout
16659 \begin_inset Formula $\diamond$
16669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16672 \begin_layout Plain Layout
16680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16683 \begin_layout Plain Layout
16684 \begin_inset Formula $\bullet$
16698 \begin_inset space \hfill{}
16702 \begin_inset Tabular
16703 <lyxtabular version="3" rows="13" columns="2">
16705 <column alignment="center" valignment="top" width="0pt">
16706 <column alignment="center" valignment="top" width="0pt">
16708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16711 \begin_layout Plain Layout
16717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16720 \begin_layout Plain Layout
16728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16731 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16743 \begin_inset Formula $\nabla$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Plain Layout
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16768 \begin_inset Formula $\bigtriangledown$
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16781 \begin_layout Plain Layout
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16792 \begin_layout Plain Layout
16793 \begin_inset Formula $\bigtriangleup$
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16806 \begin_layout Plain Layout
16814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16817 \begin_layout Plain Layout
16818 \begin_inset Formula $\Box$
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16831 \begin_layout Plain Layout
16839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16842 \begin_layout Plain Layout
16843 \begin_inset Formula $\cap$
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16856 \begin_layout Plain Layout
16864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16867 \begin_layout Plain Layout
16868 \begin_inset Formula $\cup$
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16881 \begin_layout Plain Layout
16889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16892 \begin_layout Plain Layout
16893 \begin_inset Formula $\dagger$
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16906 \begin_layout Plain Layout
16914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16917 \begin_layout Plain Layout
16918 \begin_inset Formula $\ddagger$
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16931 \begin_layout Plain Layout
16939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16942 \begin_layout Plain Layout
16943 \begin_inset Formula $\wr$
16953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16956 \begin_layout Plain Layout
16964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16967 \begin_layout Plain Layout
16968 \begin_inset Formula $\bigcirc$
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16981 \begin_layout Plain Layout
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16992 \begin_layout Plain Layout
16993 \begin_inset Formula $\wedge$
17003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17006 \begin_layout Plain Layout
17014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17018 \begin_inset Formula $\vee$
17032 \begin_inset space \hfill{}
17036 \begin_inset Tabular
17037 <lyxtabular version="3" rows="13" columns="2">
17039 <column alignment="center" valignment="top" width="0pt">
17040 <column alignment="center" valignment="top" width="0pt">
17042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17045 \begin_layout Plain Layout
17051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17054 \begin_layout Plain Layout
17062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17065 \begin_layout Plain Layout
17073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17076 \begin_layout Plain Layout
17077 \begin_inset Formula $\oplus$
17087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17090 \begin_layout Plain Layout
17098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17101 \begin_layout Plain Layout
17102 \begin_inset Formula $\ominus$
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17115 \begin_layout Plain Layout
17123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17126 \begin_layout Plain Layout
17127 \begin_inset Formula $\otimes$
17137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17140 \begin_layout Plain Layout
17148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17151 \begin_layout Plain Layout
17152 \begin_inset Formula $\oslash$
17162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17165 \begin_layout Plain Layout
17173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17176 \begin_layout Plain Layout
17177 \begin_inset Formula $\odot$
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17190 \begin_layout Plain Layout
17198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17201 \begin_layout Plain Layout
17202 \begin_inset Formula $\amalg$
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17215 \begin_layout Plain Layout
17223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17226 \begin_layout Plain Layout
17227 \begin_inset Formula $\uplus$
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17251 \begin_layout Plain Layout
17252 \begin_inset Formula $\setminus$
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17265 \begin_layout Plain Layout
17273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17276 \begin_layout Plain Layout
17277 \begin_inset Formula $\sqcap$
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17290 \begin_layout Plain Layout
17298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17301 \begin_layout Plain Layout
17302 \begin_inset Formula $\sqcup$
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17315 \begin_layout Plain Layout
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\triangleleft$
17337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17340 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17352 \begin_inset Formula $\triangleright$
17366 \begin_inset space \hfill{}
17372 \begin_layout Standard
17373 All binary operators can also be inserted via the math toolbar button
17374 \begin_inset Graphics
17375 filename ../images/math/pm.png
17383 \begin_layout Standard
17384 To typeset the Laplace operator also
17401 \begin_inset Formula $\nabla^{2}$
17404 ) can be used instead of
17413 \begin_layout Standard
17420 Insert\SpecialChar \menuseparator
17432 \begin_layout Subsection
17433 Self-defined Operators
17434 \begin_inset CommandInset label
17436 name "sub:Self-defined-Operators"
17444 \begin_layout Plain Layout
17445 Operators ! self-defined
17453 \begin_layout Standard
17454 With the help of the command
17458 DeclareMathOperator
17464 \begin_layout Plain Layout
17469 DeclareMathOperator
17474 custom operators can be defined in the LaTeX-preamble.
17475 Its command scheme is:
17478 \begin_layout Standard
17483 DeclareMathOperator{new command}{display}
17486 \begin_layout Standard
17487 Display can be characters or symbols that define how the operator looks
17489 To define a big operator a * is set behind the command.
17490 All self-defined big operators can have limits as described in
17491 \begin_inset CommandInset ref
17493 reference "sub:Operator-Limits"
17500 \begin_layout Standard
17501 For example the LaTeX-preamble line
17504 \begin_layout Standard
17509 DeclareMathOperator*{
17516 \begin_layout Standard
17517 defines the command
17523 , that inserts a big operator consisting of the lozenge symbol from
17524 \begin_inset CommandInset ref
17526 reference "sub:Miscellaneous-Symbols"
17531 \begin_inset Formula \[
17532 \Lozenge_{n=1}^{\infty}\]
17536 The command for this formula is:
17547 \begin_inset Formula $\to$
17553 \begin_layout Standard
17554 \begin_inset VSpace bigskip
17557 When self-defined operators are not used several times in the document,
17558 they can also be defined with the commands
17568 \begin_layout Plain Layout
17586 \begin_layout Plain Layout
17594 , which have the following scheme:
17597 \begin_layout Standard
17611 \begin_layout Standard
17618 defines big operators,
17627 \begin_layout Standard
17635 \begin_inset space \thinspace{}
17639 \begin_inset space ~
17642 be used to use one limit for several operators:
17645 \begin_layout Standard
17646 \begin_inset Formula \[
17647 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17654 \begin_layout Standard
17655 The command for the formula above is:
17656 \begin_inset Newline newline
17675 \begin_layout Plain Layout
17687 \begin_inset Formula $\to$
17696 \begin_layout Plain Layout
17710 \begin_layout Section
17715 \begin_layout Plain Layout
17724 \begin_layout Subsection
17726 \begin_inset CommandInset label
17728 name "sub:Font-Styles"
17736 \begin_layout Plain Layout
17745 \begin_layout Standard
17746 Latin letters in formulas can be set in one of the following font styles:
17747 \begin_inset VSpace -2mm
17753 \begin_layout Standard
17755 \begin_inset Tabular
17756 <lyxtabular version="3" rows="6" columns="3">
17758 <column alignment="center" valignment="top" width="0">
17759 <column alignment="center" valignment="top" width="0">
17760 <column alignment="center" valignment="top" width="0">
17762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17765 \begin_layout Plain Layout
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" rightline="true" usebox="none">
17783 \begin_layout Plain Layout
17791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17794 \begin_layout Plain Layout
17803 \begin_layout Plain Layout
17819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17822 \begin_layout Plain Layout
17823 \begin_inset Formula $\mathbb{ABC}$
17831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17834 \begin_layout Plain Layout
17842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17845 \begin_layout Plain Layout
17854 \begin_layout Plain Layout
17870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17873 \begin_layout Plain Layout
17874 \begin_inset Formula $\mathbf{AbC}$
17882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17885 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17896 \begin_layout Plain Layout
17905 \begin_layout Plain Layout
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17924 \begin_layout Plain Layout
17925 \begin_inset Formula $\boldsymbol{AbC}$
17933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17936 \begin_layout Plain Layout
17944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17947 \begin_layout Plain Layout
17956 \begin_layout Plain Layout
17972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17975 \begin_layout Plain Layout
17976 \begin_inset Formula $\mathcal{ABC}$
17984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17987 \begin_layout Plain Layout
17995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17998 \begin_layout Plain Layout
18007 \begin_layout Plain Layout
18023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18026 \begin_layout Plain Layout
18027 \begin_inset Formula $\mathfrak{AbC}$
18035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18038 \begin_layout Plain Layout
18052 \begin_layout Standard
18054 \begin_inset Tabular
18055 <lyxtabular version="3" rows="5" columns="3">
18057 <column alignment="center" valignment="top" width="0">
18058 <column alignment="center" valignment="top" width="0">
18059 <column alignment="center" valignment="top" width="0">
18061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18064 \begin_layout Plain Layout
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" rightline="true" usebox="none">
18082 \begin_layout Plain Layout
18090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18093 \begin_layout Plain Layout
18102 \begin_layout Plain Layout
18118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18121 \begin_layout Plain Layout
18122 \begin_inset Formula $\mathit{AbC}$
18130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18133 \begin_layout Plain Layout
18141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18144 \begin_layout Plain Layout
18153 \begin_layout Plain Layout
18169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18173 \begin_inset Formula $\mathrm{AbC}$
18181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18184 \begin_layout Plain Layout
18192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18195 \begin_layout Plain Layout
18204 \begin_layout Plain Layout
18220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18223 \begin_layout Plain Layout
18224 \begin_inset Formula $\mathsf{AbC}$
18232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18235 \begin_layout Plain Layout
18243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18246 \begin_layout Plain Layout
18255 \begin_layout Plain Layout
18271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18274 \begin_layout Plain Layout
18275 \begin_inset Formula $\mathtt{AbC}$
18283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18286 \begin_layout Plain Layout
18300 \begin_layout Standard
18301 \begin_inset Note Greyedout
18304 \begin_layout Plain Layout
18321 can only be used for big letters.
18329 \begin_layout Standard
18330 Predefined is the style
18339 \begin_layout Standard
18340 The style commands work also for letters in mathematical constructs:
18341 \begin_inset Formula \[
18342 \mathfrak{A=\frac{b}{C}}\]
18349 \begin_layout Standard
18350 Characters in mathematical text don't appear in a math font style but in
18351 the text font style
18358 That their style can't be set correctly via the text style dialog is a
18363 \begin_layout Plain Layout
18364 \begin_inset CommandInset href
18366 name "LyX-bug #4091"
18367 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18379 \begin_layout Standard
18380 Instead of the style commands the dialog
18382 Edit\SpecialChar \menuseparator
18383 Math\SpecialChar \menuseparator
18386 or the toolbar button
18387 \begin_inset Graphics
18388 filename ../images/math/font.png
18396 \begin_layout Subsection
18398 \begin_inset CommandInset label
18400 name "sub:Bold-Formulas"
18408 \begin_layout Plain Layout
18417 \begin_layout Standard
18418 To make a complete formula bold, the command
18424 from the previous subsection cannot be used, because it doesn't work for
18425 small Greek letters.
18426 Furthermore it prints Latin letters always upright, like in the following
18430 \begin_layout Standard
18431 \begin_inset Formula \[
18432 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18439 \begin_layout Standard
18440 To display the formula correctly, the command
18447 \begin_inset Formula \[
18448 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18452 It is also possible to set the formula in a
18454 boldmath environment
18457 This environment is created by inserting the command
18465 \begin_layout Plain Layout
18476 To end the environment, the command
18484 \begin_layout Plain Layout
18494 is inserted in TeX-mode.
18498 \begin_layout Plain Layout
18508 \begin_inset Formula \[
18509 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18517 \begin_layout Plain Layout
18529 \begin_layout Subsection
18531 \begin_inset CommandInset label
18533 name "sub:Font-Sizes"
18541 \begin_layout Plain Layout
18550 \begin_layout Standard
18551 For characters in formulas there are, analog to characters in text, the
18552 following size commands:
18555 \begin_layout Standard
18599 \begin_inset Newline newline
18621 \begin_layout Standard
18622 The size produced by the commands depends on the document font size, that
18623 corresponds with the command
18630 The other commands produce smaller or larger sizes than
18637 The font size can however not exceed a certain value.
18638 Is for example the document font size 12
18639 \begin_inset space \thinspace{}
18648 switches to the same size as
18658 \begin_layout Standard
18659 A size command is inserted in TeX-mode before the formula and sets the size
18660 for all following formula and text characters.
18661 To switch back to the initial size, the command
18667 is inserted behind the formula in TeX-mode.
18670 \begin_layout Standard
18671 Within a formula the size can only be changed for symbols or letters in
18673 To do this, the size command is inserted in mathematical text.
18674 All following characters until the end of the mathematical text or until
18675 another size command will have the selected size.
18677 \begin_inset VSpace -2mm
18683 \begin_layout Standard
18687 \begin_layout Plain Layout
18697 \begin_inset Formula \[
18698 A=\frac{B}{c}\cdot\maltese\]
18703 \begin_inset Formula \[
18704 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18712 \begin_layout Plain Layout
18724 \begin_layout Standard
18725 \begin_inset VSpace medskip
18728 Before both formulas the command
18735 The command for the second formula is:
18736 \begin_inset Newline newline
18747 \begin_layout Plain Layout
18762 \begin_layout Plain Layout
18777 \begin_layout Plain Layout
18792 \begin_layout Plain Layout
18802 \begin_inset Formula $\to$
18806 \begin_inset Formula $\to$
18810 \begin_inset Newline newline
18814 \begin_inset space \hspace*{}
18828 \begin_layout Plain Layout
18843 \begin_layout Plain Layout
18858 \begin_layout Plain Layout
18870 \begin_layout Standard
18871 If a symbol cannot be displayed in different sizes, it will always be displayed
18872 in the default size.
18875 \begin_layout Section
18880 \begin_layout Plain Layout
18889 \begin_layout Standard
18890 All Greek letters can also be inserted via the toolbar button
18891 \begin_inset Graphics
18892 filename ../images/math/alpha.png
18900 \begin_layout Subsection
18902 \begin_inset CommandInset label
18904 name "sub:Small-Letters"
18912 \begin_layout Plain Layout
18913 Greek letters ! small
18921 \begin_layout Standard
18922 \begin_inset space \hfill{}
18926 \begin_inset Tabular
18927 <lyxtabular version="3" rows="11" columns="2">
18929 <column alignment="center" valignment="top" width="0pt">
18930 <column alignment="center" valignment="top" width="0pt">
18932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18935 \begin_layout Plain Layout
18941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18944 \begin_layout Plain Layout
18952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18955 \begin_layout Plain Layout
18963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18966 \begin_layout Plain Layout
18967 \begin_inset Formula $\alpha$
18977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18980 \begin_layout Plain Layout
18988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18991 \begin_layout Plain Layout
18992 \begin_inset Formula $\beta$
19002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19005 \begin_layout Plain Layout
19013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19016 \begin_layout Plain Layout
19017 \begin_inset Formula $\gamma$
19027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19030 \begin_layout Plain Layout
19038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19041 \begin_layout Plain Layout
19042 \begin_inset Formula $\delta$
19052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19055 \begin_layout Plain Layout
19063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19066 \begin_layout Plain Layout
19067 \begin_inset Formula $\epsilon$
19077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19080 \begin_layout Plain Layout
19088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19091 \begin_layout Plain Layout
19092 \begin_inset Formula $\varepsilon$
19102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19105 \begin_layout Plain Layout
19113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19116 \begin_layout Plain Layout
19117 \begin_inset Formula $\zeta$
19127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19130 \begin_layout Plain Layout
19138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19141 \begin_layout Plain Layout
19142 \begin_inset Formula $\eta$
19152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19155 \begin_layout Plain Layout
19163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19166 \begin_layout Plain Layout
19167 \begin_inset Formula $\theta$
19177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19180 \begin_layout Plain Layout
19188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19191 \begin_layout Plain Layout
19192 \begin_inset Formula $\vartheta$
19206 \begin_inset space \hfill{}
19210 \begin_inset Tabular
19211 <lyxtabular version="3" rows="12" columns="2">
19213 <column alignment="center" valignment="top" width="0pt">
19214 <column alignment="center" valignment="top" width="0pt">
19216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19219 \begin_layout Plain Layout
19225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19228 \begin_layout Plain Layout
19236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19239 \begin_layout Plain Layout
19247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19250 \begin_layout Plain Layout
19251 \begin_inset Formula $\iota$
19261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19264 \begin_layout Plain Layout
19272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19275 \begin_layout Plain Layout
19276 \begin_inset Formula $\kappa$
19286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19289 \begin_layout Plain Layout
19297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19300 \begin_layout Plain Layout
19301 \begin_inset Formula $\varkappa$
19311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19314 \begin_layout Plain Layout
19322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19325 \begin_layout Plain Layout
19326 \begin_inset Formula $\lambda$
19336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19339 \begin_layout Plain Layout
19347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19350 \begin_layout Plain Layout
19351 \begin_inset Formula $\mu$
19361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19364 \begin_layout Plain Layout
19372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19375 \begin_layout Plain Layout
19376 \begin_inset Formula $\nu$
19386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19389 \begin_layout Plain Layout
19397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19400 \begin_layout Plain Layout
19401 \begin_inset Formula $\xi$
19411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19414 \begin_layout Plain Layout
19420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19423 \begin_layout Plain Layout
19424 \begin_inset Formula $o$
19434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19437 \begin_layout Plain Layout
19445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19448 \begin_layout Plain Layout
19449 \begin_inset Formula $\pi$
19459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19462 \begin_layout Plain Layout
19470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19473 \begin_layout Plain Layout
19474 \begin_inset Formula $\varpi$
19484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19487 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19499 \begin_inset Formula $\rho$
19513 \begin_inset space \hfill{}
19517 \begin_inset Tabular
19518 <lyxtabular version="3" rows="11" columns="2">
19520 <column alignment="center" valignment="top" width="0pt">
19521 <column alignment="center" valignment="top" width="0pt">
19523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19526 \begin_layout Plain Layout
19532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19535 \begin_layout Plain Layout
19543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19546 \begin_layout Plain Layout
19554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19557 \begin_layout Plain Layout
19558 \begin_inset Formula $\varrho$
19568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19571 \begin_layout Plain Layout
19579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19582 \begin_layout Plain Layout
19583 \begin_inset Formula $\sigma$
19593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19596 \begin_layout Plain Layout
19604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19607 \begin_layout Plain Layout
19608 \begin_inset Formula $\varsigma$
19618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19621 \begin_layout Plain Layout
19629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19632 \begin_layout Plain Layout
19633 \begin_inset Formula $\tau$
19643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19646 \begin_layout Plain Layout
19654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19657 \begin_layout Plain Layout
19658 \begin_inset Formula $\upsilon$
19668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19671 \begin_layout Plain Layout
19679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19682 \begin_layout Plain Layout
19683 \begin_inset Formula $\phi$
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19696 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19707 \begin_layout Plain Layout
19708 \begin_inset Formula $\varphi$
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19721 \begin_layout Plain Layout
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19732 \begin_layout Plain Layout
19733 \begin_inset Formula $\chi$
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19746 \begin_layout Plain Layout
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19757 \begin_layout Plain Layout
19758 \begin_inset Formula $\psi$
19768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19771 \begin_layout Plain Layout
19779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19782 \begin_layout Plain Layout
19783 \begin_inset Formula $\omega$
19797 \begin_inset space \hfill{}
19803 \begin_layout Standard
19804 \begin_inset VSpace medskip
19810 \begin_layout Standard
19811 How to create upright Greek letters is explained in
19812 \begin_inset CommandInset ref
19814 reference "sub:Upright-small-Greek"
19821 \begin_layout Subsection
19826 \begin_layout Plain Layout
19827 Greek letters ! big
19835 \begin_layout Standard
19836 \begin_inset space \hfill{}
19840 \begin_inset Tabular
19841 <lyxtabular version="3" rows="7" columns="2">
19843 <column alignment="center" valignment="top" width="0pt">
19844 <column alignment="center" valignment="top" width="0pt">
19846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19849 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19858 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19869 \begin_layout Plain Layout
19877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19880 \begin_layout Plain Layout
19881 \begin_inset Formula $\Gamma$
19891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19894 \begin_layout Plain Layout
19902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19905 \begin_layout Plain Layout
19906 \begin_inset Formula $\Delta$
19916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19919 \begin_layout Plain Layout
19927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19930 \begin_layout Plain Layout
19931 \begin_inset Formula $\Theta$
19941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19944 \begin_layout Plain Layout
19952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19955 \begin_layout Plain Layout
19956 \begin_inset Formula $\Lambda$
19966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19969 \begin_layout Plain Layout
19977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19980 \begin_layout Plain Layout
19981 \begin_inset Formula $\Xi$
19991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19994 \begin_layout Plain Layout
20002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20005 \begin_layout Plain Layout
20006 \begin_inset Formula $\Pi$
20020 \begin_inset space \hfill{}
20024 \begin_inset Tabular
20025 <lyxtabular version="3" rows="6" columns="2">
20027 <column alignment="center" valignment="top" width="0pt">
20028 <column alignment="center" valignment="top" width="0pt">
20030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20042 \begin_layout Plain Layout
20050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20053 \begin_layout Plain Layout
20061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20064 \begin_layout Plain Layout
20065 \begin_inset Formula $\Sigma$
20075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20078 \begin_layout Plain Layout
20086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20089 \begin_layout Plain Layout
20090 \begin_inset Formula $\Upsilon$
20100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20103 \begin_layout Plain Layout
20111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20114 \begin_layout Plain Layout
20115 \begin_inset Formula $\Phi$
20125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20128 \begin_layout Plain Layout
20136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20139 \begin_layout Plain Layout
20140 \begin_inset Formula $\Psi$
20150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20153 \begin_layout Plain Layout
20161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20164 \begin_layout Plain Layout
20165 \begin_inset Formula $\Omega$
20179 \begin_inset space \hfill{}
20185 \begin_layout Standard
20186 \begin_inset VSpace medskip
20189 That the big Greek letters appear upright is caused by a design bug when
20191 To get correct italic big letters, begin every command with
20196 For example the command
20203 \begin_inset Formula $\varGamma$
20209 \begin_layout Subsection
20214 \begin_layout Plain Layout
20215 Greek letters ! bold
20223 \begin_layout Standard
20224 Greek letters cannot be set with different font styles like Latin letters.
20225 They can only be made bold with the command
20235 \begin_layout Plain Layout
20246 \begin_layout Standard
20248 \begin_inset Tabular
20249 <lyxtabular version="3" rows="3" columns="2">
20251 <column alignment="center" valignment="top" width="0">
20252 <column alignment="center" valignment="top" width="0">
20254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20257 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20292 \begin_layout Plain Layout
20293 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20306 \begin_layout Plain Layout
20318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20321 \begin_layout Plain Layout
20322 \begin_inset Formula $\theta\boldsymbol{\theta}$
20338 \begin_layout Section
20343 \begin_layout Plain Layout
20356 \begin_layout Plain Layout
20357 A list with all symbols of most of the LaTeX-packages can be found in
20358 \begin_inset CommandInset citation
20373 \begin_layout Plain Layout
20381 \begin_inset Note Note
20384 \begin_layout Plain Layout
20387 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20390 \begin_layout Plain Layout
20393 texorpdfstring is in section
20394 \begin_inset CommandInset ref
20396 reference "sub:Formulas-in-Section"
20409 \begin_layout Plain Layout
20418 \begin_layout Standard
20419 Many of the symbols listed in this section can also be inserted via the
20421 \begin_inset Graphics
20422 filename ../images/math/nabla.png
20428 \begin_inset Graphics
20429 filename ../images/math/digamma.png
20437 \begin_layout Subsection
20438 Mathematical Symbols
20439 \begin_inset CommandInset label
20441 name "sub:Mathematical-Symbols"
20449 \begin_layout Plain Layout
20450 Symbols ! mathematical
20458 \begin_layout Standard
20459 \begin_inset space \hfill{}
20463 \begin_inset Tabular
20464 <lyxtabular version="3" rows="10" columns="2">
20466 <column alignment="center" valignment="top" width="0pt">
20467 <column alignment="center" valignment="top" width="0pt">
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20481 \begin_layout Plain Layout
20489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20492 \begin_layout Plain Layout
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20503 \begin_layout Plain Layout
20504 \begin_inset Formula $\neg$
20514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20517 \begin_layout Plain Layout
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20528 \begin_layout Plain Layout
20529 \begin_inset Formula $\Im$
20539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20542 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Plain Layout
20554 \begin_inset Formula $\Re$
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20567 \begin_layout Plain Layout
20575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20578 \begin_layout Plain Layout
20579 \begin_inset Formula $\aleph$
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20592 \begin_layout Plain Layout
20600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Plain Layout
20604 \begin_inset Formula $\partial$
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20617 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Plain Layout
20629 \begin_inset Formula $\infty$
20639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20642 \begin_layout Plain Layout
20650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Plain Layout
20654 \begin_inset Formula $\wp$
20664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\imath$
20689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\jmath$
20718 \begin_inset space \hfill{}
20722 \begin_inset Tabular
20723 <lyxtabular version="3" rows="10" columns="2">
20725 <column alignment="center" valignment="top" width="0pt">
20726 <column alignment="center" valignment="top" width="0pt">
20728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20731 \begin_layout Plain Layout
20737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20740 \begin_layout Plain Layout
20742 \begin_inset Note Note
20745 \begin_layout Plain Layout
20752 is only used as spacer.
20764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20767 \begin_layout Plain Layout
20775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20778 \begin_layout Plain Layout
20779 \begin_inset Formula $\forall$
20789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20792 \begin_layout Plain Layout
20800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20803 \begin_layout Plain Layout
20804 \begin_inset Formula $\exists$
20814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20817 \begin_layout Plain Layout
20825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20828 \begin_layout Plain Layout
20829 \begin_inset Formula $\nexists$
20839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20842 \begin_layout Plain Layout
20850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20853 \begin_layout Plain Layout
20854 \begin_inset Formula $\emptyset$
20864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20867 \begin_layout Plain Layout
20875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20878 \begin_layout Plain Layout
20879 \begin_inset Formula $\varnothing$
20889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20892 \begin_layout Plain Layout
20900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20903 \begin_layout Plain Layout
20904 \begin_inset Formula $\dag$
20914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20917 \begin_layout Plain Layout
20925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20928 \begin_layout Plain Layout
20929 \begin_inset Formula $\ddag$
20939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20942 \begin_layout Plain Layout
20950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20953 \begin_layout Plain Layout
20957 \begin_layout Plain Layout
20967 \begin_inset Formula $\complement$
20974 \begin_layout Plain Layout
20988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20991 \begin_layout Plain Layout
20999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21002 \begin_layout Plain Layout
21003 \begin_inset Formula $\Bbbk$
21017 \begin_inset space \hfill{}
21021 \begin_inset Tabular
21022 <lyxtabular version="3" rows="10" columns="2">
21024 <column alignment="center" valignment="top" width="0pt">
21025 <column alignment="center" valignment="top" width="0pt">
21027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21030 \begin_layout Plain Layout
21036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21039 \begin_layout Plain Layout
21047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21050 \begin_layout Plain Layout
21058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21061 \begin_layout Plain Layout
21062 \begin_inset Formula $\prime$
21072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21075 \begin_layout Plain Layout
21083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21086 \begin_layout Plain Layout
21087 \begin_inset Formula $\backprime$
21097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21100 \begin_layout Plain Layout
21108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21111 \begin_layout Plain Layout
21112 \begin_inset Formula $\mho$
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21125 \begin_layout Plain Layout
21133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21136 \begin_layout Plain Layout
21137 \begin_inset Formula $\triangle$
21147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21150 \begin_layout Plain Layout
21158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21161 \begin_layout Plain Layout
21162 \begin_inset Formula $\angle$
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21186 \begin_layout Plain Layout
21187 \begin_inset Formula $\measuredangle$
21197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21200 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21212 \begin_inset Formula $\sphericalangle$
21222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21225 \begin_layout Plain Layout
21233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21236 \begin_layout Plain Layout
21237 \begin_inset Formula $\top$
21247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21250 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21261 \begin_layout Plain Layout
21262 \begin_inset Formula $\bot$
21276 \begin_inset space \hfill{}
21282 \begin_layout Standard
21283 \begin_inset Newpage newpage
21289 \begin_layout Subsection
21290 Miscellaneous Symbols
21291 \begin_inset CommandInset label
21293 name "sub:Miscellaneous-Symbols"
21301 \begin_layout Plain Layout
21302 Symbols ! miscellaneous
21310 \begin_layout Standard
21313 \begin_inset Tabular
21314 <lyxtabular version="3" rows="10" columns="2">
21316 <column alignment="center" valignment="top" width="0pt">
21317 <column alignment="center" valignment="top" width="0pt">
21319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21322 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21342 \begin_layout Plain Layout
21350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21353 \begin_layout Plain Layout
21354 \begin_inset Formula $\flat$
21364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21367 \begin_layout Plain Layout
21375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21378 \begin_layout Plain Layout
21379 \begin_inset Formula $\natural$
21389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21392 \begin_layout Plain Layout
21400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21403 \begin_layout Plain Layout
21404 \begin_inset Formula $\sharp$
21414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21417 \begin_layout Plain Layout
21425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21428 \begin_layout Plain Layout
21429 \begin_inset Formula $\surd$
21439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21442 \begin_layout Plain Layout
21450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21453 \begin_layout Plain Layout
21454 \begin_inset Formula $\checkmark$
21464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21467 \begin_layout Plain Layout
21475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21478 \begin_layout Plain Layout
21479 \begin_inset Formula $\yen$
21489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21492 \begin_layout Plain Layout
21500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21503 \begin_layout Plain Layout
21504 \begin_inset Formula $\pounds$
21514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21517 \begin_layout Plain Layout
21523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21526 \begin_layout Plain Layout
21527 \begin_inset Formula $\$$
21537 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21540 \begin_layout Plain Layout
21546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21549 \begin_layout Plain Layout
21550 \begin_inset Formula $§$
21564 \begin_inset Tabular
21565 <lyxtabular version="3" rows="10" columns="2">
21567 <column alignment="center" valignment="top" width="0">
21568 <column alignment="center" valignment="top" width="0">
21570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21573 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21593 \begin_layout Plain Layout
21601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21604 \begin_layout Plain Layout
21605 \begin_inset Formula $\hbar$
21615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21618 \begin_layout Plain Layout
21626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21629 \begin_layout Plain Layout
21630 \begin_inset Formula $\hslash$
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21643 \begin_layout Plain Layout
21651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21654 \begin_layout Plain Layout
21655 \begin_inset Formula $\clubsuit$
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21668 \begin_layout Plain Layout
21676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21679 \begin_layout Plain Layout
21680 \begin_inset Formula $\spadesuit$
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21693 \begin_layout Plain Layout
21701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21704 \begin_layout Plain Layout
21705 \begin_inset Formula $\bigstar$
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21718 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21730 \begin_inset Formula $\blacklozenge$
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21754 \begin_layout Plain Layout
21755 \begin_inset Formula $\blacktriangle$
21765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21768 \begin_layout Plain Layout
21776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21779 \begin_layout Plain Layout
21780 \begin_inset Formula $\blacktriangledown$
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21793 \begin_layout Plain Layout
21801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21804 \begin_layout Plain Layout
21805 \begin_inset Formula $\bullet$
21819 \begin_inset Tabular
21820 <lyxtabular version="3" rows="10" columns="2">
21822 <column alignment="center" valignment="top" width="0pt">
21823 <column alignment="center" valignment="top" width="0pt">
21825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21828 \begin_layout Plain Layout
21834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21837 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21848 \begin_layout Plain Layout
21856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21859 \begin_layout Plain Layout
21860 \begin_inset Formula $\diamondsuit$
21870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21873 \begin_layout Plain Layout
21881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21884 \begin_layout Plain Layout
21885 \begin_inset Formula $\Diamond$
21895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21898 \begin_layout Plain Layout
21906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21909 \begin_layout Plain Layout
21910 \begin_inset Formula $\heartsuit$
21920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21923 \begin_layout Plain Layout
21931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21934 \begin_layout Plain Layout
21935 \begin_inset Formula $\P$
21945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21948 \begin_layout Plain Layout
21956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21959 \begin_layout Plain Layout
21960 \begin_inset Formula $\copyright$
21970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21973 \begin_layout Plain Layout
21981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21984 \begin_layout Plain Layout
21985 \begin_inset Formula $\circledR$
21995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21998 \begin_layout Plain Layout
22006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22009 \begin_layout Plain Layout
22010 \begin_inset Formula $\maltese$
22020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22023 \begin_layout Plain Layout
22031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22034 \begin_layout Plain Layout
22035 \begin_inset Formula $\diagup$
22045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22048 \begin_layout Plain Layout
22056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22059 \begin_layout Plain Layout
22060 \begin_inset Formula $\diagdown$
22076 \begin_layout Standard
22077 \begin_inset VSpace medskip
22080 More symbols are listed in
22081 \begin_inset CommandInset ref
22083 reference "sub:Miscellaneous-special-Characters"
22090 \begin_layout Standard
22091 Some symbols can be displayed in different sizes, see
22092 \begin_inset CommandInset ref
22094 reference "sub:Font-Sizes"
22101 \begin_layout Subsection
22106 \begin_layout Plain Layout
22107 Symbols ! Euro-symbol
22116 \begin_layout Plain Layout
22123 \begin_layout Plain Layout
22140 \begin_layout Standard
22141 To use the Euro symbol in formulas, the LaTeX-package
22149 \begin_layout Plain Layout
22155 must be installed and loaded with the LaTeX-preamble line
22158 \begin_layout Standard
22163 usepackage[gennarrow]{eurosym}
22166 \begin_layout Standard
22167 The Euro symbol can now be inserted with the command
22177 \begin_layout Plain Layout
22188 \begin_layout Standard
22189 The Euro symbol can directly be inserted with the € key in mathematical
22190 text, without having
22205 can also be inserted in TeX-mode.
22206 The official currency symbol can then be inserted with the command
22216 \begin_layout Plain Layout
22224 , that is only available in TeX-mode.
22227 \begin_layout Standard
22231 \begin_layout Plain Layout
22241 \begin_inset Note Note
22244 \begin_layout Plain Layout
22245 The following table will only be displayed when the LaTeX-package
22257 \begin_layout Standard
22258 An overview about the different Euro symbols:
22261 \begin_layout Standard
22263 \begin_inset Tabular
22264 <lyxtabular version="3" rows="4" columns="3">
22266 <column alignment="center" valignment="top" width="0pt">
22267 <column alignment="center" valignment="top" width="0pt">
22268 <column alignment="center" valignment="top" width="0pt">
22270 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22273 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22282 \begin_layout Plain Layout
22288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22291 \begin_layout Plain Layout
22299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22302 \begin_layout Plain Layout
22308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22322 \begin_layout Plain Layout
22323 \begin_inset Formula $\euro$
22333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22336 \begin_layout Plain Layout
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22345 \begin_layout Plain Layout
22351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22354 \begin_layout Plain Layout
22355 \begin_inset Formula $\mbox{€}$
22365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22368 \begin_layout Plain Layout
22374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22377 \begin_layout Plain Layout
22385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22388 \begin_layout Plain Layout
22392 \begin_layout Plain Layout
22414 \begin_layout Standard
22418 \begin_layout Plain Layout
22428 \begin_inset Note Note
22431 \begin_layout Plain Layout
22432 The following will be displayed when the LaTeX-package
22444 \begin_layout Standard
22445 You need to install the LaTeX-package
22449 to see the rest of this subsection in the output.
22452 \begin_layout Standard
22456 \begin_layout Plain Layout
22468 \begin_layout Section
22470 \begin_inset CommandInset label
22472 name "sec:Relations"
22480 \begin_layout Plain Layout
22490 \begin_layout Plain Layout
22495 \begin_layout Plain Layout
22506 \begin_layout Plain Layout
22521 \begin_layout Standard
22522 All relations can also be inserted via the toolbar button
22523 \begin_inset Graphics
22524 filename ../images/math/leq.png
22532 \begin_layout Standard
22533 \begin_inset space \hfill{}
22537 \begin_inset Tabular
22538 <lyxtabular version="3" rows="17" columns="2">
22540 <column alignment="center" valignment="top" width="0pt">
22541 <column alignment="center" valignment="top" width="0pt">
22543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22546 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22566 \begin_layout Plain Layout
22572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22575 \begin_layout Plain Layout
22576 \begin_inset Formula $<$
22586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22589 \begin_layout Plain Layout
22597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22600 \begin_layout Plain Layout
22601 \begin_inset Formula $\le$
22611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22614 \begin_layout Plain Layout
22622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22625 \begin_layout Plain Layout
22626 \begin_inset Formula $\ll$
22636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22639 \begin_layout Plain Layout
22647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22650 \begin_layout Plain Layout
22651 \begin_inset Formula $\prec$
22661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22664 \begin_layout Plain Layout
22672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22675 \begin_layout Plain Layout
22676 \begin_inset Formula $\preceq$
22686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22689 \begin_layout Plain Layout
22697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22700 \begin_layout Plain Layout
22701 \begin_inset Formula $\subset$
22711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22714 \begin_layout Plain Layout
22722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22725 \begin_layout Plain Layout
22726 \begin_inset Formula $\subseteq$
22736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22739 \begin_layout Plain Layout
22747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22750 \begin_layout Plain Layout
22751 \begin_inset Formula $\sqsubseteq$
22761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22764 \begin_layout Plain Layout
22772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22775 \begin_layout Plain Layout
22776 \begin_inset Formula $\in$
22786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22789 \begin_layout Plain Layout
22797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22800 \begin_layout Plain Layout
22801 \begin_inset Formula $\vdash$
22811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22814 \begin_layout Plain Layout
22822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22825 \begin_layout Plain Layout
22826 \begin_inset Formula $\smile$
22836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22839 \begin_layout Plain Layout
22847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22850 \begin_layout Plain Layout
22851 \begin_inset Formula $\lhd$
22861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22864 \begin_layout Plain Layout
22872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22875 \begin_layout Plain Layout
22876 \begin_inset Formula $\unlhd$
22886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22889 \begin_layout Plain Layout
22897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22900 \begin_layout Plain Layout
22901 \begin_inset Formula $\gtrless$
22911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22914 \begin_layout Plain Layout
22922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22925 \begin_layout Plain Layout
22926 \begin_inset Formula $\mid$
22936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22939 \begin_layout Plain Layout
22947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22950 \begin_layout Plain Layout
22951 \begin_inset Formula $\nmid$
22965 \begin_inset space \hfill{}
22969 \begin_inset Tabular
22970 <lyxtabular version="3" rows="17" columns="2">
22972 <column alignment="center" valignment="top" width="0pt">
22973 <column alignment="center" valignment="top" width="0pt">
22975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22978 \begin_layout Plain Layout
22984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22987 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23007 \begin_layout Plain Layout
23008 \begin_inset Formula $=$
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23021 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23032 \begin_layout Plain Layout
23033 \begin_inset Formula $\not=$
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23046 \begin_layout Plain Layout
23054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23057 \begin_layout Plain Layout
23058 \begin_inset Formula $\equiv$
23068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23071 \begin_layout Plain Layout
23079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23082 \begin_layout Plain Layout
23083 \begin_inset Formula $\sim$
23093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23096 \begin_layout Plain Layout
23104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23107 \begin_layout Plain Layout
23108 \begin_inset Formula $\simeq$
23118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23121 \begin_layout Plain Layout
23129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23132 \begin_layout Plain Layout
23133 \begin_inset Formula $\approx$
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23146 \begin_layout Plain Layout
23154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23157 \begin_layout Plain Layout
23158 \begin_inset Formula $\cong$
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23171 \begin_layout Plain Layout
23179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23182 \begin_layout Plain Layout
23183 \begin_inset Formula $\bowtie$
23193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23196 \begin_layout Plain Layout
23204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23207 \begin_layout Plain Layout
23208 \begin_inset Formula $\notin$
23218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23221 \begin_layout Plain Layout
23229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23232 \begin_layout Plain Layout
23233 \begin_inset Formula $\perp$
23243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23246 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23258 \begin_inset Formula $\propto$
23268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23271 \begin_layout Plain Layout
23279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23282 \begin_layout Plain Layout
23283 \begin_inset Formula $\asymp$
23293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23296 \begin_layout Plain Layout
23304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23307 \begin_layout Plain Layout
23308 \begin_inset Formula $\doteq$
23318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23321 \begin_layout Plain Layout
23329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23332 \begin_layout Plain Layout
23333 \begin_inset Formula $\circeq$
23343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23346 \begin_layout Plain Layout
23354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23357 \begin_layout Plain Layout
23358 \begin_inset Formula $\models$
23368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23371 \begin_layout Plain Layout
23379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23382 \begin_layout Plain Layout
23383 \begin_inset Formula $\widehat{=}$
23397 \begin_inset space \hfill{}
23401 \begin_inset Tabular
23402 <lyxtabular version="3" rows="17" columns="2">
23404 <column alignment="center" valignment="top" width="0pt">
23405 <column alignment="center" valignment="top" width="0pt">
23407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23410 \begin_layout Plain Layout
23416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23419 \begin_layout Plain Layout
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23439 \begin_layout Plain Layout
23440 \begin_inset Formula $>$
23450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23453 \begin_layout Plain Layout
23461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23464 \begin_layout Plain Layout
23465 \begin_inset Formula $\ge$
23475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23478 \begin_layout Plain Layout
23486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23489 \begin_layout Plain Layout
23490 \begin_inset Formula $\gg$
23500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23503 \begin_layout Plain Layout
23511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23514 \begin_layout Plain Layout
23515 \begin_inset Formula $\succ$
23525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23528 \begin_layout Plain Layout
23536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23539 \begin_layout Plain Layout
23540 \begin_inset Formula $\succeq$
23550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23553 \begin_layout Plain Layout
23561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23564 \begin_layout Plain Layout
23565 \begin_inset Formula $\supset$
23575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23578 \begin_layout Plain Layout
23586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23589 \begin_layout Plain Layout
23590 \begin_inset Formula $\supseteq$
23600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23603 \begin_layout Plain Layout
23611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23614 \begin_layout Plain Layout
23615 \begin_inset Formula $\sqsupseteq$
23625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23628 \begin_layout Plain Layout
23636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23639 \begin_layout Plain Layout
23640 \begin_inset Formula $\ni$
23650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23653 \begin_layout Plain Layout
23661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23664 \begin_layout Plain Layout
23665 \begin_inset Formula $\dashv$
23675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23678 \begin_layout Plain Layout
23686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23689 \begin_layout Plain Layout
23690 \begin_inset Formula $\frown$
23700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23703 \begin_layout Plain Layout
23711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23714 \begin_layout Plain Layout
23715 \begin_inset Formula $\rhd$
23725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23728 \begin_layout Plain Layout
23736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23739 \begin_layout Plain Layout
23740 \begin_inset Formula $\unrhd$
23750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23753 \begin_layout Plain Layout
23761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23764 \begin_layout Plain Layout
23765 \begin_inset Formula $\lessgtr$
23775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23778 \begin_layout Plain Layout
23786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23789 \begin_layout Plain Layout
23790 \begin_inset Formula $\parallel$
23800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23803 \begin_layout Plain Layout
23811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23814 \begin_layout Plain Layout
23815 \begin_inset Formula $\nparallel$
23829 \begin_inset space \hfill{}
23835 \begin_layout Standard
23836 \begin_inset VSpace medskip
23851 are bigger than the equal looking operators
23866 \begin_layout Standard
23867 Relations are, in contrary to symbols, always surrounded by space.
23870 \begin_layout Standard
23871 Relations with labels can be created with the command
23881 \begin_layout Plain Layout
23892 \begin_layout Standard
23894 \begin_inset Tabular
23895 <lyxtabular version="3" rows="2" columns="2">
23897 <column alignment="center" valignment="top" width="0">
23898 <column alignment="center" valignment="top" width="0">
23900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23903 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23914 \begin_inset Note Note
23917 \begin_layout Plain Layout
23924 is only used as spacer.
23936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23939 \begin_layout Plain Layout
23946 \begin_layout Plain Layout
23963 \begin_layout Plain Layout
23973 \begin_inset Formula $\downarrow$
23982 \begin_layout Plain Layout
23995 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24029 \begin_layout Section
24033 \begin_layout Subsection
24034 Predefined Functions
24035 \begin_inset CommandInset label
24037 name "sub:Predefined-Functions"
24045 \begin_layout Plain Layout
24046 Functions ! predefined
24054 \begin_layout Standard
24055 In general, variables are set
24059 in mathematical expressions, but not function names, because
24060 \begin_inset Formula $sin$
24063 could be misunderstood as
24064 \begin_inset Formula $s\cdot i\cdot n$
24068 Therefore there are predefined functions, that are additionally a bit separated
24070 They are inserted as commands starting with a backslash before their name.
24073 \begin_layout Standard
24075 \begin_inset Tabular
24076 <lyxtabular version="3" rows="2" columns="4">
24078 <column alignment="center" valignment="top" width="0pt">
24079 <column alignment="center" valignment="top" width="0pt">
24080 <column alignment="center" valignment="top" width="0pt">
24081 <column alignment="center" valignment="top" width="0pt">
24083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24086 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24095 \begin_layout Plain Layout
24101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24113 \begin_layout Plain Layout
24121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24124 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24134 \begin_inset Formula $Asin(x)+B$
24142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24145 \begin_layout Plain Layout
24153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24156 \begin_layout Plain Layout
24157 \begin_inset Formula $A\sin(x)+B$
24171 \begin_inset Newpage pagebreak
24177 \begin_layout Standard
24178 The following functions are predefined:
24181 \begin_layout Standard
24182 \begin_inset VSpace -2mm
24188 \begin_layout Standard
24190 \begin_inset Tabular
24191 <lyxtabular version="3" rows="9" columns="4">
24193 <column alignment="center" valignment="top" width="0pt">
24194 <column alignment="center" valignment="top" width="0pt">
24195 <column alignment="center" valignment="top" width="0pt">
24196 <column alignment="center" valignment="top" width="0pt">
24198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24201 \begin_layout Plain Layout
24207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24210 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24239 \begin_layout Plain Layout
24247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24250 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24285 \begin_layout Plain Layout
24293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24296 \begin_layout Plain Layout
24304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24307 \begin_layout Plain Layout
24315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24318 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24331 \begin_layout Plain Layout
24339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24342 \begin_layout Plain Layout
24350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24353 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24364 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24388 \begin_layout Plain Layout
24396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Plain Layout
24420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24434 \begin_layout Plain Layout
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24480 \begin_layout Plain Layout
24488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24502 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24515 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24537 \begin_layout Plain Layout
24545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24548 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Plain Layout
24610 \begin_layout Standard
24611 They can also be inserted with the math toolbar button
24612 \begin_inset Graphics
24613 filename ../images/math/functions.png
24621 \begin_layout Subsection
24622 Self-defined Functions
24626 \begin_layout Plain Layout
24627 Functions ! self-defined
24635 \begin_layout Standard
24636 To use a function that is not predefined, like for example the sign function
24637 sgn(x), there are two possibilities:
24640 \begin_layout Itemize
24641 Define the function by inserting the following line to the LaTeX-preamble
24645 \begin_layout Plain Layout
24650 DeclareMathOperator
24653 \begin_inset CommandInset ref
24655 reference "sub:Self-defined-Operators"
24665 \begin_inset Newline newline
24669 \begin_inset VSpace -3mm
24673 \begin_inset Newline newline
24680 DeclareMathOperator{
24688 \begin_layout Plain Layout
24693 DeclareMathOperator
24699 \begin_inset Newline newline
24703 \begin_inset VSpace -2mm
24707 \begin_inset Newline newline
24710 Now the new defined function can be called with the command
24719 \begin_layout Itemize
24720 Write the the formula as usual, mark the formula name, in our example the
24725 , and change it to mathematical text.
24726 At last a space is inserted between prefactor and function.
24729 \begin_layout Standard
24730 The result is the same with both methods as with a predefined function
24734 \begin_layout Plain Layout
24735 In LyX self-defined functions are displayed red, predefined ones black.
24743 \begin_layout Standard
24745 \begin_inset Tabular
24746 <lyxtabular version="3" rows="3" columns="2">
24748 <column alignment="center" valignment="top" width="0pt">
24749 <column alignment="center" valignment="top" width="0pt">
24751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24763 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24774 \begin_layout Plain Layout
24782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24785 \begin_layout Plain Layout
24786 \begin_inset Formula $A\sgn(x)+B$
24796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24799 \begin_layout Plain Layout
24803 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24814 \begin_layout Plain Layout
24815 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24831 \begin_layout Standard
24832 The first method is more suitable when the self-defined function should
24833 be used several times.
24836 \begin_layout Subsection
24841 \begin_layout Plain Layout
24850 \begin_layout Standard
24851 For limits there are defined besides
24861 \begin_layout Plain Layout
24881 furthermore the following functions:
24884 \begin_layout Standard
24886 \begin_inset Tabular
24887 <lyxtabular version="3" rows="5" columns="2">
24889 <column alignment="center" valignment="top" width="0">
24890 <column alignment="center" valignment="top" width="0">
24892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24895 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24904 \begin_layout Plain Layout
24906 \begin_inset Note Note
24909 \begin_layout Plain Layout
24916 is only used as spacer.
24928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24931 \begin_layout Plain Layout
24939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24942 \begin_layout Plain Layout
24943 \begin_inset Formula $\varliminf$
24953 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24956 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24967 \begin_layout Plain Layout
24968 \begin_inset Formula $\varlimsup$
24978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24981 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24992 \begin_layout Plain Layout
24993 \begin_inset Formula $\varprojlim$
25003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25006 \begin_layout Plain Layout
25014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25017 \begin_layout Plain Layout
25018 \begin_inset Formula $\varinjlim$
25022 \begin_inset Formula $\raisebox{-2.5mm}{}$
25038 \begin_layout Standard
25039 \begin_inset VSpace medskip
25042 The limit is created by inserting a subscript.
25043 It is set right beside the function in an inline formula:
25046 \begin_layout Standard
25048 \begin_inset Tabular
25049 <lyxtabular version="3" rows="2" columns="2">
25051 <column alignment="center" valignment="top" width="0pt">
25052 <column alignment="center" valignment="top" width="0pt">
25054 <cell alignment="center" valignment="top" usebox="none">
25057 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" usebox="none">
25066 \begin_layout Plain Layout
25067 \begin_inset space \hspace{}
25072 \begin_inset Note Note
25075 \begin_layout Plain Layout
25088 are used here as spacer.
25100 <cell alignment="center" valignment="top" usebox="none">
25103 \begin_layout Plain Layout
25112 \begin_layout Plain Layout
25125 \begin_layout Plain Layout
25139 <cell alignment="center" valignment="top" usebox="none">
25142 \begin_layout Plain Layout
25143 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25159 \begin_layout Standard
25160 In a displayed formula the limit is set below the formula, as usual:
25161 \begin_inset Formula \[
25169 \begin_layout Subsection
25174 \begin_layout Plain Layout
25175 Functions ! modulo-
25183 \begin_layout Standard
25184 The modulo-function is special, because it exists in four variants.
25187 \begin_layout Standard
25188 The variants in a displayed formula:
25189 \begin_inset Formula \begin{align*}
25190 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25191 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25192 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25193 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25194 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25201 \begin_layout Standard
25202 In an inline formula less space is set before the function names for all
25206 \begin_layout Section
25211 \begin_layout Plain Layout
25220 \begin_layout Subsection
25221 Special Characters in Mathematical Text
25224 \begin_layout Standard
25225 The following commands can only be used in mathematical text or in TeX-mode:
25228 \begin_layout Standard
25229 \begin_inset space \hfill{}
25233 \begin_inset Tabular
25234 <lyxtabular version="3" rows="8" columns="2">
25236 <column alignment="block" valignment="top" width="0">
25237 <column alignment="block" valignment="top" width="0">
25239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25242 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25251 \begin_layout Plain Layout
25259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25262 \begin_layout Plain Layout
25270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25273 \begin_layout Plain Layout
25274 \begin_inset Formula $\textrm{œ}$
25284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25287 \begin_layout Plain Layout
25295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25298 \begin_layout Plain Layout
25299 \begin_inset Formula $\textrm{Œ}$
25309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25312 \begin_layout Plain Layout
25320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25323 \begin_layout Plain Layout
25324 \begin_inset Formula $\textrm{æ}$
25334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25337 \begin_layout Plain Layout
25345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25348 \begin_layout Plain Layout
25349 \begin_inset Formula $\textrm{Æ}$
25359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25373 \begin_layout Plain Layout
25374 \begin_inset Formula $\textrm{\aa}$
25384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25387 \begin_layout Plain Layout
25394 \begin_layout Plain Layout
25401 \begin_layout Plain Layout
25422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25425 \begin_layout Plain Layout
25426 \begin_inset Formula $\textrm{Å}$
25436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25439 \begin_layout Plain Layout
25447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25450 \begin_layout Plain Layout
25451 \begin_inset Formula $\textrm{ı}$
25465 \begin_inset space \hfill{}
25469 \begin_inset Tabular
25470 <lyxtabular version="3" rows="8" columns="2">
25472 <column alignment="block" valignment="top" width="0">
25473 <column alignment="center" valignment="top" width="0">
25475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25478 \begin_layout Plain Layout
25480 \begin_inset Note Note
25483 \begin_layout Plain Layout
25490 is used for separation, because otherwise the output will be ¡ and ¿ respective
25501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25515 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25527 \begin_inset Formula $\textrm{ø}$
25537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25540 \begin_layout Plain Layout
25548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25551 \begin_layout Plain Layout
25552 \begin_inset Formula $\textrm{Ø}$
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25565 \begin_layout Plain Layout
25573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25576 \begin_layout Plain Layout
25577 \begin_inset Formula $\textrm{ł}$
25587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25601 \begin_layout Plain Layout
25602 \begin_inset Formula $\textrm{Ł}$
25612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25615 \begin_layout Plain Layout
25617 \begin_inset space \hspace{}
25625 \begin_layout Plain Layout
25639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25642 \begin_layout Plain Layout
25643 \begin_inset Formula $\textrm{!`}$
25653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25656 \begin_layout Plain Layout
25658 \begin_inset space \hspace{}
25666 \begin_layout Plain Layout
25680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25683 \begin_layout Plain Layout
25684 \begin_inset Formula $\textrm{?`}$
25694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25697 \begin_layout Plain Layout
25705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25708 \begin_layout Plain Layout
25709 \begin_inset Formula $\textrm{ȷ}$
25723 \begin_inset space \hfill{}
25729 \begin_layout Standard
25731 \begin_inset Formula $\textrm{\textrm{Å}}$
25735 \begin_inset Formula $\textrm{\textrm{Ø}}$
25738 can also be inserted via the math toolbar button
25739 \begin_inset Graphics
25740 filename ../images/math/digamma.png
25748 \begin_layout Standard
25749 An exception are the commands
25752 \begin_inset space \hspace{}
25761 \begin_inset space \hspace{}
25767 , because they can be inserted in LyX directly to text.
25770 \begin_layout Subsection
25772 \begin_inset CommandInset label
25774 name "sub:Accents-in-Text"
25782 \begin_layout Plain Layout
25791 \begin_layout Standard
25792 With the following commands all letters can be accented.
25793 The commands must be inserted in TeX-mode.
25796 \begin_layout Standard
25797 \begin_inset space \hfill{}
25801 \begin_inset Tabular
25802 <lyxtabular version="3" rows="8" columns="2">
25804 <column alignment="block" valignment="top" width="0">
25805 <column alignment="block" valignment="top" width="0">
25807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25810 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25830 \begin_layout Plain Layout
25834 \begin_inset Quotes grd
25842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25845 \begin_layout Plain Layout
25849 \begin_layout Plain Layout
25865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25868 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25879 \begin_layout Plain Layout
25883 \begin_layout Plain Layout
25899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25902 \begin_layout Plain Layout
25909 \begin_layout Plain Layout
25923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25926 \begin_layout Plain Layout
25930 \begin_layout Plain Layout
25946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25949 \begin_layout Plain Layout
25957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25960 \begin_layout Plain Layout
25964 \begin_layout Plain Layout
25980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25983 \begin_layout Plain Layout
25990 \begin_layout Plain Layout
26004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26007 \begin_layout Plain Layout
26011 \begin_layout Plain Layout
26027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26030 \begin_layout Plain Layout
26037 \begin_layout Plain Layout
26051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26054 \begin_layout Plain Layout
26058 \begin_layout Plain Layout
26074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26084 \begin_layout Plain Layout
26098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26101 \begin_layout Plain Layout
26105 \begin_layout Plain Layout
26125 \begin_inset space \hfill{}
26129 \begin_inset Tabular
26130 <lyxtabular version="3" rows="8" columns="2">
26132 <column alignment="block" valignment="top" width="0">
26133 <column alignment="center" valignment="top" width="0">
26135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26138 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26158 \begin_layout Plain Layout
26165 \begin_layout Plain Layout
26179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26182 \begin_layout Plain Layout
26186 \begin_layout Plain Layout
26202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26205 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26220 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26246 \begin_layout Plain Layout
26257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26260 \begin_layout Plain Layout
26264 \begin_layout Plain Layout
26280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26283 \begin_layout Plain Layout
26291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26294 \begin_layout Plain Layout
26298 \begin_layout Plain Layout
26314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26317 \begin_layout Plain Layout
26324 \begin_layout Plain Layout
26338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26341 \begin_layout Plain Layout
26345 \begin_layout Plain Layout
26361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26364 \begin_layout Plain Layout
26371 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26392 \begin_layout Plain Layout
26408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26411 \begin_layout Plain Layout
26418 \begin_layout Plain Layout
26432 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26435 \begin_layout Plain Layout
26439 \begin_layout Plain Layout
26459 \begin_inset space \hfill{}
26465 \begin_layout Standard
26466 \begin_inset VSpace medskip
26475 also two different characters can be accented.
26484 \begin_layout Plain Layout
26499 \begin_layout Plain Layout
26511 \begin_layout Standard
26524 can in combination with vowels directly be inserted with the keyboard without
26526 The same applies for the tilde
26530 \begin_layout Plain Layout
26531 This only applies for keyboards where the tilde is defined as accent.
26540 in combination with
26555 \begin_layout Standard
26598 , and accents inserted directly with the keyboard are also available in
26600 For the other accents there are special math commands to be used in formulas,
26602 \begin_inset CommandInset ref
26604 reference "sub:Accents-for-one"
26611 \begin_layout Standard
26612 \begin_inset VSpace bigskip
26615 Furthermore, with the command
26625 \begin_layout Plain Layout
26633 all numbers and letters can be set into a circle, quasi accented with a
26634 circle, similar to the the copyright symbol.
26637 \begin_layout Standard
26639 \begin_inset Tabular
26640 <lyxtabular version="3" rows="3" columns="2">
26642 <column alignment="center" valignment="top" width="0">
26643 <column alignment="center" valignment="top" width="0">
26645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26648 \begin_layout Plain Layout
26654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26657 \begin_layout Plain Layout
26659 \begin_inset Note Note
26662 \begin_layout Plain Layout
26669 is only used as spacer.
26681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26684 \begin_layout Plain Layout
26692 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26695 \begin_layout Plain Layout
26699 \begin_layout Plain Layout
26715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26729 raisebox{-1.5pt}{W}}
26734 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26737 \begin_layout Plain Layout
26738 \begin_inset Formula $\raisebox{4.5mm}{}$
26745 \begin_layout Plain Layout
26763 \begin_inset Formula $\raisebox{-2mm}{}$
26779 \begin_layout Standard
26780 One has to take care that the character fits in the circle.
26791 \begin_layout Plain Layout
26793 \begin_inset CommandInset ref
26795 reference "sub:Font-Sizes"
26804 specifies thereby the size of the circle.
26815 \begin_layout Plain Layout
26817 \begin_inset CommandInset ref
26819 reference "sub:Boxes-without-Frame"
26828 the character can be centered.
26831 \begin_layout Subsection
26836 \begin_layout Plain Layout
26845 \begin_layout Standard
26846 Minuscule numbers are created with the command
26856 \begin_layout Plain Layout
26865 The command can be used in formulas and in TeX-mode.
26866 The command scheme is:
26869 \begin_layout Standard
26874 oldstylenums{number}
26877 \begin_layout Standard
26882 oldstylenums{0123456789
26885 \begin_inset Formula $\oldstylenums{0123456789}$
26891 \begin_layout Subsection
26892 Miscellaneous special Characters
26893 \begin_inset CommandInset label
26895 name "sub:Miscellaneous-special-Characters"
26903 \begin_layout Plain Layout
26904 Special characters ! miscellaneous
26912 \begin_layout Standard
26913 The following characters can only be inserted to formulas by using commands:
26916 \begin_layout Standard
26918 \begin_inset Tabular
26919 <lyxtabular version="3" rows="4" columns="2">
26921 <column alignment="center" valignment="top" width="0">
26922 <column alignment="center" valignment="top" width="0">
26924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26927 \begin_layout Plain Layout
26933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26947 \begin_layout Plain Layout
26954 \begin_layout Plain Layout
26968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26971 \begin_layout Plain Layout
26972 \begin_inset Formula $\mathcircumflex$
26982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26985 \begin_layout Plain Layout
26993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26996 \begin_layout Plain Layout
26997 \begin_inset Formula $\_$
27007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27010 \begin_layout Plain Layout
27015 \begin_layout Plain Layout
27030 \begin_layout Plain Layout
27043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27046 \begin_layout Plain Layout
27047 \begin_inset Formula $^{\circ}$
27063 \begin_layout Standard
27064 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27065 contains the following line
27069 \begin_layout Plain Layout
27070 More about this is described in
27071 \begin_inset CommandInset ref
27073 reference "sub:Text-Characters-in"
27085 \begin_layout Standard
27090 DeclareInputtext{176}{
27103 \begin_layout Section
27105 \begin_inset CommandInset label
27107 name "sec:Formula-Styles"
27115 \begin_layout Plain Layout
27124 \begin_layout Itemize
27125 There are two different alignment styles:
27129 \begin_layout Description
27130 Centered is the predefined standard
27133 \begin_layout Description
27134 Indented for this the option
27138 must be inserted in the menu
27140 Document\SpecialChar \menuseparator
27146 \begin_inset space ~
27152 \begin_layout Standard
27157 is used, the indentation can be adjusted with the length
27167 \begin_layout Plain Layout
27176 Should the distance be 15
27177 \begin_inset space \thinspace{}
27180 mm, the following command line is inserted in the LaTeX-preamble
27183 \begin_layout Standard
27193 \begin_layout Standard
27194 When no length is specified, the predefined value of 30
27195 \begin_inset space \thinspace{}
27202 \begin_layout Itemize
27203 And two different numbering styles:
27207 \begin_layout Description
27208 Right is the predefined standard
27211 \begin_layout Description
27212 Left for this the option
27216 must be inserted in the menu
27218 Document\SpecialChar \menuseparator
27224 \begin_inset space ~
27231 \begin_layout Standard
27240 can also be used together.
27241 In this case both options are inserted, separated by a comma.
27244 \begin_layout Standard
27245 The chosen styles are used for all displayed formulas of the document.
27246 When both, centered and indented formulas should be created in a document,
27252 The indented formulas are then set in a flalign environment, see
27253 \begin_inset CommandInset ref
27255 reference "sub:Flalign-Environment"
27262 \begin_layout Section
27264 \begin_inset CommandInset label
27266 name "sec:Multiline-Formulas"
27274 \begin_layout Plain Layout
27275 Formula ! multiline
27283 \begin_layout Subsection
27287 \begin_layout Standard
27288 In LyX multiline formulas are created by pressing
27295 This creates either an
27297 eqnarray environment
27299 that is described in
27300 \begin_inset CommandInset ref
27302 reference "sub:Eqnarray-Environment"
27306 or, when the option
27308 Use AMS math package
27310 in the document settings is selected, an
27314 that is described in
27315 \begin_inset CommandInset ref
27317 reference "sub:Standard-align-Environment"
27324 \begin_layout Standard
27325 There are other multiline formula environments that can be created via the
27328 Insert\SpecialChar \menuseparator
27332 These environments are described in the following sections.
27335 \begin_layout Standard
27336 In all multiline formula environments a new line is created by pressing
27342 To add or delete lines, the math toolbar buttons
27343 \begin_inset Graphics
27344 filename ../images/tabular-feature_append-row.png
27350 \begin_inset Graphics
27351 filename ../images/tabular-feature_delete-row.png
27356 , respectively, or the menu
27358 Edit\SpecialChar \menuseparator
27364 \begin_layout Subsubsection
27366 \begin_inset CommandInset label
27368 name "sub:Line-Separation"
27376 \begin_layout Plain Layout
27377 Formula ! multiline ! Line separation
27385 \begin_layout Standard
27386 There is sometimes not enough space in multiline formulas between the lines:
27387 \begin_inset Formula \begin{eqnarray*}
27388 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}\\
27389 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*}
27396 \begin_layout Standard
27397 In LaTeX additional line space is specified as optional argument of the
27399 This is not yet possible in LyX
27403 \begin_layout Plain Layout
27405 \begin_inset CommandInset href
27407 name "LyX-bug #1505"
27408 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27417 , therefore the whole formula must be inserted in TeX-mode.
27418 To add in our example space, the command
27426 is inserted at the end of the first line.
27431 \begin_layout Plain Layout
27438 \begin_layout Plain Layout
27440 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27443 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27450 \begin_layout Plain Layout
27454 left(B^{2}+x_{0}^{2}
27462 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27467 \begin_layout Plain Layout
27479 \begin_layout Standard
27480 \begin_inset VSpace bigskip
27483 To set the the line separation for all lines in a formula, the length
27493 \begin_layout Plain Layout
27503 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27514 \begin_inset space \thinspace{}
27519 \begin_inset space \thinspace{}
27522 mm additional line separation as in the previous example, the command
27525 \begin_layout Standard
27535 \begin_layout Standard
27536 is inserted in TeX-mode before the formula.
27537 This requires that the LaTeX-package
27545 \begin_layout Plain Layout
27550 is part of every LaTeX standard installation.
27559 \begin_layout Plain Layout
27565 was loaded in LaTeX-preamble with the line
27568 \begin_layout Standard
27576 \begin_layout Standard
27581 \begin_layout Plain Layout
27593 \begin_inset Formula \begin{eqnarray*}
27594 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}\\
27595 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*}
27602 \begin_layout Standard
27606 \begin_layout Plain Layout
27617 To get back to the predefined distance,
27623 is set to the value 3
27624 \begin_inset space \thinspace{}
27630 \begin_layout Subsubsection
27632 \begin_inset CommandInset label
27634 name "sub:Column-Separation"
27642 \begin_layout Plain Layout
27643 Formula ! multiline ! Column separation
27651 \begin_layout Standard
27652 Multiline formulas form a matrix.
27653 A formula in the eqnarray environment is for example a matrix with three
27655 By changing the column separation in this environment, the space beside
27656 the relation sign can be changed.
27659 \begin_layout Standard
27660 The column separation is specified with the length
27670 \begin_layout Plain Layout
27679 \begin_inset Newline newline
27682 column separation = 2
27683 \begin_inset space \thinspace{}
27693 \begin_inset Newline newline
27699 \begin_layout Standard
27709 \begin_layout Standard
27710 inserted in TeX-mode, sets for all following formulas a column separation
27712 \begin_inset space \thinspace{}
27716 To get back to the predefined distance,
27723 \begin_inset space \thinspace{}
27729 \begin_layout Standard
27731 \begin_inset space \thinspace{}
27734 cm column separation:
27738 \begin_layout Plain Layout
27750 \begin_inset Formula \begin{eqnarray*}
27752 C & \ne & A\end{eqnarray*}
27756 A formula with the predefined column separation for matrices of 10
27757 \begin_inset space \thinspace{}
27764 \begin_layout Plain Layout
27776 \begin_inset Formula \begin{eqnarray*}
27778 C & \ne & A\end{eqnarray*}
27785 \begin_layout Subsubsection
27790 \begin_layout Plain Layout
27799 \begin_layout Standard
27800 Long formulas can be typeset using these methods:
27803 \begin_layout Itemize
27804 When one side of the equation is much shorther than the line width, this
27805 one is chosen for the left side and the right side is typeset over two
27810 \begin_layout Plain Layout
27820 \begin_inset Formula \begin{eqnarray}
27821 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 \\
27822 & & -\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}
27830 \begin_layout Plain Layout
27840 \begin_inset Newline newline
27843 The minus sign at the beginning of the second line does normally not appear
27844 as operator because it is the first character of the line.
27845 Thus it would not be surrounded by space and could not be distinguished
27846 from the fraction bar.
27847 To avoid this, space was inserted behind the minus sign with the command
27858 \begin_layout Plain Layout
27866 \begin_inset CommandInset ref
27868 reference "sub:Variable-Space"
27881 \begin_layout Plain Layout
27892 \begin_layout Itemize
27893 When both sides of the equation are too long, the command
27903 \begin_layout Plain Layout
27912 It is inserted to the first column of the first line and effects that all
27913 further insertions overwrite the following columns:
27917 \begin_layout Plain Layout
27927 \begin_inset Formula \begin{eqnarray}
27928 \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 \\
27929 & & -\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 \\
27930 & & =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}
27938 \begin_layout Plain Layout
27948 \begin_inset Newline newline
27951 After the insertion of
27957 , the cursor is in a purple box that is a bit shifted to the left from the
27959 In this the formula is inserted.
27963 \begin_layout Plain Layout
27973 \begin_inset Newline newline
27976 The content of the further lines is inserted to the second or another formula
27978 The greater the column number where it was inserted, the larger the indentation.
27982 \begin_layout Plain Layout
27992 \begin_inset Newline newline
27996 \begin_inset Note Greyedout
27999 \begin_layout Plain Layout
28000 Note the following when using
28009 \begin_layout Itemize
28010 The formula doesn't use the full page width.
28012 \begin_inset space \thinspace{}
28016 \begin_inset space ~
28020 \begin_inset Formula $-B^{2}$
28023 is added to the first line in the above example, it would have been outside
28025 To better use the width, negative space can be inserted at the beginning
28029 \begin_layout Itemize
28030 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28035 \begin_layout Plain Layout
28036 \begin_inset CommandInset href
28038 name "LyX-bug #1429"
28039 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28048 One can only set the cursor at the beginning of the line and move it with
28057 \begin_layout Itemize
28058 Other methods to set long formulas are offered by the environments described
28060 \begin_inset CommandInset ref
28062 reference "sub:Multline-Environment"
28067 \begin_inset CommandInset ref
28069 reference "sub:Multiline-Formula-Parts"
28076 \begin_layout Subsubsection
28078 \begin_inset CommandInset label
28080 name "sub:Multiline-Brackets"
28088 \begin_layout Plain Layout
28089 Brackets ! for multiline expressions
28097 \begin_layout Standard
28098 For brackets spanning multiple lines the following problem occurs:
28099 \begin_inset Formula \begin{eqnarray*}
28100 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28101 & & \left.\cdots+B-D\right]\end{eqnarray*}
28108 \begin_layout Standard
28109 The closing bracket is smaller than the opening bracket because brackets
28110 with variable size may not span multiple lines.
28113 \begin_layout Standard
28114 To set the bracket size for the second line correctly, the first line is
28125 \begin_layout Plain Layout
28133 and the second line with
28141 \begin_layout Plain Layout
28155 \begin_inset CommandInset ref
28157 reference "sub:Automatic-Bracket-Size"
28172 \begin_layout Plain Layout
28198 \begin_layout Plain Layout
28217 \begin_layout Plain Layout
28236 \begin_layout Plain Layout
28248 \begin_inset Formula $\downarrow$
28257 \begin_layout Plain Layout
28265 is inserted, because the multiplication operator with its limits is the
28266 largest symbol in the first line and this should be the size for the bracket
28267 in the second line.
28270 \begin_layout Standard
28271 The result is this:
28272 \begin_inset Formula \begin{eqnarray*}
28273 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28274 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28281 \begin_layout Subsection
28285 \begin_layout Standard
28286 Align environments can be used for every kind of multiline formulas.
28287 They are specially useful to set several formulas side by side.
28290 \begin_layout Standard
28291 Align environments consist of columns.
28292 The odd columns are right aligned, the even ones left aligned.
28293 Every line in an Align environment can be numbered.
28296 \begin_layout Standard
28297 Align environments are created via the menu
28299 Insert\SpecialChar \menuseparator
28305 Edit\SpecialChar \menuseparator
28306 Math\SpecialChar \menuseparator
28307 Change Formula Type
28309 already existing formulas can be converted to Align environments.
28312 \begin_layout Standard
28313 To add or delete columns, the math toolbar buttons
28314 \begin_inset Graphics
28315 filename ../images/tabular-feature_append-column.png
28321 \begin_inset Graphics
28322 filename ../images/tabular-feature_delete-column.png
28327 , respectively, or the menu
28329 Edit\SpecialChar \menuseparator
28335 \begin_layout Subsubsection
28336 Standard align Environment
28337 \begin_inset CommandInset label
28339 name "sub:Standard-align-Environment"
28347 \begin_layout Plain Layout
28348 Formula ! multiline ! align environment
28356 \begin_layout Standard
28357 This Align environment is created by presssing
28361 in a formula or by the menu
28363 Insert\SpecialChar \menuseparator
28364 Math\SpecialChar \menuseparator
28365 AMS align Environment
28370 \begin_layout Standard
28371 An example for two formulas set side by side, that are created with a four
28372 column align environment:
28373 \begin_inset Formula \begin{align*}
28374 A & =\sin(B) & C & =D\\
28375 C & \ne A & B & \ne D\end{align*}
28379 As it can be seen, the formulas in this environment are placed so as if
28388 \begin_layout Plain Layout
28396 \begin_inset CommandInset ref
28398 reference "sub:Variable-Space"
28409 before the first and after every even column.
28410 When the formula style
28416 \begin_layout Plain Layout
28418 \begin_inset CommandInset ref
28420 reference "sec:Formula-Styles"
28431 is used, the formula is set without the
28437 before the first column.
28440 \begin_layout Subsubsection
28441 Alignat Environment
28445 \begin_layout Plain Layout
28446 Formula ! multiline ! alignat environment
28454 \begin_layout Standard
28455 The alignat environment has no predefined column separation.
28456 It can be inserted manually with the spaces that are described
28457 \begin_inset CommandInset ref
28459 reference "sub:Space"
28466 \begin_layout Standard
28467 The above example in the alignat environment where 1
28468 \begin_inset space \thinspace{}
28471 cm space was inserted at the beginning of the second formula:
28472 \begin_inset Formula \begin{alignat*}{2}
28473 A & =\sin(B) & \hspace{1cm}C & =D\\
28474 C & \ne A & B & \ne D\end{alignat*}
28478 Because the column separation can be set separately for every column, this
28479 environment is especially suitable to set three and more formulas side
28483 \begin_layout Subsubsection
28484 Flalign Environment
28485 \begin_inset CommandInset label
28487 name "sub:Flalign-Environment"
28495 \begin_layout Plain Layout
28496 Formula ! multiline ! flalign environment
28504 \begin_layout Standard
28505 In this environment the first two columns are always set as much as possible
28506 to the left and the last two ones to the right.
28508 \begin_inset Formula \begin{flalign*}
28509 A & =1 & B & =2 & C & =3\\
28510 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28517 \begin_layout Standard
28518 By creating a flalign environment with an odd number of columns where an
28519 empty TeX-brace is inserted to the last column, several formulas in a document
28520 can be set to the left, although the formula style
28525 As example the indented formula
28526 \begin_inset CommandInset ref
28528 reference "eq:VolInt"
28533 \begin_inset Formula \begin{flalign}
28534 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28538 The first two columns contain the formula.
28539 To indent it as with the formula style
28544 \begin_inset space \thinspace{}
28547 pt space was inserted at the beginning of the first column.
28550 \begin_layout Subsection
28551 Eqnarray Environment
28552 \begin_inset CommandInset label
28554 name "sub:Eqnarray-Environment"
28562 \begin_layout Plain Layout
28563 Formula ! multiline ! eqnarray environment
28571 \begin_layout Standard
28572 When this environment has been created, three blue boxes appear.
28573 The content of the first box is right aligned, the content of the last
28575 The content of the middle box appears centered and a bit smaller, because
28576 it is designed to insert there only relation characters.
28577 \begin_inset Formula \begin{eqnarray*}
28578 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28580 A & = & A\end{eqnarray*}
28587 \begin_layout Subsection
28592 \begin_layout Plain Layout
28593 Formula ! multiline ! gather environment
28601 \begin_layout Standard
28602 This environment consists of only one centered column.
28603 Every line can be numbered.
28604 \begin_inset Formula \begin{gather}
28606 X=\textrm{-}1\end{gather}
28613 \begin_layout Subsection
28614 Multline Environment
28615 \begin_inset CommandInset label
28617 name "sub:Multline-Environment"
28625 \begin_layout Plain Layout
28626 Formula ! multiline ! multline environment
28634 \begin_layout Standard
28635 The multline environment consists, like the gather environment, of only
28637 But the first line is left aligned, the last one right aligned.
28638 All other lines are centered.
28639 Therefore this environment is suitable for long formulas.
28641 \begin_inset CommandInset ref
28643 reference "eq:lefteqn"
28647 in the multline environment:
28648 \begin_inset Formula \begin{multline}
28649 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}\\
28650 -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}\\
28651 =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}
28658 \begin_layout Standard
28659 In the output only the last (first) line of a multline environment appears
28660 numbered when the document numbering is right (left).
28664 \begin_layout Plain Layout
28665 numbering styles see
28666 \begin_inset CommandInset ref
28668 reference "sec:Formula-Styles"
28680 \begin_layout Standard
28689 \begin_layout Plain Layout
28707 \begin_layout Plain Layout
28717 a centered line can be right or left aligned, respectively.
28718 The commands are used as follows:
28721 \begin_layout Standard
28726 shoveright{line content}
28732 shoveleft{line content}
28735 \begin_layout Standard
28736 \begin_inset VSpace medskip
28747 \begin_layout Plain Layout
28757 specifies the distance of the first line from the left page margin.
28758 Predefined is the length 0
28759 \begin_inset space \thinspace{}
28765 \begin_layout Standard
28766 As example the above formula where the command
28769 \begin_layout Standard
28779 \begin_layout Standard
28780 was inserted in TeX-mode before:
28784 \begin_layout Plain Layout
28796 \begin_inset Formula \begin{multline}
28797 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}\\
28798 \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}}\\
28799 =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}
28807 \begin_layout Plain Layout
28818 The second line was left aligned using
28827 \begin_layout Subsection
28828 Multiline Formula Parts
28829 \begin_inset CommandInset label
28831 name "sub:Multiline-Formula-Parts"
28839 \begin_layout Plain Layout
28840 Formula ! multiline ! formula parts
28848 \begin_layout Standard
28849 To display only parts of a formula with multiple lines, one of the following
28850 environments are used:
28867 They can be inserted via the menu
28869 Insert\SpecialChar \menuseparator
28872 or by using the commands described in this section.
28875 \begin_layout Standard
28876 The first three have the same properties as the corresponding multiline
28877 formula environments, but it is possible to set further formula parts beside
28880 \begin_inset Formula \[
28881 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28882 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28883 \right\} \textrm{Uncertainty relations}\]
28890 \begin_layout Standard
28891 To get this formula, a displayed formula is created where the command
28899 \begin_layout Plain Layout
28910 A purple box appears around the blue formula box where now columns and
28911 lines can be added.
28912 Outside the multiline environment other formula parts can be set, like
28916 \begin_layout Standard
28917 The aligned environment is also suitable for long formulas whose lines are
28918 horizontally aligned.
28919 Using aligned in a displayed formula has the advantage that the formula
28920 number is vertically centered behind the lines.
28922 \begin_inset CommandInset ref
28924 reference "eq:kurzlang"
28928 in the aligned environment:
28929 \begin_inset Formula \begin{equation}
28930 \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}|}\\
28931 & -\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}
28939 \begin_layout Standard
28940 To use the environments
28962 \begin_layout Plain Layout
28980 \begin_layout Plain Layout
28998 \begin_layout Plain Layout
29006 are inserted, respectively.
29007 The split environment has the same properties as the aligned environment
29008 but it can only have two columns.
29011 \begin_layout Subsection
29012 Text in multiline Formulas
29013 \begin_inset CommandInset label
29015 name "sub:Text-in-multiline"
29023 \begin_layout Plain Layout
29033 \begin_layout Plain Layout
29034 Formula ! multiline ! text
29042 \begin_layout Standard
29043 In the Align environments, and the multline and gather environment, text
29044 can be inserted that will appear in a separate line and doesn't affect
29045 the column alignment.
29046 To do this, the command
29054 \begin_layout Plain Layout
29064 is used in the following scheme:
29067 \begin_layout Standard
29075 \begin_layout Standard
29076 The text should not be longer than a line because it cannot be hyphenated.
29077 As LyX doesn't yet support
29083 directly, the text is written as mathematical text.
29090 must hereby be at the beginning of a line and appears in the output above
29092 An example where the text was inserted at the beginning of the second line:
29093 \begin_inset Formula \begin{align}
29094 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29095 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29102 \begin_layout Section
29107 \begin_layout Plain Layout
29117 \begin_layout Plain Layout
29118 Formula ! numbering|see
29122 \begin_layout Plain Layout
29133 \begin_layout Plain Layout
29148 \begin_layout Subsection
29152 \begin_layout Standard
29153 Numbered formulas can be created with the menu
29155 Insert\SpecialChar \menuseparator
29156 Math\SpecialChar \menuseparator
29158 \begin_inset space ~
29166 \begin_inset space ~
29172 Existing formulas can be numbered with the menu
29174 Edit\SpecialChar \menuseparator
29175 Math\SpecialChar \menuseparator
29177 \begin_inset space ~
29185 \begin_inset space ~
29191 The formula number is displayed in LyX behind the formula as number sign
29193 The number sign is replaced in the output by the formula number.
29196 \begin_layout Standard
29197 When numbering is turned on in multiline formulas, all lines will be numbered.
29198 But the numbering can be controlled with the menu
29200 Edit\SpecialChar \menuseparator
29201 Math\SpecialChar \menuseparator
29203 \begin_inset space ~
29207 \begin_inset space ~
29211 \begin_inset space ~
29219 \begin_inset space ~
29227 \begin_layout Standard
29228 Except of inline formulas, all formulas can be numbered with two different
29230 \begin_inset CommandInset ref
29232 reference "sec:Formula-Styles"
29239 \begin_layout Subsection
29241 \begin_inset CommandInset label
29243 name "sub:Cross-References"
29251 \begin_layout Plain Layout
29252 Cross-references ! to formulas
29260 \begin_layout Standard
29261 All labeled formulas can be cross-referenced.
29262 A label is added by the menu
29264 Insert\SpecialChar \menuseparator
29267 or the toolbar button
29268 \begin_inset Graphics
29269 filename ../images/label-insert.png
29275 The cursor must hereby be inside a displayed formula.
29276 A dialog pops up displaying the prefix
29281 The label is inserted there behind the prefix.
29282 The predefined prefix means
29283 \begin_inset Quotes eld
29287 \begin_inset Quotes erd
29290 and makes it easier to find labels in large documents because it marks
29291 it as formula label to divide it from e.
29292 \begin_inset space \thinspace{}
29296 \begin_inset space ~
29300 To change a label, the menu
29302 Insert\SpecialChar \menuseparator
29308 \begin_layout Standard
29309 The name of the label is displayed in LyX within two parentheses behind
29311 A formula with a label is always numbered.
29314 \begin_layout Standard
29315 Cross-references are inserted via the menu
29317 Insert\SpecialChar \menuseparator
29320 or with the toolbar button
29321 \begin_inset Graphics
29322 filename ../images/dialog-show-new-inset_ref.png
29328 A formula cross-reference appears in the output as formula number.
29329 When in the cross-reference dialog window the format
29333 is chosen, the cross-reference appears in the output as formula number
29335 \begin_inset Newline newline
29338 By right-clicking on a cross-reference in LyX, one jumps to the formula
29339 that is referenced.
29342 \begin_layout Standard
29343 Here are as examples cross-references to formulas of the following subsections:
29344 \begin_inset Note Note
29347 \begin_layout Plain Layout
29348 Note the different cross-reference types.
29356 \begin_layout Standard
29358 \begin_inset CommandInset ref
29365 \begin_inset CommandInset ref
29373 \begin_inset CommandInset ref
29379 ) big Latin letters are used for the numbering in contrary to (
29380 \begin_inset CommandInset ref
29389 \begin_layout Standard
29390 \begin_inset VSpace medskip
29393 When the argument of
29401 \begin_layout Plain Layout
29409 \begin_inset CommandInset ref
29411 reference "sub:User-defined-Numbering"
29422 contains a box like in
29423 \begin_inset CommandInset ref
29425 reference "sub:Paragraph-Boxes"
29429 , the formula cannot be referenced.
29432 \begin_layout Subsection
29437 \begin_layout Plain Layout
29438 Formula numbering ! subnumbering
29446 \begin_layout Standard
29447 With the help of the commands
29451 begin{subequations}
29459 formulas can be subnumbered.
29460 Both commands are inserted in TeX-mode.
29463 \begin_layout Standard
29465 \begin_inset Formula \begin{equation}
29466 A=C-B\label{eq:a}\end{equation}
29474 \begin_layout Plain Layout
29478 addtocounter{equation}{-1}
29487 \begin_layout Plain Layout
29491 begin{subequations}
29497 \begin_inset VSpace -5mm
29501 \begin_inset Formula \begin{equation}
29502 B=C-A\label{eq:b}\end{equation}
29507 \begin_inset Formula \begin{equation}
29508 C=A+B\label{eq:c}\end{equation}
29515 \begin_layout Standard
29519 \begin_layout Plain Layout
29531 \begin_layout Standard
29532 To create the example, the following is done:
29535 \begin_layout Enumerate
29536 first formula is inserted
29539 \begin_layout Enumerate
29544 addtocounter{equation}{-1}
29546 begin{subequations}
29550 \begin_layout Plain Layout
29559 \begin_inset Newline newline
29564 is inserted after the first formula
29567 \begin_layout Enumerate
29568 second formula is inserted
29571 \begin_layout Enumerate
29572 third formula is inserted
29575 \begin_layout Enumerate
29582 is inserted after the third formula
29585 \begin_layout Standard
29586 Every formula between the commands
29598 is subnumbered as a, b,
29599 \begin_inset Newline linebreak
29602 c, \SpecialChar \ldots{}
29603 For multiline formulas every line will be subnumbered.
29604 All subnumbered formulas are treated as
29609 But as every numbered formula increases the counter
29613 by one, the command
29619 is needed to decrease it.
29620 Otherwise the formulas
29621 \begin_inset CommandInset ref
29628 \begin_inset CommandInset ref
29635 \begin_inset CommandInset ref
29641 would be numbered as
29642 \begin_inset CommandInset ref
29649 \begin_inset CommandInset ref
29656 \begin_inset CommandInset ref
29665 \begin_layout Standard
29666 By inserting the commands in TeX-mode, a space is created between the first
29669 \begin_inset space \thinspace{}
29672 mm vertical space is inserted after the command
29676 begin{subequations}
29679 When the formula style
29685 \begin_layout Plain Layout
29687 \begin_inset CommandInset ref
29689 reference "sec:Formula-Styles"
29701 \begin_inset space \thinspace{}
29704 mm space is inserted instead.
29707 \begin_layout Standard
29708 Here is an example for a multiline formula where the numbering was turned
29709 off for the second line:
29713 \begin_layout Plain Layout
29717 begin{subequations}
29723 \begin_inset Formula \begin{eqnarray}
29724 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29725 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29726 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29734 \begin_layout Plain Layout
29746 \begin_layout Subsection
29747 User-defined Numbering
29748 \begin_inset CommandInset label
29750 name "sub:User-defined-Numbering"
29758 \begin_layout Plain Layout
29759 Formula numbering ! user-defined
29767 \begin_layout Standard
29771 \begin_layout Plain Layout
29772 Formula numbering ! self-defined delimiters
29777 With the standard numbering parentheses are set around the formula number.
29778 To replace the parentheses for example by vertical bars, the following
29779 line is added to the LaTeX-preamble:
29782 \begin_layout Standard
29794 \begin_inset Note Note
29797 \begin_layout Plain Layout
29798 This macro is already declared in the LaTeX-preamble for testing.
29799 To activate it, remove the percent sign at the beginning.
29807 \begin_layout Standard
29808 To use other characters, the vertical bars besides the
29812 are replaced by one ore more characters.
29813 To get only the formula number the vertical bars are omitted.
29816 \begin_layout Standard
29817 \begin_inset VSpace bigskip
29820 When there should be an expression of your choice instead of the consecutive
29821 formula number in parentheses behind the formula, the command
29831 \begin_layout Plain Layout
29840 \begin_inset Formula \begin{equation}
29841 A+B=C\tag{something}\label{eq:tag}\end{equation}
29845 In this example the command
29853 \begin_layout Plain Layout
29864 was inserted to the formula.
29867 \begin_layout Standard
29876 \begin_layout Plain Layout
29887 is inserted instead, the star prevents the parentheses around the expression:
29888 \begin_inset Formula \[
29889 A+B=C\tag*{something}\]
29896 \begin_layout Standard
29897 \begin_inset VSpace bigskip
29900 To restart the formula numbering with new document parts or sections, the
29901 following command is used:
29904 \begin_layout Standard
29909 @addtoreset{equation}{part}
29915 \begin_layout Plain Layout
29920 \begin_layout Plain Layout
29931 \begin_layout Plain Layout
29944 \begin_layout Plain Layout
29955 \begin_layout Plain Layout
29968 \begin_inset Newline newline
29972 \begin_inset Newline newline
29979 @addtoreset{equation}{section}
29982 \begin_layout Standard
29983 To be able to use these commands in TeX-mode, the
29984 \begin_inset Quotes eld
29988 \begin_inset Quotes erd
29991 character has to be made
29992 \begin_inset Quotes eld
29996 \begin_inset Quotes erd
29999 for LaTeX using the command
30013 So the command sequence in TeX-mode is:
30016 \begin_layout Standard
30022 \begin_inset Newline newline
30027 @addtoreset{equation}{section}
30028 \begin_inset Newline newline
30036 \begin_layout Standard
30037 In the LaTeX-preamble
30049 can be omitted as they are automatically internally inserted by LyX.
30052 \begin_layout Standard
30067 \begin_layout Plain Layout
30072 is part of the LaTeX-package
30080 \begin_layout Plain Layout
30081 Packages ! carlisle
30086 that is part of every LaTeX standard installation.
30095 \begin_layout Plain Layout
30096 Packages ! remreset
30101 has to be loaded in the LaTeX-preamble with the line
30104 \begin_layout Standard
30109 usepackage{remreset}
30112 \begin_layout Standard
30123 \begin_layout Plain Layout
30128 \begin_layout Plain Layout
30139 \begin_layout Plain Layout
30152 \begin_layout Plain Layout
30163 \begin_layout Plain Layout
30175 can be used with the same scheme as
30184 \begin_layout Standard
30185 \begin_inset VSpace bigskip
30188 Sometimes formulas should be numbered in the following form:
30191 \begin_layout Standard
30194 (section number.formula number)
30197 \begin_layout Standard
30198 The formula number should start with every section with
30199 \begin_inset Quotes eld
30203 \begin_inset Quotes erd
30209 \begin_layout Standard
30210 For this case there is the command
30220 \begin_layout Plain Layout
30228 , which is used with the following scheme:
30231 \begin_layout Standard
30236 numberwithin{counter}{sectioning}
30239 \begin_layout Standard
30240 Counter denotes what kind of numbering is affected, sectioning denotes what
30241 number is before the dot.
30244 \begin_layout Standard
30245 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30248 \begin_layout Standard
30253 numberwithin{equation}{section}
30256 \begin_layout Standard
30257 This is the result:
30261 \begin_layout Plain Layout
30265 numberwithin{equation}{section}
30271 \begin_inset Formula \begin{equation}
30272 A+B=C\end{equation}
30279 \begin_layout Standard
30281 \begin_inset space \thinspace{}
30285 \begin_inset space ~
30288 tables so that the number of the part is the sectioning,
30289 \begin_inset Newline newline
30296 numberwithin{table}{part}
30301 \begin_layout Standard
30302 To go back to the standard numbering or to prevent this kind of numbering
30303 when it is defined by the document class, the following command is inserted
30304 as TeX-Code or to the LaTeX-preamble:
30307 \begin_layout Standard
30320 \begin_layout Plain Layout
30334 \begin_layout Plain Layout
30350 \begin_inset Newline newline
30358 \begin_inset Newline newline
30370 \begin_layout Standard
30377 uses internally the command
30383 , described above, that also needs to be reverted.
30387 \begin_layout Plain Layout
30394 \begin_layout Plain Layout
30398 @removefromreset{equation}{section}
30401 \begin_layout Plain Layout
30413 \begin_layout Subsection
30414 Numbering with Roman Numbers and Letters
30415 \begin_inset CommandInset label
30417 name "sub:Numbering-with-Roman"
30425 \begin_layout Plain Layout
30426 Formula numbering ! with letters
30435 \begin_layout Plain Layout
30436 Formula numbering ! with Roman numbers
30444 \begin_layout Standard
30445 Formulas can also be numbered with Roman numbers and Latin letters.
30446 To number for example with small Roman numbers, the command
30449 \begin_layout Standard
30461 \begin_layout Standard
30462 is inserted before the formula in TeX-mode.
30473 \begin_layout Plain Layout
30481 redefines the predefined command
30497 \begin_layout Plain Layout
30504 has the same scheme like the command
30510 that is described in
30511 \begin_inset CommandInset ref
30513 reference "sec:User-defined-Commands"
30527 is the formula counter.
30534 is used as prefix for a counter, the value of the counter is output as
30536 When a formula is numbered, LaTeX sets internally the command
30542 behind the formula.
30551 \begin_layout Plain Layout
30561 outputs the counter as small Roman number.
30564 \begin_layout Standard
30565 All formulas behind the command
30575 are now numbered Roman.
30576 To switch to numbering with big Roman numbers, the command is inserted
30593 \begin_layout Plain Layout
30605 \begin_inset Quotes eld
30609 \begin_inset Quotes erd
30612 with small Latin letters there is the command
30622 \begin_layout Plain Layout
30630 , for big ones there is the command
30640 \begin_layout Plain Layout
30653 \begin_layout Standard
30654 \begin_inset Note Greyedout
30657 \begin_layout Plain Layout
30662 Only maximal 26 formulas can be numbered with Latin letters in one document.
30670 \begin_layout Standard
30674 \begin_layout Plain Layout
30690 \begin_layout Standard
30691 \begin_inset Formula \begin{equation}
30692 A=\textrm{small roman}\label{eq:rom}\end{equation}
30700 \begin_layout Plain Layout
30714 \begin_inset Formula \begin{equation}
30715 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30723 \begin_layout Plain Layout
30737 \begin_inset Formula \begin{equation}
30738 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30746 \begin_layout Plain Layout
30760 \begin_inset Formula \begin{equation}
30761 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30768 \begin_layout Standard
30769 To switch back to the default numbering, insert the command:
30772 \begin_layout Standard
30785 \begin_layout Plain Layout
30796 \begin_layout Standard
30800 \begin_layout Plain Layout
30814 \begin_inset Formula \begin{equation}
30815 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30822 \begin_layout Standard
30823 \begin_inset VSpace medskip
30826 As you see, formulas are numbered serially independent from the numbering
30828 When then numbering should start with
30829 \begin_inset Quotes eld
30833 \begin_inset Quotes erd
30836 when the style is changed, new equation counters have to be defined.
30837 A description about this can be found in the file
30838 \begin_inset CommandInset href
30840 target "Formula-numbering.lyx"
30847 \begin_layout Section
30848 User-defined Commands
30849 \begin_inset CommandInset label
30851 name "sec:User-defined-Commands"
30859 \begin_layout Plain Layout
30860 User-defined commands
30868 \begin_layout Standard
30869 Many LaTeX-commands are too long to be used frequently.
30870 But it is possible to define with the command
30880 \begin_layout Plain Layout
30888 new shorter commands.
30891 \begin_layout Standard
30892 The command scheme of
30901 \begin_layout Standard
30906 newcommand{new command name}[number of arguments][optional
30911 \begin_inset Newline newline
30918 \begin_layout Plain Layout
30933 \begin_layout Plain Layout
30940 {command definition}
30943 \begin_layout Standard
30944 \begin_inset Note Greyedout
30947 \begin_layout Plain Layout
30952 Assure that the name of the new command is not already used in your document
30953 or by LaTeX-packages that you use.
30954 When you for example define the command
30966 , you get an error message because
30972 is already defined as command for
30973 \begin_inset Quotes eld
30977 \begin_inset Formula $\le$
30981 \begin_inset Quotes erd
30992 \begin_layout Standard
30993 \begin_inset Note Greyedout
30996 \begin_layout Plain Layout
31001 The names of user-defined commands may only consist of Latin letters.
31009 \begin_layout Standard
31010 The number of arguments is an integer in the range 0
31011 \begin_inset space \thinspace{}
31015 \begin_inset space \thinspace{}
31018 9 and specifies how many arguments the new command should have.
31019 With the optional value a value for an optional argument can be predefined.
31020 When this is done, the
31028 rgument of the new command is automatically an optional one.
31031 \begin_layout Standard
31032 Here are some examples:
31035 \begin_layout Itemize
31036 To define the command
31048 , the LaTeX-preamble line is:
31052 \begin_layout Plain Layout
31064 \begin_inset Newline newline
31076 \begin_layout Itemize
31077 To define the command
31089 , the argument (that should be underlined) must be taken into account.
31090 For this the preamble line is:
31094 \begin_layout Plain Layout
31106 \begin_inset Newline newline
31121 \begin_layout Plain Layout
31133 \begin_inset Newline newline
31142 acts as argument placeholder, the
31146 behind it denotes that it is the placeholder for the first argument.
31149 \begin_layout Itemize
31157 \begin_inset space \thinspace{}
31161 \begin_inset space ~
31174 \begin_layout Plain Layout
31186 \begin_inset Newline newline
31195 framebox#1#2{$#3$}}
31201 \begin_layout Plain Layout
31213 \begin_inset Newline newline
31218 The two Dollar signs creates the extra formula needed for
31225 \begin_inset CommandInset ref
31227 reference "sub:Boxes-with-Frame"
31234 \begin_layout Itemize
31235 To create a new command for
31241 where the color for the box needn't to be specified, the argument for the
31242 color is defined optional:
31246 \begin_layout Plain Layout
31258 \begin_inset Newline newline
31267 fcolorbox{#2}{#1}{$#3$}}
31273 \begin_layout Plain Layout
31283 \begin_inset Newline newline
31286 When the color is not specified when using
31292 , the predefined color
31299 \begin_layout Standard
31300 A test of the new defined commands:
31303 \begin_layout Standard
31305 \begin_inset Tabular
31306 <lyxtabular version="3" rows="6" columns="2">
31308 <column alignment="center" valignment="top" width="0">
31309 <column alignment="center" valignment="top" width="0">
31311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31314 \begin_layout Plain Layout
31320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31323 \begin_layout Plain Layout
31325 \begin_inset Note Note
31328 \begin_layout Plain Layout
31335 is only used as spacer.
31347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31350 \begin_layout Plain Layout
31357 \begin_layout Plain Layout
31371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31374 \begin_layout Plain Layout
31375 \begin_inset Formula $A\gr B$
31385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31388 \begin_layout Plain Layout
31396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31399 \begin_layout Plain Layout
31400 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31413 \begin_layout Plain Layout
31417 \begin_inset Formula $\to$
31423 \begin_inset Formula $\to$
31434 \begin_layout Plain Layout
31448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31451 \begin_layout Plain Layout
31452 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31465 \begin_layout Plain Layout
31469 \begin_inset Formula $\to$
31480 \begin_layout Plain Layout
31494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31497 \begin_layout Plain Layout
31498 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31511 \begin_layout Plain Layout
31517 \begin_inset Formula $\to$
31528 \begin_layout Plain Layout
31542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31545 \begin_layout Plain Layout
31546 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31562 \begin_layout Section
31566 \begin_layout Standard
31567 LyX supports two types of commutative diagrams:
31575 that are explained in the following.
31578 \begin_layout Subsection
31583 \begin_layout Plain Layout
31592 \begin_layout Standard
31593 Diagrams of this type visualize relations by vertical and horizontal lines
31595 \begin_inset Formula \[
31596 \begin{CD}A@>>>B@>>>C\\
31598 F@<<<E@<<<D\end{CD}\]
31605 \begin_layout Standard
31606 To get them, the command
31614 \begin_layout Plain Layout
31624 is inserted to a formula.
31625 A blue box appears with two dashed lines where further commands can be
31631 a new line is created.
31632 Horizontal relations are inserted in odd, vertical in even formula lines.
31635 \begin_layout Standard
31636 To create the relations there are the following commands:
31639 \begin_layout Itemize
31644 creates a left arrow,
31655 \begin_layout Itemize
31660 creates an up arrow,
31668 a vertical equal sign
31671 \begin_layout Itemize
31677 is a placeholder for non-existent relations
31680 \begin_layout Standard
31681 All arrows can be labeled as follows:
31684 \begin_layout Itemize
31685 Is text inserted between the first and second < or >, resp., it is placed
31687 When it is inserted between the second and third one, it appears under
31691 \begin_layout Itemize
31692 When text for vertical arrows is inserted between the first and second A
31693 or V, resp., it is placed left beside the arrow.
31694 When it is inserted between the second and third one, it appears right
31696 If the text contains an A or V, these letters must be set into a TeX-brace.
31699 \begin_layout Standard
31700 As example a diagram with all possible relations:
31703 \begin_layout Standard
31704 \begin_inset Formula \[
31705 \begin{CD}A@>j>>B@>>k>C@=F\\
31707 D@<<j<E@>k>>F@=C\end{CD}\]
31714 \begin_layout Standard
31715 The command for this is:
31716 \begin_inset Newline newline
31727 \begin_layout Plain Layout
31736 A@>j>>B@>>k>C@=F Ctrl-Enter
31737 \begin_inset Newline newline
31744 \begin_layout Plain Layout
31759 \begin_layout Plain Layout
31772 \begin_layout Plain Layout
31784 \begin_inset Formula $\to$
31790 \begin_inset Newline newline
31797 \begin_layout Plain Layout
31812 \begin_layout Plain Layout
31825 \begin_layout Plain Layout
31835 \begin_layout Subsection
31840 \begin_layout Plain Layout
31841 Diagrams ! xymatrix
31849 \begin_layout Standard
31850 To be able to use xymatrices, the LaTeX-package
31855 A xymatrix is created by inserting the command
31862 Then you are able to add new matrix columns and rows like for normal matrices,
31864 \begin_inset CommandInset ref
31866 reference "sec:Matrices"
31873 \begin_layout Standard
31874 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31876 All possibilities to create commutative diagrams and decorations are explained
31877 in detail in this manual:
31878 \begin_inset CommandInset href
31880 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31887 \begin_layout Standard
31888 \begin_inset Newpage newpage
31894 \begin_layout Section
31899 \begin_layout Plain Layout
31912 \begin_layout Plain Layout
31913 Other useful math tips can be found in
31914 \begin_inset CommandInset citation
31929 \begin_layout Plain Layout
31937 \begin_inset Note Note
31940 \begin_layout Plain Layout
31943 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31946 \begin_layout Plain Layout
31949 texorpdfstring is in section
31950 \begin_inset CommandInset ref
31952 reference "sub:Formulas-in-Section"
31965 \begin_layout Plain Layout
31975 \begin_layout Plain Layout
31980 \begin_layout Plain Layout
31987 Chemical characters
31991 \begin_layout Plain Layout
32006 \begin_layout Subsection
32007 Chemical Symbols and Equations
32008 \begin_inset CommandInset label
32010 name "sub:Chemical-Symbols-and"
32018 \begin_layout Plain Layout
32019 Chemical characters ! Symbols
32028 \begin_layout Plain Layout
32038 \begin_layout Plain Layout
32047 \begin_layout Standard
32048 An example text from chemistry:
32051 \begin_layout Quote
32053 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32056 -ion reacts with two
32057 \begin_inset Formula $\mathrm{Na^{+}}$
32060 -ions to sodium sulfate
32061 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32065 The chemical equation for this is:
32066 \begin_inset Formula \[
32067 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32074 \begin_layout Standard
32075 This chemical equation can directly be created as formula.
32076 To avoid that the symbols appear italic, everything is highlighted and
32077 changed by the shortcut
32080 \begin_inset space ~
32085 to the upright font style.
32089 \begin_layout Plain Layout
32095 \begin_inset CommandInset ref
32097 reference "sub:Font-Styles"
32109 \begin_layout Subsection
32114 \begin_layout Plain Layout
32123 \begin_layout Standard
32124 Negative numbers often look ugly in formulas because the minus sign before
32125 the number is set with the same length as the minus operator sign.
32126 When writing the negative number in normal text, the minus sign appears
32130 \begin_layout Standard
32131 Thus, the problem disappears when converting the minus sign to mathematical
32135 \begin_layout Standard
32136 An example to visualize the problem:
32139 \begin_layout Standard
32141 \begin_inset Tabular
32142 <lyxtabular version="3" rows="3" columns="2">
32144 <column alignment="right" valignment="top" width="0">
32145 <column alignment="left" valignment="top" width="0">
32147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32150 \begin_layout Plain Layout
32156 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32159 \begin_layout Plain Layout
32167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32170 \begin_layout Plain Layout
32176 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32179 \begin_layout Plain Layout
32180 \begin_inset Formula $x=-2$
32190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32193 \begin_layout Plain Layout
32199 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32202 \begin_layout Plain Layout
32203 \begin_inset Formula $x=\textrm{-}2$
32219 \begin_layout Subsection
32220 Comma as decimal Separator
32224 \begin_layout Plain Layout
32233 \begin_layout Standard
32234 In LaTeX a comma inside a formula is used, according to the English convention,
32235 as number group separator.
32236 So there will be space added behind all commas in formulas.
32239 \begin_layout Standard
32240 To avoid this, the comma is highlighted and changed to mathematical text
32244 \begin_inset space ~
32252 \begin_layout Standard
32253 To use all formula commas in the document as decimal separator, the file
32262 \begin_layout Plain Layout
32267 is part of the LaTeX-package
32275 \begin_layout Plain Layout
32280 \begin_layout Plain Layout
32303 \begin_layout Plain Layout
32309 is loaded with the LaTeX-preamble line
32312 \begin_layout Standard
32320 \begin_layout Subsection
32322 \begin_inset CommandInset label
32324 name "sub:Physical-Vectors"
32332 \begin_layout Plain Layout
32341 \begin_layout Standard
32342 Predefined vectors are offered by the LaTeX-package
32350 \begin_layout Plain Layout
32355 should be part of every LaTeX standard installation.
32364 \begin_layout Plain Layout
32370 that is loaded with the LaTeX-preamble line
32373 \begin_layout Standard
32381 \begin_layout Standard
32385 \begin_layout Plain Layout
32395 \begin_inset Note Note
32398 \begin_layout Plain Layout
32399 The following table will only be displayed when the LaTeX-package
32408 The following commands are defined:
32411 \begin_layout Standard
32413 \begin_inset Tabular
32414 <lyxtabular version="3" rows="4" columns="2">
32416 <column alignment="center" valignment="top" width="0">
32417 <column alignment="center" valignment="top" width="0">
32419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32422 \begin_layout Plain Layout
32428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32431 \begin_layout Plain Layout
32439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32442 \begin_layout Plain Layout
32452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32455 \begin_layout Plain Layout
32456 \begin_inset Formula $\Bra{\psi}$
32466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32469 \begin_layout Plain Layout
32479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32482 \begin_layout Plain Layout
32483 \begin_inset Formula $\Ket{\psi}$
32493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32496 \begin_layout Plain Layout
32508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32511 \begin_layout Plain Layout
32512 \begin_inset Formula $\Braket{\psi|\phi}$
32528 \begin_layout Standard
32535 assures that all vertical bars are set in the size of the surrounding brackets:
32536 \begin_inset Formula \[
32537 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32545 \begin_layout Plain Layout
32555 \begin_inset Note Note
32558 \begin_layout Plain Layout
32559 The following will be displayed when the LaTeX-package
32571 \begin_layout Standard
32572 You need to install the LaTeX-package
32576 to see the rest of this subsection in the output.
32579 \begin_layout Standard
32583 \begin_layout Plain Layout
32595 \begin_layout Standard
32602 can also be achieved using the command
32608 , that is described in
32609 \begin_inset CommandInset ref
32611 reference "sub:Automatic-Bracket-Size"
32618 \begin_layout Subsection
32619 Self-defined Fractions
32620 \begin_inset CommandInset label
32622 name "sub:Self-defined-Fractions"
32630 \begin_layout Plain Layout
32631 Fractions ! self-defined
32639 \begin_layout Standard
32640 To define custom commands for fractions, the command
32650 \begin_layout Plain Layout
32658 is used in the following scheme:
32661 \begin_layout Standard
32674 bracket}{fraction bar thickness}{style}
32675 \begin_inset Newline newline
32682 \begin_layout Plain Layout
32697 \begin_layout Plain Layout
32704 {numerator}{denominator}
32707 \begin_layout Standard
32708 The style is a number in the range of 0
32709 \begin_inset space \thinspace{}
32713 \begin_inset space \thinspace{}
32719 \begin_layout Standard
32721 \begin_inset Tabular
32722 <lyxtabular version="3" rows="5" columns="2">
32724 <column alignment="center" valignment="top" width="0">
32725 <column alignment="center" valignment="top" width="0">
32727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32730 \begin_layout Plain Layout
32736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32739 \begin_layout Plain Layout
32747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32750 \begin_layout Plain Layout
32756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32759 \begin_layout Plain Layout
32760 display style formula
32767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32770 \begin_layout Plain Layout
32776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32779 \begin_layout Plain Layout
32787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32790 \begin_layout Plain Layout
32796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32799 \begin_layout Plain Layout
32807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32810 \begin_layout Plain Layout
32816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32819 \begin_layout Plain Layout
32833 \begin_layout Standard
32834 When no style is given, the size is adjusted to the surrounding environment
32835 like for the command
32844 \begin_layout Standard
32845 When no fraction bar thickness is given, the predefined value of 0.4
32846 \begin_inset space \thinspace{}
32852 \begin_layout Standard
32853 \begin_inset VSpace medskip
32856 For example, the commands
32869 \begin_inset CommandInset ref
32871 reference "sub:Fractions"
32875 are defined with the commands
32878 \begin_layout Standard
32887 genfrac{}{}{}{0}{#1}{#2}}
32890 \begin_layout Standard
32894 \begin_layout Standard
32903 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32906 \begin_layout Standard
32907 \begin_inset VSpace medskip
32910 To define a fraction where the fraction bar thickness can be given as optional
32911 argument, the following line is inserted to the LaTeX-preamble:
32914 \begin_layout Standard
32923 genfrac{}{}{#1}{}{#2}{#3}}
32926 \begin_layout Standard
32928 \begin_inset Formula \begin{align*}
32929 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32930 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32934 As one can see, the distance of the numerator and the denominator to the
32935 fraction bar is round about three times the bar thickness.
32938 \begin_layout Subsection
32940 \begin_inset CommandInset label
32942 name "sub:Canceled-Formulas"
32950 \begin_layout Plain Layout
32959 \begin_layout Standard
32960 To cancel formulas or formula parts, the LaTeX-package
32968 \begin_layout Plain Layout
32973 is part of every LaTeX standard installation.
32982 \begin_layout Plain Layout
32988 has to be loaded with the LaTeX-preamble line
32991 \begin_layout Standard
32996 usepackage[samesize]{cancel}
32999 \begin_layout Standard
33000 There are four ways to cancel formulas:
33003 \begin_layout Standard
33005 \begin_inset Tabular
33006 <lyxtabular version="3" rows="5" columns="2">
33008 <column alignment="center" valignment="top" width="0">
33009 <column alignment="center" valignment="top" width="0">
33011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33014 \begin_layout Plain Layout
33020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33023 \begin_layout Plain Layout
33025 \begin_inset Note Note
33028 \begin_layout Plain Layout
33041 are used here as spacer.
33053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33056 \begin_layout Plain Layout
33065 \begin_layout Plain Layout
33079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33082 \begin_layout Plain Layout
33083 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33096 \begin_layout Plain Layout
33105 \begin_layout Plain Layout
33119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33122 \begin_layout Plain Layout
33123 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33136 \begin_layout Plain Layout
33145 \begin_layout Plain Layout
33159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33162 \begin_layout Plain Layout
33163 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33176 \begin_layout Plain Layout
33180 \begin_inset Formula $\to$
33191 \begin_layout Plain Layout
33205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33208 \begin_layout Plain Layout
33209 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33225 \begin_layout Standard
33232 is especially suitable to visualize the reduction of fractions within formulas:
33233 \begin_inset Formula \[
33234 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33241 \begin_layout Subsection
33242 Formulas in Section Headings
33243 \begin_inset CommandInset label
33245 name "sub:Formulas-in-Section"
33253 \begin_layout Plain Layout
33254 Formula ! in section headings
33262 \begin_layout Standard
33263 When formulas are used in section headings, the following has to be taken
33267 \begin_layout Standard
33268 \begin_inset Note Greyedout
33271 \begin_layout Plain Layout
33280 \begin_layout Plain Layout
33281 Packages ! hyperref
33286 support is enabled in the document settings dialog under
33289 \begin_inset space ~
33294 , PDF-bookmarks are created for every section heading in the table of contents.
33295 If a section heading contains formulas, they are incorrectly displayed
33296 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33305 \begin_layout Standard
33306 Both problems can be solved by inserting at the end of the section heading
33307 a short title with the menu
33309 Insert\SpecialChar \menuseparator
33311 \begin_inset space ~
33317 Short titles are used as alternative for multiline section headings to
33318 keep the table of contents clearly arranged.
33319 Only the short title appears in the table of contents and therefore also
33320 in the PDF-bookmark.
33323 \begin_layout Standard
33324 When formulas should be used in the table of contents but
33328 is used, one can use the following command in TeX-mode:
33331 \begin_layout Standard
33336 texorpdfstring{part}{alternative}
33340 \begin_layout Plain Layout
33351 \begin_layout Standard
33352 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33353 This can be characters, formulas, footnotes, but also cross-references.
33354 The alternative is used instead of the part for the bookmark.
33357 \begin_layout Standard
33358 Here are two example headings:
33359 \begin_inset VSpace -3mm
33366 \begin_layout Plain Layout
33378 \begin_layout Subsubsection
33379 Heading without formula in table of contents
33380 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33384 \begin_inset OptArg
33387 \begin_layout Plain Layout
33388 Heading without formula in table of contents
33396 \begin_layout Subsubsection
33397 Heading with formula in table of contents
33401 \begin_layout Plain Layout
33411 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33418 \begin_layout Plain Layout
33428 \begin_layout Standard
33432 \begin_layout Plain Layout
33441 In the first heading a short title was used, in the second one
33450 \begin_layout Standard
33451 To get the same formatting as for the other headings, the complete heading
33460 \begin_layout Plain Layout
33462 \begin_inset CommandInset ref
33464 reference "sub:Bold-Formulas"
33476 \begin_layout Subsection
33477 Formulas in multi-column Text
33481 \begin_layout Plain Layout
33482 Formula ! in multi-column text
33490 \begin_layout Standard
33491 Formulas in multi-column text are often too wide to fit into a column and
33492 thus need to be set over the whole page width.
33493 This is done by using the LaTeX-package
33501 \begin_layout Plain Layout
33506 is part of every LaTeX standard installation.
33515 \begin_layout Plain Layout
33516 Packages ! multicol
33521 , that is loaded with the LaTeX-preamble line
33524 \begin_layout Standard
33529 usepackage{multicol}
33532 \begin_layout Standard
33533 \begin_inset Note Greyedout
33536 \begin_layout Plain Layout
33537 Note herby that the setting
33540 \begin_inset space ~
33547 Document\SpecialChar \menuseparator
33553 \begin_inset space ~
33573 \begin_layout Standard
33574 Before the multi-column text the command
33577 \begin_layout Standard
33582 begin{multicols}{column number}
33585 \begin_layout Standard
33586 is written in TeX-mode.
33587 The column number is a number in the range of 2
33588 \begin_inset space \thinspace{}
33592 \begin_inset space \thinspace{}
33596 Before the formula the multi-column text is ended by inserting the command
33599 \begin_layout Standard
33607 \begin_layout Standard
33611 \begin_layout Standard
33612 Due to the command some space is automatically added before the formula.
33614 \begin_inset space \thinspace{}
33617 mm vertical space is inserted before the formula.
33618 When the formula style
33624 \begin_layout Plain Layout
33626 \begin_inset CommandInset ref
33628 reference "sec:Formula-Styles"
33640 \begin_inset space \thinspace{}
33643 mm space is inserted instead.
33646 \begin_layout Standard
33647 As example a multi-column text with a displayed formula:
33650 \begin_layout Standard
33654 \begin_layout Plain Layout
33658 begin{multicols}{2}
33663 Das Spektrum wird fouriertransformiert.
33664 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33665 , Lösungsmittel) zu trennen.
33666 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33667 nun das Aussehen des Ausgangssignals.
33668 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33669 über alle Phasen integrieren muss.
33671 \begin_inset Formula $S$
33674 unser normiertes Ausgangssignal and
33675 \begin_inset Formula $P$
33678 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33682 \begin_layout Plain Layout
33692 \begin_inset VSpace -6mm
33696 \begin_inset Formula \begin{equation}
33697 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33705 \begin_layout Plain Layout
33709 begin{multicols}{2}
33715 \begin_inset Formula $S_{0}$
33718 das Signal ohne Gradient ist and the Normierungsbedingung
33719 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33723 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33725 \begin_inset Formula $\nicefrac{\pi}{2}$
33729 \begin_inset space \thinspace{}
33732 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33733 das Signal zusätzlich abschwächt.
33734 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33736 \begin_inset Formula $T_{2}$
33742 \begin_layout Standard
33746 \begin_layout Plain Layout
33758 \begin_layout Subsection
33759 Formulas with Description of Variables
33763 \begin_layout Plain Layout
33764 Formula ! with description of variables
33772 \begin_layout Standard
33773 To describe variables within a formula, like in formula
33774 \begin_inset CommandInset ref
33776 reference "eq:within"
33785 \begin_inset Formula $n$
33789 \begin_inset space ~
33792 matrix is used with left aligned columns for the
33793 \begin_inset Formula $n$
33800 \begin_layout Plain Layout
33802 \begin_inset CommandInset ref
33804 reference "sec:Matrices"
33813 To set the description in a smaller size, before the matrix e.
33814 \begin_inset space \thinspace{}
33818 \begin_inset space ~
33831 \begin_layout Plain Layout
33833 \begin_inset CommandInset ref
33835 reference "sub:Font-Sizes"
33847 \begin_layout Standard
33848 When the formula style
33854 \begin_layout Plain Layout
33856 \begin_inset CommandInset ref
33858 reference "sec:Formula-Styles"
33879 \begin_layout Plain Layout
33886 only works in formulas with the style
33891 \begin_inset CommandInset ref
33893 reference "sub:Variable-Space"
33902 is inserted before and after the matrix to have the same separation of
33903 the matrix from the equation and the side margin.
33906 \begin_layout Standard
33907 When the formula style
33911 is used, the method described in
33912 \begin_inset CommandInset ref
33914 reference "sub:Flalign-Environment"
33918 is used to indent formulas.
33920 \begin_inset CommandInset ref
33922 reference "eq:within"
33926 consists of five columns whereas in the first two columns contain the equation,
33927 the third the matrix, and the last one an empty TeX-brace.
33928 \begin_inset Formula \begin{flalign}
33929 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33930 \rho & \textrm{density}\\
33931 V & \textrm{volume}\\
33932 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33939 \begin_layout Subsection
33940 Upright small Greek Letters
33941 \begin_inset CommandInset label
33943 name "sub:Upright-small-Greek"
33951 \begin_layout Plain Layout
33952 Greek letters ! upright
33960 \begin_layout Standard
33961 Most of the math fonts only provide italic small Greek letters.
33962 But for symbols of elementary particles like pions and neutrinos, upright
33963 Greek letters are needed.
33972 \begin_layout Plain Layout
33977 is part of the LaTeX-package
33985 \begin_layout Plain Layout
33990 \begin_layout Plain Layout
34013 \begin_layout Plain Layout
34019 that is loaded with the LaTeX-preamble line
34022 \begin_layout Standard
34027 usepackage{upgreek}
34030 \begin_layout Standard
34036 \begin_layout Plain Layout
34046 \begin_inset Note Note
34049 \begin_layout Plain Layout
34050 The following table will only be displayed when the LaTeX-package
34059 They are created when the command for a small Greek letters is started
34065 For example the command
34072 \begin_inset Formula $\uptau$
34078 \begin_layout Standard
34079 With these commands reactions of elementary particles can be typeset:
34080 \begin_inset Formula \[
34081 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34088 \begin_layout Standard
34089 The upright letters are more bold and wider than the italic ones.
34090 They should therefore not be used for units like
34091 \begin_inset Quotes eld
34095 \begin_inset Quotes erd
34101 \begin_layout Standard
34105 \begin_layout Plain Layout
34115 \begin_inset Note Note
34118 \begin_layout Plain Layout
34119 The following will be displayed when the LaTeX-package
34131 \begin_layout Standard
34132 You need to install the LaTeX-package
34136 to see the rest of this subsection in the output.
34139 \begin_layout Standard
34143 \begin_layout Plain Layout
34155 \begin_layout Subsection
34156 Text Characters in Formulas
34157 \begin_inset CommandInset label
34159 name "sub:Text-Characters-in"
34167 \begin_layout Plain Layout
34176 \begin_layout Standard
34177 In some cases you might want to insert text characters directly into formulas.
34178 When for example the centered dot · is often used in formulas like
34179 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34182 , one would have to insert the command
34192 \begin_layout Plain Layout
34194 \begin_inset CommandInset ref
34196 reference "sub:Binary-Operators"
34205 all the time, because this character is defined in all encodings as text
34207 But the encoding can be changed by this LaTeX-preamble line:
34210 \begin_layout Standard
34215 Declare Inputtext{183}{
34225 f\SpecialChar \textcompwordmark{}
34229 \begin_layout Standard
34230 The character encoding (menu
34232 Document\SpecialChar \menuseparator
34233 Settings\SpecialChar \menuseparator
34236 ) specifies what character appears when a keyboard key is pressed.
34237 When the key for the character '·' is pressed, internally the command
34244 But this command is not available in a formula so that you would get LaTeX-erro
34246 With the changed encoding the right command is chosen automatically, depending
34247 on if the character was inserted into a formula or not.
34250 \begin_layout Standard
34251 The encoding of several characters is saved in definition files.
34252 Fore example the encoding
34256 is defined in the file
34260 that is in the installation folder of LaTeX.
34261 Encodings should only be changed via the LaTeX-preamble and not in the
34263 Otherwise own documents could not be edited by other LyX users working
34264 on other computers.
34267 \begin_layout Standard
34268 \begin_inset VSpace medskip
34271 Besides the centered dot, in this document the degree sign ° is defined
34272 with the following LaTeX-preamble line so that it can directly be inserted
34276 \begin_layout Standard
34281 DeclareInputtext{176}{
34291 f\SpecialChar \textcompwordmark{}
34295 \begin_layout Standard
34296 \begin_inset Newpage newpage
34302 \begin_layout Section
34308 \begin_layout Plain Layout
34317 \begin_layout Standard
34318 This section is a summary of the most important typographic rules, listed
34323 \begin_layout Plain Layout
34324 This collection was partly taken from the German semi-official dictionary
34326 \begin_inset Quotes eld
34330 \begin_inset Quotes erd
34334 \begin_inset CommandInset citation
34340 that lists some of the ISO rules.
34348 \begin_layout Itemize
34357 \begin_layout Plain Layout
34358 done with font styles, see
34359 \begin_inset CommandInset ref
34361 reference "sub:Font-Styles"
34371 \begin_inset space \thinspace{}
34375 \begin_inset Newline newline
34378 Between the value and the unit is the smallest space, see
34379 \begin_inset CommandInset ref
34381 reference "sub:Predefined-Space"
34386 \begin_inset Newline newline
34389 This convention is automatically fulfilled when the command
34396 When it is entered to a formula, two boxes appear.
34397 In the first one the value is inserted, in the second one the unit, and
34399 \begin_inset Formula $\unit[30]{km/h}$
34403 \begin_inset space \thinspace{}
34413 is not a real LaTeX command but the command
34419 , therefore you cannot use it in TeX code.
34422 \begin_layout Itemize
34423 Percent and perthousand signs are set like physical units:
34424 \begin_inset Newline newline
34428 \begin_inset space \thinspace{}
34434 \begin_layout Itemize
34435 The degree sign follows directly on the value: 15°, but not when it is used
34437 \begin_inset space \thinspace{}
34443 \begin_layout Itemize
34444 In numbers with more than four digits the smallest space is inserted before
34445 every third digit to group them:
34455 \begin_inset space \thinspace{}
34459 \begin_inset space \thinspace{}
34465 \begin_layout Itemize
34466 For dimensions like 120×90×40
34467 \begin_inset space \thinspace{}
34470 cm the multiplication sign
34471 \begin_inset Quotes eld
34475 \begin_inset Quotes erd
34479 It is available with the LaTeX-command
34485 , but can also directly be inserted with some keyboard definitions.
34488 \begin_layout Itemize
34489 Functions with names consisting of several letters are set upright to avoid
34491 \begin_inset CommandInset ref
34493 reference "sub:Predefined-Functions"
34500 \begin_layout Itemize
34501 Indices consisting of several letters, are set upright:
34502 \begin_inset Formula $E_{\mathrm{kin}}$
34506 \begin_inset Newline newline
34509 Components of matrices are set italic:
34510 \begin_inset Formula $\hat{H}_{kl}$
34516 \begin_layout Itemize
34517 The differentiation/integration operator 'd', the Euler's number 'e', and
34518 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34522 \begin_layout Standard
34523 \begin_inset Newpage newpage
34529 \begin_layout Section
34534 \begin_layout Plain Layout
34543 \begin_layout Standard
34544 Some characters and symbols can be created with several commands.
34545 Here is a list of the synonym commands:
34548 \begin_layout Standard
34549 \begin_inset VSpace bigskip
34553 \begin_inset space \hfill{}
34557 \begin_inset Tabular
34558 <lyxtabular version="3" rows="12" columns="2">
34560 <column alignment="center" valignment="top" width="0pt">
34561 <column alignment="center" valignment="top" width="0pt">
34563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34566 \begin_layout Plain Layout
34572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34575 \begin_layout Plain Layout
34577 \begin_inset Note Note
34580 \begin_layout Plain Layout
34587 is only used as spacer.
34599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34602 \begin_layout Plain Layout
34610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34613 \begin_layout Plain Layout
34617 \begin_layout Plain Layout
34630 \begin_layout Plain Layout
34644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34647 \begin_layout Plain Layout
34655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34658 \begin_layout Plain Layout
34668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34671 \begin_layout Plain Layout
34679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34682 \begin_layout Plain Layout
34692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34695 \begin_layout Plain Layout
34703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34706 \begin_layout Plain Layout
34714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34717 \begin_layout Plain Layout
34725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34728 \begin_layout Plain Layout
34736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34739 \begin_layout Plain Layout
34747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34750 \begin_layout Plain Layout
34760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34763 \begin_layout Plain Layout
34771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34774 \begin_layout Plain Layout
34784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34787 \begin_layout Plain Layout
34795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34798 \begin_layout Plain Layout
34808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34811 \begin_layout Plain Layout
34819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34822 \begin_layout Plain Layout
34832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34835 \begin_layout Plain Layout
34843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34846 \begin_layout Plain Layout
34854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34857 \begin_layout Plain Layout
34865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34868 \begin_layout Plain Layout
34880 \begin_inset space \hfill{}
34884 \begin_inset Tabular
34885 <lyxtabular version="3" rows="12" columns="2">
34887 <column alignment="center" valignment="top" width="0pt">
34888 <column alignment="center" valignment="top" width="0pt">
34890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34893 \begin_layout Plain Layout
34899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34902 \begin_layout Plain Layout
34910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34913 \begin_layout Plain Layout
34921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34924 \begin_layout Plain Layout
34936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34939 \begin_layout Plain Layout
34947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34950 \begin_layout Plain Layout
34960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34963 \begin_layout Plain Layout
34971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34974 \begin_layout Plain Layout
34984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34987 \begin_layout Plain Layout
34995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34998 \begin_layout Plain Layout
35006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35009 \begin_layout Plain Layout
35017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35020 \begin_layout Plain Layout
35028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35031 \begin_layout Plain Layout
35039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35042 \begin_layout Plain Layout
35052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35055 \begin_layout Plain Layout
35063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35066 \begin_layout Plain Layout
35076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35079 \begin_layout Plain Layout
35087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35090 \begin_layout Plain Layout
35100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35103 \begin_layout Plain Layout
35111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35114 \begin_layout Plain Layout
35124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35127 \begin_layout Plain Layout
35135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35138 \begin_layout Plain Layout
35148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35151 \begin_layout Plain Layout
35159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35162 \begin_layout Plain Layout
35176 \begin_inset space \hfill{}
35182 \begin_layout Standard
35183 \begin_inset Newpage newpage
35189 \begin_layout Bibliography
35190 \begin_inset CommandInset bibitem
35191 LatexCommand bibitem
35203 The LaTeX Companion
35206 Addison Wesley, 2004
35209 \begin_layout Bibliography
35210 \begin_inset CommandInset bibitem
35211 LatexCommand bibitem
35217 \begin_inset CommandInset href
35220 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35224 of LaTeX's math abilities
35227 \begin_layout Bibliography
35228 \begin_inset CommandInset bibitem
35229 LatexCommand bibitem
35234 LaTeX tips and tricks-
35235 \begin_inset CommandInset href
35238 target "http://tug.org/TeXnik/"
35245 \begin_layout Bibliography
35246 \begin_inset CommandInset bibitem
35247 LatexCommand bibitem
35253 \begin_inset CommandInset href
35256 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35264 \begin_layout Plain Layout
35276 \begin_layout Bibliography
35277 \begin_inset CommandInset bibitem
35278 LatexCommand bibitem
35284 \begin_inset CommandInset href
35287 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35291 of all symbols available with LaTeX-packages
35294 \begin_layout Bibliography
35295 \begin_inset CommandInset bibitem
35296 LatexCommand bibitem
35302 \begin_inset CommandInset href
35304 name "Documentation"
35305 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35309 of the LaTeX-package
35317 \begin_layout Plain Layout
35318 Packages ! hyperref
35326 \begin_layout Bibliography
35327 \begin_inset CommandInset bibitem
35328 LatexCommand bibitem
35334 \begin_inset CommandInset href
35337 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35348 \begin_inset CommandInset ref
35350 reference "sub:Operator-Limits"
35358 \begin_layout Plain Layout
35369 \begin_layout Bibliography
35370 \begin_inset CommandInset bibitem
35371 LatexCommand bibitem
35382 Auflage, Duden 2001
35385 \begin_layout Subsubsection*
35386 \begin_inset CommandInset index_print
35387 LatexCommand printindex