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,
43 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
46 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
48 \settowidth{\abc}{\space}
49 \renewcommand{\equationautorefname}{\hspace{-\abc}}
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]{Contents}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
78 \usepackage[samesize]{cancel}
80 % enables calculation of values,
83 % for multiple table row and column cells
93 % center multirows (e.g. in sec. 13.3)
94 \renewcommand{\multirowsetup}{\centering}
96 % define a color, used in sec.9.3
97 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
99 % declare operators (see sec. 10.4 and sec. 15.2)
100 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
101 \DeclareMathOperator{\sgn}{sgn}
103 \newcommand{\spce}{\textvisiblespace}
105 % example definitions for sec. 20.1
106 \newcommand{\gr}{\Longrightarrow}
107 \newcommand{\us}[1]{\underline{#1}}
108 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
109 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
110 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
112 % example macro from sec. 19.4
113 %\def\tagform@#1{\maketag@@@{|#1|}}
115 % macro from sec. 10.2
116 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
117 \def\mathclap {\mathpalette \mathclapinternal}
118 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
120 % redefine the greyed out note
121 \renewenvironment{lyxgreyedout}
122 {\textcolor{blue}\bgroup}{\egroup}
124 % check for package eurosym
125 % used for the Euro symbol
127 \IfFileExists{eurosym.sty}
128 {\usepackage[gennarrow]{eurosym}
129 \setboolean{eurosym}{true}}
130 {\setboolean{eurosym}{false}}
132 % needed in sec. 22.4
133 % check for package braket
135 \IfFileExists{braket.sty}
137 \setboolean{braket}{true}}
138 {\setboolean{braket}{false}}
140 % needed in sec. 22.10
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
153 \font_typewriter default
154 \font_default_family default
163 \pdf_title "LyX's Math Manual"
164 \pdf_author "LyX Team, Uwe Stöhr"
165 \pdf_subject "LyX-documentation about math"
166 \pdf_keywords "LyX, Mathed"
168 \pdf_bookmarksnumbered true
169 \pdf_bookmarksopen true
170 \pdf_bookmarksopenlevel 1
171 \pdf_breaklinks false
175 \pdf_pagebackref false
176 \pdf_pdfusetitle false
177 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
184 \paperorientation portrait
187 \paragraph_separation skip
189 \quotes_language english
192 \paperpagestyle plain
196 \tracking_changes false
197 \output_changes false
205 LyX's detailed Math manual
213 \begin_layout Plain Layout
215 If you have comments or error corrections, please send them to the LyX Documenta
219 \begin_inset CommandInset href
221 name "lyx-docs@lists.lyx.org"
222 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
233 \begin_inset Note Note
236 \begin_layout Plain Layout
243 \begin_inset Newline newline
247 \begin_inset Newline newline
255 \begin_layout Standard
256 \begin_inset CommandInset toc
257 LatexCommand tableofcontents
264 \begin_layout Standard
265 \begin_inset Note Note
268 \begin_layout Plain Layout
269 To export this document to PDF, PS, or DVI the LaTeX-packages
282 If they are not installed you can export the document anyway but the sections
283 where the packages are required won't appear in the output.
286 \begin_layout Plain Layout
287 The latest PDF-version of this document can be found here:
288 \begin_inset Newline newline
293 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
301 \begin_layout Standard
302 \begin_inset Newpage newpage
308 \begin_layout Section
310 \begin_inset CommandInset label
312 name "sec:Introduction"
319 \begin_layout Standard
320 This document explains LyX's math features and is furthermore a collection
321 of LaTeX-commands used for mathematical characters and constructs.
322 The explanations are designed for the usage of commands.
323 It is therefore required that you have read the section
334 \begin_layout Standard
335 Most of the characters and many constructs explained in this manual are
336 also accessible via the menu
340 \SpecialChar \menuseparator
356 But everybody who has to write lots of formulas will notice that it is
357 much faster to use commands instead of the math toolbar.
358 Therefore this manual is focused on commands but also mentions the correspondin
359 g toolbar buttons when available.
362 \begin_layout Standard
363 If not specially mentioned the commands are only available within formulas.
364 To be able to use all commands explained in this document, the option
368 must be used in the document settings (menu
370 Document\SpecialChar \menuseparator
371 Settings\SpecialChar \menuseparator
382 \begin_layout Plain Layout
385 Use AMS math package automatically
391 \begin_layout Plain Layout
400 -math when math constructs are found that are supported by LyX.
408 \begin_layout Standard
409 This document doesn't list all
413 \begin_layout Plain Layout
426 \begin_layout Plain Layout
431 \begin_layout Plain Layout
440 -math commands is in the file
443 \begin_inset CommandInset href
446 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
452 , which is part of every LaTeX standard installation.
457 for lucidity reasons.
460 \begin_layout Section
462 \begin_inset CommandInset label
464 name "sec:General-Instructions"
471 \begin_layout Standard
472 To create an inline formula
476 \begin_layout Plain Layout
482 that is embedded into a text line, press
486 or the toolbar button
487 \begin_inset Graphics
488 filename ../images/math-mode.png
494 \begin_inset Newline newline
497 To create a display style formula
501 \begin_layout Plain Layout
502 Formula ! display style
507 that will appear bigger and in an own paragraph, press
514 \begin_layout Standard
515 To change a display style formula to an inline formula, set the cursor into
516 the formula and press
522 Edit\SpecialChar \menuseparator
523 Math\SpecialChar \menuseparator
527 The same way is used to change an inline formula to a display style formula.
530 \begin_layout Standard
531 To display parts of an inline formula in the size of a display style formula,
540 \begin_layout Plain Layout
551 Then a new blue box appears in which the desired formula part is inserted.
554 \begin_layout Standard
555 Only inline formulas are allowed inside tables.
558 \begin_layout Standard
563 can be turned on in the menu
565 View\SpecialChar \menuseparator
569 When you click there on
570 \begin_inset Quotes eld
574 \begin_inset Quotes erd
577 the toolbar will be shown permanently at the bottom; this state is visualized
582 menu with a checkmark.
583 When you click in this state again on
584 \begin_inset Quotes eld
588 \begin_inset Quotes erd
599 is only shown when the cursor is within a formula; this state is visualized
600 by the renaming of the menu entry from
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
609 \begin_inset Quotes eld
617 \begin_inset Quotes erd
623 \begin_layout Standard
628 \begin_layout Plain Layout
633 \begin_layout Plain Layout
641 \begin_layout Plain Layout
652 \begin_layout Plain Layout
669 is invoked by pressing the toolbar button
670 \begin_inset Graphics
671 filename ../images/ert-insert.png
678 Insert\SpecialChar \menuseparator
683 \begin_layout Plain Layout
694 \begin_layout Plain Layout
708 \begin_inset Note Note
711 \begin_layout Plain Layout
712 In LyX there are three
713 \begin_inset Quotes eld
717 \begin_inset Quotes erd
720 that appear in the output with sub- and superscript letters: TeX, LaTeX,
724 \begin_layout Plain Layout
725 To avoid that these names are recognized as proper names, TeX-braces are
726 set around one of the letters of the name.
734 \begin_layout Standard
735 To change the LaTeX-preamble
739 \begin_layout Plain Layout
747 Document\SpecialChar \menuseparator
748 Settings\SpecialChar \menuseparator
753 \begin_layout Plain Layout
764 \begin_layout Plain Layout
780 \begin_layout Standard
781 To edit matrices, case differentiations, and multiline formulas subsequently,
784 Edit\SpecialChar \menuseparator
789 Edit\SpecialChar \menuseparator
791 \begin_inset Space \thinspace{}
795 \begin_inset Space \thinspace{}
805 When lines and columns are swapped via the menu, the column or line where
806 the cursor is in is exchanged with the column to the right or the line
808 Is the cursor in the last column or row, the exchange is done with the
809 column to the left or the line above.
812 \begin_layout Standard
813 To write text in formulas
817 \begin_layout Plain Layout
818 For multiline formulas the command
825 \begin_inset CommandInset ref
827 reference "sub:Text-in-multiline"
844 \begin_layout Plain Layout
854 \begin_layout Plain Layout
861 This mode is invoked with the the shortcut
869 or by the insertion of the command
877 \begin_layout Plain Layout
888 The text appears black in LyX and can therefore be distinguished from the
889 other formula parts that appear blue.
890 In the output mathematical text is set upright, in contrary to other formula
894 \begin_layout Subsection*
898 \begin_layout Standard
899 Most of the LaTeX-commands for math constructs have the following scheme:
902 \begin_layout Standard
918 \begin_layout Standard
919 A command starts always with a backslash
920 \begin_inset Quotes gld
930 \begin_inset Quotes grd
934 To omit optional arguments, also omit the associated brackets.
935 The braces around the required arguments are named in this document as
940 \begin_layout Plain Layout
945 \begin_layout Plain Layout
953 \begin_layout Plain Layout
964 \begin_layout Plain Layout
982 If you add in a formula a left brace to a command name, LyX creates automatical
984 In all other cases TeX-braces are created in formulas with the command
992 TeX-braces appear red in LyX, in contrary to normal braces that appear
994 In TeX-mode no command is needed to get TeX-braces.
995 TeX-braces don't appear in the output.
998 \begin_layout Standard
999 When commands without arguments, like commands for symbols are entered in
1000 TeX-mode, a space character must
1004 be behind the command to end it.
1005 This space doesn't appear in the output.
1006 When the space should appear in the output, the space must be followed
1007 by a protected space in normal text.
1010 \begin_layout Standard
1011 A protected space is inserted with
1018 \begin_layout Subsection*
1019 \begin_inset Newpage newpage
1025 \begin_layout Itemize
1030 \begin_layout Plain Layout
1031 This visible space character can be created with the command
1041 \begin_layout Plain Layout
1049 , inserted in TeX-mode.
1058 \begin_layout Plain Layout
1068 \begin_inset Space ~
1071 denotes a space character to be input.
1074 \begin_layout Itemize
1076 \begin_inset Formula $\to$
1079 denotes the usage of the corresponding arrow key on the keyboard.
1082 \begin_layout Subsection*
1086 \begin_layout Standard
1088 \begin_inset Float table
1094 \begin_layout Plain Layout
1096 \begin_inset Caption
1098 \begin_layout Plain Layout
1099 \begin_inset CommandInset label
1101 name "tab:Used-units"
1113 \begin_layout Plain Layout
1115 \begin_inset Tabular
1116 <lyxtabular version="3" rows="13" columns="2">
1118 <column alignment="center" valignment="top" width="0">
1119 <column alignment="center" valignment="top" width="0">
1121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1124 \begin_layout Plain Layout
1130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1133 \begin_layout Plain Layout
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1164 \begin_layout Plain Layout
1170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1173 \begin_layout Plain Layout
1181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1184 \begin_layout Plain Layout
1190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1193 \begin_layout Plain Layout
1195 \begin_inset Space \thinspace{}
1199 \begin_inset Space \thinspace{}
1209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1212 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1221 \begin_layout Plain Layout
1223 \begin_inset Space \thinspace{}
1227 \begin_inset Space \thinspace{}
1237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1240 \begin_layout Plain Layout
1246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1249 \begin_layout Plain Layout
1251 \begin_inset Space \thinspace{}
1255 \begin_inset Space \thinspace{}
1265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1268 \begin_layout Plain Layout
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1277 \begin_layout Plain Layout
1279 \begin_inset Space \thinspace{}
1283 \begin_inset Space \thinspace{}
1293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1296 \begin_layout Plain Layout
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1305 \begin_layout Plain Layout
1307 \begin_inset Space \thinspace{}
1311 \begin_inset Space \thinspace{}
1321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1324 \begin_layout Plain Layout
1330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1333 \begin_layout Plain Layout
1335 \begin_inset Space \thinspace{}
1339 \begin_inset Formula $\approx$
1343 \begin_inset Space \thinspace{}
1353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1356 \begin_layout Plain Layout
1362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1365 \begin_layout Plain Layout
1367 \begin_inset Space \thinspace{}
1371 \begin_inset Space \thinspace{}
1381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1384 \begin_layout Plain Layout
1390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1393 \begin_layout Plain Layout
1397 \begin_inset Quotes eld
1403 \begin_inset Quotes erd
1413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1416 \begin_layout Plain Layout
1422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1425 \begin_layout Plain Layout
1427 \begin_inset Quotes eld
1435 \begin_inset Quotes erd
1445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1448 \begin_layout Plain Layout
1454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1457 \begin_layout Plain Layout
1459 \begin_inset Space \thinspace{}
1463 \begin_inset Formula $\nicefrac{1}{18}$
1467 \begin_inset Space \thinspace{}
1488 \begin_layout Standard
1489 \begin_inset Newpage newpage
1495 \begin_layout Section
1499 \begin_layout Subsection
1504 \begin_layout Plain Layout
1514 \begin_layout Plain Layout
1524 \begin_layout Plain Layout
1529 \begin_layout Plain Layout
1540 \begin_layout Plain Layout
1556 \begin_layout Plain Layout
1561 \begin_layout Plain Layout
1572 \begin_layout Plain Layout
1587 \begin_layout Standard
1588 Indices are created with an underscore
1589 \begin_inset Quotes eld
1593 \begin_inset Quotes erd
1596 or via the math toolbar button
1597 \begin_inset Graphics
1598 filename ../images/math-subscript.png
1603 , exponents with a caret
1604 \begin_inset Quotes eld
1608 \begin_inset Quotes erd
1611 or via the math toolbar button
1612 \begin_inset Graphics
1613 filename ../images/math-superscript.png
1621 \begin_layout Standard
1623 \begin_inset Tabular
1624 <lyxtabular version="3" rows="4" columns="2">
1626 <column alignment="center" valignment="top" width="0pt">
1627 <column alignment="center" valignment="top" width="0pt">
1629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1632 \begin_layout Plain Layout
1638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1641 \begin_layout Plain Layout
1643 \begin_inset Note Note
1646 \begin_layout Plain Layout
1653 is only used as spacer.
1665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1668 \begin_layout Plain Layout
1674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1677 \begin_layout Plain Layout
1678 \begin_inset Formula $B_{V}$
1688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1691 \begin_layout Plain Layout
1697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1700 \begin_layout Plain Layout
1701 \begin_inset Formula $\raisebox {5mm}{}B^{V}$
1711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1714 \begin_layout Plain Layout
1719 \begin_layout Plain Layout
1733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1736 \begin_layout Plain Layout
1737 \begin_inset Formula $\raisebox {5mm}{}B^{A}$
1753 \begin_layout Standard
1754 As the caret is in some languages an accent, vowels will be accentuated
1755 in this case and not set as exponents
1759 \begin_layout Plain Layout
1760 Depending on the used keyboard settings this can also happen for other character
1767 To get in this case exponents, press
1771 after the caret as in the last example.
1774 \begin_layout Subsection
1776 \begin_inset CommandInset label
1778 name "sub:Fractions"
1786 \begin_layout Plain Layout
1795 \begin_layout Standard
1796 Fractions are generated with the command
1806 \begin_layout Plain Layout
1814 or via the math toolbar button
1815 \begin_inset Graphics
1816 filename ../images/math/frac.png
1822 The font size is adjusted automatically, depending on whether the fraction
1823 is in an inline or display style formula.
1824 With the math toolbar button
1825 \begin_inset Graphics
1826 filename ../images/math/frac-square.png
1831 you can select different fraction types.
1834 \begin_layout Standard
1843 \begin_layout Plain Layout
1853 a fraction can be created that has in any case the size of a display style
1863 \begin_layout Plain Layout
1873 the fraction appears always with the size of an inline formula.
1877 \begin_layout Standard
1878 A line with the fraction
1879 \begin_inset Formula $\frac{1}{2}$
1882 that was created with the command
1891 \begin_layout Standard
1892 A line with the fraction
1893 \begin_inset Formula $\dfrac{1}{2}$
1896 that was created with the command
1905 \begin_layout Standard
1907 \begin_inset Tabular
1908 <lyxtabular version="3" rows="4" columns="2">
1910 <column alignment="center" valignment="top" width="0pt">
1911 <column alignment="center" valignment="top" width="0pt">
1913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1916 \begin_layout Plain Layout
1922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1925 \begin_layout Plain Layout
1927 \begin_inset Note Note
1930 \begin_layout Plain Layout
1937 is only used as spacer.
1949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1952 \begin_layout Plain Layout
1959 \begin_layout Plain Layout
1969 \begin_inset Formula $\downarrow$
1977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1980 \begin_layout Plain Layout
1981 \begin_inset Formula $\raisebox {4.5mm}{}\frac{A}{B}\raisebox {-2.5mm}{}$
1991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1994 \begin_layout Plain Layout
2001 \begin_layout Plain Layout
2011 \begin_inset Formula $\downarrow$
2019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2022 \begin_layout Plain Layout
2023 \begin_inset Formula $\raisebox {7mm}{}\dfrac{A}{B}\raisebox {-4mm}{}$
2033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2036 \begin_layout Plain Layout
2043 \begin_layout Plain Layout
2056 \begin_layout Plain Layout
2071 \begin_layout Plain Layout
2081 \begin_inset Formula $\downarrow$
2085 \begin_inset Formula $\downarrow\downarrow$
2093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2096 \begin_layout Plain Layout
2097 \begin_inset Formula $\raisebox {8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox {-4mm}{}$
2113 \begin_layout Standard
2114 \begin_inset VSpace bigskip
2118 \begin_inset Newpage newpage
2121 For nested fractions the command
2131 \begin_layout Plain Layout
2141 \begin_inset VSpace -3mm
2147 \begin_layout Standard
2148 \begin_inset Formula \begin{align*}
2149 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2150 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac {A}{B+\cfrac {C+\cfrac {E}{F}}{D}}\end{align*}
2157 \begin_layout Standard
2158 The command for the example above is:
2161 \begin_layout Standard
2167 \begin_inset Formula $\to$
2177 \begin_inset Formula $\to$
2183 \begin_inset Formula $\to\to$
2191 \begin_layout Standard
2192 \begin_inset VSpace medskip
2198 \begin_layout Standard
2205 sets the fraction always in the size of a displayed formula, also when
2206 it is part of another fraction.
2213 has the following command scheme:
2216 \begin_layout Standard
2221 cfrac[numerator position]{numerator}{denominator}
2224 \begin_layout Standard
2225 The numerator position can be
2238 l or r aligns the numerator to the left or right, resp.
2239 \begin_inset Space ~
2242 with the fraction stroke.
2247 or no position is given, the numerator appears centered.
2248 These fractions demonstrate the different alignments:
2249 \begin_inset Newline newline
2255 \begin_inset Formula $\cfrac [l]{A}{B+C}$
2259 \begin_inset Formula $\cfrac {A}{B+C}$
2263 \begin_inset Formula $\cfrac [r]{A}{B+C}$
2269 \begin_layout Standard
2270 \begin_inset VSpace medskip
2273 It is often advantageous to combine
2286 \begin_inset Formula \[
2287 \cfrac {A}{B+\cfrac {C+\frac{E}{F}}{D}}\]
2294 \begin_layout Standard
2295 For inline fractions with a sloped fraction stroke you can use the command
2304 \begin_layout Plain Layout
2315 \begin_inset Formula $\nicefrac{5}{31}$
2321 \begin_layout Standard
2322 How to define own fractions where the fraction stroke can be changed, is
2324 \begin_inset CommandInset ref
2326 reference "sub:Self-defined-Fractions"
2333 \begin_layout Subsection
2338 \begin_layout Plain Layout
2347 \begin_layout Standard
2348 Square roots are created with
2358 \begin_layout Plain Layout
2366 or the math toolbar button
2367 \begin_inset Graphics
2368 filename ../images/math/sqrt.png
2373 , all other roots with the command
2383 \begin_layout Plain Layout
2391 or with the math toolbar button
2392 \begin_inset Graphics
2393 filename ../images/math/root.png
2401 \begin_layout Standard
2403 \begin_inset Tabular
2404 <lyxtabular version="3" rows="3" columns="2">
2406 <column alignment="center" valignment="top" width="0pt">
2407 <column alignment="center" valignment="top" width="0pt">
2409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2412 \begin_layout Plain Layout
2418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2421 \begin_layout Plain Layout
2423 \begin_inset Note Note
2426 \begin_layout Plain Layout
2433 is only used as spacer.
2445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2448 \begin_layout Plain Layout
2455 \begin_layout Plain Layout
2469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2472 \begin_layout Plain Layout
2473 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt{A-B}$
2483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2486 \begin_layout Plain Layout
2493 \begin_layout Plain Layout
2503 \begin_inset Formula $\downarrow$
2511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2514 \begin_layout Plain Layout
2515 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt[3]{A-B}$
2531 \begin_layout Standard
2532 A square root can also be created with
2538 when the root index field is left empty.
2541 \begin_layout Standard
2542 With certain indices the distance to the root is too small, like in this
2544 \begin_inset Formula $\sqrt[\beta]{B}$
2548 \begin_inset Newline newline
2552 \begin_inset Formula $\beta$
2556 To avoid this, the commands
2566 \begin_layout Plain Layout
2584 \begin_layout Plain Layout
2592 are used with the following scheme:
2595 \begin_layout Standard
2609 \begin_layout Standard
2610 Distance is the number of Big Points (unit bp;
2611 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2614 ), that the index should be moved to the left or top, resp..
2615 The commands are written to the index.
2616 This way the command
2617 \begin_inset Newline newline
2627 \begin_inset Formula $\to$
2633 \begin_inset Formula $\to$
2642 \begin_layout Plain Layout
2652 \begin_inset Formula $\to$
2656 \begin_inset Newline newline
2661 produces a correct typeset formula:
2662 \begin_inset Formula $\sqrt[\leftroot {-1}\uproot {2}\beta]{B}$
2668 \begin_layout Subsection
2669 Binomial coefficients
2673 \begin_layout Plain Layout
2674 Binomial coefficient s
2682 \begin_layout Standard
2683 Binomial coefficients are inserted with the command
2693 \begin_layout Plain Layout
2701 or with the submenu of the math toolbar button
2702 \begin_inset Graphics
2703 filename ../images/math/frac-square.png
2709 Analog to fractions (
2729 \begin_layout Plain Layout
2749 \begin_layout Plain Layout
2758 For other brackets around binomial coeficients there are the commands
2768 \begin_layout Plain Layout
2786 \begin_layout Plain Layout
2797 \begin_layout Standard
2799 \begin_inset Tabular
2800 <lyxtabular version="3" rows="6" columns="2">
2802 <column alignment="center" valignment="top" width="0pt">
2803 <column alignment="center" valignment="top" width="0pt">
2805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2808 \begin_layout Plain Layout
2814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2817 \begin_layout Plain Layout
2819 \begin_inset Note Note
2822 \begin_layout Plain Layout
2829 is only used as spacer.
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 $\raisebox {5mm}{}\binom{A}{B}\raisebox {-2.5mm}{}$
2883 <cell alignment="center" valignment="top" topline="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" leftline="true" rightline="true" usebox="none">
2914 \begin_layout Plain Layout
2915 \begin_inset Formula $\raisebox {5mm}{}\dbinom{A}{B}\raisebox {-2.5mm}{}$
2925 <cell alignment="center" valignment="top" topline="true" bottomline="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" bottomline="true" leftline="true" rightline="true" usebox="none">
2956 \begin_layout Plain Layout
2957 \begin_inset Formula $\raisebox {5mm}{}\tbinom{A}{B}\raisebox {-2.5mm}{}$
2967 <cell alignment="center" valignment="top" topline="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" leftline="true" rightline="true" usebox="none">
2998 \begin_layout Plain Layout
2999 \begin_inset Formula $\raisebox {5mm}{}{A \brack B}\raisebox {-2.5mm}{}$
3009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3012 \begin_layout Plain Layout
3019 \begin_layout Plain Layout
3029 \begin_inset Formula $\downarrow$
3037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3040 \begin_layout Plain Layout
3041 \begin_inset Formula $\raisebox {5mm}{}{A \brace B}\raisebox {-2.5mm}{}$
3057 \begin_layout Subsection
3058 Case differentiations
3062 \begin_layout Plain Layout
3063 Case differentiations
3071 \begin_layout Standard
3073 \begin_inset Tabular
3074 <lyxtabular version="3" rows="3" columns="2">
3076 <column alignment="center" valignment="top" width="0pt">
3077 <column alignment="center" valignment="top" width="0pt">
3079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3082 \begin_layout Plain Layout
3088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3091 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3102 \begin_layout Plain Layout
3109 \begin_layout Plain Layout
3119 \begin_inset Formula $\to$
3126 \begin_layout Plain Layout
3139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3142 \begin_layout Plain Layout
3143 \begin_inset Formula $\begin{cases}
3154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3157 \begin_layout Plain Layout
3164 \begin_layout Plain Layout
3178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3181 \begin_layout Plain Layout
3182 \begin_inset Formula $\begin{cases}
3183 A & \textrm{for }x>0\\
3184 B & \textrm{for }x=0\end{cases}$
3200 \begin_layout Standard
3207 or the usage of the math toolbar button
3208 \begin_inset Graphics
3209 filename ../images/math/cases.png
3214 you can create new lines with the shortcut
3218 or the table toolbar button
3219 \begin_inset Graphics
3220 filename ../images/tabular-feature_append-row.png
3228 \begin_layout Standard
3235 is also available via the menu
3237 Insert\SpecialChar \menuseparator
3238 Math\SpecialChar \menuseparator
3244 \begin_layout Subsection
3249 \begin_layout Plain Layout
3258 \begin_layout Standard
3269 \begin_layout Plain Layout
3277 every character can be displayed canceled.
3278 The characters are quasi accentuated by a slash.
3281 \begin_layout Standard
3283 \begin_inset Tabular
3284 <lyxtabular version="3" rows="4" columns="2">
3286 <column alignment="center" valignment="top" width="0pt">
3287 <column alignment="center" valignment="top" width="0pt">
3289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3292 \begin_layout Plain Layout
3298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3301 \begin_layout Plain Layout
3309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3312 \begin_layout Plain Layout
3320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3323 \begin_layout Plain Layout
3324 \begin_inset Formula $\not=$
3334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3337 \begin_layout Plain Layout
3347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3350 \begin_layout Plain Layout
3351 \begin_inset Formula $\not\le$
3361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3364 \begin_layout Plain Layout
3374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3377 \begin_layout Plain Layout
3378 \begin_inset Formula $\not\parallel$
3394 \begin_layout Standard
3395 The last example shows, that not all negations look good.
3396 Therefore there are for some negations special commands (see
3397 \begin_inset CommandInset ref
3399 reference "sub:Mathematical-Symbols"
3404 \begin_inset CommandInset ref
3406 reference "sec:Relations"
3413 \begin_layout Subsection
3415 \begin_inset CommandInset label
3417 name "sub:Placeholders"
3425 \begin_layout Plain Layout
3435 \begin_layout Plain Layout
3436 Chemical characters ! Isotopes
3445 \begin_layout Plain Layout
3450 \begin_layout Plain Layout
3461 \begin_layout Plain Layout
3476 \begin_layout Standard
3478 \begin_inset Space \thinspace{}
3482 \begin_inset Space ~
3489 \begin_layout Plain Layout
3490 More about chemical symbols is written in
3491 \begin_inset CommandInset ref
3493 reference "sub:Chemical-Symbols-and"
3502 the following problem occurs:
3505 \begin_layout Standard
3507 \begin_inset Tabular
3508 <lyxtabular version="3" rows="2" columns="2">
3510 <column alignment="center" valignment="top" width="0pt">
3511 <column alignment="center" valignment="top" width="0pt">
3513 <cell alignment="center" valignment="top" usebox="none">
3516 \begin_layout Plain Layout
3517 Indices created with sub- and superscripts:
3522 <cell alignment="center" valignment="top" usebox="none">
3525 \begin_layout Plain Layout
3526 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox {-3mm}{}$
3536 <cell alignment="center" valignment="top" usebox="none">
3539 \begin_layout Plain Layout
3545 <cell alignment="center" valignment="top" usebox="none">
3548 \begin_layout Plain Layout
3549 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3563 \begin_inset Note Note
3566 \begin_layout Plain Layout
3573 is only used as spacer.
3581 \begin_layout Standard
3582 The shorter index is by default placed below or above the first character
3583 of the longer index.
3584 To avoid this there is the command
3594 \begin_layout Plain Layout
3602 or the math toolbar button
3603 \begin_inset Space \thinspace{}
3610 \begin_layout Plain Layout
3611 can be found in the submenu of the toolbar button
3612 \begin_inset Graphics
3613 filename ../images/math/space.png
3624 \begin_inset Graphics
3625 filename ../images/math/phantom.png
3630 that creates one or more phantom characters.
3637 a small blue box appears that is superposed with two red arrows.
3638 The arrows indicate that the complete width and height of the box content
3639 will be created as placeholder.
3640 Phantom characters are accordingly placeholders with the size of the characters.
3643 \begin_layout Standard
3645 \begin_inset Tabular
3646 <lyxtabular version="3" rows="4" columns="2">
3648 <column alignment="center" valignment="top" width="0">
3649 <column alignment="center" valignment="top" width="0">
3651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3654 \begin_layout Plain Layout
3660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3663 \begin_layout Plain Layout
3665 \begin_inset Note Note
3668 \begin_layout Plain Layout
3675 is only used as spacer.
3687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3690 \begin_layout Plain Layout
3695 \begin_layout Plain Layout
3710 \begin_layout Plain Layout
3720 \begin_inset Formula $\to$
3727 \begin_layout Plain Layout
3741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3744 \begin_layout Plain Layout
3745 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox {-2.5mm}{}$
3755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3758 \begin_layout Plain Layout
3763 \begin_layout Plain Layout
3778 \begin_layout Plain Layout
3788 \begin_inset Formula $\to$
3795 \begin_layout Plain Layout
3809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3812 \begin_layout Plain Layout
3813 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox {-2.5mm}{}$
3823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3826 \begin_layout Plain Layout
3833 \begin_layout Plain Layout
3848 \begin_layout Plain Layout
3858 \begin_inset Formula $\to$
3865 \begin_layout Plain Layout
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3882 \begin_layout Plain Layout
3883 \begin_inset Formula $\raisebox {4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox {-2.5mm}{}$
3899 \begin_layout Standard
3900 Furthermore there are the commands
3910 \begin_layout Plain Layout
3919 \begin_inset Space ~
3923 \begin_inset Graphics
3924 filename ../images/math/vphantom.png
3939 \begin_layout Plain Layout
3948 \begin_inset Space ~
3952 \begin_inset Graphics
3953 filename ../images/math/hphantom.png
3965 creates only space for the maximal height of the characters in the box
3966 but not for its width.
3973 creates only space for the width of the box content.
3974 Therefore the boxes of both commands have only one red arrow.
3977 \begin_layout Standard
3988 \begin_layout Plain Layout
4003 space for the height of the integral sign,
4007 \begin_layout Plain Layout
4014 creates an integral sign, see
4015 \begin_inset CommandInset ref
4017 reference "sub:Big-Operators"
4026 because this is the larger character.
4027 An example application is in
4028 \begin_inset CommandInset ref
4030 reference "sub:Multiline-Brackets"
4037 \begin_layout Subsection
4042 \begin_layout Plain Layout
4052 \begin_layout Plain Layout
4053 Formula ! underlined
4061 \begin_layout Standard
4063 \begin_inset Tabular
4064 <lyxtabular version="3" rows="4" columns="2">
4066 <column alignment="center" valignment="top" width="0pt">
4067 <column alignment="center" valignment="top" width="0pt">
4069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4072 \begin_layout Plain Layout
4078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4081 \begin_layout Plain Layout
4083 \begin_inset Note Note
4086 \begin_layout Plain Layout
4093 is only used as spacer.
4105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4108 \begin_layout Plain Layout
4115 \begin_layout Plain Layout
4128 \begin_layout Plain Layout
4141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4144 \begin_layout Plain Layout
4145 \begin_inset Formula $\raisebox {5mm}{}\overline{A+B}$
4155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4158 \begin_layout Plain Layout
4165 \begin_layout Plain Layout
4178 \begin_layout Plain Layout
4191 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4194 \begin_layout Plain Layout
4195 \begin_inset Formula $\underline{A+B}\raisebox {-2.5mm}{}$
4205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4208 \begin_layout Plain Layout
4215 \begin_layout Plain Layout
4230 \begin_layout Plain Layout
4244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4247 \begin_layout Plain Layout
4248 \begin_inset Formula $\raisebox {5mm}{}\overline{\underline{A+B}}\raisebox {-2.5mm}{}$
4264 \begin_layout Standard
4265 In the last example it doesn't matter if first
4280 \begin_layout Standard
4281 To double underline e.
4282 \begin_inset Space \thinspace{}
4295 \begin_layout Standard
4296 It is possible to place up to 6 lines above or below characters.
4299 \begin_layout Subsection
4304 \begin_layout Plain Layout
4313 \begin_layout Standard
4314 There are different types of ellipses available.
4318 \begin_layout Plain Layout
4319 In the math toolbar in the submenu of the button
4320 \begin_inset Graphics
4321 filename ../images/math/ldots.png
4331 For listings dots at the baseline are used (
4341 \begin_layout Plain Layout
4349 ), while for operations dots are needed that are on the same height as the
4360 \begin_layout Plain Layout
4369 When using the command
4379 \begin_layout Plain Layout
4387 , LaTeX decides on the basis of the next character what type is used.
4390 \begin_layout Standard
4392 \begin_inset Tabular
4393 <lyxtabular version="3" rows="8" columns="2">
4395 <column alignment="center" valignment="top" width="0pt">
4396 <column alignment="center" valignment="top" width="0pt">
4398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4401 \begin_layout Plain Layout
4407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4410 \begin_layout Plain Layout
4418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4421 \begin_layout Plain Layout
4426 \begin_layout Plain Layout
4441 \begin_layout Plain Layout
4455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4458 \begin_layout Plain Layout
4459 \begin_inset Formula $A_{1},\dots,A_{n}$
4469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4472 \begin_layout Plain Layout
4477 \begin_layout Plain Layout
4492 \begin_layout Plain Layout
4506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4509 \begin_layout Plain Layout
4510 \begin_inset Formula $A_{1}+\dots+A_{n}$
4520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4523 \begin_layout Plain Layout
4528 \begin_layout Plain Layout
4543 \begin_layout Plain Layout
4557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4560 \begin_layout Plain Layout
4561 \begin_inset Formula $A_{1},\ldots,A_{n}$
4571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4574 \begin_layout Plain Layout
4579 \begin_layout Plain Layout
4594 \begin_layout Plain Layout
4608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4611 \begin_layout Plain Layout
4612 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4625 \begin_layout Plain Layout
4633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4636 \begin_layout Plain Layout
4637 \begin_inset Formula $\vdots$
4647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4650 \begin_layout Plain Layout
4658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4661 \begin_layout Plain Layout
4662 \begin_inset Formula $\ddots$
4672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4675 \begin_layout Plain Layout
4677 \begin_inset Space \thinspace{}
4680 matrix with the different dots
4685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4688 \begin_layout Plain Layout
4689 \begin_inset Formula $\begin{array}{ccc}
4690 A_{11} & \cdots & A_{1m}\\
4691 \vdots & \ddots & \vdots\\
4692 A_{n1} & \cdots & A_{nm}\end{array}$
4708 \begin_layout Standard
4709 The ellipses available in menu
4711 Insert\SpecialChar \menuseparator
4713 \begin_inset Space ~
4727 \begin_layout Standard
4728 \begin_inset VSpace medskip
4731 Specially for matrices there are ellipses that span over several columns.
4732 They are created with the command
4742 \begin_layout Plain Layout
4750 , that has the following scheme:
4753 \begin_layout Standard
4758 hdotsfor[distance]{number of columns}
4761 \begin_layout Standard
4762 The number of columns specifies how many columns should be spanned.
4763 Distance is a factor for the distance between the dots.
4766 \begin_layout Standard
4767 In the following matrix the command
4773 was inserted in the first box of the second line, to get an ellipsis with
4774 a dot distance twice as long as with the command
4781 \begin_inset Formula \[
4782 \left(\begin{array}{cccc}
4785 q & w & e & r\end{array}\right)\]
4789 Note that the matrix fields that should be spanned must be empty, otherwise
4790 you get LaTeX-errors.
4793 \begin_layout Standard
4794 \begin_inset VSpace bigskip
4797 Furthermore you can fill with the command
4807 \begin_layout Plain Layout
4815 the rest of a line with dots.
4816 The effect of these commands is the same like with
4823 \begin_inset CommandInset ref
4825 reference "sub:Variable-Space"
4832 \begin_layout Standard
4833 For example the command
4841 \begin_layout Plain Layout
4855 \begin_layout Standard
4856 \begin_inset Formula $A\dotfill B$
4862 \begin_layout Standard
4869 there is for a line the command
4879 \begin_layout Plain Layout
4890 \begin_layout Standard
4891 \begin_inset Formula $A\hrulefill B$
4897 \begin_layout Standard
4898 To use the commands for text, they have to be inserted in TeX-mode.
4901 \begin_layout Section
4903 \begin_inset CommandInset label
4913 \begin_layout Plain Layout
4922 \begin_layout Standard
4923 Matrices can be inserted via the math toolbar button
4924 \begin_inset Graphics
4925 filename ../images/dialog-show_mathmatrix.png
4932 Insert\SpecialChar \menuseparator
4933 Math\SpecialChar \menuseparator
4937 You will be asked for the number of matrix columns and rows, and the alignment.
4938 The vertical alignment is hereby only of importance for matrices in inline
4942 \begin_layout Standard
4943 The first matrix is top
4944 \begin_inset Formula $\begin{array}[t]{cccc}
4947 C & F & I & L\end{array}$
4951 \begin_inset Formula $\begin{array}{cccc}
4954 C & F & I & L\end{array}$
4957 , and the third bottom
4958 \begin_inset Formula $\begin{array}[b]{cccc}
4961 C & F & I & L\end{array}$
4967 \begin_layout Standard
4968 The horizontal alignment specifies how the column entries should be aligned.
4969 It is set by entering a letter for every column.
4974 denotes left aligned,
4983 To create for example a 4
4988 \begin_inset Space ~
4991 matrix where the first column is left aligned, the second and third are
4992 centered, and the last one is right aligned, one enters for the horizontal
4998 Normally are in a matrix all columns centered, therefore the default is
4999 for every column is a
5006 \begin_layout Standard
5007 Horizontal alignment:
5010 \begin_layout Standard
5016 \begin_inset Formula $\begin{array}{lll}
5019 C & F & 10000\end{array}$
5027 \begin_inset Formula $\begin{array}{ccc}
5030 C & F & 10000\end{array}$
5038 \begin_inset Formula $\begin{array}{rrr}
5041 C & F & 10000\end{array}$
5047 \begin_layout Standard
5048 To add or delete rows and columns subsequently, the math toolbar buttons
5050 \begin_inset Graphics
5051 filename ../images/tabular-feature_append-row.png
5057 \begin_inset Graphics
5058 filename ../images/tabular-feature_delete-row.png
5064 \begin_inset Space \thinspace{}
5069 Edit\SpecialChar \menuseparator
5073 New rows can also be created with
5080 \begin_layout Standard
5081 \begin_inset VSpace bigskip
5084 Parentheses around a matrix can can either be created with the commands
5095 \begin_layout Plain Layout
5113 \begin_layout Plain Layout
5124 \begin_inset Space ~
5130 \begin_inset CommandInset ref
5132 reference "sub:Automatic-Bracket-Size"
5136 , or by using the following commands:
5137 \begin_inset VSpace medskip
5143 \begin_layout Standard
5144 \begin_inset Space \hfill{}
5148 \begin_inset Tabular
5149 <lyxtabular version="3" rows="4" columns="2">
5151 <column alignment="center" valignment="top" width="0">
5152 <column alignment="center" valignment="top" width="0">
5154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5157 \begin_layout Plain Layout
5163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5166 \begin_layout Plain Layout
5168 \begin_inset Note Note
5171 \begin_layout Plain Layout
5178 is only used as spacer.
5190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5193 \begin_layout Plain Layout
5200 \begin_layout Plain Layout
5214 \begin_inset Space \thinspace{}
5222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5225 \begin_layout Plain Layout
5226 \begin_inset Formula $\raisebox {7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5227 0 & \textrm{-}\mathrm{i}\\
5228 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox {-5.3mm}{}$
5238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5241 \begin_layout Plain Layout
5248 \begin_layout Plain Layout
5262 \begin_inset Space \thinspace{}
5270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5273 \begin_layout Plain Layout
5274 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5275 0 & \textrm{-}\mathrm{i}\\
5276 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox {-5.3mm}{}$
5286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5289 \begin_layout Plain Layout
5296 \begin_layout Plain Layout
5310 \begin_inset Space \thinspace{}
5318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5321 \begin_layout Plain Layout
5322 \begin_inset Formula $\raisebox {7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5323 0 & \textrm{-}\mathrm{i}\\
5324 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox {-5.3mm}{}$
5338 \begin_inset Space \hfill{}
5342 \begin_inset Tabular
5343 <lyxtabular version="3" rows="4" columns="2">
5345 <column alignment="center" valignment="top" width="0">
5346 <column alignment="center" valignment="top" width="0">
5348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5351 \begin_layout Plain Layout
5357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5360 \begin_layout Plain Layout
5368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5371 \begin_layout Plain Layout
5378 \begin_layout Plain Layout
5392 \begin_inset Space \thinspace{}
5400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5403 \begin_layout Plain Layout
5404 \begin_inset Formula $\raisebox {7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5405 0 & \textrm{-}\mathrm{i}\\
5406 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox {-5.3mm}{}$
5416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5419 \begin_layout Plain Layout
5426 \begin_layout Plain Layout
5440 \begin_inset Space \thinspace{}
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5451 \begin_layout Plain Layout
5452 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5453 0 & \textrm{-}\mathrm{i}\\
5454 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox {-5.3mm}{}$
5464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5467 \begin_layout Plain Layout
5474 \begin_layout Plain Layout
5488 \begin_inset Space \thinspace{}
5496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5499 \begin_layout Plain Layout
5500 \begin_inset Formula $\raisebox {7.5mm}{}\begin{matrix}\begin{array}{cc}
5501 0 & \textrm{-}\mathrm{i}\\
5502 \mathrm{i} & 0\end{array}\end{matrix}\raisebox {-5.3mm}{}$
5516 \begin_inset Space \hfill{}
5522 \begin_layout Standard
5523 \begin_inset VSpace medskip
5527 \begin_inset Space \thinspace{}
5531 \begin_inset Space ~
5540 is inserted, a blue box appears between two vertical lines where the matrix
5544 \begin_layout Standard
5545 \begin_inset VSpace bigskip
5548 As all multiline formulas are matrices, the length
5558 \begin_layout Plain Layout
5566 that is described in
5567 \begin_inset CommandInset ref
5569 reference "sub:Column-Separation"
5573 can also be used to change the column separation of matrices.
5576 \begin_layout Standard
5577 To change the row separation, the command
5587 \begin_layout Plain Layout
5596 It is used as follows:
5599 \begin_layout Standard
5606 arraystretch}{stretch factor}
5610 \begin_layout Plain Layout
5621 \begin_layout Standard
5628 assigns the stretch factor to the predefined command
5636 \begin_inset Space \thinspace{}
5640 \begin_inset Space ~
5643 the row separation, use the factor 2.
5644 This is then used for all following matrices.
5645 To go back to the original separation, assign the factor 1 to
5654 \begin_layout Standard
5655 To set matrices into a text line, the command
5665 \begin_layout Plain Layout
5674 When it is inserted a blue box with two dashed lines appears.
5675 In this box the matrix is inserted.
5678 \begin_layout Standard
5680 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5681 C & D\end{smallmatrix}\right)$
5687 \begin_layout Section
5688 Brackets and Delimiters
5692 \begin_layout Plain Layout
5702 \begin_layout Plain Layout
5711 \begin_layout Subsection
5712 Vertical Brackets and Delimiters
5716 \begin_layout Plain Layout
5725 \begin_layout Standard
5726 \begin_inset Space \hfill{}
5730 \begin_inset Tabular
5731 <lyxtabular version="3" rows="9" columns="2">
5733 <column alignment="center" valignment="top" width="0pt">
5734 <column alignment="center" valignment="top" width="0pt">
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5739 \begin_layout Plain Layout
5745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5748 \begin_layout Plain Layout
5756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5759 \begin_layout Plain Layout
5765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5768 \begin_layout Plain Layout
5769 \begin_inset Formula $($
5779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5782 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\{$
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
5836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5839 \begin_layout Plain Layout
5840 \begin_inset Formula $\langle$
5850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5853 \begin_layout Plain Layout
5861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5864 \begin_layout Plain Layout
5865 \begin_inset Formula $\lceil$
5875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5878 \begin_layout Plain Layout
5886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5889 \begin_layout Plain Layout
5890 \begin_inset Formula $\lfloor$
5900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5903 \begin_layout Plain Layout
5909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5912 \begin_layout Plain Layout
5913 \begin_inset Formula $/$
5923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5926 \begin_layout Plain Layout
5932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5935 \begin_layout Plain Layout
5936 \begin_inset Formula $|$
5950 \begin_inset Space \hfill{}
5954 \begin_inset Tabular
5955 <lyxtabular version="3" rows="9" columns="2">
5957 <column alignment="center" valignment="top" width="0pt">
5958 <column alignment="center" valignment="top" width="0pt">
5960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5963 \begin_layout Plain Layout
5969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5972 \begin_layout Plain Layout
5980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5983 \begin_layout Plain Layout
5989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5992 \begin_layout Plain Layout
5993 \begin_inset Formula $)$
6003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6006 \begin_layout Plain Layout
6012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6015 \begin_layout Plain Layout
6016 \begin_inset Formula $\}$
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
6060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6063 \begin_layout Plain Layout
6064 \begin_inset Formula $\rangle$
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6077 \begin_layout Plain Layout
6085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6088 \begin_layout Plain Layout
6089 \begin_inset Formula $\rceil$
6099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6102 \begin_layout Plain Layout
6110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6113 \begin_layout Plain Layout
6114 \begin_inset Formula $\rfloor$
6124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6127 \begin_layout Plain Layout
6137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6140 \begin_layout Plain Layout
6141 \begin_inset Formula $\backslash$
6151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6154 \begin_layout Plain Layout
6162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6165 \begin_layout Plain Layout
6166 \begin_inset Formula $\|$
6180 \begin_inset Space \hfill{}
6186 \begin_layout Standard
6189 \begin_inset Note Greyedout
6192 \begin_layout Plain Layout
6197 In TeX-mode the command
6207 \begin_layout Plain Layout
6215 must be used for the backslash, because the command
6223 produces there a line break.
6231 \begin_layout Standard
6232 For all characters listed above the size can be adjusted with the commands
6233 described in the following two subsections.
6234 When using these commands, the characters < and > can directly be used
6235 instead of the commands
6250 \begin_layout Subsubsection
6252 \begin_inset CommandInset label
6254 name "sub:Manual-Bracket-Size"
6262 \begin_layout Plain Layout
6263 Bracket size ! manual
6271 \begin_layout Standard
6272 The bracket size can be specified manually by the LaTeX-commands
6282 \begin_layout Plain Layout
6315 denotes the smallest and
6321 the largest bracket size.
6324 \begin_layout Standard
6325 These commands are used to emphasize levels of brackets:
6328 \begin_layout Standard
6330 \begin_inset Tabular
6331 <lyxtabular version="3" rows="2" columns="2">
6333 <column alignment="center" valignment="top" width="0pt">
6334 <column alignment="center" valignment="top" width="0pt">
6336 <cell alignment="center" valignment="top" usebox="none">
6339 \begin_layout Plain Layout
6340 all brackets in the same size:
6345 <cell alignment="center" valignment="top" usebox="none">
6348 \begin_layout Plain Layout
6349 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox {-4mm}{}$
6359 <cell alignment="center" valignment="top" usebox="none">
6362 \begin_layout Plain Layout
6368 <cell alignment="center" valignment="top" usebox="none">
6371 \begin_layout Plain Layout
6372 \begin_inset Formula $\Big ((A+B)(A-B)\Big )^{C}$
6386 \begin_inset Note Note
6389 \begin_layout Plain Layout
6396 is only used as spacer.
6404 \begin_layout Standard
6405 For the second formula the command
6415 \begin_layout Plain Layout
6429 \begin_layout Standard
6430 Here is an overview about all bracket sizes:
6433 \begin_layout Standard
6453 \begin_layout Plain Layout
6470 \begin_layout Plain Layout
6483 \begin_layout Plain Layout
6499 \begin_layout Standard
6501 \begin_inset Formula $\Bigg (\exp\bigg <\Big [\big \{\ln(3x)\big \}^{2}\sin(x)\Big ]^{A}\bigg >\Bigg )^{0,5}$
6507 \begin_layout Standard
6508 \begin_inset Newpage newpage
6517 -commands there is the variant
6527 \begin_layout Plain Layout
6535 that adds a bit more space between the bracket and its content, and the
6552 \begin_layout Plain Layout
6562 , that don't add additional space.
6567 at the end of the command
6573 is for a left bracket; for a right bracket this will be replaced by an
6579 A left or right bracket can each be an opening or closing bracket.
6582 \begin_layout Standard
6583 In the following table is a comparison of the variants:
6586 \begin_layout Standard
6588 \begin_inset Tabular
6589 <lyxtabular version="3" rows="5" columns="2">
6591 <column alignment="center" valignment="middle" width="0">
6592 <column alignment="center" valignment="middle" width="0">
6594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6597 \begin_layout Plain Layout
6603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6606 \begin_layout Plain Layout
6608 \begin_inset Note Note
6611 \begin_layout Plain Layout
6618 is only used as spacer.
6630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6633 \begin_layout Plain Layout
6648 \begin_layout Plain Layout
6666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6669 \begin_layout Plain Layout
6670 \begin_inset Formula $\raisebox {5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox {-3.25mm}{}$
6680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6683 \begin_layout Plain Layout
6698 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6719 \begin_layout Plain Layout
6720 \begin_inset Formula $\raisebox {5.5mm}{}\Big (\big (\ln(3x)\big )^{2}\Big )\raisebox {-3.25mm}{}$
6730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6733 \begin_layout Plain Layout
6748 \begin_layout Plain Layout
6766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6769 \begin_layout Plain Layout
6770 \begin_inset Formula $\raisebox {5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox {-3.25mm}{}$
6780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6783 \begin_layout Plain Layout
6795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6798 \begin_layout Plain Layout
6799 \begin_inset Formula $\raisebox {4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox {-2mm}{}$
6815 \begin_layout Subsubsection
6816 Automatic Bracket Size
6817 \begin_inset CommandInset label
6819 name "sub:Automatic-Bracket-Size"
6827 \begin_layout Plain Layout
6828 Bracket size ! automatic
6836 \begin_layout Standard
6837 Brackets with variable size can be inserted with the commands
6847 \begin_layout Plain Layout
6865 \begin_layout Plain Layout
6873 or via the math toolbar button
6874 \begin_inset Graphics
6875 filename ../images/dialog-show_mathdelimiter.png
6893 the wanted bracket must be inserted.
6894 The bracket size will then automatically be calculated for the output.
6897 \begin_layout Standard
6899 normal bracket: The command
6909 \begin_layout Plain Layout
6919 \begin_inset Formula $\downarrow$
6926 \begin_layout Plain Layout
6938 \begin_inset Formula \[
6946 \begin_layout Standard
6948 multiline bracket: The command
6960 \begin_layout Plain Layout
6970 \begin_inset Formula $\downarrow$
6977 \begin_layout Plain Layout
6991 \begin_inset Formula \[
6992 \ln\left(\frac{A}{C}\right)\]
6999 \begin_layout Standard
7015 \begin_inset Space ~
7021 This has the advantage that you can see in LyX immediately the real bracket
7022 size and that the matching right bracket will be created too.
7023 \begin_inset Newline newline
7026 The command for the last example would then be:
7040 \begin_layout Plain Layout
7050 \begin_inset Formula $\downarrow$
7056 \begin_layout Standard
7057 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7058 For example the command
7068 \begin_layout Plain Layout
7078 \begin_inset Formula $\downarrow$
7085 \begin_layout Plain Layout
7101 \begin_inset Formula \[
7102 \left.\frac{A}{B}\right\} \]
7120 will be converted by LyX to brackets in the right size when the document
7121 is reloaded and an omitted bracket will appear as dashed line.
7124 \begin_layout Standard
7125 \begin_inset VSpace bigskip
7128 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7139 \begin_layout Plain Layout
7147 is additionally available for all brackets and limits.
7148 With this command the height of the following character is adapted to the
7149 one of the surrounding brackets, what is e.
7150 \begin_inset Space \thinspace{}
7154 \begin_inset Space ~
7157 needed for physical vectors:
7158 \begin_inset Formula \[
7159 \left\langle \phi\:\middle |\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7163 For physical vectors there is a special LaTeX-package, described in
7164 \begin_inset CommandInset ref
7166 reference "sub:Physical-Vectors"
7173 \begin_layout Subsection
7178 \begin_layout Plain Layout
7179 Brackets ! horizontal
7187 \begin_layout Standard
7189 \begin_inset Tabular
7190 <lyxtabular version="3" rows="4" columns="2">
7192 <column alignment="center" valignment="top" width="0pt">
7193 <column alignment="center" valignment="top" width="0pt">
7195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7198 \begin_layout Plain Layout
7200 \begin_inset Note Note
7203 \begin_layout Plain Layout
7210 is only used as spacer.
7220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7223 \begin_layout Plain Layout
7231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7234 \begin_layout Plain Layout
7238 \begin_layout Plain Layout
7253 \begin_layout Plain Layout
7266 \begin_layout Plain Layout
7279 \begin_layout Plain Layout
7292 \begin_layout Plain Layout
7303 \begin_layout Plain Layout
7316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7319 \begin_layout Plain Layout
7320 \begin_inset Formula $\overbrace{A+B}^{3}$
7330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7333 \begin_layout Plain Layout
7337 \begin_layout Plain Layout
7352 \begin_layout Plain Layout
7365 \begin_layout Plain Layout
7378 \begin_layout Plain Layout
7389 \begin_layout Plain Layout
7402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7405 \begin_layout Plain Layout
7406 \begin_inset Formula $\underbrace{A+B}_{5}$
7416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7419 \begin_layout Plain Layout
7426 \begin_layout Plain Layout
7441 \begin_layout Plain Layout
7454 \begin_layout Plain Layout
7467 \begin_layout Plain Layout
7480 \begin_layout Plain Layout
7493 \begin_layout Plain Layout
7506 \begin_layout Plain Layout
7520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7523 \begin_layout Plain Layout
7524 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7540 \begin_layout Standard
7541 In the last example it doesn't matter if
7553 is inserted at first.
7556 \begin_layout Standard
7557 \begin_inset VSpace bigskip
7560 When brackets are needed that overlap each other, multiline formulas, as
7562 \begin_inset CommandInset ref
7564 reference "sec:Multiline-Formulas"
7569 \begin_inset Formula \begin{eqnarray*}
7570 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7571 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7575 In the first row the formula is inserted together with the first brace.
7576 It is hereby important that the space command
7580 \begin_layout Plain Layout
7581 Space commands are explained in
7582 \begin_inset CommandInset ref
7584 reference "sub:Predefined-Space"
7599 is inserted before the first
7600 \begin_inset Formula $d$
7603 , because the brace that ends behind the
7604 \begin_inset Formula $q$
7607 prevents that the following
7608 \begin_inset Quotes eld
7612 \begin_inset Quotes erd
7615 is surrounded by space.
7619 \begin_layout Plain Layout
7620 because a bracket is not handled as character, see
7621 \begin_inset CommandInset ref
7623 reference "sub:Binary-Operators"
7632 In the second row the second brace is inserted.
7633 As it should begin before the
7634 \begin_inset Formula $b$
7649 \begin_layout Plain Layout
7657 \begin_inset CommandInset ref
7659 reference "sub:Placeholders"
7668 This space is needed because the
7669 \begin_inset Quotes eld
7673 \begin_inset Quotes erd
7676 is also surrounded by space in the formula.
7677 The brace is placed under the command
7686 \begin_layout Standard
7687 It gets more complicated when brackets overlap each other, like in the following
7692 \begin_layout Plain Layout
7704 \begin_inset Formula \begin{eqnarray*}
7705 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7706 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7714 \begin_layout Plain Layout
7725 The first formula row is the same as the second row of the previous example,
7726 with the difference that the brace is above.
7727 The second row contains the formula together with the second brace.
7728 To avoid that there is space between the upper brace in the first row and
7729 the formula, the row spacing need to be reduced.
7730 This is not easily possible due to a bug in LyX
7734 \begin_layout Plain Layout
7735 \begin_inset CommandInset href
7737 name "LyX-bug #1505"
7738 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7748 As solution for the problem, the global formula row separation
7758 \begin_layout Plain Layout
7766 must be changed to -6
7767 \begin_inset Space \thinspace{}
7770 pt before the formula with the command
7785 is set back after the formula to the standard value of 3
7786 \begin_inset Space \thinspace{}
7789 pt using the same command.
7790 More about the row separation in formulas is explained in
7791 \begin_inset CommandInset ref
7793 reference "sub:Line-Separation"
7800 \begin_layout Section
7805 \begin_layout Plain Layout
7814 \begin_layout Standard
7815 Arrows can be inserted via the math toolbar button
7816 \begin_inset Graphics
7817 filename ../images/math/leftarrow.png
7822 or the commands listed in the following subsections.
7825 \begin_layout Subsection
7830 \begin_layout Plain Layout
7839 \begin_layout Standard
7840 \begin_inset Space \hfill{}
7844 \begin_inset Tabular
7845 <lyxtabular version="3" rows="8" columns="2">
7847 <column alignment="center" valignment="top" width="0pt">
7848 <column alignment="center" valignment="top" width="0pt">
7850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7853 \begin_layout Plain Layout
7859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7862 \begin_layout Plain Layout
7870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7873 \begin_layout Plain Layout
7881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7884 \begin_layout Plain Layout
7885 \begin_inset Formula $\gets$
7895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7898 \begin_layout Plain Layout
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7909 \begin_layout Plain Layout
7910 \begin_inset Formula $\Leftarrow$
7920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7923 \begin_layout Plain Layout
7931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7934 \begin_layout Plain Layout
7935 \begin_inset Formula $\longleftarrow$
7945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7948 \begin_layout Plain Layout
7956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7959 \begin_layout Plain Layout
7960 \begin_inset Formula $\Longleftarrow$
7970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7984 \begin_layout Plain Layout
7985 \begin_inset Formula $\leftharpoonup$
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 $\leftharpoondown$
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 $\hookleftarrow$
8049 \begin_inset Space \hfill{}
8053 \begin_inset Tabular
8054 <lyxtabular version="3" rows="8" columns="2">
8056 <column alignment="center" valignment="top" width="0pt">
8057 <column alignment="center" valignment="top" width="0pt">
8059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8062 \begin_layout Plain Layout
8068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8082 \begin_layout Plain Layout
8090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8093 \begin_layout Plain Layout
8094 \begin_inset Formula $\to$
8104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8118 \begin_layout Plain Layout
8119 \begin_inset Formula $\Rightarrow$
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 $\longrightarrow$
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 $\Longrightarrow$
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 $\rightharpoonup$
8204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\rightharpoondown$
8229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8244 \begin_inset Formula $\hookrightarrow$
8258 \begin_inset Space \hfill{}
8264 \begin_layout Standard
8265 \begin_inset Space \hfill{}
8269 \begin_inset Tabular
8270 <lyxtabular version="3" rows="6" columns="2">
8272 <column alignment="center" valignment="top" width="0pt">
8273 <column alignment="center" valignment="top" width="0pt">
8275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8278 \begin_layout Plain Layout
8284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8287 \begin_layout Plain Layout
8295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8298 \begin_layout Plain Layout
8306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8309 \begin_layout Plain Layout
8310 \begin_inset Formula $\leftrightarrow$
8320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8323 \begin_layout Plain Layout
8331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8334 \begin_layout Plain Layout
8335 \begin_inset Formula $\Leftrightarrow$
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 $\longleftrightarrow$
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 $\Longleftrightarrow$
8395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8398 \begin_layout Plain Layout
8406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8409 \begin_layout Plain Layout
8410 \begin_inset Formula $\rightleftharpoons$
8424 \begin_inset Space \hspace{}
8429 \begin_inset Space \hfill{}
8433 \begin_inset Tabular
8434 <lyxtabular version="3" rows="5" columns="2">
8436 <column alignment="center" valignment="top" width="0pt">
8437 <column alignment="center" valignment="top" width="0pt">
8439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8442 \begin_layout Plain Layout
8448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8451 \begin_layout Plain Layout
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\mapsto$
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8498 \begin_layout Plain Layout
8499 \begin_inset Formula $\longmapsto$
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 $\leadsto$
8534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8537 \begin_layout Plain Layout
8545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Plain Layout
8549 \begin_inset Formula $\dasharrow$
8563 \begin_inset Space \hfill{}
8569 \begin_layout Standard
8570 \begin_inset VSpace medskip
8573 Arrows used as accent like e.
8574 \begin_inset Space \thinspace{}
8578 \begin_inset Space ~
8581 vector arrows are listed in
8582 \begin_inset CommandInset ref
8584 reference "sec:Accents"
8591 \begin_layout Standard
8592 \begin_inset VSpace bigskip
8595 Furthermore there are the labeled arrows
8599 \begin_layout Plain Layout
8615 \begin_layout Plain Layout
8633 \begin_layout Plain Layout
8637 \begin_inset VSpace 4mm
8646 When inserting one of these commands in a formula, an arrow with two blue
8647 boxes appear where the label can be inserted.
8648 The length of the arrow adapts to the label width.
8651 \begin_layout Standard
8653 \begin_inset Tabular
8654 <lyxtabular version="3" rows="3" columns="2">
8656 <column alignment="center" valignment="top" width="0pt">
8657 <column alignment="center" valignment="top" width="0pt">
8659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8662 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8673 \begin_inset Note Note
8676 \begin_layout Plain Layout
8683 is only used as spacer.
8695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8698 \begin_layout Plain Layout
8705 \begin_layout Plain Layout
8715 \begin_inset Formula $\downarrow$
8719 \begin_inset Formula $\to$
8727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8730 \begin_layout Plain Layout
8731 \begin_inset Formula $\raisebox {5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox {-4mm}{}$
8741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8744 \begin_layout Plain Layout
8751 \begin_layout Plain Layout
8761 \begin_inset Formula $\downarrow$
8765 \begin_inset Formula $\to$
8773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8776 \begin_layout Plain Layout
8777 \begin_inset Formula $\raisebox {5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox {-4mm}{}$
8793 \begin_layout Subsection
8794 Vertical and diagonal Arrows
8798 \begin_layout Plain Layout
8808 \begin_layout Plain Layout
8817 \begin_layout Standard
8818 \begin_inset Space \hfill{}
8822 \begin_inset Tabular
8823 <lyxtabular version="3" rows="7" columns="2">
8825 <column alignment="center" valignment="top" width="0pt">
8826 <column alignment="center" valignment="top" width="0pt">
8828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8831 \begin_layout Plain Layout
8837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8840 \begin_layout Plain Layout
8848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8851 \begin_layout Plain Layout
8859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8862 \begin_layout Plain Layout
8863 \begin_inset Formula $\uparrow$
8873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8876 \begin_layout Plain Layout
8884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8887 \begin_layout Plain Layout
8888 \begin_inset Formula $\Uparrow$
8898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8901 \begin_layout Plain Layout
8909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8912 \begin_layout Plain Layout
8913 \begin_inset Formula $\updownarrow$
8923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8926 \begin_layout Plain Layout
8934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8937 \begin_layout Plain Layout
8938 \begin_inset Formula $\Updownarrow$
8948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8951 \begin_layout Plain Layout
8959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8962 \begin_layout Plain Layout
8963 \begin_inset Formula $\Downarrow$
8973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8976 \begin_layout Plain Layout
8984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8987 \begin_layout Plain Layout
8988 \begin_inset Formula $\downarrow$
9002 \begin_inset Space \hfill{}
9006 \begin_inset Tabular
9007 <lyxtabular version="3" rows="5" columns="2">
9009 <column alignment="center" valignment="top" width="0pt">
9010 <column alignment="center" valignment="top" width="0pt">
9012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9015 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9035 \begin_layout Plain Layout
9043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9046 \begin_layout Plain Layout
9047 \begin_inset Formula $\nearrow$
9057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9060 \begin_layout Plain Layout
9068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9071 \begin_layout Plain Layout
9072 \begin_inset Formula $\searrow$
9082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9085 \begin_layout Plain Layout
9093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9096 \begin_layout Plain Layout
9097 \begin_inset Formula $\swarrow$
9107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9110 \begin_layout Plain Layout
9118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9121 \begin_layout Plain Layout
9122 \begin_inset Formula $\nwarrow$
9136 \begin_inset Space \hfill{}
9142 \begin_layout Standard
9143 \begin_inset VSpace medskip
9146 Vertical arrows can be used also as delimiter together with the commands
9148 \begin_inset CommandInset ref
9150 reference "sub:Manual-Bracket-Size"
9155 \begin_inset CommandInset ref
9157 reference "sub:Automatic-Bracket-Size"
9164 \begin_layout Standard
9165 \begin_inset Newpage newpage
9171 \begin_layout Section
9173 \begin_inset CommandInset label
9183 \begin_layout Plain Layout
9192 \begin_layout Standard
9193 Accents can be inserted via the math toolbar button
9194 \begin_inset Graphics
9195 filename ../images/math/hat.png
9200 or the commands listed in the following subsections.
9203 \begin_layout Subsection
9204 Accents for one Character
9208 \begin_layout Plain Layout
9221 \begin_layout Plain Layout
9223 \begin_inset CommandInset ref
9225 reference "sub:Accents-in-Text"
9238 \begin_layout Plain Layout
9246 \begin_inset Note Note
9249 \begin_layout Plain Layout
9252 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9255 \begin_layout Plain Layout
9258 texorpdfstring is in section
9259 \begin_inset CommandInset ref
9261 reference "sub:Formulas-in-Section"
9271 \begin_inset CommandInset label
9273 name "sub:Accents-for-one"
9281 \begin_layout Plain Layout
9282 Accents ! for one character
9290 \begin_layout Standard
9291 \begin_inset Space \hfill{}
9295 \begin_inset Tabular
9296 <lyxtabular version="3" rows="8" columns="2">
9298 <column alignment="center" valignment="top" width="0pt">
9299 <column alignment="center" valignment="top" width="0pt">
9301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9304 \begin_layout Plain Layout
9310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9313 \begin_layout Plain Layout
9315 \begin_inset Note Note
9318 \begin_layout Plain Layout
9325 is only used as spacer.
9337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9340 \begin_layout Plain Layout
9347 \begin_layout Plain Layout
9361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9364 \begin_layout Plain Layout
9365 \begin_inset Formula $\raisebox {5mm}{}\dot{A}$
9375 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9378 \begin_layout Plain Layout
9385 \begin_layout Plain Layout
9399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9402 \begin_layout Plain Layout
9403 \begin_inset Formula $\raisebox {5mm}{}\ddot{A}$
9413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9416 \begin_layout Plain Layout
9423 \begin_layout Plain Layout
9437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9440 \begin_layout Plain Layout
9441 \begin_inset Formula $\raisebox {5mm}{}\dddot{A}$
9451 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9454 \begin_layout Plain Layout
9462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9465 \begin_layout Plain Layout
9466 \begin_inset Formula $\raisebox {5mm}{}\ddddot {A}$
9476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9479 \begin_layout Plain Layout
9486 \begin_layout Plain Layout
9499 \begin_layout Plain Layout
9510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9513 \begin_layout Plain Layout
9514 \begin_inset Formula $\raisebox {5mm}{}\vec{A}$
9524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9527 \begin_layout Plain Layout
9534 \begin_layout Plain Layout
9548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9551 \begin_layout Plain Layout
9552 \begin_inset Formula $\raisebox {5mm}{}\bar{A}$
9562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9565 \begin_layout Plain Layout
9572 \begin_layout Plain Layout
9586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9589 \begin_layout Plain Layout
9590 \begin_inset Formula $\raisebox {5mm}{}\mathring{A}$
9604 \begin_inset Space \hfill{}
9608 \begin_inset Tabular
9609 <lyxtabular version="3" rows="7" columns="2">
9611 <column alignment="center" valignment="top" width="0pt">
9612 <column alignment="center" valignment="top" width="0pt">
9614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9617 \begin_layout Plain Layout
9623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9626 \begin_layout Plain Layout
9634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9637 \begin_layout Plain Layout
9644 \begin_layout Plain Layout
9658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9661 \begin_layout Plain Layout
9662 \begin_inset Formula $\raisebox {5mm}{}\tilde{A}$
9672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9675 \begin_layout Plain Layout
9682 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9699 \begin_layout Plain Layout
9700 \begin_inset Formula $\raisebox {5mm}{}\hat{A}$
9710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9713 \begin_layout Plain Layout
9720 \begin_layout Plain Layout
9734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9737 \begin_layout Plain Layout
9738 \begin_inset Formula $\raisebox {5mm}{}\check{A}$
9748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9751 \begin_layout Plain Layout
9758 \begin_layout Plain Layout
9772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9775 \begin_layout Plain Layout
9776 \begin_inset Formula $\raisebox {5mm}{}\acute{A}$
9786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9789 \begin_layout Plain Layout
9796 \begin_layout Plain Layout
9810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9813 \begin_layout Plain Layout
9814 \begin_inset Formula $\raisebox {5mm}{}\grave{A}$
9824 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9827 \begin_layout Plain Layout
9834 \begin_layout Plain Layout
9848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9851 \begin_layout Plain Layout
9852 \begin_inset Formula $\raisebox {5mm}{}\breve{A}$
9866 \begin_inset Space \hfill{}
9872 \begin_layout Standard
9873 \begin_inset VSpace bigskip
9880 \begin_layout Plain Layout
9886 in formulas, a quotation mark is inserted before the vowel.
9887 These two characters are then treated by LaTeX as
9891 character when the formula part with the umlaut is marked as German.
9899 \begin_inset Quotes eld
9903 \begin_inset Quotes erd
9906 umlauts are created as demonstrated in the following example:
9909 \begin_layout Standard
9910 \begin_inset VSpace -2mm
9916 \begin_layout Standard
9918 \begin_inset Tabular
9919 <lyxtabular version="3" rows="3" columns="2">
9921 <column alignment="center" valignment="top" width="0">
9922 <column alignment="center" valignment="top" width="0">
9924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9927 \begin_layout Plain Layout
9933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9936 \begin_layout Plain Layout
9938 \begin_inset Note Note
9941 \begin_layout Plain Layout
9948 is only used as spacer.
9960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9963 \begin_layout Plain Layout
9966 \begin_inset Quotes grd
9974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9977 \begin_layout Plain Layout
9980 \begin_inset Formula $"i$
9990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox {5mm}{}\ddot{i}$
10034 \begin_layout Standard
10035 Another advantage to
10041 is that umlauts can directly be converted to mathematical text because
10042 the accent commands above are
10048 in mathematical text
10051 To convert an accented character to mathematical text, only the character
10052 under the accent may be converted.
10053 This applies also for all other conversions, e.
10054 \begin_inset Space \thinspace{}
10058 \begin_inset Space ~
10064 \begin_layout Standard
10065 In mathematical text, umlauts and other accented characters can directly
10069 \begin_layout Subsection
10070 Accents for Operators
10074 \begin_layout Plain Layout
10075 Accents ! for operators
10083 \begin_layout Standard
10094 \begin_layout Plain Layout
10112 \begin_layout Plain Layout
10120 characters can be placed above or below an operator, respectively, to accent
10132 \begin_layout Plain Layout
10140 characters can be set before and behind an operator.
10141 The command scheme is:
10144 \begin_layout Standard
10160 \begin_layout Standard
10167 must always be before the operator that should be accented.
10168 You can accent with several characters and even with other operators and
10176 for example only characters behind an operator, write nothing between the
10177 first braces but don't omit the braces.
10180 \begin_layout Standard
10181 For example the command
10186 \begin_inset Formula $\to$
10196 \begin_inset Formula $\to$
10205 \begin_layout Plain Layout
10221 \begin_inset Formula \[
10222 \sideset {}{'}\sum_{k=1}^{n}\]
10229 \begin_layout Standard
10238 \begin_layout Plain Layout
10253 \begin_layout Plain Layout
10265 \begin_inset Formula $\uparrow$
10273 \begin_inset Formula \[
10274 \overset{a}{\maltese}\]
10278 As seen in the last example, with
10290 also symbols and characters can be accented; with
10296 this is not possible.
10299 \begin_layout Subsection
10300 Accents for several Characters
10301 \begin_inset CommandInset label
10303 name "sub:Accents-for-several"
10311 \begin_layout Plain Layout
10312 Accents ! for several characters
10320 \begin_layout Standard
10321 \begin_inset Space \hfill{}
10325 \begin_inset Tabular
10326 <lyxtabular version="3" rows="5" columns="2">
10328 <column alignment="center" valignment="top" width="0pt">
10329 <column alignment="center" valignment="top" width="0pt">
10331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10334 \begin_layout Plain Layout
10340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10343 \begin_layout Plain Layout
10345 \begin_inset Note Note
10348 \begin_layout Plain Layout
10355 is only used as spacer.
10367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10370 \begin_layout Plain Layout
10377 \begin_layout Plain Layout
10391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10394 \begin_layout Plain Layout
10395 \begin_inset Formula $\raisebox {6mm}{}\overleftarrow{A=B}\raisebox {-2mm}{}$
10405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10408 \begin_layout Plain Layout
10415 \begin_layout Plain Layout
10429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10432 \begin_layout Plain Layout
10433 \begin_inset Formula $\raisebox {5mm}{}\underleftarrow{A=B}\raisebox {-3mm}{}$
10443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10446 \begin_layout Plain Layout
10453 \begin_layout Plain Layout
10467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10470 \begin_layout Plain Layout
10471 \begin_inset Formula $\raisebox {6mm}{}\overleftrightarrow{A=B}\raisebox {-2mm}{}$
10481 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10484 \begin_layout Plain Layout
10487 underleftrightarrow
10491 \begin_layout Plain Layout
10505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Formula $\raisebox {5mm}{}\underleftrightarrow{A=B}\raisebox {-3mm}{}$
10523 \begin_inset Space \hfill{}
10527 \begin_inset Tabular
10528 <lyxtabular version="3" rows="5" columns="2">
10530 <column alignment="center" valignment="top" width="0pt">
10531 <column alignment="center" valignment="top" width="0pt">
10533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10536 \begin_layout Plain Layout
10542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10545 \begin_layout Plain Layout
10553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10556 \begin_layout Plain Layout
10563 \begin_layout Plain Layout
10577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10580 \begin_layout Plain Layout
10581 \begin_inset Formula $\raisebox {6mm}{}\overrightarrow{A=B}\raisebox {-2mm}{}$
10591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10594 \begin_layout Plain Layout
10601 \begin_layout Plain Layout
10615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10618 \begin_layout Plain Layout
10619 \begin_inset Formula $\raisebox {5mm}{}\underrightarrow{A=B}\raisebox {-3mm}{}$
10629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10632 \begin_layout Plain Layout
10639 \begin_layout Plain Layout
10653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10656 \begin_layout Plain Layout
10657 \begin_inset Formula $\raisebox {6mm}{}\widetilde{A=B}\raisebox {-2mm}{}$
10667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10670 \begin_layout Plain Layout
10677 \begin_layout Plain Layout
10691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10694 \begin_layout Plain Layout
10695 \begin_inset Formula $\raisebox {6mm}{}\widehat{A=B}\raisebox {-2mm}{}$
10709 \begin_inset Space \hfill{}
10715 \begin_layout Standard
10716 \begin_inset VSpace medskip
10719 With these commands as many characters as you like can be accented.
10732 will only be set in the output with a length of three characters, as shown
10733 in the following example:
10734 \begin_inset Formula \[
10735 \widetilde{A+B=C-D}\]
10742 \begin_layout Standard
10753 \begin_layout Plain Layout
10771 \begin_layout Plain Layout
10779 described in the previous subsection it is also possible to accent several
10789 \begin_layout Plain Layout
10799 \begin_inset Formula $\downarrow$
10805 \begin_inset Formula \[
10806 \underset{***}{A=B}\]
10813 \begin_layout Section
10815 \begin_inset CommandInset label
10825 \begin_layout Plain Layout
10834 \begin_layout Subsection
10836 \begin_inset CommandInset label
10838 name "sub:Predefined-Space"
10846 \begin_layout Plain Layout
10847 Space ! horizontal ! predefined
10855 \begin_layout Standard
10856 Sometimes it is necessary to insert horizontal space to a formula.
10857 This is done by inserting a protected space (shortcut
10863 \begin_inset Quotes eld
10873 \begin_layout Plain Layout
10886 \begin_inset Quotes erd
10889 appears and by pressing
10893 several times one can select one of eight different space sizes.
10894 The spaces can also be inserted using the math toolbar button
10895 \begin_inset Graphics
10896 filename ../images/math/space.png
10901 or special commands.
10902 Independent from the inserted command, one can select the size again by
10910 \begin_layout Standard
10913 \begin_inset VSpace -5mm
10917 \begin_inset Tabular
10918 <lyxtabular version="3" rows="3" columns="7">
10920 <column alignment="center" valignment="middle" width="6.8cm">
10921 <column alignment="center" valignment="top" width="0">
10922 <column alignment="center" valignment="top" width="0">
10923 <column alignment="center" valignment="top" width="0">
10924 <column alignment="center" valignment="top" width="0">
10925 <column alignment="center" valignment="top" width="0">
10926 <column alignment="center" valignment="top" width="0">
10928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10931 \begin_layout Plain Layout
10937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10940 \begin_layout Plain Layout
10948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10951 \begin_layout Plain Layout
10959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10962 \begin_layout Plain Layout
10970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10973 \begin_layout Plain Layout
10981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10984 \begin_layout Plain Layout
10992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10995 \begin_layout Plain Layout
11005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11008 \begin_layout Plain Layout
11013 keystrokes after inserting the protected space
11018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11021 \begin_layout Plain Layout
11027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11030 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11048 \begin_layout Plain Layout
11054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11057 \begin_layout Plain Layout
11063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11066 \begin_layout Plain Layout
11074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11077 \begin_layout Plain Layout
11083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11086 \begin_layout Plain Layout
11087 \begin_inset Formula $A\, B$
11095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11099 \begin_inset Formula $A\: B$
11107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11111 \begin_inset Formula $A\; B$
11119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11122 \begin_layout Plain Layout
11123 \begin_inset Formula $A\quad B$
11131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11134 \begin_layout Plain Layout
11135 \begin_inset Formula $A\qquad B$
11143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11146 \begin_layout Plain Layout
11147 \begin_inset Formula $A\! B$
11163 \begin_layout Standard
11164 The last size seem to produce no space.
11165 It is displayed red in LyX contrary to the other sizes, because it is a
11167 There are two more negative spaces:
11170 \begin_layout Standard
11172 \begin_inset Tabular
11173 <lyxtabular version="3" rows="3" columns="3">
11175 <column alignment="center" valignment="middle" width="6.8cm">
11176 <column alignment="center" valignment="top" width="0pt">
11177 <column alignment="center" valignment="top" width="0pt">
11179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11182 \begin_layout Plain Layout
11188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11191 \begin_layout Plain Layout
11199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11202 \begin_layout Plain Layout
11212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11215 \begin_layout Plain Layout
11220 keystrokes after inserting the protected space
11225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11228 \begin_layout Plain Layout
11234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11237 \begin_layout Plain Layout
11245 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11248 \begin_layout Plain Layout
11254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11258 \begin_inset Formula $A\negmedspace B$
11266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11269 \begin_layout Plain Layout
11270 \begin_inset Formula $A\negthickspace B$
11286 \begin_layout Standard
11287 Negative spaces can lead to characters overlapping each other.
11288 Thus they can be used to enforce ligatures, what is e.
11289 \begin_inset Space \thinspace{}
11293 \begin_inset Space ~
11296 useful for summation operators:
11299 \begin_layout Standard
11301 \begin_inset Tabular
11302 <lyxtabular version="3" rows="3" columns="2">
11304 <column alignment="center" valignment="top" width="0">
11305 <column alignment="center" valignment="top" width="0">
11307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11319 \begin_layout Plain Layout
11321 \begin_inset Note Note
11324 \begin_layout Plain Layout
11331 is only used as spacer.
11343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11346 \begin_layout Plain Layout
11355 \begin_layout Plain Layout
11369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11372 \begin_layout Plain Layout
11373 \begin_inset Formula $\raisebox {4.5mm}{}\sum\sum f_{kl}\raisebox {-2.5mm}{}$
11383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11386 \begin_layout Plain Layout
11397 \begin_layout Plain Layout
11411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11414 \begin_layout Plain Layout
11415 \begin_inset Formula $\raisebox {4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox {-2.5mm}{}$
11431 \begin_layout Standard
11432 Relations like for example equal signs, are always surrounded by space.
11433 To suppress this, the equal sign is placed into a TeX-brace.
11434 The following example demonstrates this:
11437 \begin_layout Standard
11439 \begin_inset Tabular
11440 <lyxtabular version="3" rows="2" columns="2">
11442 <column alignment="center" valignment="top" width="0pt">
11443 <column alignment="center" valignment="top" width="0pt">
11445 <cell alignment="center" valignment="top" usebox="none">
11448 \begin_layout Plain Layout
11454 <cell alignment="center" valignment="top" usebox="none">
11457 \begin_layout Plain Layout
11458 \begin_inset Formula $A=B$
11468 <cell alignment="center" valignment="top" usebox="none">
11471 \begin_layout Plain Layout
11472 \begin_inset Note Note
11475 \begin_layout Plain Layout
11482 is only used as spacer.
11488 \begin_inset Formula $\raisebox {5mm}{}$
11491 equation without space
11496 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11499 \begin_layout Plain Layout
11500 \begin_inset Formula $A{=}B$
11516 \begin_layout Standard
11518 The command for the last formula is:
11523 \begin_inset Formula $\to$
11529 \begin_layout Standard
11530 \begin_inset VSpace bigskip
11533 Spaces are needed for physical units, because the space between the value
11534 and the unit is the smallest one and not a normal space.
11535 For units in text, the smallest space is inserted via the menu
11537 Insert\SpecialChar \menuseparator
11538 Formatting\SpecialChar \menuseparator
11540 \begin_inset Space ~
11552 \begin_layout Standard
11553 An example to visualize the difference:
11556 \begin_layout Standard
11557 \begin_inset Tabular
11558 <lyxtabular version="3" rows="2" columns="2">
11560 <column alignment="left" valignment="top" width="0">
11561 <column alignment="left" valignment="top" width="0">
11563 <cell alignment="center" valignment="top" usebox="none">
11566 \begin_layout Plain Layout
11568 \begin_inset Formula $\cdot$
11576 <cell alignment="center" valignment="top" usebox="none">
11579 \begin_layout Plain Layout
11580 space between value and unit
11587 <cell alignment="center" valignment="top" usebox="none">
11590 \begin_layout Plain Layout
11592 \begin_inset Space \thinspace{}
11596 \begin_inset Formula $\cdot$
11604 <cell alignment="center" valignment="top" usebox="none">
11607 \begin_layout Plain Layout
11608 smallest space between value and unit
11621 \begin_layout Subsection
11626 \begin_layout Plain Layout
11639 \begin_layout Plain Layout
11640 for vertical space in formulas see
11641 \begin_inset CommandInset ref
11643 reference "sub:Line-Separation"
11656 \begin_layout Plain Layout
11664 \begin_inset Note Note
11667 \begin_layout Plain Layout
11670 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11673 \begin_layout Plain Layout
11676 texorpdfstring is in section
11677 \begin_inset CommandInset ref
11679 reference "sub:Formulas-in-Section"
11689 \begin_inset CommandInset label
11691 name "sub:Variable-Space"
11699 \begin_layout Plain Layout
11700 Space ! horizontal ! variable
11708 \begin_layout Standard
11709 Space with a defined length can be inserted in LyX with the command
11710 \begin_inset Newline newline
11723 \begin_layout Plain Layout
11732 For the length all units listed in
11733 \begin_inset CommandInset ref
11735 reference "tab:Used-units"
11739 are allowed, except of the unit
11740 \begin_inset Quotes eld
11744 \begin_inset Quotes erd
11748 The length may also be negative.
11749 To insert so many space that the formula uses all available space, the
11760 \begin_layout Plain Layout
11771 \begin_layout Standard
11772 \begin_inset VSpace -1mm
11778 \begin_layout Standard
11780 \begin_inset Tabular
11781 <lyxtabular version="3" rows="4" columns="2">
11783 <column alignment="center" valignment="top" width="0">
11784 <column alignment="center" valignment="top" width="0">
11786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11789 \begin_layout Plain Layout
11795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11798 \begin_layout Plain Layout
11806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11809 \begin_layout Plain Layout
11813 \begin_inset Formula $\to$
11823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11826 \begin_layout Plain Layout
11827 \begin_inset Formula $A=B\hspace {3cm}A\not=C$
11837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11840 \begin_layout Plain Layout
11844 \begin_inset Formula $\to$
11854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11857 \begin_layout Plain Layout
11858 \begin_inset Formula $A\hspace {-1mm}A\not=A$
11868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11871 \begin_layout Plain Layout
11878 \begin_layout Plain Layout
11892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11895 \begin_layout Plain Layout
11896 \begin_inset Formula $A=A\hfill B=B$
11912 \begin_layout Standard
11913 In the last example the available space is given by the longest column entry
11915 In an inline formula the space depends on the length of the line in which
11923 Thus, when the line uses the full width, no space will be created.
11930 only has an effect on displayed formulas when the formula style
11935 (Formula styles are explained in
11936 \begin_inset CommandInset ref
11938 reference "sec:Formula-Styles"
11945 \begin_layout Standard
11946 For text, variable space can be inserted via the menu
11948 Insert\SpecialChar \menuseparator
11949 Formatting\SpecialChar \menuseparator
11951 \begin_inset Space ~
11956 , what is not possible in formulas:
11959 \begin_layout Standard
11960 This is a line with
11961 \begin_inset Space \hspace{}
11966 \begin_inset Space \thinspace{}
11972 \begin_layout Standard
11973 This is a line with
11974 \begin_inset Space \hfill{}
11980 \begin_layout Subsection
11981 Space besides inline Formulas
11985 \begin_layout Plain Layout
11986 Space ! besides inline formulas
11994 \begin_layout Standard
11995 The space that surrounds inline formulas can be adjusted with the length
12004 \begin_layout Plain Layout
12015 The value of a length is set with the command
12023 \begin_layout Plain Layout
12033 that has the following scheme:
12036 \begin_layout Standard
12041 setlength{length name}{value}
12044 \begin_layout Standard
12052 \begin_inset Space \thinspace{}
12058 \begin_layout Standard
12068 \begin_layout Standard
12069 is inserted in TeX-mode.
12071 \begin_inset Space \thinspace{}
12074 mm space will now be set around all inline formulas:
12078 \begin_layout Plain Layout
12092 \begin_layout Standard
12093 This is a line with an inline formula
12094 \begin_inset Formula $A=B$
12098 \begin_inset Space \thinspace{}
12101 mm surrounding space.
12105 \begin_layout Plain Layout
12119 \begin_layout Standard
12120 To return to the predefined value,
12126 is set to the value 0
12127 \begin_inset Space \thinspace{}
12133 \begin_layout Section
12138 \begin_layout Plain Layout
12148 \begin_layout Plain Layout
12153 \begin_layout Plain Layout
12164 \begin_layout Plain Layout
12179 \begin_layout Standard
12180 Boxes for text are described in chapter
12187 \begin_inset Space ~
12195 \begin_layout Subsection
12197 \begin_inset CommandInset label
12199 name "sub:Boxes-with-Frame"
12207 \begin_layout Plain Layout
12216 \begin_layout Standard
12217 It is possible to frame formulas or parts of it with the commands
12227 \begin_layout Plain Layout
12245 \begin_layout Plain Layout
12256 \begin_layout Standard
12257 When one of these commands is inserted to a formula, a blue box appears
12258 within a frame to enter formula parts.
12265 an additional formula has to be created by
12273 \begin_layout Plain Layout
12274 Due to a bug in LyX it is not possible to create a new formula with
12279 \begin_inset CommandInset href
12281 name "LyX-bug #1435"
12282 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12291 , because the box content will otherwise be treated as mathematical text.
12298 is used, a new formula is automatically created inside the frame.
12301 \begin_layout Standard
12308 is not suitable to frame displayed formulas, because the formula will always
12309 be set in the size of the text.
12316 is in contrary not suitable to frame inline formulas, because the formula
12317 will always be set in the size of a displayed formula.
12320 \begin_layout Standard
12327 there is the command
12337 \begin_layout Plain Layout
12345 where additionally the frame width and the alignment can be specified.
12352 is used in the following scheme:
12355 \begin_layout Standard
12360 framebox[frame width][position]{box content}
12363 \begin_layout Standard
12364 The position can either be
12381 right aligns the formula in the box.
12382 When no position is given, the formula will be centered.
12383 \begin_inset Newline newline
12386 Is no width given, also no position can be given.
12387 In this case the frame width is adjusted to the box content like for
12396 \begin_layout Standard
12403 is inserted, a box appears containing three blue boxes.
12404 The first two boxes are surrounded by brackets and denote the two optional
12406 The third box is for formula parts like for
12415 \begin_layout Standard
12417 \begin_inset Note Note
12420 \begin_layout Plain Layout
12421 The table has been set into a minipage to make the footnote appearing.
12422 Otherwise the footnote text would not be displayed.
12428 \begin_inset Box Frameless
12437 height_special "totalheight"
12440 \begin_layout Plain Layout
12442 \begin_inset Tabular
12443 <lyxtabular version="3" rows="5" columns="2">
12445 <column alignment="center" valignment="top" width="0">
12446 <column alignment="center" valignment="top" width="0">
12448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12451 \begin_layout Plain Layout
12456 \begin_layout Plain Layout
12457 Due to a bug in LyX it is not possible to create a new formula with
12462 \begin_inset CommandInset href
12464 name "LyX-bug #1435"
12465 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12482 \begin_layout Plain Layout
12484 \begin_inset Note Note
12487 \begin_layout Plain Layout
12494 is only used as spacer.
12506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12509 \begin_layout Plain Layout
12516 \begin_layout Plain Layout
12535 \begin_layout Plain Layout
12549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12552 \begin_layout Plain Layout
12553 \begin_inset Formula \raisebox {6mm}{}\fbox{$\int A=B$}\raisebox {-4mm}{}
12564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12567 \begin_layout Plain Layout
12574 \begin_layout Plain Layout
12589 \begin_layout Plain Layout
12603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12606 \begin_layout Plain Layout
12607 \begin_inset Formula $\raisebox {8.5mm}{}\boxed{\int A=B}\raisebox {-6.5mm}{}$
12617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12620 \begin_layout Plain Layout
12627 \begin_layout Plain Layout
12641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12644 \begin_layout Plain Layout
12645 \begin_inset Formula $\raisebox {6mm}{}A+\fbox{B}\raisebox {-3mm}{}$
12655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12658 \begin_layout Plain Layout
12665 \begin_layout Plain Layout
12675 \begin_inset Formula $\to$
12679 \begin_inset Formula $\to$
12692 \begin_layout Plain Layout
12702 \begin_inset Formula $\downarrow$
12710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12713 \begin_layout Plain Layout
12714 \begin_inset Formula $\raisebox {6mm}{}$
12718 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12722 \begin_inset Formula $\raisebox {-4mm}{}$
12743 \begin_layout Standard
12744 The frame thickness can also be adjusted.
12745 To do this the following commands have to be inserted in TeX-mode before
12749 \begin_layout Standard
12759 \begin_inset Quotes eld
12763 \begin_inset Quotes erd
12777 \begin_inset Quotes eld
12781 \begin_inset Quotes erd
12787 \begin_layout Standard
12788 \begin_inset Quotes eld
12792 \begin_inset Quotes erd
12795 specifies the minimal distance between the frame and the first character
12797 An example for this is the following framed formula:
12801 \begin_layout Plain Layout
12813 \begin_inset Formula \[
12818 Before this formula the commands
12821 \begin_layout Standard
12843 \begin_layout Standard
12844 were inserted in TeX-mode.
12845 The given values are used for all following boxes.
12848 \begin_layout Standard
12849 To return to the standard frame size, the command
12852 \begin_layout Standard
12877 \begin_layout Plain Layout
12891 \begin_layout Standard
12892 is inserted in TeX-mode before the next formula.
12895 \begin_layout Subsection
12896 Boxes without Frame
12897 \begin_inset CommandInset label
12899 name "sub:Boxes-without-Frame"
12907 \begin_layout Plain Layout
12908 Boxes ! without frame
12916 \begin_layout Standard
12917 For boxes without a frame there are the following box commands:
12927 \begin_layout Plain Layout
12945 \begin_layout Plain Layout
12963 \begin_layout Plain Layout
12974 \begin_layout Standard
12981 a box can be super- or subscripted.
12982 But in contrary to normal super- and subscripting, the characters in the
12983 box keep their font size.
12990 is used in the following scheme:
12993 \begin_layout Standard
12998 raisebox{height}{box content}
13001 \begin_layout Standard
13002 When the box should contain a formula, an extra formula is needed like for
13012 \begin_layout Standard
13014 \begin_inset Tabular
13015 <lyxtabular version="3" rows="4" columns="2">
13017 <column alignment="center" valignment="top" width="0">
13018 <column alignment="center" valignment="top" width="0">
13020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13023 \begin_layout Plain Layout
13029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13032 \begin_layout Plain Layout
13040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13043 \begin_layout Plain Layout
13047 \begin_inset Formula $\to$
13053 \begin_inset Formula $\to$
13061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13064 \begin_layout Plain Layout
13065 \begin_inset Formula $H\raisebox {2mm}{al}lo$
13075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13078 \begin_layout Plain Layout
13082 \begin_inset Formula $\to$
13088 \begin_inset Formula $\to$
13096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13099 \begin_layout Plain Layout
13100 \begin_inset Formula $H\raisebox {-2mm}{al}lo$
13110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13113 \begin_layout Plain Layout
13117 \begin_inset Formula $\to$
13132 \begin_layout Plain Layout
13146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13149 \begin_layout Plain Layout
13153 \begin_layout Plain Layout
13177 \begin_layout Standard
13178 The last formula can currently only be created using TeX-mode because LyX
13179 inserts a box instead of the needed extra formula.
13183 \begin_layout Plain Layout
13185 \begin_inset CommandInset href
13187 name "LyX-bug #1435"
13188 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13200 \begin_layout Standard
13225 , with the difference that there is no frame.
13228 \begin_layout Subsection
13230 \begin_inset CommandInset label
13232 name "sub:Colored-Boxes"
13240 \begin_layout Plain Layout
13249 \begin_layout Standard
13250 To be able to use all commands explained in this section, the LaTeX-package
13259 \begin_layout Plain Layout
13264 is part of every LaTeX standard installation.
13273 \begin_layout Plain Layout
13279 has to be loaded in the LaTeX-preamble with the line
13283 \begin_layout Plain Layout
13284 When text is colored somewhere in the document with a predefined color,
13285 LyX loads the LaTeX-package
13290 Thus it is possible that the package is loaded twice, but this doesn't
13297 \begin_inset Note Note
13300 \begin_layout Plain Layout
13301 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13310 \begin_layout Standard
13318 \begin_layout Standard
13319 \begin_inset VSpace medskip
13322 To color boxes, the command
13332 \begin_layout Plain Layout
13340 is used in the following scheme:
13343 \begin_layout Standard
13348 colorbox{color}{box content}
13351 \begin_layout Standard
13352 The box content can also be a box and a
13358 can also be part of another box (see the 2nd and 3rd example).
13359 When the box should contain a formula, an extra formula has to be created,
13370 \begin_layout Plain Layout
13371 This also applies for the command
13379 \begin_inset CommandInset href
13381 name "LyX-bug #1435"
13382 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13394 \begin_layout Standard
13395 One of the following predefined colors can be chosen:
13398 \begin_layout Standard
13432 \begin_layout Standard
13434 \begin_inset Tabular
13435 <lyxtabular version="3" rows="4" columns="2">
13437 <column alignment="center" valignment="top" width="0">
13438 <column alignment="center" valignment="top" width="0">
13440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13443 \begin_layout Plain Layout
13449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13452 \begin_layout Plain Layout
13454 \begin_inset Note Note
13457 \begin_layout Plain Layout
13464 is only used as spacer.
13476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13479 \begin_layout Plain Layout
13483 \begin_inset Formula $\to$
13493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13496 \begin_layout Plain Layout
13497 \begin_inset Formula $\raisebox {6mm}{}\colorbox {yellow}{A=B}\raisebox {-3mm}{}$
13507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13510 \begin_layout Plain Layout
13514 \begin_inset Formula $\to$
13525 \begin_layout Plain Layout
13539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13542 \begin_layout Plain Layout
13543 \begin_inset Formula $\raisebox {6mm}{}\colorbox {green}{\fbox{A=B}}\raisebox {-3mm}{}$
13553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13556 \begin_layout Plain Layout
13563 \begin_layout Plain Layout
13575 \begin_inset Formula $\to$
13585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13588 \begin_layout Plain Layout
13589 \begin_inset Formula $\raisebox {6mm}{}\fbox{\colorbox {green}{A=B}}\raisebox {-3mm}{}$
13605 \begin_layout Standard
13612 only colors the box but not the characters in the box.
13613 To color all characters, the whole formula is highlighted and the wanted
13614 color is chosen in the
13617 \begin_inset Space ~
13623 The dialog can be called with the toolbar button
13624 \begin_inset Graphics
13625 filename ../images/dialog-show_character.png
13632 Edit\SpecialChar \menuseparator
13634 \begin_inset Space ~
13637 Style\SpecialChar \menuseparator
13641 The formula number has then the same color as the formula.
13642 When the formula number should get another color than the formula characters,
13643 the color must be changed within the formula.
13646 \begin_layout Standard
13650 \begin_layout Standard
13653 \begin_inset Formula \begin{equation}
13654 \int A=B\label{eq:red}\end{equation}
13661 \begin_inset Formula \begin{equation}
13662 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13669 \begin_layout Standard
13671 \begin_inset CommandInset ref
13677 is completely colored red.
13678 \begin_inset Newline newline
13682 \begin_inset CommandInset ref
13684 reference "eq:redgreen"
13688 was first completely colored green to set the color for the formula number.
13689 Subsequently the formula characters were colored red.
13692 \begin_layout Standard
13693 \begin_inset VSpace bigskip
13696 To color the frame different than the rest of the box, the command
13706 \begin_layout Plain Layout
13714 is used in the following scheme:
13717 \begin_layout Standard
13722 fcolorbox{frame color}{color}{box content}
13725 \begin_layout Standard
13732 is an extension of the command
13739 The frame width is set, like for
13762 \begin_layout Plain Layout
13774 \begin_inset Formula \[
13775 \fcolorbox {cyan}{magenta}{A=B}\]
13783 \begin_layout Plain Layout
13797 \begin_layout Standard
13798 This formula was created with the command
13799 \begin_inset Newline newline
13807 \begin_inset Formula $\to$
13813 \begin_inset Formula $\to$
13823 \begin_layout Standard
13824 \begin_inset VSpace bigskip
13827 To use other colors than the predefined ones, they have to be defined first.
13830 \begin_layout Standard
13831 One can for example define the color
13832 \begin_inset Quotes eld
13840 \begin_inset Quotes erd
13843 with the LaTeX-preamble line:
13846 \begin_layout Standard
13851 definecolor{darkgreen}{cmyk}{0.5,
13869 \begin_layout Plain Layout
13880 \begin_layout Standard
13885 is the color space that denotes the colors
13902 The four comma separated numbers are the portion factor for the corresponding
13903 colors of the color space.
13904 The factors can be in the range of 0
13905 \begin_inset Space \thinspace{}
13909 \begin_inset Space \thinspace{}
13917 also the color space
13921 can be used for definitions.
13938 , so that there are in this case three portion factors for the corresponding
13940 Furthermore there is the color space
13944 with one portion factor for the gray value.
13947 \begin_layout Standard
13948 As example a framed box with the new defined color
13952 where the characters have been colored
13957 \begin_inset Formula \begin{equation}
13958 \colorbox {darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13965 \begin_layout Standard
13966 Self-defined colors can also be used for text with the help of the command
13977 \begin_layout Plain Layout
13986 \begin_layout Standard
13990 \begin_layout Plain Layout
13994 textcolor{darkgreen}{
14000 \begin_inset Quotes eld
14004 \begin_inset Quotes erd
14011 \begin_layout Plain Layout
14021 \begin_layout Standard
14032 \begin_layout Plain Layout
14040 is used in the scheme
14044 textcolor{color}{characters to color}
14049 \begin_layout Subsection
14051 \begin_inset CommandInset label
14053 name "sub:Paragraph-Boxes"
14061 \begin_layout Plain Layout
14062 Boxes ! as paragraph
14070 \begin_layout Standard
14071 A box that can contain several lines and paragraphs, a so called paragraph
14072 box (parbox), can be created with the menu
14074 Insert\SpecialChar \menuseparator
14077 or the toolbar button
14078 \begin_inset Graphics
14079 filename ../images/box-insert.png
14087 \begin_layout Standard
14088 The following example shows a framed parbox in a line:
14091 \begin_layout Standard
14092 \begin_inset VSpace medskip
14096 \begin_inset Box Boxed
14105 height_special "totalheight"
14108 \begin_layout Plain Layout
14109 This is a paragraph box.
14111 \begin_inset Space \thinspace{}
14114 cm long and can also contain formulas:
14115 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14126 \begin_layout Standard
14127 \begin_inset VSpace medskip
14133 \begin_layout Standard
14134 Such a box is created by right-clicking on the gray box inset.
14135 A dialog pops up showing the box properties.
14149 \begin_inset Space \thinspace{}
14154 Vertical Box Alignment
14159 \begin_layout Standard
14160 \begin_inset VSpace medskip
14163 In LaTeX a parbox is created with the command
14173 \begin_layout Plain Layout
14181 that has the following scheme:
14184 \begin_layout Standard
14189 parbox[position]{width}{box content}
14192 \begin_layout Standard
14206 for bottom means that the box is aligned within the surrounding text with
14212 for top this is done with the first line.
14213 When no position is given, the box will be vertically centered, see section
14221 \begin_inset Space ~
14226 manual for examples.
14229 \begin_layout Standard
14230 \begin_inset VSpace bigskip
14233 To frame formulas completely, including the formula number, the formula
14234 must be set into a parbox.
14235 To do this, the command
14249 is inserted in TeX-mode before the formula.
14258 \begin_layout Plain Layout
14268 is hereby the line width set for the document.
14269 Because the frame is outside the parbox, 2
14270 \begin_inset Space \thinspace{}
14273 times the frame separation and the frame thickness must be subtracted from
14275 As this is not automatically done by LyX due to a bug
14279 \begin_layout Plain Layout
14280 \begin_inset CommandInset href
14282 name "LyX-bug #4483"
14283 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14292 , TeX-mode has to be used.
14293 To be able to multiply and subtract in arguments, the LaTeX-package
14301 \begin_layout Plain Layout
14306 is part of every LaTeX standard installation.
14315 \begin_layout Plain Layout
14321 must be loaded in the LaTeX-preamble with the line
14324 \begin_layout Standard
14332 \begin_layout Standard
14333 Behind the formula both boxes are closed by entering
14338 Here is an example:
14342 \begin_layout Plain Layout
14356 \begin_layout Standard
14360 \begin_layout Plain Layout
14378 \begin_inset Formula \begin{equation}
14379 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14387 \begin_layout Plain Layout
14398 \begin_layout Plain Layout
14412 \begin_layout Standard
14413 \begin_inset VSpace medskip
14416 As a parbox is used as argument of
14422 , there is in this case no difference between
14437 \begin_layout Standard
14438 \begin_inset VSpace bigskip
14441 Paragraph boxes are very useful to comment formulas directly.
14448 is used in combination with the command
14462 \begin_inset CommandInset ref
14464 reference "sub:User-defined-Numbering"
14471 \begin_layout Standard
14472 An example of a formula commented with
14481 \begin_layout Standard
14485 \begin_layout Plain Layout
14498 This is a description.
14499 It is distinctly separated from the formula and multiline.
14503 \begin_layout Plain Layout
14515 \begin_layout Standard
14516 Such a formula must be inserted completely in TeX-mode because LyX does
14517 not yet support the command
14524 The formula is created with the following command sequence:
14527 \begin_layout Standard
14540 is inserted in TeX-mode.
14544 \begin_layout Plain Layout
14545 When the formula style
14557 can also be replaced by
14564 (formula styles see
14565 \begin_inset CommandInset ref
14567 reference "sec:Formula-Styles"
14576 Then the description follows as normal text, and finally
14582 is inserted in TeX-mode.
14595 hereby create a displayed formula.
14598 \begin_layout Standard
14605 can be seen in this example that was
14606 \begin_inset Quotes eld
14610 \begin_inset Quotes erd
14613 using the mathematical textmode:
14614 \begin_inset Formula \[
14615 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14622 \begin_layout Section
14627 \begin_layout Plain Layout
14636 \begin_layout Subsection
14638 \begin_inset CommandInset label
14640 name "sub:Big-Operators"
14648 \begin_layout Plain Layout
14658 \begin_layout Plain Layout
14668 \begin_layout Plain Layout
14677 \begin_layout Standard
14678 To be able to use all integral operators listed here, the option
14680 Use esint package automatically
14682 must be set in the document settings under
14685 \begin_inset Space ~
14693 \begin_layout Standard
14694 \begin_inset Space \hfill{}
14698 \begin_inset Tabular
14699 <lyxtabular version="3" rows="11" columns="2">
14701 <column alignment="center" valignment="top" width="0pt">
14702 <column alignment="center" valignment="top" width="0pt">
14704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14707 \begin_layout Plain Layout
14713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14716 \begin_layout Plain Layout
14724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14727 \begin_layout Plain Layout
14734 \begin_layout Plain Layout
14747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14750 \begin_layout Plain Layout
14751 \begin_inset Formula $\sum$
14761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14764 \begin_layout Plain Layout
14771 \begin_layout Plain Layout
14784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14787 \begin_layout Plain Layout
14788 \begin_inset Formula $\int$
14798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14801 \begin_layout Plain Layout
14809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14812 \begin_layout Plain Layout
14813 \begin_inset Formula $\intop$
14823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14826 \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 $\oint$
14848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14851 \begin_layout Plain Layout
14859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14862 \begin_layout Plain Layout
14863 \begin_inset Formula $\ointop$
14873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14876 \begin_layout Plain Layout
14884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14887 \begin_layout Plain Layout
14888 \begin_inset Formula $\ointctrclockwise$
14898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14901 \begin_layout Plain Layout
14909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14912 \begin_layout Plain Layout
14913 \begin_inset Formula $\ointclockwise$
14923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14926 \begin_layout Plain Layout
14934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14937 \begin_layout Plain Layout
14938 \begin_inset Formula $\sqint$
14948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14951 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14962 \begin_layout Plain Layout
14963 \begin_inset Formula $\bigcap$
14973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14987 \begin_layout Plain Layout
14988 \begin_inset Formula $\bigcup$
15002 \begin_inset Space \hfill{}
15006 \begin_inset Tabular
15007 <lyxtabular version="3" rows="10" columns="2">
15009 <column alignment="center" valignment="top" width="0pt">
15010 <column alignment="center" valignment="top" width="0pt">
15012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15015 \begin_layout Plain Layout
15021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15024 \begin_layout Plain Layout
15032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15035 \begin_layout Plain Layout
15042 \begin_layout Plain Layout
15055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15058 \begin_layout Plain Layout
15059 \begin_inset Formula $\prod$
15069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15072 \begin_layout Plain Layout
15080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15083 \begin_layout Plain Layout
15084 \begin_inset Formula $\coprod$
15094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15097 \begin_layout Plain Layout
15105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15108 \begin_layout Plain Layout
15109 \begin_inset Formula $\bigodot$
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15134 \begin_inset Formula $\bigotimes$
15144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15147 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\bigoplus$
15169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15172 \begin_layout Plain Layout
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15183 \begin_layout Plain Layout
15184 \begin_inset Formula $\bigwedge$
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15197 \begin_layout Plain Layout
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15208 \begin_layout Plain Layout
15209 \begin_inset Formula $\bigvee$
15219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15222 \begin_layout Plain Layout
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15233 \begin_layout Plain Layout
15234 \begin_inset Formula $\bigsqcup$
15244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15247 \begin_layout Plain Layout
15255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15258 \begin_layout Plain Layout
15259 \begin_inset Formula $\biguplus$
15273 \begin_inset Space \hfill{}
15279 \begin_layout Standard
15280 All big operators can also be inserted via the math toolbar button
15281 \begin_inset Graphics
15282 filename ../images/math/intop.png
15290 \begin_layout Standard
15291 The operators are called big because they are bigger than the sometimes
15292 equal looking binary operators.
15293 All big operators can have limits as described in the next subsection.
15296 \begin_layout Standard
15322 \begin_inset Space ~
15325 in the style the operator limits are displayed, see
15326 \begin_inset CommandInset ref
15328 reference "sub:Operator-Limits"
15336 \begin_layout Subsubsection*
15337 Advices for Integrals
15340 \begin_layout Standard
15345 in an integral is an operator, that therefore has to be set upright.
15346 This is done by highlighting the
15350 and using the keyboard shortcut
15353 \begin_inset Space ~
15362 \begin_layout Plain Layout
15368 \begin_inset CommandInset ref
15370 reference "sub:Font-Styles"
15380 Finally the smallest space is inserted before the
15384 , as this is usual for operators.
15388 \begin_layout Standard
15390 \begin_inset Formula $\int A(x)dx$
15394 \begin_inset Newline newline
15401 \begin_layout Plain Layout
15411 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15417 \begin_layout Standard
15418 For multiple integrals there are the following commands:
15419 \begin_inset VSpace medskip
15425 \begin_layout Standard
15426 \begin_inset Space \hfill{}
15430 \begin_inset Tabular
15431 <lyxtabular version="3" rows="4" columns="2">
15433 <column alignment="center" valignment="top" width="0">
15434 <column alignment="center" valignment="top" width="0">
15436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15448 \begin_layout Plain Layout
15450 \begin_inset Note Note
15453 \begin_layout Plain Layout
15460 is only used as spacer.
15472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15475 \begin_layout Plain Layout
15483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15486 \begin_layout Plain Layout
15487 \begin_inset Formula $\raisebox {4.5mm}{}\iint\raisebox {-2.5mm}{}$
15497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15500 \begin_layout Plain Layout
15508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15511 \begin_layout Plain Layout
15512 \begin_inset Formula $\raisebox {4.5mm}{}\oiint\raisebox {-2.5mm}{}$
15522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15525 \begin_layout Plain Layout
15533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15536 \begin_layout Plain Layout
15537 \begin_inset Formula $\raisebox {4.5mm}{}\sqiint\raisebox {-2.5mm}{}$
15551 \begin_inset Space \hfill{}
15555 \begin_inset Tabular
15556 <lyxtabular version="3" rows="4" columns="2">
15558 <column alignment="center" valignment="top" width="0">
15559 <column alignment="center" valignment="top" width="0">
15561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15564 \begin_layout Plain Layout
15570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15573 \begin_layout Plain Layout
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15584 \begin_layout Plain Layout
15592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15595 \begin_layout Plain Layout
15596 \begin_inset Formula $\raisebox {4.5mm}{}\iiint\raisebox {-2.5mm}{}$
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15609 \begin_layout Plain Layout
15617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15620 \begin_layout Plain Layout
15621 \begin_inset Formula $\raisebox {4.5mm}{}\iiiint\raisebox {-2.5mm}{}$
15631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15634 \begin_layout Plain Layout
15642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15645 \begin_layout Plain Layout
15646 \begin_inset Formula $\raisebox {4.5mm}{}\dotsint\raisebox {-2.5mm}{}$
15660 \begin_inset Space \hfill{}
15666 \begin_layout Subsection
15668 \begin_inset CommandInset label
15670 name "sub:Operator-Limits"
15678 \begin_layout Plain Layout
15687 \begin_layout Standard
15688 Limits are created by super- and subscripts:
15691 \begin_layout Standard
15693 \begin_inset Tabular
15694 <lyxtabular version="3" rows="2" columns="2">
15696 <column alignment="center" valignment="top" width="0pt">
15697 <column alignment="center" valignment="top" width="0pt">
15699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15702 \begin_layout Plain Layout
15708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15711 \begin_layout Plain Layout
15713 \begin_inset Note Note
15716 \begin_layout Plain Layout
15723 is only used as spacer.
15735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15738 \begin_layout Plain Layout
15747 \begin_layout Plain Layout
15757 \begin_inset Formula $\to$
15761 \begin_inset Formula $\to$
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15773 \begin_inset Formula $\raisebox {5mm}{}\prod_{0}^{\infty}A(x)\raisebox {-2.5mm}{}$
15789 \begin_layout Standard
15790 Limits of inline formulas are set right beside the operator.
15791 Limits in displayed formulas are set above or below the operator, except
15792 of integral limits.
15795 \begin_layout Standard
15796 To force that the limits are set beside the operator, the cursor is set
15797 directly behind the operator and the limits type is changed with the menu
15800 Edit\SpecialChar \menuseparator
15801 Math\SpecialChar \menuseparator
15813 \begin_inset Space ~
15822 \begin_layout Standard
15823 The default limits type is this:
15824 \begin_inset Formula \[
15825 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15829 This is how it looks when the limits type was changed to
15836 \begin_inset Formula \[
15837 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15841 For integrals, except of
15853 , the limits are by default set beside the operator.
15854 But for multiple integrals the limits are often set below the operator.
15855 In the following example the limits type was therefore set to
15859 and so set below the integrals:
15860 \begin_inset Formula \begin{equation}
15861 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15868 \begin_layout Standard
15869 \begin_inset VSpace medskip
15872 To specify conditions for limits, the commands
15882 \begin_layout Plain Layout
15900 \begin_layout Plain Layout
15909 To create for example this expression
15910 \begin_inset Formula \begin{equation}
15911 \sum_{\begin{subarray}{c}
15913 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15920 \begin_layout Standard
15921 the following has to be done:
15922 \begin_inset Newline newline
15937 \begin_layout Plain Layout
15949 One is now in a blue box under the summation operator and insert there
15958 \begin_layout Plain Layout
15970 The blue box is now within a purple box and now several lines can be written
15972 A new line is created by inserting a line break (
15978 \begin_inset Newline newline
15983 0<k<1000 Ctrl-Return
15984 \begin_inset Newline newline
15989 is typed in, a new box appears below for the new line.
15992 \begin_layout Standard
15993 The alignment of the lines can be changed to left aligned with the
16003 Edit\SpecialChar \menuseparator
16007 To get right alignment,
16015 \begin_layout Plain Layout
16026 is inserted at the beginning of the line.
16029 \begin_layout Standard
16042 with the difference that the lines are always centered.
16045 \begin_layout Standard
16046 \begin_inset VSpace bigskip
16050 \begin_inset CommandInset ref
16052 reference "eq:substack"
16056 there can be too much space beside an operator, because the characters
16057 following the operator are set beside the limits.
16060 \begin_layout Standard
16061 To avoid this, the following macro can be used in the LaTeX-preamble:
16064 \begin_layout Standard
16078 \begin_inset Newline newline
16090 \begin_inset Newline newline
16097 mathclapinternal #1#2{
16101 mathsurround =0pt #1{#2}$}}
16104 \begin_layout Standard
16105 This defines the command
16115 \begin_layout Plain Layout
16123 that sets the width of the limit to 0
16124 \begin_inset Space \thinspace{}
16128 The command scheme is
16131 \begin_layout Standard
16139 \begin_layout Standard
16140 where the limit can consist of several conditions.
16143 \begin_layout Standard
16145 \begin_inset CommandInset ref
16147 reference "eq:substack"
16151 , one uses the command
16154 \begin_layout Standard
16167 \begin_layout Plain Layout
16176 0<k<1000 Ctrl-Enter
16179 \begin_layout Standard
16180 to create the lower limit.
16181 The summand is now directly behind the summation operator:
16182 \begin_inset Formula \[
16183 \sum_{\mathclap {\substack{0<k<1000\\
16184 \\k\,\in\,\mathbb{N}}
16192 \begin_layout Standard
16193 \begin_inset VSpace bigskip
16196 How to use one limit for several operators is described in
16197 \begin_inset CommandInset ref
16199 reference "sub:Self-defined-Operators"
16206 \begin_layout Subsection
16208 \begin_inset CommandInset label
16210 name "sub:Binary-Operators"
16218 \begin_layout Plain Layout
16227 \begin_layout Standard
16228 Binary operators are surrounded by space when there is a character before
16230 \begin_inset VSpace medskip
16236 \begin_layout Standard
16237 \begin_inset Space \hfill{}
16241 \begin_inset Tabular
16242 <lyxtabular version="3" rows="13" columns="2">
16244 <column alignment="center" valignment="top" width="0pt">
16245 <column alignment="center" valignment="top" width="0pt">
16247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16250 \begin_layout Plain Layout
16252 \begin_inset Note Note
16255 \begin_layout Plain Layout
16262 is only used as spacer.
16272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16275 \begin_layout Plain Layout
16283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16286 \begin_layout Plain Layout
16292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16295 \begin_layout Plain Layout
16296 \begin_inset Formula $+$
16306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16309 \begin_layout Plain Layout
16315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16318 \begin_layout Plain Layout
16319 \begin_inset Formula $-$
16329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16332 \begin_layout Plain Layout
16340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16343 \begin_layout Plain Layout
16344 \begin_inset Formula $\pm$
16354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16357 \begin_layout Plain Layout
16365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16368 \begin_layout Plain Layout
16369 \begin_inset Formula $\mp$
16379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16382 \begin_layout Plain Layout
16390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16393 \begin_layout Plain Layout
16394 \begin_inset Formula $\cdot$
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16407 \begin_layout Plain Layout
16415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16418 \begin_layout Plain Layout
16419 \begin_inset Formula $\times$
16429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16432 \begin_layout Plain Layout
16440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16443 \begin_layout Plain Layout
16444 \begin_inset Formula $\div$
16454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16457 \begin_layout Plain Layout
16461 \begin_layout Plain Layout
16474 \begin_layout Plain Layout
16486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16489 \begin_layout Plain Layout
16490 \begin_inset Formula $*$
16500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16503 \begin_layout Plain Layout
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16514 \begin_layout Plain Layout
16515 \begin_inset Formula $\star$
16525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16528 \begin_layout Plain Layout
16536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16539 \begin_layout Plain Layout
16540 \begin_inset Formula $\circ$
16550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16553 \begin_layout Plain Layout
16561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16564 \begin_layout Plain Layout
16565 \begin_inset Formula $\diamond$
16575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16578 \begin_layout Plain Layout
16586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16589 \begin_layout Plain Layout
16590 \begin_inset Formula $\bullet$
16604 \begin_inset Space \hfill{}
16608 \begin_inset Tabular
16609 <lyxtabular version="3" rows="13" columns="2">
16611 <column alignment="center" valignment="top" width="0pt">
16612 <column alignment="center" valignment="top" width="0pt">
16614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16617 \begin_layout Plain Layout
16623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16626 \begin_layout Plain Layout
16634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16637 \begin_layout Plain Layout
16645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16648 \begin_layout Plain Layout
16649 \begin_inset Formula $\nabla$
16659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16662 \begin_layout Plain Layout
16670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16673 \begin_layout Plain Layout
16674 \begin_inset Formula $\bigtriangledown$
16684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16687 \begin_layout Plain Layout
16695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16698 \begin_layout Plain Layout
16699 \begin_inset Formula $\bigtriangleup$
16709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16712 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16723 \begin_layout Plain Layout
16724 \begin_inset Formula $\Box$
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16737 \begin_layout Plain Layout
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16748 \begin_layout Plain Layout
16749 \begin_inset Formula $\cap$
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16762 \begin_layout Plain Layout
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16774 \begin_inset Formula $\cup$
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16787 \begin_layout Plain Layout
16795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16798 \begin_layout Plain Layout
16799 \begin_inset Formula $\dagger$
16809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16812 \begin_layout Plain Layout
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16823 \begin_layout Plain Layout
16824 \begin_inset Formula $\ddagger$
16834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16837 \begin_layout Plain Layout
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16848 \begin_layout Plain Layout
16849 \begin_inset Formula $\wr$
16859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16862 \begin_layout Plain Layout
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16873 \begin_layout Plain Layout
16874 \begin_inset Formula $\bigcirc$
16884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16887 \begin_layout Plain Layout
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16898 \begin_layout Plain Layout
16899 \begin_inset Formula $\wedge$
16909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16912 \begin_layout Plain Layout
16920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16923 \begin_layout Plain Layout
16924 \begin_inset Formula $\vee$
16938 \begin_inset Space \hfill{}
16942 \begin_inset Tabular
16943 <lyxtabular version="3" rows="13" columns="2">
16945 <column alignment="center" valignment="top" width="0pt">
16946 <column alignment="center" valignment="top" width="0pt">
16948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16951 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\oplus$
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\ominus$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\otimes$
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\oslash$
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\odot$
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17096 \begin_layout Plain Layout
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17107 \begin_layout Plain Layout
17108 \begin_inset Formula $\amalg$
17118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17121 \begin_layout Plain Layout
17129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17132 \begin_layout Plain Layout
17133 \begin_inset Formula $\uplus$
17143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17146 \begin_layout Plain Layout
17154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17157 \begin_layout Plain Layout
17158 \begin_inset Formula $\setminus$
17168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17171 \begin_layout Plain Layout
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17182 \begin_layout Plain Layout
17183 \begin_inset Formula $\sqcap$
17193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17196 \begin_layout Plain Layout
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17207 \begin_layout Plain Layout
17208 \begin_inset Formula $\sqcup$
17218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17221 \begin_layout Plain Layout
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17232 \begin_layout Plain Layout
17233 \begin_inset Formula $\triangleleft$
17243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17246 \begin_layout Plain Layout
17254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17257 \begin_layout Plain Layout
17258 \begin_inset Formula $\triangleright$
17272 \begin_inset Space \hfill{}
17278 \begin_layout Standard
17279 All binary operators can also be inserted via the math toolbar button
17280 \begin_inset Graphics
17281 filename ../images/math/pm.png
17289 \begin_layout Standard
17290 To typeset the Laplace operator also
17307 \begin_inset Formula $\nabla^{2}$
17310 ) can be used instead of
17319 \begin_layout Standard
17326 Insert\SpecialChar \menuseparator
17338 \begin_layout Subsection
17339 Self-defined Operators
17340 \begin_inset CommandInset label
17342 name "sub:Self-defined-Operators"
17350 \begin_layout Plain Layout
17351 Operators ! self-defined
17359 \begin_layout Standard
17360 With the help of the command
17364 DeclareMathOperator
17370 \begin_layout Plain Layout
17375 DeclareMathOperator
17380 custom operators can be defined in the LaTeX-preamble.
17381 Its command scheme is:
17384 \begin_layout Standard
17389 DeclareMathOperator{new command}{display}
17392 \begin_layout Standard
17393 Display can be characters or symbols that define how the operator looks
17395 To define a big operator a * is set behind the command.
17396 All self-defined big operators can have limits as described in
17397 \begin_inset CommandInset ref
17399 reference "sub:Operator-Limits"
17406 \begin_layout Standard
17407 For example the LaTeX-preamble line
17410 \begin_layout Standard
17415 DeclareMathOperator*{
17422 \begin_layout Standard
17423 defines the command
17429 , that inserts a big operator consisting of the lozenge symbol from
17430 \begin_inset CommandInset ref
17432 reference "sub:Miscellaneous-Symbols"
17437 \begin_inset Formula \[
17438 \Lozenge _{n=1}^{\infty}\]
17442 The command for this formula is:
17453 \begin_inset Formula $\to$
17459 \begin_layout Standard
17460 \begin_inset VSpace bigskip
17463 When self-defined operators are not used several times in the document,
17464 they can also be defined with the commands
17474 \begin_layout Plain Layout
17492 \begin_layout Plain Layout
17500 , which have the following scheme:
17503 \begin_layout Standard
17517 \begin_layout Standard
17524 defines big operators,
17533 \begin_layout Standard
17541 \begin_inset Space \thinspace{}
17545 \begin_inset Space ~
17548 be used to use one limit for several operators:
17551 \begin_layout Standard
17552 \begin_inset Formula \[
17553 \mathop {\sum\negmedspace\sum}_{i,j=1}^{N}\]
17560 \begin_layout Standard
17561 The command for the formula above is:
17562 \begin_inset Newline newline
17581 \begin_layout Plain Layout
17593 \begin_inset Formula $\to$
17602 \begin_layout Plain Layout
17616 \begin_layout Section
17621 \begin_layout Plain Layout
17630 \begin_layout Subsection
17632 \begin_inset CommandInset label
17634 name "sub:Font-Styles"
17642 \begin_layout Plain Layout
17651 \begin_layout Standard
17652 Latin letters in formulas can be set in one of the following font styles:
17653 \begin_inset VSpace -2mm
17659 \begin_layout Standard
17661 \begin_inset Tabular
17662 <lyxtabular version="3" rows="6" columns="3">
17664 <column alignment="center" valignment="top" width="0">
17665 <column alignment="center" valignment="top" width="0">
17666 <column alignment="center" valignment="top" width="0">
17668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17671 \begin_layout Plain Layout
17677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17680 \begin_layout Plain Layout
17686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17689 \begin_layout Plain Layout
17697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17700 \begin_layout Plain Layout
17709 \begin_layout Plain Layout
17725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17728 \begin_layout Plain Layout
17729 \begin_inset Formula $\mathbb{ABC}$
17737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17740 \begin_layout Plain Layout
17748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17751 \begin_layout Plain Layout
17760 \begin_layout Plain Layout
17776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17779 \begin_layout Plain Layout
17780 \begin_inset Formula $\mathbf{AbC}$
17788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17791 \begin_layout Plain Layout
17799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17802 \begin_layout Plain Layout
17811 \begin_layout Plain Layout
17827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17830 \begin_layout Plain Layout
17831 \begin_inset Formula $\boldsymbol{AbC}$
17839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17842 \begin_layout Plain Layout
17850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17853 \begin_layout Plain Layout
17862 \begin_layout Plain Layout
17878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17881 \begin_layout Plain Layout
17882 \begin_inset Formula $\mathcal{ABC}$
17890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17893 \begin_layout Plain Layout
17901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17904 \begin_layout Plain Layout
17913 \begin_layout Plain Layout
17929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17932 \begin_layout Plain Layout
17933 \begin_inset Formula $\mathfrak{AbC}$
17941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17944 \begin_layout Plain Layout
17958 \begin_layout Standard
17960 \begin_inset Tabular
17961 <lyxtabular version="3" rows="5" columns="3">
17963 <column alignment="center" valignment="top" width="0">
17964 <column alignment="center" valignment="top" width="0">
17965 <column alignment="center" valignment="top" width="0">
17967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17970 \begin_layout Plain Layout
17976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17988 \begin_layout Plain Layout
17996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17999 \begin_layout Plain Layout
18008 \begin_layout Plain Layout
18024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18027 \begin_layout Plain Layout
18028 \begin_inset Formula $\mathit{AbC}$
18036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18039 \begin_layout Plain Layout
18047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18050 \begin_layout Plain Layout
18059 \begin_layout Plain Layout
18075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18078 \begin_layout Plain Layout
18079 \begin_inset Formula $\mathrm{AbC}$
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18090 \begin_layout Plain Layout
18098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18101 \begin_layout Plain Layout
18110 \begin_layout Plain Layout
18126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18129 \begin_layout Plain Layout
18130 \begin_inset Formula $\mathsf{AbC}$
18138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18141 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18152 \begin_layout Plain Layout
18161 \begin_layout Plain Layout
18177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18180 \begin_layout Plain Layout
18181 \begin_inset Formula $\mathtt{AbC}$
18189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18192 \begin_layout Plain Layout
18206 \begin_layout Standard
18207 \begin_inset Note Greyedout
18210 \begin_layout Plain Layout
18227 can only be used for big letters.
18235 \begin_layout Standard
18236 Predefined is the style
18245 \begin_layout Standard
18246 The style commands work also for letters in mathematical constructs:
18247 \begin_inset Formula \[
18248 \mathfrak{A=\frac{b}{C}}\]
18255 \begin_layout Standard
18256 Characters in mathematical text don't appear in a math font style but in
18257 the text font style
18264 That their style can't be set correctly via the text style dialog is a
18269 \begin_layout Plain Layout
18270 \begin_inset CommandInset href
18272 name "LyX-bug #4091"
18273 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18285 \begin_layout Standard
18286 Instead of the style commands the dialog
18288 Edit\SpecialChar \menuseparator
18289 Math\SpecialChar \menuseparator
18292 or the toolbar button
18293 \begin_inset Graphics
18294 filename ../images/math/font.png
18302 \begin_layout Subsection
18304 \begin_inset CommandInset label
18306 name "sub:Bold-Formulas"
18314 \begin_layout Plain Layout
18323 \begin_layout Standard
18324 To make a complete formula bold, the command
18330 from the previous subsection cannot be used, because it doesn't work for
18331 small Greek letters.
18332 Furthermore it prints Latin letters always upright, like in the following
18336 \begin_layout Standard
18337 \begin_inset Formula \[
18338 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18345 \begin_layout Standard
18346 To display the formula correctly, the command
18353 \begin_inset Formula \[
18354 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18358 It is also possible to set the formula in a
18360 boldmath environment
18363 This environment is created by inserting the command
18371 \begin_layout Plain Layout
18382 To end the environment, the command
18390 \begin_layout Plain Layout
18400 is inserted in TeX-mode.
18404 \begin_layout Plain Layout
18414 \begin_inset Formula \[
18415 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18423 \begin_layout Plain Layout
18435 \begin_layout Subsection
18437 \begin_inset CommandInset label
18439 name "sub:Font-Sizes"
18447 \begin_layout Plain Layout
18456 \begin_layout Standard
18457 For characters in formulas there are, analog to characters in text, the
18458 following size commands:
18461 \begin_layout Standard
18505 \begin_inset Newline newline
18527 \begin_layout Standard
18528 The size produced by the commands depends on the document font size, that
18529 corresponds with the command
18536 The other commands produce smaller or larger sizes than
18543 The font size can however not exceed a certain value.
18544 Is for example the document font size 12
18545 \begin_inset Space \thinspace{}
18554 switches to the same size as
18564 \begin_layout Standard
18565 A size command is inserted in TeX-mode before the formula and sets the size
18566 for all following formula and text characters.
18567 To switch back to the initial size, the command
18573 is inserted behind the formula in TeX-mode.
18576 \begin_layout Standard
18577 Within a formula the size can only be changed for symbols or letters in
18579 To do this, the size command is inserted in mathematical text.
18580 All following characters until the end of the mathematical text or until
18581 another size command will have the selected size.
18583 \begin_inset VSpace -2mm
18589 \begin_layout Standard
18593 \begin_layout Plain Layout
18603 \begin_inset Formula \[
18604 A=\frac{B}{c}\cdot\maltese\]
18609 \begin_inset Formula \[
18610 \maltese A\textrm{\Large \maltese\textit{A}}\textrm{\tiny \maltese\textit{A}}\]
18618 \begin_layout Plain Layout
18630 \begin_layout Standard
18631 \begin_inset VSpace medskip
18634 Before both formulas the command
18641 The command for the second formula is:
18642 \begin_inset Newline newline
18653 \begin_layout Plain Layout
18668 \begin_layout Plain Layout
18683 \begin_layout Plain Layout
18698 \begin_layout Plain Layout
18708 \begin_inset Formula $\to$
18712 \begin_inset Formula $\to$
18716 \begin_inset Newline newline
18720 \begin_inset Space \hspace*{}
18734 \begin_layout Plain Layout
18749 \begin_layout Plain Layout
18764 \begin_layout Plain Layout
18776 \begin_layout Standard
18777 If a symbol cannot be displayed in different sizes, it will always be displayed
18778 in the default size.
18781 \begin_layout Section
18786 \begin_layout Plain Layout
18795 \begin_layout Standard
18796 All Greek letters can also be inserted via the toolbar button
18797 \begin_inset Graphics
18798 filename ../images/math/alpha.png
18806 \begin_layout Subsection
18808 \begin_inset CommandInset label
18810 name "sub:Small-Letters"
18818 \begin_layout Plain Layout
18819 Greek letters ! small
18827 \begin_layout Standard
18828 \begin_inset Space \hfill{}
18832 \begin_inset Tabular
18833 <lyxtabular version="3" rows="11" columns="2">
18835 <column alignment="center" valignment="top" width="0pt">
18836 <column alignment="center" valignment="top" width="0pt">
18838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18841 \begin_layout Plain Layout
18847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18850 \begin_layout Plain Layout
18858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18861 \begin_layout Plain Layout
18869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18872 \begin_layout Plain Layout
18873 \begin_inset Formula $\alpha$
18883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18886 \begin_layout Plain Layout
18894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18897 \begin_layout Plain Layout
18898 \begin_inset Formula $\beta$
18908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18911 \begin_layout Plain Layout
18919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18922 \begin_layout Plain Layout
18923 \begin_inset Formula $\gamma$
18933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18936 \begin_layout Plain Layout
18944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18947 \begin_layout Plain Layout
18948 \begin_inset Formula $\delta$
18958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18961 \begin_layout Plain Layout
18969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18972 \begin_layout Plain Layout
18973 \begin_inset Formula $\epsilon$
18983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18986 \begin_layout Plain Layout
18994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18997 \begin_layout Plain Layout
18998 \begin_inset Formula $\varepsilon$
19008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19011 \begin_layout Plain Layout
19019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19022 \begin_layout Plain Layout
19023 \begin_inset Formula $\zeta$
19033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19036 \begin_layout Plain Layout
19044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19047 \begin_layout Plain Layout
19048 \begin_inset Formula $\eta$
19058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19061 \begin_layout Plain Layout
19069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19072 \begin_layout Plain Layout
19073 \begin_inset Formula $\theta$
19083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19086 \begin_layout Plain Layout
19094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19097 \begin_layout Plain Layout
19098 \begin_inset Formula $\vartheta$
19112 \begin_inset Space \hfill{}
19116 \begin_inset Tabular
19117 <lyxtabular version="3" rows="12" columns="2">
19119 <column alignment="center" valignment="top" width="0pt">
19120 <column alignment="center" valignment="top" width="0pt">
19122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19125 \begin_layout Plain Layout
19131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19134 \begin_layout Plain Layout
19142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19145 \begin_layout Plain Layout
19153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19156 \begin_layout Plain Layout
19157 \begin_inset Formula $\iota$
19167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19170 \begin_layout Plain Layout
19178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19181 \begin_layout Plain Layout
19182 \begin_inset Formula $\kappa$
19192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19195 \begin_layout Plain Layout
19203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19206 \begin_layout Plain Layout
19207 \begin_inset Formula $\varkappa$
19217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19220 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19231 \begin_layout Plain Layout
19232 \begin_inset Formula $\lambda$
19242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19245 \begin_layout Plain Layout
19253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19256 \begin_layout Plain Layout
19257 \begin_inset Formula $\mu$
19267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19270 \begin_layout Plain Layout
19278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19281 \begin_layout Plain Layout
19282 \begin_inset Formula $\nu$
19292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19295 \begin_layout Plain Layout
19303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19306 \begin_layout Plain Layout
19307 \begin_inset Formula $\xi$
19317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19320 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula $o$
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19343 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula $\pi$
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula $\varpi$
19390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19393 \begin_layout Plain Layout
19401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Plain Layout
19405 \begin_inset Formula $\rho$
19419 \begin_inset Space \hfill{}
19423 \begin_inset Tabular
19424 <lyxtabular version="3" rows="11" columns="2">
19426 <column alignment="center" valignment="top" width="0pt">
19427 <column alignment="center" valignment="top" width="0pt">
19429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19432 \begin_layout Plain Layout
19438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19441 \begin_layout Plain Layout
19449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19452 \begin_layout Plain Layout
19460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19463 \begin_layout Plain Layout
19464 \begin_inset Formula $\varrho$
19474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19477 \begin_layout Plain Layout
19485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19488 \begin_layout Plain Layout
19489 \begin_inset Formula $\sigma$
19499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19502 \begin_layout Plain Layout
19510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19513 \begin_layout Plain Layout
19514 \begin_inset Formula $\varsigma$
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19527 \begin_layout Plain Layout
19535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19538 \begin_layout Plain Layout
19539 \begin_inset Formula $\tau$
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19552 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19563 \begin_layout Plain Layout
19564 \begin_inset Formula $\upsilon$
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19589 \begin_inset Formula $\phi$
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19602 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19614 \begin_inset Formula $\varphi$
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19627 \begin_layout Plain Layout
19635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19638 \begin_layout Plain Layout
19639 \begin_inset Formula $\chi$
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19652 \begin_layout Plain Layout
19660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19663 \begin_layout Plain Layout
19664 \begin_inset Formula $\psi$
19674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19677 \begin_layout Plain Layout
19685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19688 \begin_layout Plain Layout
19689 \begin_inset Formula $\omega$
19703 \begin_inset Space \hfill{}
19709 \begin_layout Standard
19710 \begin_inset VSpace medskip
19716 \begin_layout Standard
19717 How to create upright Greek letters is explained in
19718 \begin_inset CommandInset ref
19720 reference "sub:Upright-small-Greek"
19727 \begin_layout Subsection
19732 \begin_layout Plain Layout
19733 Greek letters ! big
19741 \begin_layout Standard
19742 \begin_inset Space \hfill{}
19746 \begin_inset Tabular
19747 <lyxtabular version="3" rows="7" columns="2">
19749 <column alignment="center" valignment="top" width="0pt">
19750 <column alignment="center" valignment="top" width="0pt">
19752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19755 \begin_layout Plain Layout
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19764 \begin_layout Plain Layout
19772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19775 \begin_layout Plain Layout
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19786 \begin_layout Plain Layout
19787 \begin_inset Formula $\Gamma$
19797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19800 \begin_layout Plain Layout
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Plain Layout
19812 \begin_inset Formula $\Delta$
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19825 \begin_layout Plain Layout
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Plain Layout
19837 \begin_inset Formula $\Theta$
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Plain Layout
19862 \begin_inset Formula $\Lambda$
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19875 \begin_layout Plain Layout
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19886 \begin_layout Plain Layout
19887 \begin_inset Formula $\Xi$
19897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19900 \begin_layout Plain Layout
19908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19911 \begin_layout Plain Layout
19912 \begin_inset Formula $\Pi$
19926 \begin_inset Space \hfill{}
19930 \begin_inset Tabular
19931 <lyxtabular version="3" rows="6" columns="2">
19933 <column alignment="center" valignment="top" width="0pt">
19934 <column alignment="center" valignment="top" width="0pt">
19936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19939 \begin_layout Plain Layout
19945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19948 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19959 \begin_layout Plain Layout
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19970 \begin_layout Plain Layout
19971 \begin_inset Formula $\Sigma$
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19984 \begin_layout Plain Layout
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19995 \begin_layout Plain Layout
19996 \begin_inset Formula $\Upsilon$
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20009 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20021 \begin_inset Formula $\Phi$
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $\Psi$
20056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\Omega$
20085 \begin_inset Space \hfill{}
20091 \begin_layout Standard
20092 \begin_inset VSpace medskip
20095 That the big Greek letters appear upright is caused by a design bug when
20097 To get correct italic big letters, begin every command with
20102 For example the command
20109 \begin_inset Formula $\varGamma $
20115 \begin_layout Subsection
20120 \begin_layout Plain Layout
20121 Greek letters ! bold
20129 \begin_layout Standard
20130 Greek letters cannot be set with different font styles like Latin letters.
20131 They can only be made bold with the command
20141 \begin_layout Plain Layout
20152 \begin_layout Standard
20154 \begin_inset Tabular
20155 <lyxtabular version="3" rows="3" columns="2">
20157 <column alignment="center" valignment="top" width="0">
20158 <column alignment="center" valignment="top" width="0">
20160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20163 \begin_layout Plain Layout
20169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Plain Layout
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20183 \begin_layout Plain Layout
20195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20198 \begin_layout Plain Layout
20199 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20212 \begin_layout Plain Layout
20224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20227 \begin_layout Plain Layout
20228 \begin_inset Formula $\theta\boldsymbol{\theta}$
20244 \begin_layout Section
20249 \begin_layout Plain Layout
20262 \begin_layout Plain Layout
20263 A list with all symbols of most of the LaTeX-packages can be found in
20264 \begin_inset CommandInset citation
20279 \begin_layout Plain Layout
20287 \begin_inset Note Note
20290 \begin_layout Plain Layout
20293 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20296 \begin_layout Plain Layout
20299 texorpdfstring is in section
20300 \begin_inset CommandInset ref
20302 reference "sub:Formulas-in-Section"
20315 \begin_layout Plain Layout
20324 \begin_layout Standard
20325 Many of the symbols listed in this section can also be inserted via the
20327 \begin_inset Graphics
20328 filename ../images/math/nabla.png
20334 \begin_inset Graphics
20335 filename ../images/math/digamma.png
20343 \begin_layout Subsection
20344 Mathematical Symbols
20345 \begin_inset CommandInset label
20347 name "sub:Mathematical-Symbols"
20355 \begin_layout Plain Layout
20356 Symbols ! mathematical
20364 \begin_layout Standard
20365 \begin_inset Space \hfill{}
20369 \begin_inset Tabular
20370 <lyxtabular version="3" rows="10" columns="2">
20372 <column alignment="center" valignment="top" width="0pt">
20373 <column alignment="center" valignment="top" width="0pt">
20375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20378 \begin_layout Plain Layout
20384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20387 \begin_layout Plain Layout
20395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\neg$
20420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\Im$
20445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20459 \begin_layout Plain Layout
20460 \begin_inset Formula $\Re$
20470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20473 \begin_layout Plain Layout
20481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20484 \begin_layout Plain Layout
20485 \begin_inset Formula $\aleph$
20495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20498 \begin_layout Plain Layout
20506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20509 \begin_layout Plain Layout
20510 \begin_inset Formula $\partial$
20520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20523 \begin_layout Plain Layout
20531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20534 \begin_layout Plain Layout
20535 \begin_inset Formula $\infty$
20545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20548 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20559 \begin_layout Plain Layout
20560 \begin_inset Formula $\wp$
20570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20573 \begin_layout Plain Layout
20581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20584 \begin_layout Plain Layout
20585 \begin_inset Formula $\imath$
20595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20598 \begin_layout Plain Layout
20606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20609 \begin_layout Plain Layout
20610 \begin_inset Formula $\jmath$
20624 \begin_inset Space \hfill{}
20628 \begin_inset Tabular
20629 <lyxtabular version="3" rows="10" columns="2">
20631 <column alignment="center" valignment="top" width="0pt">
20632 <column alignment="center" valignment="top" width="0pt">
20634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20637 \begin_layout Plain Layout
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20646 \begin_layout Plain Layout
20648 \begin_inset Note Note
20651 \begin_layout Plain Layout
20658 is only used as spacer.
20670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20673 \begin_layout Plain Layout
20681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20684 \begin_layout Plain Layout
20685 \begin_inset Formula $\forall$
20695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20698 \begin_layout Plain Layout
20706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20709 \begin_layout Plain Layout
20710 \begin_inset Formula $\exists$
20720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20723 \begin_layout Plain Layout
20731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20734 \begin_layout Plain Layout
20735 \begin_inset Formula $\nexists$
20745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20748 \begin_layout Plain Layout
20756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20759 \begin_layout Plain Layout
20760 \begin_inset Formula $\emptyset$
20770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20773 \begin_layout Plain Layout
20781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20784 \begin_layout Plain Layout
20785 \begin_inset Formula $\varnothing$
20795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20798 \begin_layout Plain Layout
20806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20809 \begin_layout Plain Layout
20810 \begin_inset Formula $\dag $
20820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20823 \begin_layout Plain Layout
20831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20834 \begin_layout Plain Layout
20835 \begin_inset Formula $\ddag $
20845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20848 \begin_layout Plain Layout
20856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20859 \begin_layout Plain Layout
20863 \begin_layout Plain Layout
20873 \begin_inset Formula $\complement$
20880 \begin_layout Plain Layout
20894 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20897 \begin_layout Plain Layout
20905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20908 \begin_layout Plain Layout
20909 \begin_inset Formula $\Bbbk$
20923 \begin_inset Space \hfill{}
20927 \begin_inset Tabular
20928 <lyxtabular version="3" rows="10" columns="2">
20930 <column alignment="center" valignment="top" width="0pt">
20931 <column alignment="center" valignment="top" width="0pt">
20933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20936 \begin_layout Plain Layout
20942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20967 \begin_layout Plain Layout
20968 \begin_inset Formula $\prime$
20978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20981 \begin_layout Plain Layout
20989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20992 \begin_layout Plain Layout
20993 \begin_inset Formula $\backprime$
21003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21006 \begin_layout Plain Layout
21014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21017 \begin_layout Plain Layout
21018 \begin_inset Formula $\mho$
21028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21031 \begin_layout Plain Layout
21039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21042 \begin_layout Plain Layout
21043 \begin_inset Formula $\triangle$
21053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21056 \begin_layout Plain Layout
21064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21067 \begin_layout Plain Layout
21068 \begin_inset Formula $\angle$
21078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21081 \begin_layout Plain Layout
21089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21092 \begin_layout Plain Layout
21093 \begin_inset Formula $\measuredangle$
21103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21106 \begin_layout Plain Layout
21114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21117 \begin_layout Plain Layout
21118 \begin_inset Formula $\sphericalangle$
21128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21131 \begin_layout Plain Layout
21139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21142 \begin_layout Plain Layout
21143 \begin_inset Formula $\top$
21153 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21156 \begin_layout Plain Layout
21164 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21167 \begin_layout Plain Layout
21168 \begin_inset Formula $\bot$
21182 \begin_inset Space \hfill{}
21188 \begin_layout Standard
21189 \begin_inset Newpage newpage
21195 \begin_layout Subsection
21196 Miscellaneous Symbols
21197 \begin_inset CommandInset label
21199 name "sub:Miscellaneous-Symbols"
21207 \begin_layout Plain Layout
21208 Symbols ! miscellaneous
21216 \begin_layout Standard
21219 \begin_inset Tabular
21220 <lyxtabular version="3" rows="10" columns="2">
21222 <column alignment="center" valignment="top" width="0pt">
21223 <column alignment="center" valignment="top" width="0pt">
21225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21228 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21237 \begin_layout Plain Layout
21245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21248 \begin_layout Plain Layout
21256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21259 \begin_layout Plain Layout
21260 \begin_inset Formula $\flat$
21270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21273 \begin_layout Plain Layout
21281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21284 \begin_layout Plain Layout
21285 \begin_inset Formula $\natural$
21295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21298 \begin_layout Plain Layout
21306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Plain Layout
21310 \begin_inset Formula $\sharp$
21320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21335 \begin_inset Formula $\surd$
21345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21348 \begin_layout Plain Layout
21356 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21359 \begin_layout Plain Layout
21360 \begin_inset Formula $\checkmark$
21370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21373 \begin_layout Plain Layout
21381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21384 \begin_layout Plain Layout
21385 \begin_inset Formula $\yen$
21395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21398 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21410 \begin_inset Formula $\pounds $
21420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21432 \begin_layout Plain Layout
21433 \begin_inset Formula $\$$
21443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21446 \begin_layout Plain Layout
21452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21455 \begin_layout Plain Layout
21456 \begin_inset Formula $§$
21470 \begin_inset Tabular
21471 <lyxtabular version="3" rows="10" columns="2">
21473 <column alignment="center" valignment="top" width="0">
21474 <column alignment="center" valignment="top" width="0">
21476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21479 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21499 \begin_layout Plain Layout
21507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21510 \begin_layout Plain Layout
21511 \begin_inset Formula $\hbar$
21521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21524 \begin_layout Plain Layout
21532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21535 \begin_layout Plain Layout
21536 \begin_inset Formula $\hslash$
21546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21549 \begin_layout Plain Layout
21557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21560 \begin_layout Plain Layout
21561 \begin_inset Formula $\clubsuit$
21571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21574 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21585 \begin_layout Plain Layout
21586 \begin_inset Formula $\spadesuit$
21596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21599 \begin_layout Plain Layout
21607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21610 \begin_layout Plain Layout
21611 \begin_inset Formula $\bigstar$
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21636 \begin_inset Formula $\blacklozenge$
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21649 \begin_layout Plain Layout
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21660 \begin_layout Plain Layout
21661 \begin_inset Formula $\blacktriangle$
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\blacktriangledown$
21696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Plain Layout
21711 \begin_inset Formula $\bullet$
21725 \begin_inset Tabular
21726 <lyxtabular version="3" rows="10" columns="2">
21728 <column alignment="center" valignment="top" width="0pt">
21729 <column alignment="center" valignment="top" width="0pt">
21731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21743 \begin_layout Plain Layout
21751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21754 \begin_layout Plain Layout
21762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21765 \begin_layout Plain Layout
21766 \begin_inset Formula $\diamondsuit$
21776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21779 \begin_layout Plain Layout
21787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21790 \begin_layout Plain Layout
21791 \begin_inset Formula $\Diamond$
21801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21804 \begin_layout Plain Layout
21812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21815 \begin_layout Plain Layout
21816 \begin_inset Formula $\heartsuit$
21826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21829 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21841 \begin_inset Formula $\P $
21851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21854 \begin_layout Plain Layout
21862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21865 \begin_layout Plain Layout
21866 \begin_inset Formula $\copyright $
21876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21879 \begin_layout Plain Layout
21887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21890 \begin_layout Plain Layout
21891 \begin_inset Formula $\circledR$
21901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21904 \begin_layout Plain Layout
21912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21915 \begin_layout Plain Layout
21916 \begin_inset Formula $\maltese$
21926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21929 \begin_layout Plain Layout
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21940 \begin_layout Plain Layout
21941 \begin_inset Formula $\diagup$
21951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21954 \begin_layout Plain Layout
21962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21965 \begin_layout Plain Layout
21966 \begin_inset Formula $\diagdown$
21982 \begin_layout Standard
21983 \begin_inset VSpace medskip
21986 More symbols are listed in
21987 \begin_inset CommandInset ref
21989 reference "sub:Miscellaneous-Special-Characters"
21996 \begin_layout Standard
21997 Some symbols can be displayed in different sizes, see
21998 \begin_inset CommandInset ref
22000 reference "sub:Font-Sizes"
22007 \begin_layout Subsection
22012 \begin_layout Plain Layout
22013 Symbols ! Euro-symbol
22022 \begin_layout Plain Layout
22026 \begin_layout Plain Layout
22043 \begin_layout Standard
22044 To use the Euro symbol in formulas, the LaTeX-package
22052 \begin_layout Plain Layout
22058 must be installed and loaded with the LaTeX-preamble line
22061 \begin_layout Standard
22066 usepackage[gennarrow]{eurosym}
22069 \begin_layout Standard
22070 The Euro symbol can now be inserted with the command
22080 \begin_layout Plain Layout
22091 \begin_layout Standard
22092 The Euro symbol can directly be inserted with the € key in mathematical
22093 text, without having
22108 can also be inserted in TeX-mode.
22109 The official currency symbol can then be inserted with the command
22119 \begin_layout Plain Layout
22127 , that is only available in TeX-mode.
22130 \begin_layout Standard
22134 \begin_layout Plain Layout
22144 \begin_inset Note Note
22147 \begin_layout Plain Layout
22148 The following table will only be displayed when the LaTeX-package
22160 \begin_layout Standard
22161 An overview about the different Euro symbols:
22164 \begin_layout Standard
22166 \begin_inset Tabular
22167 <lyxtabular version="3" rows="4" columns="3">
22169 <column alignment="center" valignment="top" width="0pt">
22170 <column alignment="center" valignment="top" width="0pt">
22171 <column alignment="center" valignment="top" width="0pt">
22173 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22176 \begin_layout Plain Layout
22182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22185 \begin_layout Plain Layout
22191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22194 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22205 \begin_layout Plain Layout
22211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22214 \begin_layout Plain Layout
22222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22225 \begin_layout Plain Layout
22226 \begin_inset Formula $\euro $
22236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22239 \begin_layout Plain Layout
22245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22248 \begin_layout Plain Layout
22254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22257 \begin_layout Plain Layout
22258 \begin_inset Formula $\mbox{€}$
22268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22280 \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
22295 \begin_layout Plain Layout
22317 \begin_layout Standard
22321 \begin_layout Plain Layout
22331 \begin_inset Note Note
22334 \begin_layout Plain Layout
22335 The following will be displayed when the LaTeX-package
22347 \begin_layout Standard
22348 You need to install the LaTeX-package
22352 to see the rest of this subsection in the output.
22355 \begin_layout Standard
22359 \begin_layout Plain Layout
22371 \begin_layout Section
22373 \begin_inset CommandInset label
22375 name "sec:Relations"
22383 \begin_layout Plain Layout
22393 \begin_layout Plain Layout
22398 \begin_layout Plain Layout
22409 \begin_layout Plain Layout
22424 \begin_layout Standard
22425 All relations can also be inserted via the toolbar button
22426 \begin_inset Graphics
22427 filename ../images/math/leq.png
22435 \begin_layout Standard
22436 \begin_inset Space \hfill{}
22440 \begin_inset Tabular
22441 <lyxtabular version="3" rows="17" columns="2">
22443 <column alignment="center" valignment="top" width="0pt">
22444 <column alignment="center" valignment="top" width="0pt">
22446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22449 \begin_layout Plain Layout
22455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22458 \begin_layout Plain Layout
22466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22478 \begin_layout Plain Layout
22479 \begin_inset Formula $<$
22489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22504 \begin_inset Formula $\le$
22514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22517 \begin_layout Plain Layout
22525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22528 \begin_layout Plain Layout
22529 \begin_inset Formula $\ll$
22539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22542 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22554 \begin_inset Formula $\prec$
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22567 \begin_layout Plain Layout
22575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22578 \begin_layout Plain Layout
22579 \begin_inset Formula $\preceq$
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22592 \begin_layout Plain Layout
22600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22603 \begin_layout Plain Layout
22604 \begin_inset Formula $\subset$
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22617 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22628 \begin_layout Plain Layout
22629 \begin_inset Formula $\subseteq$
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22654 \begin_inset Formula $\sqsubseteq$
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22678 \begin_layout Plain Layout
22679 \begin_inset Formula $\in$
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22703 \begin_layout Plain Layout
22704 \begin_inset Formula $\vdash$
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\smile$
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\lhd$
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\unlhd$
22789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\gtrless$
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\mid$
22839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\nmid$
22868 \begin_inset Space \hfill{}
22872 \begin_inset Tabular
22873 <lyxtabular version="3" rows="17" columns="2">
22875 <column alignment="center" valignment="top" width="0pt">
22876 <column alignment="center" valignment="top" width="0pt">
22878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22881 \begin_layout Plain Layout
22887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22890 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22901 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22910 \begin_layout Plain Layout
22911 \begin_inset Formula $=$
22921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22924 \begin_layout Plain Layout
22932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22935 \begin_layout Plain Layout
22936 \begin_inset Formula $\not=$
22946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22949 \begin_layout Plain Layout
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22960 \begin_layout Plain Layout
22961 \begin_inset Formula $\equiv$
22971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22974 \begin_layout Plain Layout
22982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22985 \begin_layout Plain Layout
22986 \begin_inset Formula $\sim$
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23010 \begin_layout Plain Layout
23011 \begin_inset Formula $\simeq$
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23024 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23035 \begin_layout Plain Layout
23036 \begin_inset Formula $\approx$
23046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23049 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23060 \begin_layout Plain Layout
23061 \begin_inset Formula $\cong$
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23086 \begin_inset Formula $\bowtie$
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23099 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23110 \begin_layout Plain Layout
23111 \begin_inset Formula $\notin$
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\perp$
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23161 \begin_inset Formula $\propto$
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23174 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\asymp$
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\doteq$
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23235 \begin_layout Plain Layout
23236 \begin_inset Formula $\circeq$
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23261 \begin_inset Formula $\models$
23271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23285 \begin_layout Plain Layout
23286 \begin_inset Formula $\widehat{=}$
23300 \begin_inset Space \hfill{}
23304 \begin_inset Tabular
23305 <lyxtabular version="3" rows="17" columns="2">
23307 <column alignment="center" valignment="top" width="0pt">
23308 <column alignment="center" valignment="top" width="0pt">
23310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23313 \begin_layout Plain Layout
23319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23333 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23342 \begin_layout Plain Layout
23343 \begin_inset Formula $>$
23353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23356 \begin_layout Plain Layout
23364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23367 \begin_layout Plain Layout
23368 \begin_inset Formula $\ge$
23378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23381 \begin_layout Plain Layout
23389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23392 \begin_layout Plain Layout
23393 \begin_inset Formula $\gg$
23403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23406 \begin_layout Plain Layout
23414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23417 \begin_layout Plain Layout
23418 \begin_inset Formula $\succ$
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $\succeq$
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\supset$
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\supseteq$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\sqsupseteq$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\ni$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\dashv$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\frown$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\rhd$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\unrhd$
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\lessgtr$
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23693 \begin_inset Formula $\parallel$
23703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23717 \begin_layout Plain Layout
23718 \begin_inset Formula $\nparallel$
23732 \begin_inset Space \hfill{}
23738 \begin_layout Standard
23739 \begin_inset VSpace medskip
23754 are bigger than the equal looking operators
23769 \begin_layout Standard
23770 Relations are, in contrary to symbols, always surrounded by space.
23773 \begin_layout Standard
23774 Relations with labels can be created with the command
23784 \begin_layout Plain Layout
23795 \begin_layout Standard
23797 \begin_inset Tabular
23798 <lyxtabular version="3" rows="2" columns="2">
23800 <column alignment="center" valignment="top" width="0">
23801 <column alignment="center" valignment="top" width="0">
23803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23806 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23817 \begin_inset Note Note
23820 \begin_layout Plain Layout
23827 is only used as spacer.
23839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23842 \begin_layout Plain Layout
23849 \begin_layout Plain Layout
23866 \begin_layout Plain Layout
23876 \begin_inset Formula $\downarrow$
23885 \begin_layout Plain Layout
23898 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\raisebox {5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23932 \begin_layout Section
23936 \begin_layout Subsection
23937 Predefined Functions
23938 \begin_inset CommandInset label
23940 name "sub:Predefined-Functions"
23948 \begin_layout Plain Layout
23949 Functions ! predefined
23957 \begin_layout Standard
23958 In general, variables are set
23962 in mathematical expressions, but not function names, because
23963 \begin_inset Formula $sin$
23966 could be misunderstood as
23967 \begin_inset Formula $s\cdot i\cdot n$
23971 Therefore there are predefined functions, that are additionally a bit separated
23973 They are inserted as commands starting with a backslash before their name.
23976 \begin_layout Standard
23978 \begin_inset Tabular
23979 <lyxtabular version="3" rows="2" columns="4">
23981 <column alignment="center" valignment="top" width="0pt">
23982 <column alignment="center" valignment="top" width="0pt">
23983 <column alignment="center" valignment="top" width="0pt">
23984 <column alignment="center" valignment="top" width="0pt">
23986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23989 \begin_layout Plain Layout
23995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Plain Layout
24004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24007 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24027 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24036 \begin_layout Plain Layout
24037 \begin_inset Formula $Asin(x)+B$
24045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24048 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Plain Layout
24060 \begin_inset Formula $A\sin(x)+B$
24074 \begin_inset Newpage pagebreak
24080 \begin_layout Standard
24081 The following functions are predefined:
24084 \begin_layout Standard
24085 \begin_inset VSpace -2mm
24091 \begin_layout Standard
24093 \begin_inset Tabular
24094 <lyxtabular version="3" rows="9" columns="4">
24096 <column alignment="center" valignment="top" width="0pt">
24097 <column alignment="center" valignment="top" width="0pt">
24098 <column alignment="center" valignment="top" width="0pt">
24099 <column alignment="center" valignment="top" width="0pt">
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" usebox="none">
24113 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24131 \begin_layout Plain Layout
24139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24153 \begin_layout Plain Layout
24161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24164 \begin_layout Plain Layout
24172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24175 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24188 \begin_layout Plain Layout
24196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24199 \begin_layout Plain Layout
24207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24210 \begin_layout Plain Layout
24218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24221 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24234 \begin_layout Plain Layout
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24245 \begin_layout Plain Layout
24253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24256 \begin_layout Plain Layout
24264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24267 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24291 \begin_layout Plain Layout
24299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24302 \begin_layout Plain Layout
24310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24313 \begin_layout Plain Layout
24323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24337 \begin_layout Plain Layout
24345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24348 \begin_layout Plain Layout
24356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24359 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24405 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24418 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24440 \begin_layout Plain Layout
24448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24451 \begin_layout Plain Layout
24461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24464 \begin_layout Plain Layout
24472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24475 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24513 \begin_layout Standard
24514 They can also be inserted with the math toolbar button
24515 \begin_inset Graphics
24516 filename ../images/math/functions.png
24524 \begin_layout Subsection
24525 Self-defined Functions
24529 \begin_layout Plain Layout
24530 Functions ! self-defined
24538 \begin_layout Standard
24539 To use a function that is not predefined, like for example the sign function
24540 sgn(x), there are two possibilities:
24543 \begin_layout Itemize
24544 Define the function by inserting the following line to the LaTeX-preamble
24548 \begin_layout Plain Layout
24553 DeclareMathOperator
24556 \begin_inset CommandInset ref
24558 reference "sub:Self-defined-Operators"
24568 \begin_inset Newline newline
24572 \begin_inset VSpace -3mm
24576 \begin_inset Newline newline
24583 DeclareMathOperator{
24591 \begin_layout Plain Layout
24596 DeclareMathOperator
24602 \begin_inset Newline newline
24606 \begin_inset VSpace -2mm
24610 \begin_inset Newline newline
24613 Now the new defined function can be called with the command
24622 \begin_layout Itemize
24623 Write the the formula as usual, mark the formula name, in our example the
24628 , and change it to mathematical text.
24629 At last a space is inserted between prefactor and function.
24632 \begin_layout Standard
24633 The result is the same with both methods as with a predefined function
24637 \begin_layout Plain Layout
24638 In LyX self-defined functions are displayed red, predefined ones black.
24646 \begin_layout Standard
24648 \begin_inset Tabular
24649 <lyxtabular version="3" rows="3" columns="2">
24651 <column alignment="center" valignment="top" width="0pt">
24652 <column alignment="center" valignment="top" width="0pt">
24654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24657 \begin_layout Plain Layout
24663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24666 \begin_layout Plain Layout
24674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24677 \begin_layout Plain Layout
24685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24688 \begin_layout Plain Layout
24689 \begin_inset Formula $A\sgn (x)+B$
24699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24702 \begin_layout Plain Layout
24706 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24717 \begin_layout Plain Layout
24718 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24734 \begin_layout Standard
24735 The first method is more suitable when the self-defined function should
24736 be used several times.
24739 \begin_layout Subsection
24744 \begin_layout Plain Layout
24753 \begin_layout Standard
24754 For limits there are defined besides
24764 \begin_layout Plain Layout
24784 furthermore the following functions:
24787 \begin_layout Standard
24789 \begin_inset Tabular
24790 <lyxtabular version="3" rows="5" columns="2">
24792 <column alignment="center" valignment="top" width="0">
24793 <column alignment="center" valignment="top" width="0">
24795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24798 \begin_layout Plain Layout
24804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24807 \begin_layout Plain Layout
24809 \begin_inset Note Note
24812 \begin_layout Plain Layout
24819 is only used as spacer.
24831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24834 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24845 \begin_layout Plain Layout
24846 \begin_inset Formula $\varliminf $
24856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24871 \begin_inset Formula $\varlimsup $
24881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24884 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24895 \begin_layout Plain Layout
24896 \begin_inset Formula $\varprojlim $
24906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24909 \begin_layout Plain Layout
24917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24920 \begin_layout Plain Layout
24921 \begin_inset Formula $\varinjlim $
24925 \begin_inset Formula $\raisebox {-2.5mm}{}$
24941 \begin_layout Standard
24942 \begin_inset VSpace medskip
24945 The limit is created by inserting a subscript.
24946 It is set right beside the function in an inline formula:
24949 \begin_layout Standard
24951 \begin_inset Tabular
24952 <lyxtabular version="3" rows="2" columns="2">
24954 <column alignment="center" valignment="top" width="0pt">
24955 <column alignment="center" valignment="top" width="0pt">
24957 <cell alignment="center" valignment="top" usebox="none">
24960 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" usebox="none">
24969 \begin_layout Plain Layout
24970 \begin_inset Space \hspace{}
24975 \begin_inset Note Note
24978 \begin_layout Plain Layout
24991 are used here as spacer.
25003 <cell alignment="center" valignment="top" usebox="none">
25006 \begin_layout Plain Layout
25015 \begin_layout Plain Layout
25028 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" usebox="none">
25045 \begin_layout Plain Layout
25046 \begin_inset Formula $\hspace {1cm}\raisebox {5mm}{}\lim_{x\to A}x=B$
25062 \begin_layout Standard
25063 In a displayed formula the limit is set below the formula, as usual:
25064 \begin_inset Formula \[
25072 \begin_layout Subsection
25077 \begin_layout Plain Layout
25078 Functions ! modulo-
25086 \begin_layout Standard
25087 The modulo-function is special, because it exists in four variants.
25090 \begin_layout Standard
25091 The variants in a displayed formula:
25092 \begin_inset Formula \begin{align*}
25093 \underline{\textrm{Command}\raisebox {-0.9mm}{}} & & \underline{\textrm{Result}}\\
25094 \mathrm{a\backslash mod\textrm{\spce }b} & & a\mod b\\
25095 \mathrm{a\backslash pmod\textrm{\spce }b} & & a\pmod b\\
25096 \mathrm{a\backslash bmod\textrm{\spce }b} & & a\bmod b\\
25097 \mathrm{a\backslash pod\textrm{\spce }b} & & a\pod b\end{align*}
25104 \begin_layout Standard
25105 In an inline formula less space is set before the function names for all
25109 \begin_layout Section
25114 \begin_layout Plain Layout
25123 \begin_layout Subsection
25124 Special Characters in Mathematical Text
25127 \begin_layout Standard
25128 The following commands can only be used in mathematical text or in TeX-mode:
25131 \begin_layout Standard
25132 \begin_inset Space \hfill{}
25136 \begin_inset Tabular
25137 <lyxtabular version="3" rows="8" columns="2">
25139 <column alignment="block" valignment="top" width="0">
25140 <column alignment="block" valignment="top" width="0">
25142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25145 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25165 \begin_layout Plain Layout
25173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25176 \begin_layout Plain Layout
25177 \begin_inset Formula $\textrm{\oe }$
25187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25190 \begin_layout Plain Layout
25198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25201 \begin_layout Plain Layout
25202 \begin_inset Formula $\textrm{\OE }$
25212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25226 \begin_layout Plain Layout
25227 \begin_inset Formula $\textrm{\ae }$
25237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25251 \begin_layout Plain Layout
25252 \begin_inset Formula $\textrm{\AE }$
25262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25276 \begin_layout Plain Layout
25277 \begin_inset Formula $\textrm{\aa }$
25287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25290 \begin_layout Plain Layout
25297 \begin_layout Plain Layout
25301 \begin_layout Plain Layout
25309 \begin_layout Plain Layout
25320 \begin_layout Plain Layout
25336 \begin_layout Plain Layout
25344 \begin_layout Plain Layout
25355 \begin_layout Plain Layout
25371 \begin_layout Plain Layout
25382 \begin_layout Plain Layout
25390 \begin_layout Plain Layout
25401 \begin_layout Plain Layout
25417 \begin_layout Plain Layout
25434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25437 \begin_layout Plain Layout
25438 \begin_inset Formula $\textrm{\AA}$
25448 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25451 \begin_layout Plain Layout
25459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25462 \begin_layout Plain Layout
25463 \begin_inset Formula $\textrm{\i }$
25477 \begin_inset Space \hfill{}
25481 \begin_inset Tabular
25482 <lyxtabular version="3" rows="8" columns="2">
25484 <column alignment="block" valignment="top" width="0">
25485 <column alignment="center" valignment="top" width="0">
25487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25490 \begin_layout Plain Layout
25492 \begin_inset Note Note
25495 \begin_layout Plain Layout
25502 is used for separation, because otherwise the output will be ¡ and ¿ respective
25513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25527 \begin_layout Plain Layout
25535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25538 \begin_layout Plain Layout
25539 \begin_inset Formula $\textrm{\o }$
25549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25552 \begin_layout Plain Layout
25560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25563 \begin_layout Plain Layout
25564 \begin_inset Formula $\textrm{\O}$
25574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25577 \begin_layout Plain Layout
25585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25588 \begin_layout Plain Layout
25589 \begin_inset Formula $\textrm{\l }$
25599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25602 \begin_layout Plain Layout
25610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25613 \begin_layout Plain Layout
25614 \begin_inset Formula $\textrm{\L }$
25624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25627 \begin_layout Plain Layout
25629 \begin_inset Space \hspace{}
25637 \begin_layout Plain Layout
25651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25654 \begin_layout Plain Layout
25655 \begin_inset Formula $\textrm{!`}$
25665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25668 \begin_layout Plain Layout
25670 \begin_inset Space \hspace{}
25678 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25695 \begin_layout Plain Layout
25696 \begin_inset Formula $\textrm{?`}$
25706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25709 \begin_layout Plain Layout
25717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25720 \begin_layout Plain Layout
25721 \begin_inset Formula $\textrm{\j }$
25735 \begin_inset Space \hfill{}
25741 \begin_layout Standard
25743 \begin_inset Formula $\textrm{\textrm{Å}}$
25747 \begin_inset Formula $\textrm{\textrm{Ø}}$
25750 can also be inserted via the math toolbar button
25751 \begin_inset Graphics
25752 filename ../images/math/digamma.png
25760 \begin_layout Standard
25761 An exception are the commands
25764 \begin_inset Space \hspace{}
25773 \begin_inset Space \hspace{}
25779 , because they can be inserted in LyX directly to text.
25782 \begin_layout Subsection
25784 \begin_inset CommandInset label
25786 name "sub:Accents-in-Text"
25794 \begin_layout Plain Layout
25803 \begin_layout Standard
25804 With the following commands all letters can be accented.
25805 The commands must be inserted in TeX-mode.
25808 \begin_layout Standard
25809 \begin_inset Space \hfill{}
25813 \begin_inset Tabular
25814 <lyxtabular version="3" rows="8" columns="2">
25816 <column alignment="block" valignment="top" width="0">
25817 <column alignment="block" valignment="top" width="0">
25819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25822 \begin_layout Plain Layout
25828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25831 \begin_layout Plain Layout
25839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25842 \begin_layout Plain Layout
25846 \begin_inset Quotes grd
25854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25857 \begin_layout Plain Layout
25861 \begin_layout Plain Layout
25877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25880 \begin_layout Plain Layout
25888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25891 \begin_layout Plain Layout
25895 \begin_layout Plain Layout
25911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25914 \begin_layout Plain Layout
25921 \begin_layout Plain Layout
25935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25938 \begin_layout Plain Layout
25942 \begin_layout Plain Layout
25958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25961 \begin_layout Plain Layout
25969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25972 \begin_layout Plain Layout
25976 \begin_layout Plain Layout
25992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26002 \begin_layout Plain Layout
26016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26019 \begin_layout Plain Layout
26023 \begin_layout Plain Layout
26039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26042 \begin_layout Plain Layout
26049 \begin_layout Plain Layout
26063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26066 \begin_layout Plain Layout
26070 \begin_layout Plain Layout
26086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26089 \begin_layout Plain Layout
26096 \begin_layout Plain Layout
26110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26117 \begin_layout Plain Layout
26137 \begin_inset Space \hfill{}
26141 \begin_inset Tabular
26142 <lyxtabular version="3" rows="8" columns="2">
26144 <column alignment="block" valignment="top" width="0">
26145 <column alignment="center" valignment="top" width="0">
26147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26150 \begin_layout Plain Layout
26156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26159 \begin_layout Plain Layout
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26177 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26194 \begin_layout Plain Layout
26198 \begin_layout Plain Layout
26214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26217 \begin_layout Plain Layout
26225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26228 \begin_layout Plain Layout
26232 \begin_layout Plain Layout
26248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26251 \begin_layout Plain Layout
26258 \begin_layout Plain Layout
26269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26272 \begin_layout Plain Layout
26276 \begin_layout Plain Layout
26292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26295 \begin_layout Plain Layout
26303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26306 \begin_layout Plain Layout
26310 \begin_layout Plain Layout
26326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26329 \begin_layout Plain Layout
26336 \begin_layout Plain Layout
26350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26353 \begin_layout Plain Layout
26357 \begin_layout Plain Layout
26373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26376 \begin_layout Plain Layout
26383 \begin_layout Plain Layout
26397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26400 \begin_layout Plain Layout
26404 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26430 \begin_layout Plain Layout
26444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26447 \begin_layout Plain Layout
26451 \begin_layout Plain Layout
26471 \begin_inset Space \hfill{}
26477 \begin_layout Standard
26478 \begin_inset VSpace medskip
26487 also two different characters can be accented.
26496 \begin_layout Plain Layout
26511 \begin_layout Plain Layout
26523 \begin_layout Standard
26536 can in combination with vowels directly be inserted with the keyboard without
26538 The same applies for the tilde
26542 \begin_layout Plain Layout
26543 This only applies for keyboards where the tilde is defined as accent.
26552 in combination with
26567 \begin_layout Standard
26610 , and accents inserted directly with the keyboard are also available in
26612 For the other accents there are special math commands to be used in formulas,
26614 \begin_inset CommandInset ref
26616 reference "sub:Accents-for-one"
26623 \begin_layout Standard
26624 \begin_inset VSpace bigskip
26627 Furthermore, with the command
26637 \begin_layout Plain Layout
26645 all numbers and letters can be set into a circle, quasi accented with a
26646 circle, similar to the the copyright symbol.
26649 \begin_layout Standard
26651 \begin_inset Tabular
26652 <lyxtabular version="3" rows="3" columns="2">
26654 <column alignment="center" valignment="top" width="0">
26655 <column alignment="center" valignment="top" width="0">
26657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26660 \begin_layout Plain Layout
26666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26671 \begin_inset Note Note
26674 \begin_layout Plain Layout
26681 is only used as spacer.
26693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26696 \begin_layout Plain Layout
26704 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26707 \begin_layout Plain Layout
26711 \begin_layout Plain Layout
26727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26730 \begin_layout Plain Layout
26741 raisebox{-1.5pt}{W}}
26746 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26749 \begin_layout Plain Layout
26750 \begin_inset Formula $\raisebox {4.5mm}{}$
26757 \begin_layout Plain Layout
26775 \begin_inset Formula $\raisebox {-2mm}{}$
26791 \begin_layout Standard
26792 One has to take care that the character fits in the circle.
26803 \begin_layout Plain Layout
26805 \begin_inset CommandInset ref
26807 reference "sub:Font-Sizes"
26816 specifies thereby the size of the circle.
26827 \begin_layout Plain Layout
26829 \begin_inset CommandInset ref
26831 reference "sub:Boxes-without-Frame"
26840 the character can be centered.
26843 \begin_layout Subsection
26848 \begin_layout Plain Layout
26857 \begin_layout Standard
26858 Minuscule numbers are created with the command
26868 \begin_layout Plain Layout
26877 The command can be used in formulas and in TeX-mode.
26878 The command scheme is:
26881 \begin_layout Standard
26886 oldstylenums{number}
26889 \begin_layout Standard
26894 oldstylenums{0123456789
26897 \begin_inset Formula $\oldstylenums {0123456789}$
26903 \begin_layout Subsection
26904 Miscellaneous Special Characters
26905 \begin_inset CommandInset label
26907 name "sub:Miscellaneous-Special-Characters"
26915 \begin_layout Plain Layout
26916 Special characters ! miscellaneous
26924 \begin_layout Standard
26925 The following characters can only be inserted to formulas by using commands:
26928 \begin_layout Standard
26930 \begin_inset Tabular
26931 <lyxtabular version="3" rows="4" columns="2">
26933 <column alignment="center" valignment="top" width="0">
26934 <column alignment="center" valignment="top" width="0">
26936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26939 \begin_layout Plain Layout
26945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26948 \begin_layout Plain Layout
26956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26959 \begin_layout Plain Layout
26966 \begin_layout Plain Layout
26980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26983 \begin_layout Plain Layout
26984 \begin_inset Formula $\mathcircumflex$
26994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26997 \begin_layout Plain Layout
27005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27008 \begin_layout Plain Layout
27009 \begin_inset Formula $\_{} {}{}{}{}{}{}{}$
27019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27022 \begin_layout Plain Layout
27027 \begin_layout Plain Layout
27042 \begin_layout Plain Layout
27053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27056 \begin_layout Plain Layout
27057 \begin_inset Formula $^{\circ}$
27073 \begin_layout Standard
27074 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27075 contains the following line
27079 \begin_layout Plain Layout
27080 More about this is described in
27081 \begin_inset CommandInset ref
27083 reference "sub:Text-Characters-in"
27095 \begin_layout Standard
27100 DeclareInputtext{176}{
27110 f\SpecialChar \textcompwordmark{}
27114 \begin_layout Section
27116 \begin_inset CommandInset label
27118 name "sec:Formula-Styles"
27126 \begin_layout Plain Layout
27135 \begin_layout Itemize
27136 There are two different alignment styles:
27140 \begin_layout Description
27141 Centered is the predefined standard
27144 \begin_layout Description
27145 Indented for this the option
27149 must be inserted in the menu
27151 Document\SpecialChar \menuseparator
27157 \begin_inset Space ~
27163 \begin_layout Standard
27168 is used, the indentation can be adjusted with the length
27178 \begin_layout Plain Layout
27187 Should the distance be 15
27188 \begin_inset Space \thinspace{}
27191 mm, the following command line is inserted in the LaTeX-preamble
27194 \begin_layout Standard
27204 \begin_layout Standard
27205 When no length is specified, the predefined value of 30
27206 \begin_inset Space \thinspace{}
27213 \begin_layout Itemize
27214 And two different numbering styles:
27218 \begin_layout Description
27219 Right is the predefined standard
27222 \begin_layout Description
27223 Left for this the option
27227 must be inserted in the menu
27229 Document\SpecialChar \menuseparator
27235 \begin_inset Space ~
27242 \begin_layout Standard
27251 can also be used together.
27252 In this case both options are inserted, separated by a comma.
27255 \begin_layout Standard
27256 The chosen styles are used for all displayed formulas of the document.
27257 When both, centered and indented formulas should be created in a document,
27263 The indented formulas are then set in a flalign environment, see
27264 \begin_inset CommandInset ref
27266 reference "sub:Flalign-Environment"
27273 \begin_layout Section
27275 \begin_inset CommandInset label
27277 name "sec:Multiline-Formulas"
27285 \begin_layout Plain Layout
27286 Formula ! multiline
27294 \begin_layout Subsection
27298 \begin_layout Standard
27299 In LyX multiline formulas are created by pressing
27310 that is described in
27311 \begin_inset CommandInset ref
27313 reference "sub:Standard-align-Environment"
27320 \begin_layout Standard
27321 There are other multiline formula environments that can be created via the
27324 Insert\SpecialChar \menuseparator
27328 These environments are described in the following sections.
27331 \begin_layout Standard
27332 In all multiline formula environments a new line is created by pressing
27338 To add or delete lines, the math toolbar buttons
27339 \begin_inset Graphics
27340 filename ../images/tabular-feature_append-row.png
27346 \begin_inset Graphics
27347 filename ../images/tabular-feature_delete-row.png
27352 , respectively, or the menu
27354 Edit\SpecialChar \menuseparator
27360 \begin_layout Subsubsection
27362 \begin_inset CommandInset label
27364 name "sub:Line-Separation"
27372 \begin_layout Plain Layout
27373 Formula ! multiline ! Line separation
27381 \begin_layout Standard
27382 There is sometimes not enough space in multiline formulas between the lines:
27383 \begin_inset Formula \begin{eqnarray*}
27384 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}\\
27385 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*}
27392 \begin_layout Standard
27393 In LaTeX additional line space is specified as optional argument of the
27395 This is not yet possible in LyX
27399 \begin_layout Plain Layout
27401 \begin_inset CommandInset href
27403 name "LyX-bug #1505"
27404 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27413 , therefore the whole formula must be inserted in TeX-mode.
27414 To add in our example space, the command
27422 is inserted at the end of the first line.
27427 \begin_layout Plain Layout
27434 \begin_layout Plain Layout
27436 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27439 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27446 \begin_layout Plain Layout
27450 left(B^{2}+x_{0}^{2}
27458 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27463 \begin_layout Plain Layout
27475 \begin_layout Standard
27476 \begin_inset VSpace bigskip
27479 To set the the line separation for all lines in a formula, the length
27489 \begin_layout Plain Layout
27499 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27510 \begin_inset Space \thinspace{}
27515 \begin_inset Space \thinspace{}
27518 mm additional line separation as in the previous example, the command
27521 \begin_layout Standard
27531 \begin_layout Standard
27532 is inserted in TeX-mode before the formula.
27533 This requires that the LaTeX-package
27541 \begin_layout Plain Layout
27546 is part of every LaTeX standard installation.
27555 \begin_layout Plain Layout
27561 was loaded in LaTeX-preamble with the line
27564 \begin_layout Standard
27572 \begin_layout Standard
27577 \begin_layout Plain Layout
27589 \begin_inset Formula \begin{eqnarray*}
27590 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}\\
27591 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*}
27598 \begin_layout Standard
27602 \begin_layout Plain Layout
27613 To get back to the predefined distance,
27619 is set to the value 3
27620 \begin_inset Space \thinspace{}
27626 \begin_layout Subsubsection
27628 \begin_inset CommandInset label
27630 name "sub:Column-Separation"
27638 \begin_layout Plain Layout
27639 Formula ! multiline ! Column separation
27647 \begin_layout Standard
27648 Multiline formulas form a matrix.
27649 A formula in the eqnarray environment is for example a matrix with three
27651 By changing the column separation in this environment, the space beside
27652 the relation sign can be changed.
27655 \begin_layout Standard
27656 The column separation is specified with the length
27666 \begin_layout Plain Layout
27675 \begin_inset Newline newline
27678 column separation = 2
27679 \begin_inset Space \thinspace{}
27689 \begin_inset Newline newline
27695 \begin_layout Standard
27705 \begin_layout Standard
27706 inserted in TeX-mode, sets for all following formulas a column separation
27708 \begin_inset Space \thinspace{}
27712 To get back to the predefined distance,
27719 \begin_inset Space \thinspace{}
27725 \begin_layout Standard
27727 \begin_inset Space \thinspace{}
27730 cm column separation:
27734 \begin_layout Plain Layout
27746 \begin_inset Formula \begin{eqnarray*}
27748 C & \ne & A\end{eqnarray*}
27752 A formula with the predefined column separation for matrices of 10
27753 \begin_inset Space \thinspace{}
27760 \begin_layout Plain Layout
27772 \begin_inset Formula \begin{eqnarray*}
27774 C & \ne & A\end{eqnarray*}
27781 \begin_layout Subsubsection
27786 \begin_layout Plain Layout
27795 \begin_layout Standard
27796 Long formulas can be typeset using these methods:
27799 \begin_layout Itemize
27800 When one side of the equation is much shorther than the line width, this
27801 one is chosen for the left side and the right side is typeset over two
27806 \begin_layout Plain Layout
27816 \begin_inset Formula \begin{eqnarray}
27817 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 \\
27818 & & -\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}
27826 \begin_layout Plain Layout
27836 \begin_inset Newline newline
27839 The minus sign at the beginning of the second line does normally not appear
27840 as operator because it is the first character of the line.
27841 Thus it would not be surrounded by space and could not be distinguished
27842 from the fraction bar.
27843 To avoid this, space was inserted behind the minus sign with the command
27854 \begin_layout Plain Layout
27862 \begin_inset CommandInset ref
27864 reference "sub:Variable-Space"
27877 \begin_layout Plain Layout
27888 \begin_layout Itemize
27889 When both sides of the equation are too long, the command
27899 \begin_layout Plain Layout
27908 It is inserted to the first column of the first line and effects that all
27909 further insertions overwrite the following columns:
27913 \begin_layout Plain Layout
27923 \begin_inset Formula \begin{eqnarray}
27924 \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 \\
27925 & & -\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 \\
27926 & & =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}
27934 \begin_layout Plain Layout
27944 \begin_inset Newline newline
27947 After the insertion of
27953 , the cursor is in a purple box that is a bit shifted to the left from the
27955 In this the formula is inserted.
27959 \begin_layout Plain Layout
27969 \begin_inset Newline newline
27972 The content of the further lines is inserted to the second or another formula
27974 The greater the column number where it was inserted, the larger the indentation.
27978 \begin_layout Plain Layout
27988 \begin_inset Newline newline
27992 \begin_inset Note Greyedout
27995 \begin_layout Plain Layout
27996 Note the following when using
28005 \begin_layout Itemize
28006 The formula doesn't use the full page width.
28008 \begin_inset Space \thinspace{}
28012 \begin_inset Space ~
28016 \begin_inset Formula $-B^{2}$
28019 is added to the first line in the above example, it would have been outside
28021 To better use the width, negative space can be inserted at the beginning
28025 \begin_layout Itemize
28026 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28031 \begin_layout Plain Layout
28032 \begin_inset CommandInset href
28034 name "LyX-bug #1429"
28035 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28044 One can only set the cursor at the beginning of the line and move it with
28053 \begin_layout Itemize
28054 Other methods to set long formulas are offered by the environments described
28056 \begin_inset CommandInset ref
28058 reference "sub:Multline-Environment"
28063 \begin_inset CommandInset ref
28065 reference "sub:Multiline-Formula-Parts"
28072 \begin_layout Subsubsection
28074 \begin_inset CommandInset label
28076 name "sub:Multiline-Brackets"
28084 \begin_layout Plain Layout
28085 Brackets ! for multiline expressions
28093 \begin_layout Standard
28094 For brackets spanning multiple lines the following problem occurs:
28095 \begin_inset Formula \begin{eqnarray*}
28096 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28097 & & \left.\cdots+B-D\right]\end{eqnarray*}
28104 \begin_layout Standard
28105 The closing bracket is smaller than the opening bracket because brackets
28106 with variable size may not span multiple lines.
28109 \begin_layout Standard
28110 To set the bracket size for the second line correctly, the first line is
28121 \begin_layout Plain Layout
28129 and the second line with
28137 \begin_layout Plain Layout
28151 \begin_inset CommandInset ref
28153 reference "sub:Automatic-Bracket-Size"
28168 \begin_layout Plain Layout
28194 \begin_layout Plain Layout
28213 \begin_layout Plain Layout
28232 \begin_layout Plain Layout
28244 \begin_inset Formula $\downarrow$
28253 \begin_layout Plain Layout
28261 is inserted, because the multiplication operator with its limits is the
28262 largest symbol in the first line and this should be the size for the bracket
28263 in the second line.
28266 \begin_layout Standard
28267 The result is this:
28268 \begin_inset Formula \begin{eqnarray*}
28269 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28270 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28277 \begin_layout Subsection
28281 \begin_layout Standard
28282 Align environments can be used for every kind of multiline formulas.
28283 They are specially useful to set several formulas side by side.
28286 \begin_layout Standard
28287 Align environments consist of columns.
28288 The odd columns are right aligned, the even ones left aligned.
28289 Every line in an Align environment can be numbered.
28292 \begin_layout Standard
28293 Align environments are created via the menu
28295 Insert\SpecialChar \menuseparator
28301 Edit\SpecialChar \menuseparator
28302 Math\SpecialChar \menuseparator
28303 Change Formula Type
28305 already existing formulas can be converted to Align environments.
28308 \begin_layout Standard
28309 To add or delete columns, the math toolbar buttons
28310 \begin_inset Graphics
28311 filename ../images/tabular-feature_append-column.png
28317 \begin_inset Graphics
28318 filename ../images/tabular-feature_delete-column.png
28323 , respectively, or the menu
28325 Edit\SpecialChar \menuseparator
28331 \begin_layout Subsubsection
28332 Standard align Environment
28333 \begin_inset CommandInset label
28335 name "sub:Standard-align-Environment"
28343 \begin_layout Plain Layout
28344 Formula ! multiline ! align environment
28352 \begin_layout Standard
28353 This Align environment is created by presssing
28357 in a formula or by the menu
28359 Insert\SpecialChar \menuseparator
28360 Math\SpecialChar \menuseparator
28361 AMS align Environment
28366 \begin_layout Standard
28367 An example for two formulas set side by side, that are created with a four
28368 column align environment:
28369 \begin_inset Formula \begin{align*}
28370 A & =\sin(B) & C & =D\\
28371 C & \ne A & B & \ne D\end{align*}
28375 As it can be seen, the formulas in this environment are placed so as if
28384 \begin_layout Plain Layout
28392 \begin_inset CommandInset ref
28394 reference "sub:Variable-Space"
28405 before the first and after every even column.
28406 When the formula style
28412 \begin_layout Plain Layout
28414 \begin_inset CommandInset ref
28416 reference "sec:Formula-Styles"
28427 is used, the formula is set without the
28433 before the first column.
28436 \begin_layout Subsubsection
28437 Alignat Environment
28441 \begin_layout Plain Layout
28442 Formula ! multiline ! alignat environment
28450 \begin_layout Standard
28451 The alignat environment has no predefined column separation.
28452 It can be inserted manually with the spaces that are described
28453 \begin_inset CommandInset ref
28455 reference "sub:Space"
28462 \begin_layout Standard
28463 The above example in the alignat environment where 1
28464 \begin_inset Space \thinspace{}
28467 cm space was inserted at the beginning of the second formula:
28468 \begin_inset Formula \begin{alignat*}{2}
28469 A & =\sin(B) & \hspace {1cm}C & =D\\
28470 C & \ne A & B & \ne D\end{alignat*}
28474 Because the column separation can be set separately for every column, this
28475 environment is especially suitable to set three and more formulas side
28479 \begin_layout Subsubsection
28480 Flalign Environment
28481 \begin_inset CommandInset label
28483 name "sub:Flalign-Environment"
28491 \begin_layout Plain Layout
28492 Formula ! multiline ! flalign environment
28500 \begin_layout Standard
28501 In this environment the first two columns are always set as much as possible
28502 to the left and the last two ones to the right.
28504 \begin_inset Formula \begin{flalign*}
28505 A & =1 & B & =2 & C & =3\\
28506 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28513 \begin_layout Standard
28514 By creating a flalign environment with an odd number of columns where an
28515 empty TeX-brace is inserted to the last column, several formulas in a document
28516 can be set to the left, although the formula style
28521 As example the indented formula
28522 \begin_inset CommandInset ref
28524 reference "eq:VolInt"
28529 \begin_inset Formula \begin{flalign}
28530 \hspace {30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28534 The first two columns contain the formula.
28535 To indent it as with the formula style
28540 \begin_inset Space \thinspace{}
28543 pt space was inserted at the beginning of the first column.
28546 \begin_layout Subsection
28547 Eqnarray Environment
28551 \begin_layout Plain Layout
28552 Formula ! multiline ! eqnarray environment
28560 \begin_layout Standard
28561 When this environment has been created, three blue boxes appear.
28562 The content of the first box is right aligned, the content of the last
28564 The content of the middle box appears centered and a bit smaller, because
28565 it is designed to insert there only relation characters.
28566 \begin_inset Formula \begin{eqnarray*}
28567 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28569 A & = & A\end{eqnarray*}
28576 \begin_layout Subsection
28581 \begin_layout Plain Layout
28582 Formula ! multiline ! gather environment
28590 \begin_layout Standard
28591 This environment consists of only one centered column.
28592 Every line can be numbered.
28593 \begin_inset Formula \begin{gather}
28595 X=\textrm{-}1\end{gather}
28602 \begin_layout Subsection
28603 Multline Environment
28604 \begin_inset CommandInset label
28606 name "sub:Multline-Environment"
28614 \begin_layout Plain Layout
28615 Formula ! multiline ! multline environment
28623 \begin_layout Standard
28624 The multline environment consists, like the gather environment, of only
28626 But the first line is left aligned, the last one right aligned.
28627 All other lines are centered.
28628 Therefore this environment is suitable for long formulas.
28630 \begin_inset CommandInset ref
28632 reference "eq:lefteqn"
28636 in the multline environment:
28637 \begin_inset Formula \begin{multline}
28638 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}\\
28639 -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}\\
28640 =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}
28647 \begin_layout Standard
28648 In the output only the last (first) line of a multline environment appears
28649 numbered when the document numbering is right (left).
28653 \begin_layout Plain Layout
28654 numbering styles see
28655 \begin_inset CommandInset ref
28657 reference "sec:Formula-Styles"
28669 \begin_layout Standard
28678 \begin_layout Plain Layout
28696 \begin_layout Plain Layout
28706 a centered line can be right or left aligned, respectively.
28707 The commands are used as follows:
28710 \begin_layout Standard
28715 shoveright{line content}
28721 shoveleft{line content}
28724 \begin_layout Standard
28725 \begin_inset VSpace medskip
28736 \begin_layout Plain Layout
28746 specifies the distance of the first line from the left page margin.
28747 Predefined is the length 0
28748 \begin_inset Space \thinspace{}
28754 \begin_layout Standard
28755 As example the above formula where the command
28758 \begin_layout Standard
28768 \begin_layout Standard
28769 was inserted in TeX-mode before:
28773 \begin_layout Plain Layout
28785 \begin_inset Formula \begin{multline}
28786 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}\\
28787 \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}}\\
28788 =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}
28796 \begin_layout Plain Layout
28807 The second line was left aligned using
28816 \begin_layout Subsection
28817 Multiline Formula Parts
28818 \begin_inset CommandInset label
28820 name "sub:Multiline-Formula-Parts"
28828 \begin_layout Plain Layout
28829 Formula ! multiline ! formula parts
28837 \begin_layout Standard
28838 To display only parts of a formula with multiple lines, one of the following
28839 environments are used:
28856 They can be inserted via the menu
28858 Insert\SpecialChar \menuseparator
28861 or by using the commands described in this section.
28864 \begin_layout Standard
28865 The first three have the same properties as the corresponding multiline
28866 formula environments, but it is possible to set further formula parts beside
28869 \begin_inset Formula \[
28870 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28871 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28872 \right\} \textrm{Uncertainty relations}\]
28879 \begin_layout Standard
28880 To get this formula, a displayed formula is created where the command
28888 \begin_layout Plain Layout
28899 A purple box appears around the blue formula box where now columns and
28900 lines can be added.
28901 Outside the multiline environment other formula parts can be set, like
28905 \begin_layout Standard
28906 The aligned environment is also suitable for long formulas whose lines are
28907 horizontally aligned.
28908 Using aligned in a displayed formula has the advantage that the formula
28909 number is vertically centered behind the lines.
28911 \begin_inset CommandInset ref
28913 reference "eq:kurzlang"
28917 in the aligned environment:
28918 \begin_inset Formula \begin{equation}
28919 \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}|}\\
28920 & -\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}
28928 \begin_layout Standard
28929 To use the environments
28951 \begin_layout Plain Layout
28969 \begin_layout Plain Layout
28987 \begin_layout Plain Layout
28995 are inserted, respectively.
28996 The split environment has the same properties as the aligned environment
28997 but it can only have two columns.
29000 \begin_layout Subsection
29001 Text in multiline Formulas
29002 \begin_inset CommandInset label
29004 name "sub:Text-in-multiline"
29012 \begin_layout Plain Layout
29022 \begin_layout Plain Layout
29023 Formula ! multiline ! text
29031 \begin_layout Standard
29032 In the Align environments, and the multline and gather environment, text
29033 can be inserted that will appear in a separate line and doesn't affect
29034 the column alignment.
29035 To do this, the command
29043 \begin_layout Plain Layout
29053 is used in the following scheme:
29056 \begin_layout Standard
29064 \begin_layout Standard
29065 The text should not be longer than a line because it cannot be hyphenated.
29066 As LyX doesn't yet support
29072 directly, the text is written as mathematical text.
29079 must hereby be at the beginning of a line and appears in the output above
29081 An example where the text was inserted at the beginning of the second line:
29082 \begin_inset Formula \begin{align}
29083 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29084 \intertext {\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29091 \begin_layout Section
29096 \begin_layout Plain Layout
29106 \begin_layout Plain Layout
29107 Formula ! numbering|see
29111 \begin_layout Plain Layout
29122 \begin_layout Plain Layout
29137 \begin_layout Subsection
29141 \begin_layout Standard
29142 Numbered formulas can be created with the menu
29144 Insert\SpecialChar \menuseparator
29145 Math\SpecialChar \menuseparator
29147 \begin_inset Space ~
29155 \begin_inset Space ~
29161 Existing formulas can be numbered with the menu
29163 Edit\SpecialChar \menuseparator
29164 Math\SpecialChar \menuseparator
29166 \begin_inset Space ~
29174 \begin_inset Space ~
29180 The formula number is displayed in LyX behind the formula as number sign
29182 The number sign is replaced in the output by the formula number.
29185 \begin_layout Standard
29186 When numbering is turned on in multiline formulas, all lines will be numbered.
29187 But the numbering can be controlled with the menu
29189 Edit\SpecialChar \menuseparator
29190 Math\SpecialChar \menuseparator
29192 \begin_inset Space ~
29196 \begin_inset Space ~
29200 \begin_inset Space ~
29208 \begin_inset Space ~
29216 \begin_layout Standard
29217 Except of inline formulas, all formulas can be numbered with two different
29219 \begin_inset CommandInset ref
29221 reference "sec:Formula-Styles"
29228 \begin_layout Subsection
29230 \begin_inset CommandInset label
29232 name "sub:Cross-References"
29240 \begin_layout Plain Layout
29241 Cross-references ! to formulas
29249 \begin_layout Standard
29250 All labeled formulas can be cross-referenced.
29251 A label is added by the menu
29253 Insert\SpecialChar \menuseparator
29256 or the toolbar button
29257 \begin_inset Graphics
29258 filename ../images/label-insert.png
29264 The cursor must hereby be inside a displayed formula.
29265 A dialog pops up displaying the prefix
29270 The label is inserted there behind the prefix.
29271 The predefined prefix means
29272 \begin_inset Quotes eld
29276 \begin_inset Quotes erd
29279 and makes it easier to find labels in large documents because it marks
29280 it as formula label to divide it from e.
29281 \begin_inset Space \thinspace{}
29285 \begin_inset Space ~
29289 To change a label, the menu
29291 Insert\SpecialChar \menuseparator
29297 \begin_layout Standard
29298 The name of the label is displayed in LyX within two parentheses behind
29300 A formula with a label is always numbered.
29303 \begin_layout Standard
29304 Cross-references are inserted via the menu
29306 Insert\SpecialChar \menuseparator
29309 or with the toolbar button
29310 \begin_inset Graphics
29311 filename ../images/dialog-show-new-inset_ref.png
29317 A formula cross-reference appears in the output as formula number.
29318 When in the cross-reference dialog window the format
29322 is chosen, the cross-reference appears in the output as formula number
29324 \begin_inset Newline newline
29327 By right-clicking on a cross-reference in LyX, one jumps to the formula
29328 that is referenced.
29331 \begin_layout Standard
29332 Here are as examples cross-references to formulas of the following subsections:
29333 \begin_inset Note Note
29336 \begin_layout Plain Layout
29337 Note the different cross-reference types.
29345 \begin_layout Standard
29347 \begin_inset CommandInset ref
29354 \begin_inset CommandInset ref
29362 \begin_inset CommandInset ref
29368 ) big Latin letters are used for the numbering in contrary to (
29369 \begin_inset CommandInset ref
29378 \begin_layout Standard
29379 \begin_inset VSpace medskip
29382 When the argument of
29390 \begin_layout Plain Layout
29398 \begin_inset CommandInset ref
29400 reference "sub:User-defined-Numbering"
29411 contains a box like in
29412 \begin_inset CommandInset ref
29414 reference "sub:Paragraph-Boxes"
29418 , the formula cannot be referenced.
29421 \begin_layout Subsection
29426 \begin_layout Plain Layout
29427 Formula numbering ! subnumbering
29435 \begin_layout Standard
29436 With the help of the commands
29440 begin{subequations}
29448 formulas can be subnumbered.
29449 Both commands are inserted in TeX-mode.
29452 \begin_layout Standard
29454 \begin_inset Formula \begin{equation}
29455 A=C-B\label{eq:a}\end{equation}
29463 \begin_layout Plain Layout
29467 addtocounter{equation}{-1}
29476 \begin_layout Plain Layout
29480 begin{subequations}
29486 \begin_inset VSpace -5mm
29490 \begin_inset Formula \begin{equation}
29491 B=C-A\label{eq:b}\end{equation}
29496 \begin_inset Formula \begin{equation}
29497 C=A+B\label{eq:c}\end{equation}
29504 \begin_layout Standard
29508 \begin_layout Plain Layout
29520 \begin_layout Standard
29521 To create the example, the following is done:
29524 \begin_layout Enumerate
29525 first formula is inserted
29528 \begin_layout Enumerate
29533 addtocounter{equation}{-1}
29535 begin{subequations}
29539 \begin_layout Plain Layout
29548 \begin_inset Newline newline
29553 is inserted after the first formula
29556 \begin_layout Enumerate
29557 second formula is inserted
29560 \begin_layout Enumerate
29561 third formula is inserted
29564 \begin_layout Enumerate
29571 is inserted after the third formula
29574 \begin_layout Standard
29575 Every formula between the commands
29587 is subnumbered as a, b,
29588 \begin_inset Newline linebreak
29591 c, \SpecialChar \ldots{}
29592 For multiline formulas every line will be subnumbered.
29593 All subnumbered formulas are treated as
29598 But as every numbered formula increases the counter
29602 by one, the command
29608 is needed to decrease it.
29609 Otherwise the formulas
29610 \begin_inset CommandInset ref
29617 \begin_inset CommandInset ref
29624 \begin_inset CommandInset ref
29630 would be numbered as
29631 \begin_inset CommandInset ref
29638 \begin_inset CommandInset ref
29645 \begin_inset CommandInset ref
29654 \begin_layout Standard
29655 By inserting the commands in TeX-mode, a space is created between the first
29658 \begin_inset Space \thinspace{}
29661 mm vertical space is inserted after the command
29665 begin{subequations}
29668 When the formula style
29674 \begin_layout Plain Layout
29676 \begin_inset CommandInset ref
29678 reference "sec:Formula-Styles"
29690 \begin_inset Space \thinspace{}
29693 mm space is inserted instead.
29696 \begin_layout Standard
29697 Here is an example for a multiline formula where the numbering was turned
29698 off for the second line:
29702 \begin_layout Plain Layout
29706 begin{subequations}
29712 \begin_inset Formula \begin{eqnarray}
29713 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29714 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
29715 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29723 \begin_layout Plain Layout
29735 \begin_layout Subsection
29736 User-defined Numbering
29737 \begin_inset CommandInset label
29739 name "sub:User-defined-Numbering"
29747 \begin_layout Plain Layout
29748 Formula numbering ! user-defined
29756 \begin_layout Standard
29760 \begin_layout Plain Layout
29761 Formula numbering ! self-defined delimiters
29766 With the standard numbering parentheses are set around the formula number.
29767 To replace the parentheses for example by vertical bars, the following
29768 line is added to the LaTeX-preamble:
29771 \begin_layout Standard
29783 \begin_inset Note Note
29786 \begin_layout Plain Layout
29787 This macro is already declared in the LaTeX-preamble for testing.
29788 To activate it, remove the percent sign at the beginning.
29796 \begin_layout Standard
29797 To use other characters, the vertical bars besides the
29801 are replaced by one ore more characters.
29802 To get only the formula number the vertical bars are omitted.
29805 \begin_layout Standard
29806 \begin_inset VSpace bigskip
29809 When there should be an expression of your choice instead of the consecutive
29810 formula number in parentheses behind the formula, the command
29820 \begin_layout Plain Layout
29829 \begin_inset Formula \begin{equation}
29830 A+B=C\tag{something}\label{eq:tag}\end{equation}
29834 In this example the command
29842 \begin_layout Plain Layout
29853 was inserted to the formula.
29856 \begin_layout Standard
29865 \begin_layout Plain Layout
29876 is inserted instead, the star prevents the parentheses around the expression:
29877 \begin_inset Formula \[
29878 A+B=C\tag*{something}\]
29885 \begin_layout Standard
29886 \begin_inset VSpace bigskip
29889 To restart the formula numbering with new document parts or sections, the
29890 following command is used:
29893 \begin_layout Standard
29898 @addtoreset{equation}{part}
29904 \begin_layout Plain Layout
29909 \begin_layout Plain Layout
29920 \begin_layout Plain Layout
29933 \begin_layout Plain Layout
29944 \begin_layout Plain Layout
29957 \begin_inset Newline newline
29961 \begin_inset Newline newline
29968 @addtoreset{equation}{section}
29971 \begin_layout Standard
29972 To be able to use these commands in TeX-mode, the
29973 \begin_inset Quotes eld
29977 \begin_inset Quotes erd
29980 character has to be made
29981 \begin_inset Quotes eld
29985 \begin_inset Quotes erd
29988 for LaTeX using the command
30002 So the command sequence in TeX-mode is:
30005 \begin_layout Standard
30011 \begin_inset Newline newline
30016 @addtoreset{equation}{section}
30017 \begin_inset Newline newline
30025 \begin_layout Standard
30026 In the LaTeX-preamble
30038 can be omitted as they are automatically internally inserted by LyX.
30041 \begin_layout Standard
30056 \begin_layout Plain Layout
30061 is part of the LaTeX-package
30069 \begin_layout Plain Layout
30070 Packages ! carlisle
30075 that is part of every LaTeX standard installation.
30084 \begin_layout Plain Layout
30085 Packages ! remreset
30090 has to be loaded in the LaTeX-preamble with the line
30093 \begin_layout Standard
30098 usepackage{remreset}
30101 \begin_layout Standard
30112 \begin_layout Plain Layout
30117 \begin_layout Plain Layout
30128 \begin_layout Plain Layout
30141 \begin_layout Plain Layout
30152 \begin_layout Plain Layout
30164 can be used with the same scheme as
30173 \begin_layout Standard
30174 \begin_inset VSpace bigskip
30177 Sometimes formulas should be numbered in the following form:
30180 \begin_layout Standard
30183 (section number.formula number)
30186 \begin_layout Standard
30187 The formula number should start with every section with
30188 \begin_inset Quotes eld
30192 \begin_inset Quotes erd
30198 \begin_layout Standard
30199 For this case there is the command
30209 \begin_layout Plain Layout
30217 , which is used with the following scheme:
30220 \begin_layout Standard
30225 numberwithin{counter}{sectioning}
30228 \begin_layout Standard
30229 Counter denotes what kind of numbering is affected, sectioning denotes what
30230 number is before the dot.
30233 \begin_layout Standard
30234 Thus in our case the following LaTeX-preamble or ERT line is used:
30237 \begin_layout Standard
30242 numberwithin{equation}{section}
30245 \begin_layout Standard
30246 This is the result:
30250 \begin_layout Plain Layout
30254 numberwithin{equation}{section}
30260 \begin_inset Formula \begin{equation}
30261 A+B=C\end{equation}
30268 \begin_layout Standard
30270 \begin_inset Space \thinspace{}
30274 \begin_inset Space ~
30277 tables so that the number of the part is the sectioning,
30278 \begin_inset Newline newline
30285 numberwithin{table}{part}
30290 \begin_layout Standard
30291 To go back to the standard numbering or to prevent this kind of numbering
30292 when it is defined by the document class, the following command is inserted
30293 as ERT or to the LaTeX-preamble:
30296 \begin_layout Standard
30309 \begin_layout Plain Layout
30323 \begin_layout Plain Layout
30339 \begin_inset Newline newline
30347 \begin_inset Newline newline
30359 \begin_layout Standard
30366 uses internally the command
30372 , described above, that also needs to be reverted.
30376 \begin_layout Plain Layout
30383 \begin_layout Plain Layout
30387 @removefromreset{equation}{section}
30390 \begin_layout Plain Layout
30402 \begin_layout Subsection
30403 Numbering with Roman Numbers and Letters
30404 \begin_inset CommandInset label
30406 name "sub:Numbering-with-Roman"
30414 \begin_layout Plain Layout
30415 Formula numbering ! with letters
30424 \begin_layout Plain Layout
30425 Formula numbering ! with Roman numbers
30433 \begin_layout Standard
30434 Formulas can also be numbered with Roman numbers and Latin letters.
30435 To number for example with small Roman numbers, the command
30438 \begin_layout Standard
30450 \begin_layout Standard
30451 is inserted before the formula in TeX-mode.
30462 \begin_layout Plain Layout
30470 redefines the predefined command
30486 \begin_layout Plain Layout
30493 has the same scheme like the command
30499 that is described in
30500 \begin_inset CommandInset ref
30502 reference "sec:User-defined-commands"
30516 is the formula counter.
30523 is used as prefix for a counter, the value of the counter is output as
30525 When a formula is numbered, LaTeX sets internally the command
30531 behind the formula.
30540 \begin_layout Plain Layout
30550 outputs the counter as small Roman number.
30553 \begin_layout Standard
30554 All formulas behind the command
30564 are now numbered Roman.
30565 To switch to numbering with big Roman numbers, the command is inserted
30582 \begin_layout Plain Layout
30594 \begin_inset Quotes eld
30598 \begin_inset Quotes erd
30601 with small Latin letters there is the command
30611 \begin_layout Plain Layout
30619 , for big ones there is the command
30629 \begin_layout Plain Layout
30642 \begin_layout Standard
30643 \begin_inset Note Greyedout
30646 \begin_layout Plain Layout
30651 Only maximal 26 formulas can be numbered with Latin letters in one document.
30659 \begin_layout Standard
30663 \begin_layout Plain Layout
30679 \begin_layout Standard
30680 \begin_inset Formula \begin{equation}
30681 A=\textrm{small roman}\label{eq:rom}\end{equation}
30689 \begin_layout Plain Layout
30703 \begin_inset Formula \begin{equation}
30704 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30712 \begin_layout Plain Layout
30726 \begin_inset Formula \begin{equation}
30727 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30735 \begin_layout Plain Layout
30749 \begin_inset Formula \begin{equation}
30750 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30757 \begin_layout Standard
30758 To switch back to the default numbering, insert the command:
30761 \begin_layout Standard
30774 \begin_layout Plain Layout
30785 \begin_layout Standard
30789 \begin_layout Plain Layout
30803 \begin_inset Formula \begin{equation}
30804 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30811 \begin_layout Standard
30812 \begin_inset VSpace medskip
30815 As you see, formulas are numbered serially independent from the numbering
30817 When then numbering should start with
30818 \begin_inset Quotes eld
30822 \begin_inset Quotes erd
30825 when the style is changed, new equation counters have to be defined.
30826 A description about this can be found in the file
30827 \begin_inset CommandInset href
30829 target "Formula-numbering.lyx"
30836 \begin_layout Section
30837 User-defined commands
30838 \begin_inset CommandInset label
30840 name "sec:User-defined-commands"
30848 \begin_layout Plain Layout
30849 User-defined commands
30857 \begin_layout Standard
30858 Many LaTeX-commands are too long to be used frequently.
30859 But it is possible to define with the command
30869 \begin_layout Plain Layout
30877 new shorter commands.
30880 \begin_layout Standard
30881 The command scheme of
30890 \begin_layout Standard
30895 newcommand{new command name}[number of arguments][optional
30900 \begin_inset Newline newline
30907 \begin_layout Plain Layout
30922 \begin_layout Plain Layout
30929 {command definition}
30932 \begin_layout Standard
30933 \begin_inset Note Greyedout
30936 \begin_layout Plain Layout
30941 Assure that the name of the new command is not already used in your document
30942 or by LaTeX-packages that you use.
30943 When you for example define the command
30955 , you get an error message because
30961 is already defined as command for
30962 \begin_inset Quotes eld
30966 \begin_inset Formula $\le$
30970 \begin_inset Quotes erd
30981 \begin_layout Standard
30982 \begin_inset Note Greyedout
30985 \begin_layout Plain Layout
30990 The names of user-defined commands may only consist of Latin letters.
30998 \begin_layout Standard
30999 The number of arguments is an integer in the range 0
31000 \begin_inset Space \thinspace{}
31004 \begin_inset Space \thinspace{}
31007 9 and specifies how many arguments the new command should have.
31008 With the optional value a value for an optional argument can be predefined.
31009 When this is done, the
31017 rgument of the new command is automatically an optional one.
31020 \begin_layout Standard
31021 Here are some examples:
31024 \begin_layout Itemize
31025 To define the command
31037 , the LaTeX-preamble line is:
31041 \begin_layout Plain Layout
31053 \begin_inset Newline newline
31065 \begin_layout Itemize
31066 To define the command
31078 , the argument (that should be underlined) must be taken into account.
31079 For this the preamble line is:
31083 \begin_layout Plain Layout
31095 \begin_inset Newline newline
31110 \begin_layout Plain Layout
31122 \begin_inset Newline newline
31131 acts as argument placeholder, the
31135 behind it denotes that it is the placeholder for the first argument.
31138 \begin_layout Itemize
31146 \begin_inset Space \thinspace{}
31150 \begin_inset Space ~
31163 \begin_layout Plain Layout
31175 \begin_inset Newline newline
31184 framebox#1#2{$#3$}}
31190 \begin_layout Plain Layout
31202 \begin_inset Newline newline
31207 The two Dollar signs creates the extra formula needed for
31214 \begin_inset CommandInset ref
31216 reference "sub:Boxes-with-Frame"
31223 \begin_layout Itemize
31224 To create a new command for
31230 where the color for the box needn't to be specified, the argument for the
31231 color is defined optional:
31235 \begin_layout Plain Layout
31247 \begin_inset Newline newline
31256 fcolorbox{#2}{#1}{$#3$}}
31262 \begin_layout Plain Layout
31272 \begin_inset Newline newline
31275 When the color is not specified when using
31281 , the predefined color
31288 \begin_layout Standard
31289 A test of the new defined commands:
31292 \begin_layout Standard
31294 \begin_inset Tabular
31295 <lyxtabular version="3" rows="6" columns="2">
31297 <column alignment="center" valignment="top" width="0">
31298 <column alignment="center" valignment="top" width="0">
31300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31303 \begin_layout Plain Layout
31309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31312 \begin_layout Plain Layout
31314 \begin_inset Note Note
31317 \begin_layout Plain Layout
31324 is only used as spacer.
31336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31339 \begin_layout Plain Layout
31346 \begin_layout Plain Layout
31360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31363 \begin_layout Plain Layout
31364 \begin_inset Formula $A\gr B$
31374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31377 \begin_layout Plain Layout
31385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31388 \begin_layout Plain Layout
31389 \begin_inset Formula $\raisebox {4.5mm}{}\us {ABcd}\raisebox {-2mm}{}$
31399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31402 \begin_layout Plain Layout
31406 \begin_inset Formula $\to$
31412 \begin_inset Formula $\to$
31423 \begin_layout Plain Layout
31437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31440 \begin_layout Plain Layout
31441 \begin_inset Formula $\raisebox {6mm}{}\fb {[2cm]}{}{\int A=B}\raisebox {-4mm}{}$
31451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31454 \begin_layout Plain Layout
31458 \begin_inset Formula $\to$
31469 \begin_layout Plain Layout
31483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31486 \begin_layout Plain Layout
31487 \begin_inset Formula $\raisebox {6mm}{}\cb {red}{\int A=B}\raisebox {-4mm}{}$
31497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31500 \begin_layout Plain Layout
31506 \begin_inset Formula $\to$
31517 \begin_layout Plain Layout
31531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31534 \begin_layout Plain Layout
31535 \begin_inset Formula $\raisebox {6mm}{}\cb [green]{red}{\int A=B}\raisebox {-4mm}{}$
31551 \begin_layout Section
31556 \begin_layout Plain Layout
31565 \begin_layout Standard
31566 To create diagrams, the LaTeX-package
31572 \begin_layout Plain Layout
31577 is part of every LaTeX standard installation.
31588 \begin_layout Plain Layout
31595 It is loaded in the LaTeX-preamble with the line
31598 \begin_layout Standard
31606 \begin_layout Standard
31607 Diagrams visualize relations and look like this:
31608 \begin_inset Formula \[
31609 \begin{CD}A@>>>B@>>>C\\
31611 F@<<<E@<<<D\end{CD}\]
31618 \begin_layout Standard
31619 To get them, the command
31627 \begin_layout Plain Layout
31637 is inserted to a formula.
31638 A blue box appears with two dashed lines where further commands can be
31644 a new line is created.
31645 Horizontal relations are inserted in odd, vertical in even formula lines.
31648 \begin_layout Standard
31649 To create the relations there are the following commands:
31652 \begin_layout Itemize
31657 creates a left arrow,
31668 \begin_layout Itemize
31673 creates an up arrow,
31681 a vertical equal sign
31684 \begin_layout Itemize
31690 is a placeholder for non-existent relations
31693 \begin_layout Standard
31694 All arrows can be labeled as follows:
31697 \begin_layout Itemize
31698 Is text inserted between the first and second < or >, resp., it is placed
31700 When it is inserted between the second and third one, it appears under
31704 \begin_layout Itemize
31705 When text for vertical arrows is inserted between the first and second A
31706 or V, resp., it is placed left beside the arrow.
31707 When it is inserted between the second and third one, it appears right
31709 If the text contains an A or V, these letters must be set into a TeX-brace.
31712 \begin_layout Standard
31713 As example a diagram with all possible relations:
31716 \begin_layout Standard
31717 \begin_inset Formula \[
31718 \begin{CD}A@>j>>B@>>k>C@=F\\
31720 D@<<j<E@>k>>F@=C\end{CD}\]
31727 \begin_layout Standard
31728 The command for this is:
31729 \begin_inset Newline newline
31740 \begin_layout Plain Layout
31749 A@>j>>B@>>k>C@=F Ctrl-Enter
31750 \begin_inset Newline newline
31757 \begin_layout Plain Layout
31772 \begin_layout Plain Layout
31785 \begin_layout Plain Layout
31797 \begin_inset Formula $\to$
31803 \begin_inset Newline newline
31810 \begin_layout Plain Layout
31825 \begin_layout Plain Layout
31838 \begin_layout Plain Layout
31848 \begin_layout Standard
31849 \begin_inset Newpage newpage
31855 \begin_layout Section
31860 \begin_layout Plain Layout
31873 \begin_layout Plain Layout
31874 Other useful math tips can be found in
31875 \begin_inset CommandInset citation
31890 \begin_layout Plain Layout
31898 \begin_inset Note Note
31901 \begin_layout Plain Layout
31904 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31907 \begin_layout Plain Layout
31910 texorpdfstring is in section
31911 \begin_inset CommandInset ref
31913 reference "sub:Formulas-in-Section"
31926 \begin_layout Plain Layout
31936 \begin_layout Plain Layout
31941 \begin_layout Plain Layout
31948 Chemical characters
31952 \begin_layout Plain Layout
31967 \begin_layout Subsection
31968 Chemical Symbols and Equations
31969 \begin_inset CommandInset label
31971 name "sub:Chemical-Symbols-and"
31979 \begin_layout Plain Layout
31980 Chemical characters ! Symbols
31989 \begin_layout Plain Layout
31999 \begin_layout Plain Layout
32008 \begin_layout Standard
32009 An example text from chemistry:
32012 \begin_layout Quote
32014 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32017 -ion reacts with two
32018 \begin_inset Formula $\mathrm{Na^{+}}$
32021 -ions to sodium sulfate
32022 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32026 The chemical equation for this is:
32027 \begin_inset Formula \[
32028 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32035 \begin_layout Standard
32036 This chemical equation can directly be created as formula.
32037 To avoid that the symbols appear italic, everything is highlighted and
32038 changed by the shortcut
32041 \begin_inset Space ~
32046 to the upright font style.
32050 \begin_layout Plain Layout
32056 \begin_inset CommandInset ref
32058 reference "sub:Font-Styles"
32070 \begin_layout Subsection
32075 \begin_layout Plain Layout
32084 \begin_layout Standard
32085 Negative numbers often look ugly in formulas because the minus sign before
32086 the number is set with the same length as the minus operator sign.
32087 When writing the negative number in normal text, the minus sign appears
32091 \begin_layout Standard
32092 Thus, the problem disappears when converting the minus sign to mathematical
32096 \begin_layout Standard
32097 An example to visualize the problem:
32100 \begin_layout Standard
32102 \begin_inset Tabular
32103 <lyxtabular version="3" rows="3" columns="2">
32105 <column alignment="right" valignment="top" width="0">
32106 <column alignment="left" valignment="top" width="0">
32108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32111 \begin_layout Plain Layout
32117 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32120 \begin_layout Plain Layout
32128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32131 \begin_layout Plain Layout
32137 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32140 \begin_layout Plain Layout
32141 \begin_inset Formula $x=-2$
32151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32154 \begin_layout Plain Layout
32160 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32163 \begin_layout Plain Layout
32164 \begin_inset Formula $x=\textrm{-}2$
32180 \begin_layout Subsection
32181 Comma as Decimal Separator
32185 \begin_layout Plain Layout
32194 \begin_layout Standard
32195 In LaTeX a comma inside a formula is used, according to the English convention,
32196 as number group separator.
32197 So there will be space added behind all commas in formulas.
32200 \begin_layout Standard
32201 To avoid this, the comma is highlighted and changed to mathematical text
32205 \begin_inset Space ~
32213 \begin_layout Standard
32214 To use all formula commas in the document as decimal separator, the file
32223 \begin_layout Plain Layout
32228 is part of the LaTeX-package
32236 \begin_layout Plain Layout
32238 \begin_inset VSpace 4mm
32255 \begin_layout Plain Layout
32261 is loaded with the LaTeX-preamble line
32264 \begin_layout Standard
32272 \begin_layout Subsection
32274 \begin_inset CommandInset label
32276 name "sub:Physical-Vectors"
32284 \begin_layout Plain Layout
32293 \begin_layout Standard
32294 Predefined vectors are offered by the LaTeX-package
32302 \begin_layout Plain Layout
32307 should be part of every LaTeX standard installation.
32316 \begin_layout Plain Layout
32322 that is loaded with the LaTeX-preamble line
32325 \begin_layout Standard
32333 \begin_layout Standard
32337 \begin_layout Plain Layout
32347 \begin_inset Note Note
32350 \begin_layout Plain Layout
32351 The following table will only be displayed when the LaTeX-package
32360 The following commands are defined:
32363 \begin_layout Standard
32365 \begin_inset Tabular
32366 <lyxtabular version="3" rows="4" columns="2">
32368 <column alignment="center" valignment="top" width="0">
32369 <column alignment="center" valignment="top" width="0">
32371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32374 \begin_layout Plain Layout
32380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32383 \begin_layout Plain Layout
32391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32394 \begin_layout Plain Layout
32404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32407 \begin_layout Plain Layout
32408 \begin_inset Formula $\Bra {\psi}$
32418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32421 \begin_layout Plain Layout
32431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32434 \begin_layout Plain Layout
32435 \begin_inset Formula $\Ket {\psi}$
32445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32448 \begin_layout Plain Layout
32460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32463 \begin_layout Plain Layout
32464 \begin_inset Formula $\Braket {\psi|\phi}$
32480 \begin_layout Standard
32487 assures that all vertical bars are set in the size of the surrounding brackets:
32488 \begin_inset Formula \[
32489 \Braket {\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32497 \begin_layout Plain Layout
32507 \begin_inset Note Note
32510 \begin_layout Plain Layout
32511 The following will be displayed when the LaTeX-package
32523 \begin_layout Standard
32524 You need to install the LaTeX-package
32528 to see the rest of this subsection in the output.
32531 \begin_layout Standard
32535 \begin_layout Plain Layout
32547 \begin_layout Standard
32554 can also be achieved using the command
32560 , that is described in
32561 \begin_inset CommandInset ref
32563 reference "sub:Automatic-Bracket-Size"
32570 \begin_layout Subsection
32571 Self-defined Fractions
32572 \begin_inset CommandInset label
32574 name "sub:Self-defined-Fractions"
32582 \begin_layout Plain Layout
32583 Fractions ! self-defined
32591 \begin_layout Standard
32592 To define custom commands for fractions, the command
32602 \begin_layout Plain Layout
32610 is used in the following scheme:
32613 \begin_layout Standard
32626 bracket}{fraction bar thickness}{style}
32627 \begin_inset Newline newline
32634 \begin_layout Plain Layout
32649 \begin_layout Plain Layout
32656 {numerator}{denominator}
32659 \begin_layout Standard
32660 The style is a number in the range of 0
32661 \begin_inset Space \thinspace{}
32665 \begin_inset Space \thinspace{}
32671 \begin_layout Standard
32673 \begin_inset Tabular
32674 <lyxtabular version="3" rows="5" columns="2">
32676 <column alignment="center" valignment="top" width="0">
32677 <column alignment="center" valignment="top" width="0">
32679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32682 \begin_layout Plain Layout
32688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32691 \begin_layout Plain Layout
32699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32702 \begin_layout Plain Layout
32708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32711 \begin_layout Plain Layout
32712 display style formula
32719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32722 \begin_layout Plain Layout
32728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32731 \begin_layout Plain Layout
32739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32742 \begin_layout Plain Layout
32748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32751 \begin_layout Plain Layout
32759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32762 \begin_layout Plain Layout
32768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32771 \begin_layout Plain Layout
32785 \begin_layout Standard
32786 When no style is given, the size is adjusted to the surrounding environment
32787 like for the command
32796 \begin_layout Standard
32797 When no fraction bar thickness is given, the predefined value of 0.4
32798 \begin_inset Space \thinspace{}
32804 \begin_layout Standard
32805 \begin_inset VSpace medskip
32808 For example, the commands
32821 \begin_inset CommandInset ref
32823 reference "sub:Fractions"
32827 are defined with the commands
32830 \begin_layout Standard
32839 genfrac{}{}{}{0}{#1}{#2}}
32842 \begin_layout Standard
32846 \begin_layout Standard
32855 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32858 \begin_layout Standard
32859 \begin_inset VSpace medskip
32862 To define a fraction where the fraction bar thickness can be given as optional
32863 argument, the following line is inserted to the LaTeX-preamble:
32866 \begin_layout Standard
32875 genfrac{}{}{#1}{}{#2}{#3}}
32878 \begin_layout Standard
32880 \begin_inset Formula \begin{align*}
32881 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32882 \text{Result} & & \fracS [1mm]{A}{B} & & \fracS [5mm]{A}{B}\end{align*}
32886 As one can see, the distance of the numerator and the denominator to the
32887 fraction bar is round about three times the bar thickness.
32890 \begin_layout Subsection
32892 \begin_inset CommandInset label
32894 name "sub:Canceled-Formulas"
32902 \begin_layout Plain Layout
32911 \begin_layout Standard
32912 To cancel formulas or formula parts, the LaTeX-package
32920 \begin_layout Plain Layout
32925 is part of every LaTeX standard installation.
32934 \begin_layout Plain Layout
32940 has to be loaded with the LaTeX-preamble line
32943 \begin_layout Standard
32948 usepackage[samesize]{cancel}
32951 \begin_layout Standard
32952 There are four ways to cancel formulas:
32955 \begin_layout Standard
32957 \begin_inset Tabular
32958 <lyxtabular version="3" rows="5" columns="2">
32960 <column alignment="center" valignment="top" width="0">
32961 <column alignment="center" valignment="top" width="0">
32963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32966 \begin_layout Plain Layout
32972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32975 \begin_layout Plain Layout
32977 \begin_inset Note Note
32980 \begin_layout Plain Layout
32993 are used here as spacer.
33005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33008 \begin_layout Plain Layout
33017 \begin_layout Plain Layout
33031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33034 \begin_layout Plain Layout
33035 \begin_inset Formula $\raisebox {4.5mm}{}\cancel {\int A=B}\raisebox {-2.5mm}{}$
33045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33048 \begin_layout Plain Layout
33057 \begin_layout Plain Layout
33071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33074 \begin_layout Plain Layout
33075 \begin_inset Formula $\raisebox {4.5mm}{}\bcancel {\int A=B}\raisebox {-2.5mm}{}$
33085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33088 \begin_layout Plain Layout
33097 \begin_layout Plain Layout
33111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33114 \begin_layout Plain Layout
33115 \begin_inset Formula $\raisebox {4.5mm}{}\xcancel {\int A=B}\raisebox {-2.5mm}{}$
33125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33128 \begin_layout Plain Layout
33132 \begin_inset Formula $\to$
33143 \begin_layout Plain Layout
33157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33160 \begin_layout Plain Layout
33161 \begin_inset Formula $\raisebox {7mm}{}\cancelto {1}{\int A=B}\raisebox {-2.5mm}{}\hspace {3mm}$
33177 \begin_layout Standard
33184 is especially suitable to visualize the reduction of fractions within formulas:
33185 \begin_inset Formula \[
33186 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto {2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel {1+b^{2}}}\]
33193 \begin_layout Subsection
33194 Formulas in Section Headings
33195 \begin_inset CommandInset label
33197 name "sub:Formulas-in-Section"
33205 \begin_layout Plain Layout
33206 Formula ! in section headings
33214 \begin_layout Standard
33215 When formulas are used in section headings, the following has to be taken
33219 \begin_layout Standard
33220 \begin_inset Note Greyedout
33223 \begin_layout Plain Layout
33232 \begin_layout Plain Layout
33233 Packages ! hyperref
33238 support is enabled in the document settings dialog under
33241 \begin_inset Space ~
33246 , PDF-bookmarks are created for every section heading in the table of contents.
33247 If a section heading contains formulas, they are incorrectly displayed
33248 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33257 \begin_layout Standard
33258 Both problems can be solved by inserting at the end of the section heading
33259 a short title with the menu
33261 Insert\SpecialChar \menuseparator
33263 \begin_inset Space ~
33269 Short titles are used as alternative for multiline section headings to
33270 keep the table of contents clearly arranged.
33271 Only the short title appears in the table of contents and therefore also
33272 in the PDF-bookmark.
33275 \begin_layout Standard
33276 When formulas should be used in the table of contents but
33280 is used, one can use the following command in TeX-mode:
33283 \begin_layout Standard
33288 texorpdfstring{part}{alternative}
33292 \begin_layout Plain Layout
33303 \begin_layout Standard
33304 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33305 This can be characters, formulas, footnotes, but also cross-references.
33306 The alternative is used instead of the part for the bookmark.
33309 \begin_layout Standard
33310 Here are two example headings:
33311 \begin_inset VSpace -3mm
33318 \begin_layout Plain Layout
33330 \begin_layout Subsubsection
33331 Heading without formula in table of contents
33332 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33336 \begin_inset OptArg
33339 \begin_layout Plain Layout
33340 Heading without formula in table of contents
33348 \begin_layout Subsubsection
33349 Heading with formula in table of contents
33353 \begin_layout Plain Layout
33363 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33370 \begin_layout Plain Layout
33380 \begin_layout Standard
33384 \begin_layout Plain Layout
33393 In the first heading a short title was used, in the second one
33402 \begin_layout Standard
33403 To get the same formatting as for the other headings, the complete heading
33406 boldmath environment
33412 \begin_layout Plain Layout
33414 \begin_inset CommandInset ref
33416 reference "sub:Bold-Formulas"
33428 \begin_layout Subsection
33429 Formulas in multi-column Text
33433 \begin_layout Plain Layout
33434 Formula ! in multi-column text
33442 \begin_layout Standard
33443 Formulas in multi-column text are often too wide to fit into a column and
33444 thus need to be set over the whole page width.
33445 This is done by using the LaTeX-package
33453 \begin_layout Plain Layout
33458 is part of every LaTeX standard installation.
33467 \begin_layout Plain Layout
33468 Packages ! multicol
33473 , that is loaded with the LaTeX-preamble line
33476 \begin_layout Standard
33481 usepackage{multicol}
33484 \begin_layout Standard
33485 \begin_inset Note Greyedout
33488 \begin_layout Plain Layout
33489 Note herby that the setting
33492 \begin_inset Space ~
33499 Document\SpecialChar \menuseparator
33505 \begin_inset Space ~
33525 \begin_layout Standard
33526 Before the multi-column text the command
33529 \begin_layout Standard
33534 begin{multicols}{column number}
33537 \begin_layout Standard
33538 is written in TeX-mode.
33539 The column number is a number in the range of 2
33540 \begin_inset Space \thinspace{}
33544 \begin_inset Space \thinspace{}
33548 Before the formula the multi-column text is ended by inserting the command
33551 \begin_layout Standard
33559 \begin_layout Standard
33563 \begin_layout Standard
33564 Due to the command some space is automatically added before the formula.
33566 \begin_inset Space \thinspace{}
33569 mm vertical space is inserted before the formula.
33570 When the formula style
33576 \begin_layout Plain Layout
33578 \begin_inset CommandInset ref
33580 reference "sec:Formula-Styles"
33592 \begin_inset Space \thinspace{}
33595 mm space is inserted instead.
33598 \begin_layout Standard
33599 As example a multi-column text with a displayed formula:
33602 \begin_layout Standard
33606 \begin_layout Plain Layout
33610 begin{multicols}{2}
33615 Das Spektrum wird fouriertransformiert.
33616 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33617 , Lösungsmittel) zu trennen.
33618 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33619 nun das Aussehen des Ausgangssignals.
33620 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33621 über alle Phasen integrieren muss.
33623 \begin_inset Formula $S$
33626 unser normiertes Ausgangssignal and
33627 \begin_inset Formula $P$
33630 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33634 \begin_layout Plain Layout
33644 \begin_inset VSpace -6mm
33648 \begin_inset Formula \begin{equation}
33649 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33657 \begin_layout Plain Layout
33661 begin{multicols}{2}
33667 \begin_inset Formula $S_{0}$
33670 das Signal ohne Gradient ist and the Normierungsbedingung
33671 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33675 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33677 \begin_inset Formula $\nicefrac{\pi}{2}$
33681 \begin_inset Space \thinspace{}
33684 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33685 das Signal zusätzlich abschwächt.
33686 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33688 \begin_inset Formula $T_{2}$
33694 \begin_layout Standard
33698 \begin_layout Plain Layout
33710 \begin_layout Subsection
33711 Formulas with Description of Variables
33715 \begin_layout Plain Layout
33716 Formula ! with description of variables
33724 \begin_layout Standard
33725 To describe variables within a formula, like in formula
33726 \begin_inset CommandInset ref
33728 reference "eq:within"
33737 \begin_inset Formula $n$
33741 \begin_inset Space ~
33744 matrix is used with left aligned columns for the
33745 \begin_inset Formula $n$
33752 \begin_layout Plain Layout
33754 \begin_inset CommandInset ref
33756 reference "sec:Matrices"
33765 To set the description in a smaller size, before the matrix e.
33766 \begin_inset Space \thinspace{}
33770 \begin_inset Space ~
33783 \begin_layout Plain Layout
33785 \begin_inset CommandInset ref
33787 reference "sub:Font-Sizes"
33799 \begin_layout Standard
33800 When the formula style
33806 \begin_layout Plain Layout
33808 \begin_inset CommandInset ref
33810 reference "sec:Formula-Styles"
33831 \begin_layout Plain Layout
33838 only works in formulas with the style
33843 \begin_inset CommandInset ref
33845 reference "sub:Variable-Space"
33854 is inserted before and after the matrix to have the same separation of
33855 the matrix from the equation and the side margin.
33858 \begin_layout Standard
33859 When the formula style
33863 is used, the method described in
33864 \begin_inset CommandInset ref
33866 reference "sub:Flalign-Environment"
33870 is used to indent formulas.
33872 \begin_inset CommandInset ref
33874 reference "eq:within"
33878 consists of five columns whereas in the first two columns contain the equation,
33879 the third the matrix, and the last one an empty TeX-brace.
33880 \begin_inset Formula \begin{flalign}
33881 \hspace {30pt}F_{A} & =\rho·V·g & \footnotesize \begin{array}{ll}
33882 \rho & \textrm{density}\\
33883 V & \textrm{volume}\\
33884 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33891 \begin_layout Subsection
33892 Upright small Greek Letters
33893 \begin_inset CommandInset label
33895 name "sub:Upright-small-Greek"
33903 \begin_layout Plain Layout
33904 Greek letters ! upright
33912 \begin_layout Standard
33913 Most of the math fonts only provide italic small Greek letters.
33914 But for symbols of elementary particles like pions and neutrinos, upright
33915 Greek letters are needed.
33924 \begin_layout Plain Layout
33929 is part of the LaTeX-package
33937 \begin_layout Plain Layout
33939 \begin_inset VSpace 4mm
33956 \begin_layout Plain Layout
33962 that is loaded with the LaTeX-preamble line
33965 \begin_layout Standard
33970 usepackage{upgreek}
33973 \begin_layout Standard
33979 \begin_layout Plain Layout
33989 \begin_inset Note Note
33992 \begin_layout Plain Layout
33993 The following table will only be displayed when the LaTeX-package
34002 They are created when the command for a small Greek letters is started
34008 For example the command
34015 \begin_inset Formula $\uptau $
34021 \begin_layout Standard
34022 With these commands reactions of elementary particles can be typeset:
34023 \begin_inset Formula \[
34024 \uppi ^{+}\to\upmu ^{+}+\upnu _{\upmu }\]
34031 \begin_layout Standard
34032 The upright letters are more bold and wider than the italic ones.
34033 They should therefore not be used for units like
34034 \begin_inset Quotes eld
34038 \begin_inset Quotes erd
34044 \begin_layout Standard
34048 \begin_layout Plain Layout
34058 \begin_inset Note Note
34061 \begin_layout Plain Layout
34062 The following will be displayed when the LaTeX-package
34074 \begin_layout Standard
34075 You need to install the LaTeX-package
34079 to see the rest of this subsection in the output.
34082 \begin_layout Standard
34086 \begin_layout Plain Layout
34098 \begin_layout Subsection
34099 Text Characters in Formulas
34100 \begin_inset CommandInset label
34102 name "sub:Text-Characters-in"
34110 \begin_layout Plain Layout
34119 \begin_layout Standard
34120 In some cases you might want to insert text characters directly into formulas.
34121 When for example the centered dot · is often used in formulas like
34122 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34125 , one would have to insert the command
34135 \begin_layout Plain Layout
34137 \begin_inset CommandInset ref
34139 reference "sub:Binary-Operators"
34148 all the time, because this character is defined in all encodings as text
34150 But the encoding can be changed by this LaTeX-preamble line:
34153 \begin_layout Standard
34158 Declare Inputtext{183}{
34168 f\SpecialChar \textcompwordmark{}
34172 \begin_layout Standard
34173 The character encoding (menu
34175 Document\SpecialChar \menuseparator
34176 Settings\SpecialChar \menuseparator
34179 ) specifies what character appears when a keyboard key is pressed.
34180 When the key for the character '·' is pressed, internally the command
34187 But this command is not available in a formula so that you would get LaTeX-erro
34189 With the changed encoding the right command is chosen automatically, depending
34190 on if the character was inserted into a formula or not.
34193 \begin_layout Standard
34194 The encoding of several characters is saved in definition files.
34195 Fore example the encoding
34199 is defined in the file
34203 that is in the installation folder of LaTeX.
34204 Encodings should only be changed via the LaTeX-preamble and not in the
34206 Otherwise own documents could not be edited by other LyX users working
34207 on other computers.
34210 \begin_layout Standard
34211 \begin_inset VSpace medskip
34214 Besides the centered dot, in this document the degree sign ° is defined
34215 with the following LaTeX-preamble line so that it can directly be inserted
34219 \begin_layout Standard
34224 DeclareInputtext{176}{
34234 f\SpecialChar \textcompwordmark{}
34238 \begin_layout Standard
34239 \begin_inset Newpage newpage
34245 \begin_layout Section
34247 Typographic Advises
34251 \begin_layout Plain Layout
34252 Typographic Advises
34260 \begin_layout Standard
34261 This section is a summary of the most important typographic rules, listed
34266 \begin_layout Plain Layout
34267 This collection was partly taken from the German semi-official dictionary
34269 \begin_inset Quotes eld
34273 \begin_inset Quotes erd
34277 \begin_inset CommandInset citation
34283 that lists some of the ISO rules.
34291 \begin_layout Itemize
34300 \begin_layout Plain Layout
34301 done with font styles, see
34302 \begin_inset CommandInset ref
34304 reference "sub:Font-Styles"
34314 \begin_inset Space \thinspace{}
34318 \begin_inset Newline newline
34321 Between the value and the unit is the smallest space, see
34322 \begin_inset CommandInset ref
34324 reference "sub:Predefined-Space"
34331 \begin_layout Itemize
34332 Percent and perthousand signs are set like physical units:
34333 \begin_inset Newline newline
34337 \begin_inset Space \thinspace{}
34343 \begin_layout Itemize
34344 The degree sign follows directly on the value: 15°, but not when it is used
34346 \begin_inset Space \thinspace{}
34352 \begin_layout Itemize
34353 In numbers with more than four digits the smallest space is inserted before
34354 every third digit to group them:
34364 \begin_inset Space \thinspace{}
34368 \begin_inset Space \thinspace{}
34374 \begin_layout Itemize
34375 For dimensionings like 120×90×40
34376 \begin_inset Space \thinspace{}
34379 cm the multiplication sign
34380 \begin_inset Quotes eld
34384 \begin_inset Quotes erd
34388 It is available with the LaTeX-command
34394 , but can also directly be inserted with some keyboard definitions.
34397 \begin_layout Itemize
34398 Functions with names consisting of several letters are set upright to avoid
34400 \begin_inset CommandInset ref
34402 reference "sub:Predefined-Functions"
34409 \begin_layout Itemize
34410 Indices consisting of several letters, are set upright:
34411 \begin_inset Formula $E_{\mathrm{kin}}$
34415 \begin_inset Newline newline
34418 Components of matrices are set italic:
34419 \begin_inset Formula $\hat{H}_{kl}$
34425 \begin_layout Itemize
34426 The differentiation/integration operator 'd', the Euler's number 'e', and
34427 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34431 \begin_layout Standard
34432 \begin_inset Newpage newpage
34438 \begin_layout Section
34443 \begin_layout Plain Layout
34452 \begin_layout Standard
34453 Some characters and symbols can be created with several commands.
34454 Here is a list of the synonym commands:
34457 \begin_layout Standard
34458 \begin_inset VSpace bigskip
34462 \begin_inset Space \hfill{}
34466 \begin_inset Tabular
34467 <lyxtabular version="3" rows="12" columns="2">
34469 <column alignment="center" valignment="top" width="0pt">
34470 <column alignment="center" valignment="top" width="0pt">
34472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34475 \begin_layout Plain Layout
34481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34484 \begin_layout Plain Layout
34486 \begin_inset Note Note
34489 \begin_layout Plain Layout
34496 is only used as spacer.
34508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34511 \begin_layout Plain Layout
34519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34522 \begin_layout Plain Layout
34526 \begin_layout Plain Layout
34539 \begin_layout Plain Layout
34553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34556 \begin_layout Plain Layout
34564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34567 \begin_layout Plain Layout
34577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34580 \begin_layout Plain Layout
34588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34591 \begin_layout Plain Layout
34601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34604 \begin_layout Plain Layout
34612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34615 \begin_layout Plain Layout
34623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34626 \begin_layout Plain Layout
34634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34637 \begin_layout Plain Layout
34645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34648 \begin_layout Plain Layout
34656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34659 \begin_layout Plain Layout
34669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34672 \begin_layout Plain Layout
34680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34683 \begin_layout Plain Layout
34693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34696 \begin_layout Plain Layout
34704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34707 \begin_layout Plain Layout
34717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34720 \begin_layout Plain Layout
34728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34731 \begin_layout Plain Layout
34741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34744 \begin_layout Plain Layout
34752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34755 \begin_layout Plain Layout
34763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34766 \begin_layout Plain Layout
34774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34777 \begin_layout Plain Layout
34789 \begin_inset Space \hfill{}
34793 \begin_inset Tabular
34794 <lyxtabular version="3" rows="12" columns="2">
34796 <column alignment="center" valignment="top" width="0pt">
34797 <column alignment="center" valignment="top" width="0pt">
34799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34802 \begin_layout Plain Layout
34808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34811 \begin_layout Plain Layout
34819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34822 \begin_layout Plain Layout
34830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34833 \begin_layout Plain Layout
34845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34848 \begin_layout Plain Layout
34856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34859 \begin_layout Plain Layout
34869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34872 \begin_layout Plain Layout
34880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34883 \begin_layout Plain Layout
34893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34896 \begin_layout Plain Layout
34904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34907 \begin_layout Plain Layout
34915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34918 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34929 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34940 \begin_layout Plain Layout
34948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34951 \begin_layout Plain Layout
34961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34964 \begin_layout Plain Layout
34972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34975 \begin_layout Plain Layout
34985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34988 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34999 \begin_layout Plain Layout
35009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35012 \begin_layout Plain Layout
35020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35023 \begin_layout Plain Layout
35033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35036 \begin_layout Plain Layout
35044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35047 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35060 \begin_layout Plain Layout
35068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35071 \begin_layout Plain Layout
35085 \begin_inset Space \hfill{}
35091 \begin_layout Standard
35092 \begin_inset Newpage newpage
35098 \begin_layout Bibliography
35099 \begin_inset CommandInset bibitem
35100 LatexCommand bibitem
35112 The LaTeX Companion
35115 Addison Wesley, 2004
35118 \begin_layout Bibliography
35119 \begin_inset CommandInset bibitem
35120 LatexCommand bibitem
35126 \begin_inset CommandInset href
35129 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35133 of LaTeX's math abilities
35136 \begin_layout Bibliography
35137 \begin_inset CommandInset bibitem
35138 LatexCommand bibitem
35143 LaTeX tips and tricks-
35144 \begin_inset CommandInset href
35147 target "http://tug.org/TeXnik/"
35154 \begin_layout Bibliography
35155 \begin_inset CommandInset bibitem
35156 LatexCommand bibitem
35162 \begin_inset CommandInset href
35165 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35173 \begin_layout Plain Layout
35185 \begin_layout Bibliography
35186 \begin_inset CommandInset bibitem
35187 LatexCommand bibitem
35193 \begin_inset CommandInset href
35196 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35200 of all symbols available with LaTeX-packages
35203 \begin_layout Bibliography
35204 \begin_inset CommandInset bibitem
35205 LatexCommand bibitem
35211 \begin_inset CommandInset href
35213 name "Documentation"
35214 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35218 of the LaTeX-package
35226 \begin_layout Plain Layout
35227 Packages ! hyperref
35235 \begin_layout Bibliography
35236 \begin_inset CommandInset bibitem
35237 LatexCommand bibitem
35243 \begin_inset CommandInset href
35246 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35257 \begin_inset CommandInset ref
35259 reference "sub:Operator-Limits"
35267 \begin_layout Plain Layout
35278 \begin_layout Bibliography
35279 \begin_inset CommandInset bibitem
35280 LatexCommand bibitem
35291 Auflage, Duden 2001
35294 \begin_layout Subsubsection*
35295 \begin_inset CommandInset index_print
35296 LatexCommand printindex