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
8640 \begin_layout Plain Layout
8655 When inserting one of these commands in a formula, an arrow with two blue
8656 boxes appear where the label can be inserted.
8657 The length of the arrow adapts to the label width.
8660 \begin_layout Standard
8662 \begin_inset Tabular
8663 <lyxtabular version="3" rows="3" columns="2">
8665 <column alignment="center" valignment="top" width="0pt">
8666 <column alignment="center" valignment="top" width="0pt">
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8671 \begin_layout Plain Layout
8677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8680 \begin_layout Plain Layout
8682 \begin_inset Note Note
8685 \begin_layout Plain Layout
8692 is only used as spacer.
8704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8714 \begin_layout Plain Layout
8724 \begin_inset Formula $\downarrow$
8728 \begin_inset Formula $\to$
8736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8739 \begin_layout Plain Layout
8740 \begin_inset Formula $\raisebox {5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox {-4mm}{}$
8750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8753 \begin_layout Plain Layout
8760 \begin_layout Plain Layout
8770 \begin_inset Formula $\downarrow$
8774 \begin_inset Formula $\to$
8782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8785 \begin_layout Plain Layout
8786 \begin_inset Formula $\raisebox {5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox {-4mm}{}$
8802 \begin_layout Subsection
8803 Vertical and diagonal Arrows
8807 \begin_layout Plain Layout
8817 \begin_layout Plain Layout
8826 \begin_layout Standard
8827 \begin_inset Space \hfill{}
8831 \begin_inset Tabular
8832 <lyxtabular version="3" rows="7" columns="2">
8834 <column alignment="center" valignment="top" width="0pt">
8835 <column alignment="center" valignment="top" width="0pt">
8837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8840 \begin_layout Plain Layout
8846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8849 \begin_layout Plain Layout
8857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8860 \begin_layout Plain Layout
8868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8871 \begin_layout Plain Layout
8872 \begin_inset Formula $\uparrow$
8882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8885 \begin_layout Plain Layout
8893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8896 \begin_layout Plain Layout
8897 \begin_inset Formula $\Uparrow$
8907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8910 \begin_layout Plain Layout
8918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8921 \begin_layout Plain Layout
8922 \begin_inset Formula $\updownarrow$
8932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8935 \begin_layout Plain Layout
8943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8946 \begin_layout Plain Layout
8947 \begin_inset Formula $\Updownarrow$
8957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8960 \begin_layout Plain Layout
8968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8971 \begin_layout Plain Layout
8972 \begin_inset Formula $\Downarrow$
8982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8985 \begin_layout Plain Layout
8993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8996 \begin_layout Plain Layout
8997 \begin_inset Formula $\downarrow$
9011 \begin_inset Space \hfill{}
9015 \begin_inset Tabular
9016 <lyxtabular version="3" rows="5" columns="2">
9018 <column alignment="center" valignment="top" width="0pt">
9019 <column alignment="center" valignment="top" width="0pt">
9021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9024 \begin_layout Plain Layout
9030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9033 \begin_layout Plain Layout
9041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9044 \begin_layout Plain Layout
9052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9055 \begin_layout Plain Layout
9056 \begin_inset Formula $\nearrow$
9066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9069 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9080 \begin_layout Plain Layout
9081 \begin_inset Formula $\searrow$
9091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9094 \begin_layout Plain Layout
9102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9105 \begin_layout Plain Layout
9106 \begin_inset Formula $\swarrow$
9116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9119 \begin_layout Plain Layout
9127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9130 \begin_layout Plain Layout
9131 \begin_inset Formula $\nwarrow$
9145 \begin_inset Space \hfill{}
9151 \begin_layout Standard
9152 \begin_inset VSpace medskip
9155 Vertical arrows can be used also as delimiter together with the commands
9157 \begin_inset CommandInset ref
9159 reference "sub:Manual-Bracket-Size"
9164 \begin_inset CommandInset ref
9166 reference "sub:Automatic-Bracket-Size"
9173 \begin_layout Standard
9174 \begin_inset Newpage newpage
9180 \begin_layout Section
9182 \begin_inset CommandInset label
9192 \begin_layout Plain Layout
9201 \begin_layout Standard
9202 Accents can be inserted via the math toolbar button
9203 \begin_inset Graphics
9204 filename ../images/math/hat.png
9209 or the commands listed in the following subsections.
9212 \begin_layout Subsection
9213 Accents for one Character
9217 \begin_layout Plain Layout
9230 \begin_layout Plain Layout
9232 \begin_inset CommandInset ref
9234 reference "sub:Accents-in-Text"
9247 \begin_layout Plain Layout
9255 \begin_inset Note Note
9258 \begin_layout Plain Layout
9261 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9264 \begin_layout Plain Layout
9267 texorpdfstring is in section
9268 \begin_inset CommandInset ref
9270 reference "sub:Formulas-in-Section"
9280 \begin_inset CommandInset label
9282 name "sub:Accents-for-one"
9290 \begin_layout Plain Layout
9291 Accents ! for one character
9299 \begin_layout Standard
9300 \begin_inset Space \hfill{}
9304 \begin_inset Tabular
9305 <lyxtabular version="3" rows="8" columns="2">
9307 <column alignment="center" valignment="top" width="0pt">
9308 <column alignment="center" valignment="top" width="0pt">
9310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9313 \begin_layout Plain Layout
9319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9322 \begin_layout Plain Layout
9324 \begin_inset Note Note
9327 \begin_layout Plain Layout
9334 is only used as spacer.
9346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9349 \begin_layout Plain Layout
9356 \begin_layout Plain Layout
9370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9373 \begin_layout Plain Layout
9374 \begin_inset Formula $\raisebox {5mm}{}\dot{A}$
9384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9387 \begin_layout Plain Layout
9394 \begin_layout Plain Layout
9408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9411 \begin_layout Plain Layout
9412 \begin_inset Formula $\raisebox {5mm}{}\ddot{A}$
9422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9425 \begin_layout Plain Layout
9432 \begin_layout Plain Layout
9446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9449 \begin_layout Plain Layout
9450 \begin_inset Formula $\raisebox {5mm}{}\dddot{A}$
9460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9463 \begin_layout Plain Layout
9471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9474 \begin_layout Plain Layout
9475 \begin_inset Formula $\raisebox {5mm}{}\ddddot {A}$
9485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9488 \begin_layout Plain Layout
9495 \begin_layout Plain Layout
9508 \begin_layout Plain Layout
9519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9522 \begin_layout Plain Layout
9523 \begin_inset Formula $\raisebox {5mm}{}\vec{A}$
9533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9536 \begin_layout Plain Layout
9543 \begin_layout Plain Layout
9557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9560 \begin_layout Plain Layout
9561 \begin_inset Formula $\raisebox {5mm}{}\bar{A}$
9571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9574 \begin_layout Plain Layout
9581 \begin_layout Plain Layout
9595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9598 \begin_layout Plain Layout
9599 \begin_inset Formula $\raisebox {5mm}{}\mathring{A}$
9613 \begin_inset Space \hfill{}
9617 \begin_inset Tabular
9618 <lyxtabular version="3" rows="7" columns="2">
9620 <column alignment="center" valignment="top" width="0pt">
9621 <column alignment="center" valignment="top" width="0pt">
9623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9626 \begin_layout Plain Layout
9632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9635 \begin_layout Plain Layout
9643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9646 \begin_layout Plain Layout
9653 \begin_layout Plain Layout
9667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9670 \begin_layout Plain Layout
9671 \begin_inset Formula $\raisebox {5mm}{}\tilde{A}$
9681 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9684 \begin_layout Plain Layout
9691 \begin_layout Plain Layout
9705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\raisebox {5mm}{}\hat{A}$
9719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9722 \begin_layout Plain Layout
9729 \begin_layout Plain Layout
9743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9746 \begin_layout Plain Layout
9747 \begin_inset Formula $\raisebox {5mm}{}\check{A}$
9757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9767 \begin_layout Plain Layout
9781 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9784 \begin_layout Plain Layout
9785 \begin_inset Formula $\raisebox {5mm}{}\acute{A}$
9795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9798 \begin_layout Plain Layout
9805 \begin_layout Plain Layout
9819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9822 \begin_layout Plain Layout
9823 \begin_inset Formula $\raisebox {5mm}{}\grave{A}$
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9836 \begin_layout Plain Layout
9843 \begin_layout Plain Layout
9857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\raisebox {5mm}{}\breve{A}$
9875 \begin_inset Space \hfill{}
9881 \begin_layout Standard
9882 \begin_inset VSpace bigskip
9889 \begin_layout Plain Layout
9895 in formulas, a quotation mark is inserted before the vowel.
9896 These two characters are then treated by LaTeX as
9900 character when the formula part with the umlaut is marked as German.
9908 \begin_inset Quotes eld
9912 \begin_inset Quotes erd
9915 umlauts are created as demonstrated in the following example:
9918 \begin_layout Standard
9919 \begin_inset VSpace -2mm
9925 \begin_layout Standard
9927 \begin_inset Tabular
9928 <lyxtabular version="3" rows="3" columns="2">
9930 <column alignment="center" valignment="top" width="0">
9931 <column alignment="center" valignment="top" width="0">
9933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9936 \begin_layout Plain Layout
9942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9945 \begin_layout Plain Layout
9947 \begin_inset Note Note
9950 \begin_layout Plain Layout
9957 is only used as spacer.
9969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9972 \begin_layout Plain Layout
9975 \begin_inset Quotes grd
9983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9986 \begin_layout Plain Layout
9989 \begin_inset Formula $"i$
9999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10002 \begin_layout Plain Layout
10009 \begin_layout Plain Layout
10023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10026 \begin_layout Plain Layout
10027 \begin_inset Formula $\raisebox {5mm}{}\ddot{i}$
10043 \begin_layout Standard
10044 Another advantage to
10050 is that umlauts can directly be converted to mathematical text because
10051 the accent commands above are
10057 in mathematical text
10060 To convert an accented character to mathematical text, only the character
10061 under the accent may be converted.
10062 This applies also for all other conversions, e.
10063 \begin_inset Space \thinspace{}
10067 \begin_inset Space ~
10073 \begin_layout Standard
10074 In mathematical text, umlauts and other accented characters can directly
10078 \begin_layout Subsection
10079 Accents for Operators
10083 \begin_layout Plain Layout
10084 Accents ! for operators
10092 \begin_layout Standard
10103 \begin_layout Plain Layout
10121 \begin_layout Plain Layout
10129 characters can be placed above or below an operator, respectively, to accent
10141 \begin_layout Plain Layout
10149 characters can be set before and behind an operator.
10150 The command scheme is:
10153 \begin_layout Standard
10169 \begin_layout Standard
10176 must always be before the operator that should be accented.
10177 You can accent with several characters and even with other operators and
10185 for example only characters behind an operator, write nothing between the
10186 first braces but don't omit the braces.
10189 \begin_layout Standard
10190 For example the command
10195 \begin_inset Formula $\to$
10205 \begin_inset Formula $\to$
10214 \begin_layout Plain Layout
10230 \begin_inset Formula \[
10231 \sideset {}{'}\sum_{k=1}^{n}\]
10238 \begin_layout Standard
10247 \begin_layout Plain Layout
10262 \begin_layout Plain Layout
10274 \begin_inset Formula $\uparrow$
10282 \begin_inset Formula \[
10283 \overset{a}{\maltese}\]
10287 As seen in the last example, with
10299 also symbols and characters can be accented; with
10305 this is not possible.
10308 \begin_layout Subsection
10309 Accents for several Characters
10310 \begin_inset CommandInset label
10312 name "sub:Accents-for-several"
10320 \begin_layout Plain Layout
10321 Accents ! for several characters
10329 \begin_layout Standard
10330 \begin_inset Space \hfill{}
10334 \begin_inset Tabular
10335 <lyxtabular version="3" rows="5" columns="2">
10337 <column alignment="center" valignment="top" width="0pt">
10338 <column alignment="center" valignment="top" width="0pt">
10340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10343 \begin_layout Plain Layout
10349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10352 \begin_layout Plain Layout
10354 \begin_inset Note Note
10357 \begin_layout Plain Layout
10364 is only used as spacer.
10376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10379 \begin_layout Plain Layout
10386 \begin_layout Plain Layout
10400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10403 \begin_layout Plain Layout
10404 \begin_inset Formula $\raisebox {6mm}{}\overleftarrow{A=B}\raisebox {-2mm}{}$
10414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10417 \begin_layout Plain Layout
10424 \begin_layout Plain Layout
10438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10441 \begin_layout Plain Layout
10442 \begin_inset Formula $\raisebox {5mm}{}\underleftarrow{A=B}\raisebox {-3mm}{}$
10452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10455 \begin_layout Plain Layout
10462 \begin_layout Plain Layout
10476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10479 \begin_layout Plain Layout
10480 \begin_inset Formula $\raisebox {6mm}{}\overleftrightarrow{A=B}\raisebox {-2mm}{}$
10490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10493 \begin_layout Plain Layout
10496 underleftrightarrow
10500 \begin_layout Plain Layout
10514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10517 \begin_layout Plain Layout
10518 \begin_inset Formula $\raisebox {5mm}{}\underleftrightarrow{A=B}\raisebox {-3mm}{}$
10532 \begin_inset Space \hfill{}
10536 \begin_inset Tabular
10537 <lyxtabular version="3" rows="5" columns="2">
10539 <column alignment="center" valignment="top" width="0pt">
10540 <column alignment="center" valignment="top" width="0pt">
10542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10545 \begin_layout Plain Layout
10551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10554 \begin_layout Plain Layout
10562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10565 \begin_layout Plain Layout
10572 \begin_layout Plain Layout
10586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10589 \begin_layout Plain Layout
10590 \begin_inset Formula $\raisebox {6mm}{}\overrightarrow{A=B}\raisebox {-2mm}{}$
10600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10603 \begin_layout Plain Layout
10610 \begin_layout Plain Layout
10624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10627 \begin_layout Plain Layout
10628 \begin_inset Formula $\raisebox {5mm}{}\underrightarrow{A=B}\raisebox {-3mm}{}$
10638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10641 \begin_layout Plain Layout
10648 \begin_layout Plain Layout
10662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10665 \begin_layout Plain Layout
10666 \begin_inset Formula $\raisebox {6mm}{}\widetilde{A=B}\raisebox {-2mm}{}$
10676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10686 \begin_layout Plain Layout
10700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10703 \begin_layout Plain Layout
10704 \begin_inset Formula $\raisebox {6mm}{}\widehat{A=B}\raisebox {-2mm}{}$
10718 \begin_inset Space \hfill{}
10724 \begin_layout Standard
10725 \begin_inset VSpace medskip
10728 With these commands as many characters as you like can be accented.
10741 will only be set in the output with a length of three characters, as shown
10742 in the following example:
10743 \begin_inset Formula \[
10744 \widetilde{A+B=C-D}\]
10751 \begin_layout Standard
10762 \begin_layout Plain Layout
10780 \begin_layout Plain Layout
10788 described in the previous subsection it is also possible to accent several
10798 \begin_layout Plain Layout
10808 \begin_inset Formula $\downarrow$
10814 \begin_inset Formula \[
10815 \underset{***}{A=B}\]
10822 \begin_layout Section
10824 \begin_inset CommandInset label
10834 \begin_layout Plain Layout
10843 \begin_layout Subsection
10845 \begin_inset CommandInset label
10847 name "sub:Predefined-Space"
10855 \begin_layout Plain Layout
10856 Space ! horizontal ! predefined
10864 \begin_layout Standard
10865 Sometimes it is necessary to insert horizontal space to a formula.
10866 This is done by inserting a protected space (shortcut
10872 \begin_inset Quotes eld
10882 \begin_layout Plain Layout
10895 \begin_inset Quotes erd
10898 appears and by pressing
10902 several times one can select one of eight different space sizes.
10903 The spaces can also be inserted using the math toolbar button
10904 \begin_inset Graphics
10905 filename ../images/math/space.png
10910 or special commands.
10911 Independent from the inserted command, one can select the size again by
10919 \begin_layout Standard
10922 \begin_inset VSpace -5mm
10926 \begin_inset Tabular
10927 <lyxtabular version="3" rows="3" columns="7">
10929 <column alignment="center" valignment="middle" width="6.8cm">
10930 <column alignment="center" valignment="top" width="0">
10931 <column alignment="center" valignment="top" width="0">
10932 <column alignment="center" valignment="top" width="0">
10933 <column alignment="center" valignment="top" width="0">
10934 <column alignment="center" valignment="top" width="0">
10935 <column alignment="center" valignment="top" width="0">
10937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10940 \begin_layout Plain Layout
10946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10949 \begin_layout Plain Layout
10957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10960 \begin_layout Plain Layout
10968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10971 \begin_layout Plain Layout
10979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10982 \begin_layout Plain Layout
10990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10993 \begin_layout Plain Layout
11001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11004 \begin_layout Plain Layout
11014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11017 \begin_layout Plain Layout
11022 keystrokes after inserting the protected space
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" usebox="none">
11066 \begin_layout Plain Layout
11072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11075 \begin_layout Plain Layout
11083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11086 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11096 \begin_inset Formula $A\, B$
11104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11108 \begin_inset Formula $A\: B$
11116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11120 \begin_inset Formula $A\; B$
11128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11132 \begin_inset Formula $A\quad B$
11140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11143 \begin_layout Plain Layout
11144 \begin_inset Formula $A\qquad B$
11152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11155 \begin_layout Plain Layout
11156 \begin_inset Formula $A\! B$
11172 \begin_layout Standard
11173 The last size seem to produce no space.
11174 It is displayed red in LyX contrary to the other sizes, because it is a
11176 There are two more negative spaces:
11179 \begin_layout Standard
11181 \begin_inset Tabular
11182 <lyxtabular version="3" rows="3" columns="3">
11184 <column alignment="center" valignment="middle" width="6.8cm">
11185 <column alignment="center" valignment="top" width="0pt">
11186 <column alignment="center" valignment="top" width="0pt">
11188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11191 \begin_layout Plain Layout
11197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11200 \begin_layout Plain Layout
11208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11211 \begin_layout Plain Layout
11221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11224 \begin_layout Plain Layout
11229 keystrokes after inserting the protected space
11234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11246 \begin_layout Plain Layout
11254 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11267 \begin_inset Formula $A\negmedspace B$
11275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11278 \begin_layout Plain Layout
11279 \begin_inset Formula $A\negthickspace B$
11295 \begin_layout Standard
11296 Negative spaces can lead to characters overlapping each other.
11297 Thus they can be used to enforce ligatures, what is e.
11298 \begin_inset Space \thinspace{}
11302 \begin_inset Space ~
11305 useful for summation operators:
11308 \begin_layout Standard
11310 \begin_inset Tabular
11311 <lyxtabular version="3" rows="3" columns="2">
11313 <column alignment="center" valignment="top" width="0">
11314 <column alignment="center" valignment="top" width="0">
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11328 \begin_layout Plain Layout
11330 \begin_inset Note Note
11333 \begin_layout Plain Layout
11340 is only used as spacer.
11352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11364 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11381 \begin_layout Plain Layout
11382 \begin_inset Formula $\raisebox {4.5mm}{}\sum\sum f_{kl}\raisebox {-2.5mm}{}$
11392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11395 \begin_layout Plain Layout
11406 \begin_layout Plain Layout
11420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11423 \begin_layout Plain Layout
11424 \begin_inset Formula $\raisebox {4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox {-2.5mm}{}$
11440 \begin_layout Standard
11441 Relations like for example equal signs, are always surrounded by space.
11442 To suppress this, the equal sign is placed into a TeX-brace.
11443 The following example demonstrates this:
11446 \begin_layout Standard
11448 \begin_inset Tabular
11449 <lyxtabular version="3" rows="2" columns="2">
11451 <column alignment="center" valignment="top" width="0pt">
11452 <column alignment="center" valignment="top" width="0pt">
11454 <cell alignment="center" valignment="top" usebox="none">
11457 \begin_layout Plain Layout
11463 <cell alignment="center" valignment="top" usebox="none">
11466 \begin_layout Plain Layout
11467 \begin_inset Formula $A=B$
11477 <cell alignment="center" valignment="top" usebox="none">
11480 \begin_layout Plain Layout
11481 \begin_inset Note Note
11484 \begin_layout Plain Layout
11491 is only used as spacer.
11497 \begin_inset Formula $\raisebox {5mm}{}$
11500 equation without space
11505 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11508 \begin_layout Plain Layout
11509 \begin_inset Formula $A{=}B$
11525 \begin_layout Standard
11527 The command for the last formula is:
11532 \begin_inset Formula $\to$
11538 \begin_layout Standard
11539 \begin_inset VSpace bigskip
11542 Spaces are needed for physical units, because the space between the value
11543 and the unit is the smallest one and not a normal space.
11544 For units in text, the smallest space is inserted via the menu
11546 Insert\SpecialChar \menuseparator
11547 Formatting\SpecialChar \menuseparator
11549 \begin_inset Space ~
11561 \begin_layout Standard
11562 An example to visualize the difference:
11565 \begin_layout Standard
11566 \begin_inset Tabular
11567 <lyxtabular version="3" rows="2" columns="2">
11569 <column alignment="left" valignment="top" width="0">
11570 <column alignment="left" valignment="top" width="0">
11572 <cell alignment="center" valignment="top" usebox="none">
11575 \begin_layout Plain Layout
11577 \begin_inset Formula $\cdot$
11585 <cell alignment="center" valignment="top" usebox="none">
11588 \begin_layout Plain Layout
11589 space between value and unit
11596 <cell alignment="center" valignment="top" usebox="none">
11599 \begin_layout Plain Layout
11601 \begin_inset Space \thinspace{}
11605 \begin_inset Formula $\cdot$
11613 <cell alignment="center" valignment="top" usebox="none">
11616 \begin_layout Plain Layout
11617 smallest space between value and unit
11630 \begin_layout Subsection
11635 \begin_layout Plain Layout
11648 \begin_layout Plain Layout
11649 for vertical space in formulas see
11650 \begin_inset CommandInset ref
11652 reference "sub:Line-Separation"
11665 \begin_layout Plain Layout
11673 \begin_inset Note Note
11676 \begin_layout Plain Layout
11679 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11682 \begin_layout Plain Layout
11685 texorpdfstring is in section
11686 \begin_inset CommandInset ref
11688 reference "sub:Formulas-in-Section"
11698 \begin_inset CommandInset label
11700 name "sub:Variable-Space"
11708 \begin_layout Plain Layout
11709 Space ! horizontal ! variable
11717 \begin_layout Standard
11718 Space with a defined length can be inserted in LyX with the command
11719 \begin_inset Newline newline
11732 \begin_layout Plain Layout
11741 For the length all units listed in
11742 \begin_inset CommandInset ref
11744 reference "tab:Used-units"
11748 are allowed, except of the unit
11749 \begin_inset Quotes eld
11753 \begin_inset Quotes erd
11757 The length may also be negative.
11758 To insert so many space that the formula uses all available space, the
11769 \begin_layout Plain Layout
11780 \begin_layout Standard
11781 \begin_inset VSpace -1mm
11787 \begin_layout Standard
11789 \begin_inset Tabular
11790 <lyxtabular version="3" rows="4" columns="2">
11792 <column alignment="center" valignment="top" width="0">
11793 <column alignment="center" valignment="top" width="0">
11795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11798 \begin_layout Plain Layout
11804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11807 \begin_layout Plain Layout
11815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11818 \begin_layout Plain Layout
11822 \begin_inset Formula $\to$
11832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11835 \begin_layout Plain Layout
11836 \begin_inset Formula $A=B\hspace {3cm}A\not=C$
11846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11849 \begin_layout Plain Layout
11853 \begin_inset Formula $\to$
11863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11866 \begin_layout Plain Layout
11867 \begin_inset Formula $A\hspace {-1mm}A\not=A$
11877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11880 \begin_layout Plain Layout
11887 \begin_layout Plain Layout
11901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11904 \begin_layout Plain Layout
11905 \begin_inset Formula $A=A\hfill B=B$
11921 \begin_layout Standard
11922 In the last example the available space is given by the longest column entry
11924 In an inline formula the space depends on the length of the line in which
11932 Thus, when the line uses the full width, no space will be created.
11939 only has an effect on displayed formulas when the formula style
11944 (Formula styles are explained in
11945 \begin_inset CommandInset ref
11947 reference "sec:Formula-Styles"
11954 \begin_layout Standard
11955 For text, variable space can be inserted via the menu
11957 Insert\SpecialChar \menuseparator
11958 Formatting\SpecialChar \menuseparator
11960 \begin_inset Space ~
11965 , what is not possible in formulas:
11968 \begin_layout Standard
11969 This is a line with
11970 \begin_inset Space \hspace{}
11975 \begin_inset Space \thinspace{}
11981 \begin_layout Standard
11982 This is a line with
11983 \begin_inset Space \hfill{}
11989 \begin_layout Subsection
11990 Space besides inline Formulas
11994 \begin_layout Plain Layout
11995 Space ! besides inline formulas
12003 \begin_layout Standard
12004 The space that surrounds inline formulas can be adjusted with the length
12013 \begin_layout Plain Layout
12024 The value of a length is set with the command
12032 \begin_layout Plain Layout
12042 that has the following scheme:
12045 \begin_layout Standard
12050 setlength{length name}{value}
12053 \begin_layout Standard
12061 \begin_inset Space \thinspace{}
12067 \begin_layout Standard
12077 \begin_layout Standard
12078 is inserted in TeX-mode.
12080 \begin_inset Space \thinspace{}
12083 mm space will now be set around all inline formulas:
12087 \begin_layout Plain Layout
12101 \begin_layout Standard
12102 This is a line with an inline formula
12103 \begin_inset Formula $A=B$
12107 \begin_inset Space \thinspace{}
12110 mm surrounding space.
12114 \begin_layout Plain Layout
12128 \begin_layout Standard
12129 To return to the predefined value,
12135 is set to the value 0
12136 \begin_inset Space \thinspace{}
12142 \begin_layout Section
12147 \begin_layout Plain Layout
12157 \begin_layout Plain Layout
12162 \begin_layout Plain Layout
12173 \begin_layout Plain Layout
12188 \begin_layout Standard
12189 Boxes for text are described in chapter
12196 \begin_inset Space ~
12204 \begin_layout Subsection
12206 \begin_inset CommandInset label
12208 name "sub:Boxes-with-Frame"
12216 \begin_layout Plain Layout
12225 \begin_layout Standard
12226 It is possible to frame formulas or parts of it with the commands
12236 \begin_layout Plain Layout
12254 \begin_layout Plain Layout
12265 \begin_layout Standard
12266 When one of these commands is inserted to a formula, a blue box appears
12267 within a frame to enter formula parts.
12274 an additional formula has to be created by
12282 \begin_layout Plain Layout
12283 Due to a bug in LyX it is not possible to create a new formula with
12288 \begin_inset CommandInset href
12290 name "LyX-bug #1435"
12291 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12300 , because the box content will otherwise be treated as mathematical text.
12307 is used, a new formula is automatically created inside the frame.
12310 \begin_layout Standard
12317 is not suitable to frame displayed formulas, because the formula will always
12318 be set in the size of the text.
12325 is in contrary not suitable to frame inline formulas, because the formula
12326 will always be set in the size of a displayed formula.
12329 \begin_layout Standard
12336 there is the command
12346 \begin_layout Plain Layout
12354 where additionally the frame width and the alignment can be specified.
12361 is used in the following scheme:
12364 \begin_layout Standard
12369 framebox[frame width][position]{box content}
12372 \begin_layout Standard
12373 The position can either be
12390 right aligns the formula in the box.
12391 When no position is given, the formula will be centered.
12392 \begin_inset Newline newline
12395 Is no width given, also no position can be given.
12396 In this case the frame width is adjusted to the box content like for
12405 \begin_layout Standard
12412 is inserted, a box appears containing three blue boxes.
12413 The first two boxes are surrounded by brackets and denote the two optional
12415 The third box is for formula parts like for
12424 \begin_layout Standard
12426 \begin_inset Note Note
12429 \begin_layout Plain Layout
12430 The table has been set into a minipage to make the footnote appearing.
12431 Otherwise the footnote text would not be displayed.
12437 \begin_inset Box Frameless
12446 height_special "totalheight"
12449 \begin_layout Plain Layout
12451 \begin_inset Tabular
12452 <lyxtabular version="3" rows="5" columns="2">
12454 <column alignment="center" valignment="top" width="0">
12455 <column alignment="center" valignment="top" width="0">
12457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12460 \begin_layout Plain Layout
12465 \begin_layout Plain Layout
12466 Due to a bug in LyX it is not possible to create a new formula with
12471 \begin_inset CommandInset href
12473 name "LyX-bug #1435"
12474 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12491 \begin_layout Plain Layout
12493 \begin_inset Note Note
12496 \begin_layout Plain Layout
12503 is only used as spacer.
12515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12518 \begin_layout Plain Layout
12525 \begin_layout Plain Layout
12544 \begin_layout Plain Layout
12558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12561 \begin_layout Plain Layout
12562 \begin_inset Formula \raisebox {6mm}{}\fbox{$\int A=B$}\raisebox {-4mm}{}
12573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12576 \begin_layout Plain Layout
12583 \begin_layout Plain Layout
12598 \begin_layout Plain Layout
12612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12615 \begin_layout Plain Layout
12616 \begin_inset Formula $\raisebox {8.5mm}{}\boxed{\int A=B}\raisebox {-6.5mm}{}$
12626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12629 \begin_layout Plain Layout
12636 \begin_layout Plain Layout
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12653 \begin_layout Plain Layout
12654 \begin_inset Formula $\raisebox {6mm}{}A+\fbox{B}\raisebox {-3mm}{}$
12664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12667 \begin_layout Plain Layout
12674 \begin_layout Plain Layout
12684 \begin_inset Formula $\to$
12688 \begin_inset Formula $\to$
12701 \begin_layout Plain Layout
12711 \begin_inset Formula $\downarrow$
12719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12722 \begin_layout Plain Layout
12723 \begin_inset Formula $\raisebox {6mm}{}$
12727 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12731 \begin_inset Formula $\raisebox {-4mm}{}$
12752 \begin_layout Standard
12753 The frame thickness can also be adjusted.
12754 To do this the following commands have to be inserted in TeX-mode before
12758 \begin_layout Standard
12768 \begin_inset Quotes eld
12772 \begin_inset Quotes erd
12786 \begin_inset Quotes eld
12790 \begin_inset Quotes erd
12796 \begin_layout Standard
12797 \begin_inset Quotes eld
12801 \begin_inset Quotes erd
12804 specifies the minimal distance between the frame and the first character
12806 An example for this is the following framed formula:
12810 \begin_layout Plain Layout
12822 \begin_inset Formula \[
12827 Before this formula the commands
12830 \begin_layout Standard
12852 \begin_layout Standard
12853 were inserted in TeX-mode.
12854 The given values are used for all following boxes.
12857 \begin_layout Standard
12858 To return to the standard frame size, the command
12861 \begin_layout Standard
12886 \begin_layout Plain Layout
12900 \begin_layout Standard
12901 is inserted in TeX-mode before the next formula.
12904 \begin_layout Subsection
12905 Boxes without Frame
12906 \begin_inset CommandInset label
12908 name "sub:Boxes-without-Frame"
12916 \begin_layout Plain Layout
12917 Boxes ! without frame
12925 \begin_layout Standard
12926 For boxes without a frame there are the following box commands:
12936 \begin_layout Plain Layout
12954 \begin_layout Plain Layout
12972 \begin_layout Plain Layout
12983 \begin_layout Standard
12990 a box can be super- or subscripted.
12991 But in contrary to normal super- and subscripting, the characters in the
12992 box keep their font size.
12999 is used in the following scheme:
13002 \begin_layout Standard
13007 raisebox{height}{box content}
13010 \begin_layout Standard
13011 When the box should contain a formula, an extra formula is needed like for
13021 \begin_layout Standard
13023 \begin_inset Tabular
13024 <lyxtabular version="3" rows="4" columns="2">
13026 <column alignment="center" valignment="top" width="0">
13027 <column alignment="center" valignment="top" width="0">
13029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13032 \begin_layout Plain Layout
13038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13041 \begin_layout Plain Layout
13049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13052 \begin_layout Plain Layout
13056 \begin_inset Formula $\to$
13062 \begin_inset Formula $\to$
13070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13073 \begin_layout Plain Layout
13074 \begin_inset Formula $H\raisebox {2mm}{al}lo$
13084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13087 \begin_layout Plain Layout
13091 \begin_inset Formula $\to$
13097 \begin_inset Formula $\to$
13105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13108 \begin_layout Plain Layout
13109 \begin_inset Formula $H\raisebox {-2mm}{al}lo$
13119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13122 \begin_layout Plain Layout
13126 \begin_inset Formula $\to$
13141 \begin_layout Plain Layout
13155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13158 \begin_layout Plain Layout
13162 \begin_layout Plain Layout
13186 \begin_layout Standard
13187 The last formula can currently only be created using TeX-mode because LyX
13188 inserts a box instead of the needed extra formula.
13192 \begin_layout Plain Layout
13194 \begin_inset CommandInset href
13196 name "LyX-bug #1435"
13197 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13209 \begin_layout Standard
13234 , with the difference that there is no frame.
13237 \begin_layout Subsection
13239 \begin_inset CommandInset label
13241 name "sub:Colored-Boxes"
13249 \begin_layout Plain Layout
13258 \begin_layout Standard
13259 To be able to use all commands explained in this section, the LaTeX-package
13268 \begin_layout Plain Layout
13273 is part of every LaTeX standard installation.
13282 \begin_layout Plain Layout
13288 has to be loaded in the LaTeX-preamble with the line
13292 \begin_layout Plain Layout
13293 When text is colored somewhere in the document with a predefined color,
13294 LyX loads the LaTeX-package
13299 Thus it is possible that the package is loaded twice, but this doesn't
13306 \begin_inset Note Note
13309 \begin_layout Plain Layout
13310 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13319 \begin_layout Standard
13327 \begin_layout Standard
13328 \begin_inset VSpace medskip
13331 To color boxes, the command
13341 \begin_layout Plain Layout
13349 is used in the following scheme:
13352 \begin_layout Standard
13357 colorbox{color}{box content}
13360 \begin_layout Standard
13361 The box content can also be a box and a
13367 can also be part of another box (see the 2nd and 3rd example).
13368 When the box should contain a formula, an extra formula has to be created,
13379 \begin_layout Plain Layout
13380 This also applies for the command
13388 \begin_inset CommandInset href
13390 name "LyX-bug #1435"
13391 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13403 \begin_layout Standard
13404 One of the following predefined colors can be chosen:
13407 \begin_layout Standard
13441 \begin_layout Standard
13443 \begin_inset Tabular
13444 <lyxtabular version="3" rows="4" columns="2">
13446 <column alignment="center" valignment="top" width="0">
13447 <column alignment="center" valignment="top" width="0">
13449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13452 \begin_layout Plain Layout
13458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13461 \begin_layout Plain Layout
13463 \begin_inset Note Note
13466 \begin_layout Plain Layout
13473 is only used as spacer.
13485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13488 \begin_layout Plain Layout
13492 \begin_inset Formula $\to$
13502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13505 \begin_layout Plain Layout
13506 \begin_inset Formula $\raisebox {6mm}{}\colorbox {yellow}{A=B}\raisebox {-3mm}{}$
13516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13519 \begin_layout Plain Layout
13523 \begin_inset Formula $\to$
13534 \begin_layout Plain Layout
13548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13551 \begin_layout Plain Layout
13552 \begin_inset Formula $\raisebox {6mm}{}\colorbox {green}{\fbox{A=B}}\raisebox {-3mm}{}$
13562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13565 \begin_layout Plain Layout
13572 \begin_layout Plain Layout
13584 \begin_inset Formula $\to$
13594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13597 \begin_layout Plain Layout
13598 \begin_inset Formula $\raisebox {6mm}{}\fbox{\colorbox {green}{A=B}}\raisebox {-3mm}{}$
13614 \begin_layout Standard
13621 only colors the box but not the characters in the box.
13622 To color all characters, the whole formula is highlighted and the wanted
13623 color is chosen in the
13626 \begin_inset Space ~
13632 The dialog can be called with the toolbar button
13633 \begin_inset Graphics
13634 filename ../images/dialog-show_character.png
13641 Edit\SpecialChar \menuseparator
13643 \begin_inset Space ~
13646 Style\SpecialChar \menuseparator
13650 The formula number has then the same color as the formula.
13651 When the formula number should get another color than the formula characters,
13652 the color must be changed within the formula.
13655 \begin_layout Standard
13659 \begin_layout Standard
13662 \begin_inset Formula \begin{equation}
13663 \int A=B\label{eq:red}\end{equation}
13670 \begin_inset Formula \begin{equation}
13671 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13678 \begin_layout Standard
13680 \begin_inset CommandInset ref
13686 is completely colored red.
13687 \begin_inset Newline newline
13691 \begin_inset CommandInset ref
13693 reference "eq:redgreen"
13697 was first completely colored green to set the color for the formula number.
13698 Subsequently the formula characters were colored red.
13701 \begin_layout Standard
13702 \begin_inset VSpace bigskip
13705 To color the frame different than the rest of the box, the command
13715 \begin_layout Plain Layout
13723 is used in the following scheme:
13726 \begin_layout Standard
13731 fcolorbox{frame color}{color}{box content}
13734 \begin_layout Standard
13741 is an extension of the command
13748 The frame width is set, like for
13771 \begin_layout Plain Layout
13783 \begin_inset Formula \[
13784 \fcolorbox {cyan}{magenta}{A=B}\]
13792 \begin_layout Plain Layout
13806 \begin_layout Standard
13807 This formula was created with the command
13808 \begin_inset Newline newline
13816 \begin_inset Formula $\to$
13822 \begin_inset Formula $\to$
13832 \begin_layout Standard
13833 \begin_inset VSpace bigskip
13836 To use other colors than the predefined ones, they have to be defined first.
13839 \begin_layout Standard
13840 One can for example define the color
13841 \begin_inset Quotes eld
13849 \begin_inset Quotes erd
13852 with the LaTeX-preamble line:
13855 \begin_layout Standard
13860 definecolor{darkgreen}{cmyk}{0.5,
13878 \begin_layout Plain Layout
13889 \begin_layout Standard
13894 is the color space that denotes the colors
13911 The four comma separated numbers are the portion factor for the corresponding
13912 colors of the color space.
13913 The factors can be in the range of 0
13914 \begin_inset Space \thinspace{}
13918 \begin_inset Space \thinspace{}
13926 also the color space
13930 can be used for definitions.
13947 , so that there are in this case three portion factors for the corresponding
13949 Furthermore there is the color space
13953 with one portion factor for the gray value.
13956 \begin_layout Standard
13957 As example a framed box with the new defined color
13961 where the characters have been colored
13966 \begin_inset Formula \begin{equation}
13967 \colorbox {darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13974 \begin_layout Standard
13975 Self-defined colors can also be used for text with the help of the command
13986 \begin_layout Plain Layout
13995 \begin_layout Standard
13999 \begin_layout Plain Layout
14003 textcolor{darkgreen}{
14009 \begin_inset Quotes eld
14013 \begin_inset Quotes erd
14020 \begin_layout Plain Layout
14030 \begin_layout Standard
14041 \begin_layout Plain Layout
14049 is used in the scheme
14053 textcolor{color}{characters to color}
14058 \begin_layout Subsection
14060 \begin_inset CommandInset label
14062 name "sub:Paragraph-Boxes"
14070 \begin_layout Plain Layout
14071 Boxes ! as paragraph
14079 \begin_layout Standard
14080 A box that can contain several lines and paragraphs, a so called paragraph
14081 box (parbox), can be created with the menu
14083 Insert\SpecialChar \menuseparator
14086 or the toolbar button
14087 \begin_inset Graphics
14088 filename ../images/box-insert.png
14096 \begin_layout Standard
14097 The following example shows a framed parbox in a line:
14100 \begin_layout Standard
14101 \begin_inset VSpace medskip
14105 \begin_inset Box Boxed
14114 height_special "totalheight"
14117 \begin_layout Plain Layout
14118 This is a paragraph box.
14120 \begin_inset Space \thinspace{}
14123 cm long and can also contain formulas:
14124 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14135 \begin_layout Standard
14136 \begin_inset VSpace medskip
14142 \begin_layout Standard
14143 Such a box is created by right-clicking on the gray box inset.
14144 A dialog pops up showing the box properties.
14158 \begin_inset Space \thinspace{}
14163 Vertical Box Alignment
14168 \begin_layout Standard
14169 \begin_inset VSpace medskip
14172 In LaTeX a parbox is created with the command
14182 \begin_layout Plain Layout
14190 that has the following scheme:
14193 \begin_layout Standard
14198 parbox[position]{width}{box content}
14201 \begin_layout Standard
14215 for bottom means that the box is aligned within the surrounding text with
14221 for top this is done with the first line.
14222 When no position is given, the box will be vertically centered, see section
14230 \begin_inset Space ~
14235 manual for examples.
14238 \begin_layout Standard
14239 \begin_inset VSpace bigskip
14242 To frame formulas completely, including the formula number, the formula
14243 must be set into a parbox.
14244 To do this, the command
14258 is inserted in TeX-mode before the formula.
14267 \begin_layout Plain Layout
14277 is hereby the line width set for the document.
14278 Because the frame is outside the parbox, 2
14279 \begin_inset Space \thinspace{}
14282 times the frame separation and the frame thickness must be subtracted from
14284 As this is not automatically done by LyX due to a bug
14288 \begin_layout Plain Layout
14289 \begin_inset CommandInset href
14291 name "LyX-bug #4483"
14292 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14301 , TeX-mode has to be used.
14302 To be able to multiply and subtract in arguments, the LaTeX-package
14310 \begin_layout Plain Layout
14315 is part of every LaTeX standard installation.
14324 \begin_layout Plain Layout
14330 must be loaded in the LaTeX-preamble with the line
14333 \begin_layout Standard
14341 \begin_layout Standard
14342 Behind the formula both boxes are closed by entering
14347 Here is an example:
14351 \begin_layout Plain Layout
14365 \begin_layout Standard
14369 \begin_layout Plain Layout
14387 \begin_inset Formula \begin{equation}
14388 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14396 \begin_layout Plain Layout
14407 \begin_layout Plain Layout
14421 \begin_layout Standard
14422 \begin_inset VSpace medskip
14425 As a parbox is used as argument of
14431 , there is in this case no difference between
14446 \begin_layout Standard
14447 \begin_inset VSpace bigskip
14450 Paragraph boxes are very useful to comment formulas directly.
14457 is used in combination with the command
14471 \begin_inset CommandInset ref
14473 reference "sub:User-defined-Numbering"
14480 \begin_layout Standard
14481 An example of a formula commented with
14490 \begin_layout Standard
14494 \begin_layout Plain Layout
14507 This is a description.
14508 It is distinctly separated from the formula and multiline.
14512 \begin_layout Plain Layout
14524 \begin_layout Standard
14525 Such a formula must be inserted completely in TeX-mode because LyX does
14526 not yet support the command
14533 The formula is created with the following command sequence:
14536 \begin_layout Standard
14549 is inserted in TeX-mode.
14553 \begin_layout Plain Layout
14554 When the formula style
14566 can also be replaced by
14573 (formula styles see
14574 \begin_inset CommandInset ref
14576 reference "sec:Formula-Styles"
14585 Then the description follows as normal text, and finally
14591 is inserted in TeX-mode.
14604 hereby create a displayed formula.
14607 \begin_layout Standard
14614 can be seen in this example that was
14615 \begin_inset Quotes eld
14619 \begin_inset Quotes erd
14622 using the mathematical textmode:
14623 \begin_inset Formula \[
14624 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14631 \begin_layout Section
14636 \begin_layout Plain Layout
14645 \begin_layout Subsection
14647 \begin_inset CommandInset label
14649 name "sub:Big-Operators"
14657 \begin_layout Plain Layout
14667 \begin_layout Plain Layout
14677 \begin_layout Plain Layout
14686 \begin_layout Standard
14687 To be able to use all integral operators listed here, the option
14689 Use esint package automatically
14691 must be set in the document settings under
14694 \begin_inset Space ~
14702 \begin_layout Standard
14703 \begin_inset Space \hfill{}
14707 \begin_inset Tabular
14708 <lyxtabular version="3" rows="11" columns="2">
14710 <column alignment="center" valignment="top" width="0pt">
14711 <column alignment="center" valignment="top" width="0pt">
14713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14716 \begin_layout Plain Layout
14722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14725 \begin_layout Plain Layout
14733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14736 \begin_layout Plain Layout
14743 \begin_layout Plain Layout
14756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14759 \begin_layout Plain Layout
14760 \begin_inset Formula $\sum$
14770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14773 \begin_layout Plain Layout
14780 \begin_layout Plain Layout
14793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14796 \begin_layout Plain Layout
14797 \begin_inset Formula $\int$
14807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14810 \begin_layout Plain Layout
14818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14821 \begin_layout Plain Layout
14822 \begin_inset Formula $\intop$
14832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14835 \begin_layout Plain Layout
14843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14846 \begin_layout Plain Layout
14847 \begin_inset Formula $\oint$
14857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14860 \begin_layout Plain Layout
14868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14871 \begin_layout Plain Layout
14872 \begin_inset Formula $\ointop$
14882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14885 \begin_layout Plain Layout
14893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14896 \begin_layout Plain Layout
14897 \begin_inset Formula $\ointctrclockwise$
14907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14910 \begin_layout Plain Layout
14918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14921 \begin_layout Plain Layout
14922 \begin_inset Formula $\ointclockwise$
14932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14935 \begin_layout Plain Layout
14943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14946 \begin_layout Plain Layout
14947 \begin_inset Formula $\sqint$
14957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14960 \begin_layout Plain Layout
14968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14971 \begin_layout Plain Layout
14972 \begin_inset Formula $\bigcap$
14982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14985 \begin_layout Plain Layout
14993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14996 \begin_layout Plain Layout
14997 \begin_inset Formula $\bigcup$
15011 \begin_inset Space \hfill{}
15015 \begin_inset Tabular
15016 <lyxtabular version="3" rows="10" columns="2">
15018 <column alignment="center" valignment="top" width="0pt">
15019 <column alignment="center" valignment="top" width="0pt">
15021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15024 \begin_layout Plain Layout
15030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15033 \begin_layout Plain Layout
15041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15044 \begin_layout Plain Layout
15051 \begin_layout Plain Layout
15064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15067 \begin_layout Plain Layout
15068 \begin_inset Formula $\prod$
15078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15081 \begin_layout Plain Layout
15089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15092 \begin_layout Plain Layout
15093 \begin_inset Formula $\coprod$
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15117 \begin_layout Plain Layout
15118 \begin_inset Formula $\bigodot$
15128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15131 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15142 \begin_layout Plain Layout
15143 \begin_inset Formula $\bigotimes$
15153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15156 \begin_layout Plain Layout
15164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15167 \begin_layout Plain Layout
15168 \begin_inset Formula $\bigoplus$
15178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15181 \begin_layout Plain Layout
15189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15192 \begin_layout Plain Layout
15193 \begin_inset Formula $\bigwedge$
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15206 \begin_layout Plain Layout
15214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15217 \begin_layout Plain Layout
15218 \begin_inset Formula $\bigvee$
15228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15231 \begin_layout Plain Layout
15239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15242 \begin_layout Plain Layout
15243 \begin_inset Formula $\bigsqcup$
15253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15256 \begin_layout Plain Layout
15264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15267 \begin_layout Plain Layout
15268 \begin_inset Formula $\biguplus$
15282 \begin_inset Space \hfill{}
15288 \begin_layout Standard
15289 All big operators can also be inserted via the math toolbar button
15290 \begin_inset Graphics
15291 filename ../images/math/intop.png
15299 \begin_layout Standard
15300 The operators are called big because they are bigger than the sometimes
15301 equal looking binary operators.
15302 All big operators can have limits as described in the next subsection.
15305 \begin_layout Standard
15331 \begin_inset Space ~
15334 in the style the operator limits are displayed, see
15335 \begin_inset CommandInset ref
15337 reference "sub:Operator-Limits"
15345 \begin_layout Subsubsection*
15346 Advices for Integrals
15349 \begin_layout Standard
15354 in an integral is an operator, that therefore has to be set upright.
15355 This is done by highlighting the
15359 and using the keyboard shortcut
15362 \begin_inset Space ~
15371 \begin_layout Plain Layout
15377 \begin_inset CommandInset ref
15379 reference "sub:Font-Styles"
15389 Finally the smallest space is inserted before the
15393 , as this is usual for operators.
15397 \begin_layout Standard
15399 \begin_inset Formula $\int A(x)dx$
15403 \begin_inset Newline newline
15410 \begin_layout Plain Layout
15420 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15426 \begin_layout Standard
15427 For multiple integrals there are the following commands:
15428 \begin_inset VSpace medskip
15434 \begin_layout Standard
15435 \begin_inset Space \hfill{}
15439 \begin_inset Tabular
15440 <lyxtabular version="3" rows="4" columns="2">
15442 <column alignment="center" valignment="top" width="0">
15443 <column alignment="center" valignment="top" width="0">
15445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15448 \begin_layout Plain Layout
15454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15457 \begin_layout Plain Layout
15459 \begin_inset Note Note
15462 \begin_layout Plain Layout
15469 is only used as spacer.
15481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15484 \begin_layout Plain Layout
15492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15495 \begin_layout Plain Layout
15496 \begin_inset Formula $\raisebox {4.5mm}{}\iint\raisebox {-2.5mm}{}$
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15509 \begin_layout Plain Layout
15517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15520 \begin_layout Plain Layout
15521 \begin_inset Formula $\raisebox {4.5mm}{}\oiint\raisebox {-2.5mm}{}$
15531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15534 \begin_layout Plain Layout
15542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15545 \begin_layout Plain Layout
15546 \begin_inset Formula $\raisebox {4.5mm}{}\sqiint\raisebox {-2.5mm}{}$
15560 \begin_inset Space \hfill{}
15564 \begin_inset Tabular
15565 <lyxtabular version="3" rows="4" columns="2">
15567 <column alignment="center" valignment="top" width="0">
15568 <column alignment="center" valignment="top" width="0">
15570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15573 \begin_layout Plain Layout
15579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15582 \begin_layout Plain Layout
15590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15593 \begin_layout Plain Layout
15601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15604 \begin_layout Plain Layout
15605 \begin_inset Formula $\raisebox {4.5mm}{}\iiint\raisebox {-2.5mm}{}$
15615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15618 \begin_layout Plain Layout
15626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15629 \begin_layout Plain Layout
15630 \begin_inset Formula $\raisebox {4.5mm}{}\iiiint\raisebox {-2.5mm}{}$
15640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15643 \begin_layout Plain Layout
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15654 \begin_layout Plain Layout
15655 \begin_inset Formula $\raisebox {4.5mm}{}\dotsint\raisebox {-2.5mm}{}$
15669 \begin_inset Space \hfill{}
15675 \begin_layout Subsection
15677 \begin_inset CommandInset label
15679 name "sub:Operator-Limits"
15687 \begin_layout Plain Layout
15696 \begin_layout Standard
15697 Limits are created by super- and subscripts:
15700 \begin_layout Standard
15702 \begin_inset Tabular
15703 <lyxtabular version="3" rows="2" columns="2">
15705 <column alignment="center" valignment="top" width="0pt">
15706 <column alignment="center" valignment="top" width="0pt">
15708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15711 \begin_layout Plain Layout
15717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15720 \begin_layout Plain Layout
15722 \begin_inset Note Note
15725 \begin_layout Plain Layout
15732 is only used as spacer.
15744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15747 \begin_layout Plain Layout
15756 \begin_layout Plain Layout
15766 \begin_inset Formula $\to$
15770 \begin_inset Formula $\to$
15778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15781 \begin_layout Plain Layout
15782 \begin_inset Formula $\raisebox {5mm}{}\prod_{0}^{\infty}A(x)\raisebox {-2.5mm}{}$
15798 \begin_layout Standard
15799 Limits of inline formulas are set right beside the operator.
15800 Limits in displayed formulas are set above or below the operator, except
15801 of integral limits.
15804 \begin_layout Standard
15805 To force that the limits are set beside the operator, the cursor is set
15806 directly behind the operator and the limits type is changed with the menu
15809 Edit\SpecialChar \menuseparator
15810 Math\SpecialChar \menuseparator
15822 \begin_inset Space ~
15831 \begin_layout Standard
15832 The default limits type is this:
15833 \begin_inset Formula \[
15834 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15838 This is how it looks when the limits type was changed to
15845 \begin_inset Formula \[
15846 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15850 For integrals, except of
15862 , the limits are by default set beside the operator.
15863 But for multiple integrals the limits are often set below the operator.
15864 In the following example the limits type was therefore set to
15868 and so set below the integrals:
15869 \begin_inset Formula \begin{equation}
15870 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15877 \begin_layout Standard
15878 \begin_inset VSpace medskip
15881 To specify conditions for limits, the commands
15891 \begin_layout Plain Layout
15909 \begin_layout Plain Layout
15918 To create for example this expression
15919 \begin_inset Formula \begin{equation}
15920 \sum_{\begin{subarray}{c}
15922 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15929 \begin_layout Standard
15930 the following has to be done:
15931 \begin_inset Newline newline
15946 \begin_layout Plain Layout
15958 One is now in a blue box under the summation operator and insert there
15967 \begin_layout Plain Layout
15979 The blue box is now within a purple box and now several lines can be written
15981 A new line is created by inserting a line break (
15987 \begin_inset Newline newline
15992 0<k<1000 Ctrl-Return
15993 \begin_inset Newline newline
15998 is typed in, a new box appears below for the new line.
16001 \begin_layout Standard
16002 The alignment of the lines can be changed to left aligned with the
16012 Edit\SpecialChar \menuseparator
16016 To get right alignment,
16024 \begin_layout Plain Layout
16035 is inserted at the beginning of the line.
16038 \begin_layout Standard
16051 with the difference that the lines are always centered.
16054 \begin_layout Standard
16055 \begin_inset VSpace bigskip
16059 \begin_inset CommandInset ref
16061 reference "eq:substack"
16065 there can be too much space beside an operator, because the characters
16066 following the operator are set beside the limits.
16069 \begin_layout Standard
16070 To avoid this, the following macro can be used in the LaTeX-preamble:
16073 \begin_layout Standard
16087 \begin_inset Newline newline
16099 \begin_inset Newline newline
16106 mathclapinternal #1#2{
16110 mathsurround =0pt #1{#2}$}}
16113 \begin_layout Standard
16114 This defines the command
16124 \begin_layout Plain Layout
16132 that sets the width of the limit to 0
16133 \begin_inset Space \thinspace{}
16137 The command scheme is
16140 \begin_layout Standard
16148 \begin_layout Standard
16149 where the limit can consist of several conditions.
16152 \begin_layout Standard
16154 \begin_inset CommandInset ref
16156 reference "eq:substack"
16160 , one uses the command
16163 \begin_layout Standard
16176 \begin_layout Plain Layout
16185 0<k<1000 Ctrl-Enter
16188 \begin_layout Standard
16189 to create the lower limit.
16190 The summand is now directly behind the summation operator:
16191 \begin_inset Formula \[
16192 \sum_{\mathclap {\substack{0<k<1000\\
16193 \\k\,\in\,\mathbb{N}}
16201 \begin_layout Standard
16202 \begin_inset VSpace bigskip
16205 How to use one limit for several operators is described in
16206 \begin_inset CommandInset ref
16208 reference "sub:Self-defined-Operators"
16215 \begin_layout Subsection
16217 \begin_inset CommandInset label
16219 name "sub:Binary-Operators"
16227 \begin_layout Plain Layout
16236 \begin_layout Standard
16237 Binary operators are surrounded by space when there is a character before
16239 \begin_inset VSpace medskip
16245 \begin_layout Standard
16246 \begin_inset Space \hfill{}
16250 \begin_inset Tabular
16251 <lyxtabular version="3" rows="13" columns="2">
16253 <column alignment="center" valignment="top" width="0pt">
16254 <column alignment="center" valignment="top" width="0pt">
16256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16259 \begin_layout Plain Layout
16261 \begin_inset Note Note
16264 \begin_layout Plain Layout
16271 is only used as spacer.
16281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16284 \begin_layout Plain Layout
16292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16295 \begin_layout Plain Layout
16301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16304 \begin_layout Plain Layout
16305 \begin_inset Formula $+$
16315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16318 \begin_layout Plain Layout
16324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16327 \begin_layout Plain Layout
16328 \begin_inset Formula $-$
16338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16341 \begin_layout Plain Layout
16349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16352 \begin_layout Plain Layout
16353 \begin_inset Formula $\pm$
16363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16366 \begin_layout Plain Layout
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16377 \begin_layout Plain Layout
16378 \begin_inset Formula $\mp$
16388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16391 \begin_layout Plain Layout
16399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16402 \begin_layout Plain Layout
16403 \begin_inset Formula $\cdot$
16413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16416 \begin_layout Plain Layout
16424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16427 \begin_layout Plain Layout
16428 \begin_inset Formula $\times$
16438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16441 \begin_layout Plain Layout
16449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16452 \begin_layout Plain Layout
16453 \begin_inset Formula $\div$
16463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16466 \begin_layout Plain Layout
16470 \begin_layout Plain Layout
16483 \begin_layout Plain Layout
16495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16498 \begin_layout Plain Layout
16499 \begin_inset Formula $*$
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16512 \begin_layout Plain Layout
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16523 \begin_layout Plain Layout
16524 \begin_inset Formula $\star$
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16537 \begin_layout Plain Layout
16545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16548 \begin_layout Plain Layout
16549 \begin_inset Formula $\circ$
16559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16562 \begin_layout Plain Layout
16570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16573 \begin_layout Plain Layout
16574 \begin_inset Formula $\diamond$
16584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16587 \begin_layout Plain Layout
16595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16598 \begin_layout Plain Layout
16599 \begin_inset Formula $\bullet$
16613 \begin_inset Space \hfill{}
16617 \begin_inset Tabular
16618 <lyxtabular version="3" rows="13" columns="2">
16620 <column alignment="center" valignment="top" width="0pt">
16621 <column alignment="center" valignment="top" width="0pt">
16623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16626 \begin_layout Plain Layout
16632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16635 \begin_layout Plain Layout
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16657 \begin_layout Plain Layout
16658 \begin_inset Formula $\nabla$
16668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16682 \begin_layout Plain Layout
16683 \begin_inset Formula $\bigtriangledown$
16693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16696 \begin_layout Plain Layout
16704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16707 \begin_layout Plain Layout
16708 \begin_inset Formula $\bigtriangleup$
16718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16721 \begin_layout Plain Layout
16729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16732 \begin_layout Plain Layout
16733 \begin_inset Formula $\Box$
16743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16746 \begin_layout Plain Layout
16754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16757 \begin_layout Plain Layout
16758 \begin_inset Formula $\cap$
16768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16771 \begin_layout Plain Layout
16779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16782 \begin_layout Plain Layout
16783 \begin_inset Formula $\cup$
16793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16796 \begin_layout Plain Layout
16804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16807 \begin_layout Plain Layout
16808 \begin_inset Formula $\dagger$
16818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16821 \begin_layout Plain Layout
16829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16832 \begin_layout Plain Layout
16833 \begin_inset Formula $\ddagger$
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16846 \begin_layout Plain Layout
16854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16858 \begin_inset Formula $\wr$
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16882 \begin_layout Plain Layout
16883 \begin_inset Formula $\bigcirc$
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16896 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $\wedge$
16918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\vee$
16947 \begin_inset Space \hfill{}
16951 \begin_inset Tabular
16952 <lyxtabular version="3" rows="13" columns="2">
16954 <column alignment="center" valignment="top" width="0pt">
16955 <column alignment="center" valignment="top" width="0pt">
16957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16960 \begin_layout Plain Layout
16966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16969 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\oplus$
17002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\ominus$
17027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17030 \begin_layout Plain Layout
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17041 \begin_layout Plain Layout
17042 \begin_inset Formula $\otimes$
17052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17055 \begin_layout Plain Layout
17063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17066 \begin_layout Plain Layout
17067 \begin_inset Formula $\oslash$
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17080 \begin_layout Plain Layout
17088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17091 \begin_layout Plain Layout
17092 \begin_inset Formula $\odot$
17102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17105 \begin_layout Plain Layout
17113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17116 \begin_layout Plain Layout
17117 \begin_inset Formula $\amalg$
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17130 \begin_layout Plain Layout
17138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17141 \begin_layout Plain Layout
17142 \begin_inset Formula $\uplus$
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17166 \begin_layout Plain Layout
17167 \begin_inset Formula $\setminus$
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\sqcap$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\sqcup$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\triangleleft$
17252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\triangleright$
17281 \begin_inset Space \hfill{}
17287 \begin_layout Standard
17288 All binary operators can also be inserted via the math toolbar button
17289 \begin_inset Graphics
17290 filename ../images/math/pm.png
17298 \begin_layout Standard
17299 To typeset the Laplace operator also
17316 \begin_inset Formula $\nabla^{2}$
17319 ) can be used instead of
17328 \begin_layout Standard
17335 Insert\SpecialChar \menuseparator
17347 \begin_layout Subsection
17348 Self-defined Operators
17349 \begin_inset CommandInset label
17351 name "sub:Self-defined-Operators"
17359 \begin_layout Plain Layout
17360 Operators ! self-defined
17368 \begin_layout Standard
17369 With the help of the command
17373 DeclareMathOperator
17379 \begin_layout Plain Layout
17384 DeclareMathOperator
17389 custom operators can be defined in the LaTeX-preamble.
17390 Its command scheme is:
17393 \begin_layout Standard
17398 DeclareMathOperator{new command}{display}
17401 \begin_layout Standard
17402 Display can be characters or symbols that define how the operator looks
17404 To define a big operator a * is set behind the command.
17405 All self-defined big operators can have limits as described in
17406 \begin_inset CommandInset ref
17408 reference "sub:Operator-Limits"
17415 \begin_layout Standard
17416 For example the LaTeX-preamble line
17419 \begin_layout Standard
17424 DeclareMathOperator*{
17431 \begin_layout Standard
17432 defines the command
17438 , that inserts a big operator consisting of the lozenge symbol from
17439 \begin_inset CommandInset ref
17441 reference "sub:Miscellaneous-Symbols"
17446 \begin_inset Formula \[
17447 \Lozenge _{n=1}^{\infty}\]
17451 The command for this formula is:
17462 \begin_inset Formula $\to$
17468 \begin_layout Standard
17469 \begin_inset VSpace bigskip
17472 When self-defined operators are not used several times in the document,
17473 they can also be defined with the commands
17483 \begin_layout Plain Layout
17501 \begin_layout Plain Layout
17509 , which have the following scheme:
17512 \begin_layout Standard
17526 \begin_layout Standard
17533 defines big operators,
17542 \begin_layout Standard
17550 \begin_inset Space \thinspace{}
17554 \begin_inset Space ~
17557 be used to use one limit for several operators:
17560 \begin_layout Standard
17561 \begin_inset Formula \[
17562 \mathop {\sum\negmedspace\sum}_{i,j=1}^{N}\]
17569 \begin_layout Standard
17570 The command for the formula above is:
17571 \begin_inset Newline newline
17590 \begin_layout Plain Layout
17602 \begin_inset Formula $\to$
17611 \begin_layout Plain Layout
17625 \begin_layout Section
17630 \begin_layout Plain Layout
17639 \begin_layout Subsection
17641 \begin_inset CommandInset label
17643 name "sub:Font-Styles"
17651 \begin_layout Plain Layout
17660 \begin_layout Standard
17661 Latin letters in formulas can be set in one of the following font styles:
17662 \begin_inset VSpace -2mm
17668 \begin_layout Standard
17670 \begin_inset Tabular
17671 <lyxtabular version="3" rows="6" columns="3">
17673 <column alignment="center" valignment="top" width="0">
17674 <column alignment="center" valignment="top" width="0">
17675 <column alignment="center" valignment="top" width="0">
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" usebox="none">
17689 \begin_layout Plain Layout
17695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17698 \begin_layout Plain Layout
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17709 \begin_layout Plain Layout
17718 \begin_layout Plain Layout
17734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17737 \begin_layout Plain Layout
17738 \begin_inset Formula $\mathbb{ABC}$
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17769 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17789 \begin_inset Formula $\mathbf{AbC}$
17797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Plain Layout
17808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17820 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17840 \begin_inset Formula $\boldsymbol{AbC}$
17848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17862 \begin_layout Plain Layout
17871 \begin_layout Plain Layout
17887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17891 \begin_inset Formula $\mathcal{ABC}$
17899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17902 \begin_layout Plain Layout
17910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17913 \begin_layout Plain Layout
17922 \begin_layout Plain Layout
17938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17941 \begin_layout Plain Layout
17942 \begin_inset Formula $\mathfrak{AbC}$
17950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17953 \begin_layout Plain Layout
17967 \begin_layout Standard
17969 \begin_inset Tabular
17970 <lyxtabular version="3" rows="5" columns="3">
17972 <column alignment="center" valignment="top" width="0">
17973 <column alignment="center" valignment="top" width="0">
17974 <column alignment="center" valignment="top" width="0">
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" usebox="none">
17988 \begin_layout Plain Layout
17994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17997 \begin_layout Plain Layout
18005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18008 \begin_layout Plain Layout
18017 \begin_layout Plain Layout
18033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18036 \begin_layout Plain Layout
18037 \begin_inset Formula $\mathit{AbC}$
18045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18048 \begin_layout Plain Layout
18056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18059 \begin_layout Plain Layout
18068 \begin_layout Plain Layout
18084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18087 \begin_layout Plain Layout
18088 \begin_inset Formula $\mathrm{AbC}$
18096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18099 \begin_layout Plain Layout
18107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18110 \begin_layout Plain Layout
18119 \begin_layout Plain Layout
18135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18138 \begin_layout Plain Layout
18139 \begin_inset Formula $\mathsf{AbC}$
18147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18150 \begin_layout Plain Layout
18158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18161 \begin_layout Plain Layout
18170 \begin_layout Plain Layout
18186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18189 \begin_layout Plain Layout
18190 \begin_inset Formula $\mathtt{AbC}$
18198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18201 \begin_layout Plain Layout
18215 \begin_layout Standard
18216 \begin_inset Note Greyedout
18219 \begin_layout Plain Layout
18236 can only be used for big letters.
18244 \begin_layout Standard
18245 Predefined is the style
18254 \begin_layout Standard
18255 The style commands work also for letters in mathematical constructs:
18256 \begin_inset Formula \[
18257 \mathfrak{A=\frac{b}{C}}\]
18264 \begin_layout Standard
18265 Characters in mathematical text don't appear in a math font style but in
18266 the text font style
18273 That their style can't be set correctly via the text style dialog is a
18278 \begin_layout Plain Layout
18279 \begin_inset CommandInset href
18281 name "LyX-bug #4091"
18282 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18294 \begin_layout Standard
18295 Instead of the style commands the dialog
18297 Edit\SpecialChar \menuseparator
18298 Math\SpecialChar \menuseparator
18301 or the toolbar button
18302 \begin_inset Graphics
18303 filename ../images/math/font.png
18311 \begin_layout Subsection
18313 \begin_inset CommandInset label
18315 name "sub:Bold-Formulas"
18323 \begin_layout Plain Layout
18332 \begin_layout Standard
18333 To make a complete formula bold, the command
18339 from the previous subsection cannot be used, because it doesn't work for
18340 small Greek letters.
18341 Furthermore it prints Latin letters always upright, like in the following
18345 \begin_layout Standard
18346 \begin_inset Formula \[
18347 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18354 \begin_layout Standard
18355 To display the formula correctly, the command
18362 \begin_inset Formula \[
18363 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18367 It is also possible to set the formula in a
18369 boldmath environment
18372 This environment is created by inserting the command
18380 \begin_layout Plain Layout
18391 To end the environment, the command
18399 \begin_layout Plain Layout
18409 is inserted in TeX-mode.
18413 \begin_layout Plain Layout
18423 \begin_inset Formula \[
18424 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18432 \begin_layout Plain Layout
18444 \begin_layout Subsection
18446 \begin_inset CommandInset label
18448 name "sub:Font-Sizes"
18456 \begin_layout Plain Layout
18465 \begin_layout Standard
18466 For characters in formulas there are, analog to characters in text, the
18467 following size commands:
18470 \begin_layout Standard
18514 \begin_inset Newline newline
18536 \begin_layout Standard
18537 The size produced by the commands depends on the document font size, that
18538 corresponds with the command
18545 The other commands produce smaller or larger sizes than
18552 The font size can however not exceed a certain value.
18553 Is for example the document font size 12
18554 \begin_inset Space \thinspace{}
18563 switches to the same size as
18573 \begin_layout Standard
18574 A size command is inserted in TeX-mode before the formula and sets the size
18575 for all following formula and text characters.
18576 To switch back to the initial size, the command
18582 is inserted behind the formula in TeX-mode.
18585 \begin_layout Standard
18586 Within a formula the size can only be changed for symbols or letters in
18588 To do this, the size command is inserted in mathematical text.
18589 All following characters until the end of the mathematical text or until
18590 another size command will have the selected size.
18592 \begin_inset VSpace -2mm
18598 \begin_layout Standard
18602 \begin_layout Plain Layout
18612 \begin_inset Formula \[
18613 A=\frac{B}{c}\cdot\maltese\]
18618 \begin_inset Formula \[
18619 \maltese A\textrm{\Large \maltese\textit{A}}\textrm{\tiny \maltese\textit{A}}\]
18627 \begin_layout Plain Layout
18639 \begin_layout Standard
18640 \begin_inset VSpace medskip
18643 Before both formulas the command
18650 The command for the second formula is:
18651 \begin_inset Newline newline
18662 \begin_layout Plain Layout
18677 \begin_layout Plain Layout
18692 \begin_layout Plain Layout
18707 \begin_layout Plain Layout
18717 \begin_inset Formula $\to$
18721 \begin_inset Formula $\to$
18725 \begin_inset Newline newline
18729 \begin_inset Space \hspace*{}
18743 \begin_layout Plain Layout
18758 \begin_layout Plain Layout
18773 \begin_layout Plain Layout
18785 \begin_layout Standard
18786 If a symbol cannot be displayed in different sizes, it will always be displayed
18787 in the default size.
18790 \begin_layout Section
18795 \begin_layout Plain Layout
18804 \begin_layout Standard
18805 All Greek letters can also be inserted via the toolbar button
18806 \begin_inset Graphics
18807 filename ../images/math/alpha.png
18815 \begin_layout Subsection
18817 \begin_inset CommandInset label
18819 name "sub:Small-Letters"
18827 \begin_layout Plain Layout
18828 Greek letters ! small
18836 \begin_layout Standard
18837 \begin_inset Space \hfill{}
18841 \begin_inset Tabular
18842 <lyxtabular version="3" rows="11" columns="2">
18844 <column alignment="center" valignment="top" width="0pt">
18845 <column alignment="center" valignment="top" width="0pt">
18847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18850 \begin_layout Plain Layout
18856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18859 \begin_layout Plain Layout
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18870 \begin_layout Plain Layout
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18881 \begin_layout Plain Layout
18882 \begin_inset Formula $\alpha$
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18895 \begin_layout Plain Layout
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18906 \begin_layout Plain Layout
18907 \begin_inset Formula $\beta$
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18920 \begin_layout Plain Layout
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18931 \begin_layout Plain Layout
18932 \begin_inset Formula $\gamma$
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18945 \begin_layout Plain Layout
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18956 \begin_layout Plain Layout
18957 \begin_inset Formula $\delta$
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18970 \begin_layout Plain Layout
18978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18981 \begin_layout Plain Layout
18982 \begin_inset Formula $\epsilon$
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18995 \begin_layout Plain Layout
19003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19006 \begin_layout Plain Layout
19007 \begin_inset Formula $\varepsilon$
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19020 \begin_layout Plain Layout
19028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19031 \begin_layout Plain Layout
19032 \begin_inset Formula $\zeta$
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19045 \begin_layout Plain Layout
19053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19056 \begin_layout Plain Layout
19057 \begin_inset Formula $\eta$
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19070 \begin_layout Plain Layout
19078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19081 \begin_layout Plain Layout
19082 \begin_inset Formula $\theta$
19092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19095 \begin_layout Plain Layout
19103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19106 \begin_layout Plain Layout
19107 \begin_inset Formula $\vartheta$
19121 \begin_inset Space \hfill{}
19125 \begin_inset Tabular
19126 <lyxtabular version="3" rows="12" columns="2">
19128 <column alignment="center" valignment="top" width="0pt">
19129 <column alignment="center" valignment="top" width="0pt">
19131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19134 \begin_layout Plain Layout
19140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19143 \begin_layout Plain Layout
19151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19154 \begin_layout Plain Layout
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19165 \begin_layout Plain Layout
19166 \begin_inset Formula $\iota$
19176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19179 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19191 \begin_inset Formula $\kappa$
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19204 \begin_layout Plain Layout
19212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19215 \begin_layout Plain Layout
19216 \begin_inset Formula $\varkappa$
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19229 \begin_layout Plain Layout
19237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19240 \begin_layout Plain Layout
19241 \begin_inset Formula $\lambda$
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19254 \begin_layout Plain Layout
19262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19265 \begin_layout Plain Layout
19266 \begin_inset Formula $\mu$
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19279 \begin_layout Plain Layout
19287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19290 \begin_layout Plain Layout
19291 \begin_inset Formula $\nu$
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19304 \begin_layout Plain Layout
19312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19315 \begin_layout Plain Layout
19316 \begin_inset Formula $\xi$
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19329 \begin_layout Plain Layout
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19338 \begin_layout Plain Layout
19339 \begin_inset Formula $o$
19349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19363 \begin_layout Plain Layout
19364 \begin_inset Formula $\pi$
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19377 \begin_layout Plain Layout
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19388 \begin_layout Plain Layout
19389 \begin_inset Formula $\varpi$
19399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19402 \begin_layout Plain Layout
19410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19413 \begin_layout Plain Layout
19414 \begin_inset Formula $\rho$
19428 \begin_inset Space \hfill{}
19432 \begin_inset Tabular
19433 <lyxtabular version="3" rows="11" columns="2">
19435 <column alignment="center" valignment="top" width="0pt">
19436 <column alignment="center" valignment="top" width="0pt">
19438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19441 \begin_layout Plain Layout
19447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Plain Layout
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Plain Layout
19473 \begin_inset Formula $\varrho$
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19486 \begin_layout Plain Layout
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Plain Layout
19498 \begin_inset Formula $\sigma$
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Plain Layout
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Plain Layout
19523 \begin_inset Formula $\varsigma$
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Plain Layout
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Plain Layout
19548 \begin_inset Formula $\tau$
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Plain Layout
19573 \begin_inset Formula $\upsilon$
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Plain Layout
19598 \begin_inset Formula $\phi$
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19611 \begin_layout Plain Layout
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Plain Layout
19623 \begin_inset Formula $\varphi$
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19636 \begin_layout Plain Layout
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19647 \begin_layout Plain Layout
19648 \begin_inset Formula $\chi$
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19661 \begin_layout Plain Layout
19669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19672 \begin_layout Plain Layout
19673 \begin_inset Formula $\psi$
19683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19686 \begin_layout Plain Layout
19694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19697 \begin_layout Plain Layout
19698 \begin_inset Formula $\omega$
19712 \begin_inset Space \hfill{}
19718 \begin_layout Standard
19719 \begin_inset VSpace medskip
19725 \begin_layout Standard
19726 How to create upright Greek letters is explained in
19727 \begin_inset CommandInset ref
19729 reference "sub:Upright-small-Greek"
19736 \begin_layout Subsection
19741 \begin_layout Plain Layout
19742 Greek letters ! big
19750 \begin_layout Standard
19751 \begin_inset Space \hfill{}
19755 \begin_inset Tabular
19756 <lyxtabular version="3" rows="7" columns="2">
19758 <column alignment="center" valignment="top" width="0pt">
19759 <column alignment="center" valignment="top" width="0pt">
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19764 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\Gamma$
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Plain Layout
19821 \begin_inset Formula $\Delta$
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19834 \begin_layout Plain Layout
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19845 \begin_layout Plain Layout
19846 \begin_inset Formula $\Theta$
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19859 \begin_layout Plain Layout
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19870 \begin_layout Plain Layout
19871 \begin_inset Formula $\Lambda$
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19884 \begin_layout Plain Layout
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19895 \begin_layout Plain Layout
19896 \begin_inset Formula $\Xi$
19906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19909 \begin_layout Plain Layout
19917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19920 \begin_layout Plain Layout
19921 \begin_inset Formula $\Pi$
19935 \begin_inset Space \hfill{}
19939 \begin_inset Tabular
19940 <lyxtabular version="3" rows="6" columns="2">
19942 <column alignment="center" valignment="top" width="0pt">
19943 <column alignment="center" valignment="top" width="0pt">
19945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19957 \begin_layout Plain Layout
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\Sigma$
19990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\Upsilon$
20015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20030 \begin_inset Formula $\Phi$
20040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20043 \begin_layout Plain Layout
20051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20054 \begin_layout Plain Layout
20055 \begin_inset Formula $\Psi$
20065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20068 \begin_layout Plain Layout
20076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20079 \begin_layout Plain Layout
20080 \begin_inset Formula $\Omega$
20094 \begin_inset Space \hfill{}
20100 \begin_layout Standard
20101 \begin_inset VSpace medskip
20104 That the big Greek letters appear upright is caused by a design bug when
20106 To get correct italic big letters, begin every command with
20111 For example the command
20118 \begin_inset Formula $\varGamma $
20124 \begin_layout Subsection
20129 \begin_layout Plain Layout
20130 Greek letters ! bold
20138 \begin_layout Standard
20139 Greek letters cannot be set with different font styles like Latin letters.
20140 They can only be made bold with the command
20150 \begin_layout Plain Layout
20161 \begin_layout Standard
20163 \begin_inset Tabular
20164 <lyxtabular version="3" rows="3" columns="2">
20166 <column alignment="center" valignment="top" width="0">
20167 <column alignment="center" valignment="top" width="0">
20169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20172 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20207 \begin_layout Plain Layout
20208 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20221 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20236 \begin_layout Plain Layout
20237 \begin_inset Formula $\theta\boldsymbol{\theta}$
20253 \begin_layout Section
20258 \begin_layout Plain Layout
20271 \begin_layout Plain Layout
20272 A list with all symbols of most of the LaTeX-packages can be found in
20273 \begin_inset CommandInset citation
20288 \begin_layout Plain Layout
20296 \begin_inset Note Note
20299 \begin_layout Plain Layout
20302 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20305 \begin_layout Plain Layout
20308 texorpdfstring is in section
20309 \begin_inset CommandInset ref
20311 reference "sub:Formulas-in-Section"
20324 \begin_layout Plain Layout
20333 \begin_layout Standard
20334 Many of the symbols listed in this section can also be inserted via the
20336 \begin_inset Graphics
20337 filename ../images/math/nabla.png
20343 \begin_inset Graphics
20344 filename ../images/math/digamma.png
20352 \begin_layout Subsection
20353 Mathematical Symbols
20354 \begin_inset CommandInset label
20356 name "sub:Mathematical-Symbols"
20364 \begin_layout Plain Layout
20365 Symbols ! mathematical
20373 \begin_layout Standard
20374 \begin_inset Space \hfill{}
20378 \begin_inset Tabular
20379 <lyxtabular version="3" rows="10" columns="2">
20381 <column alignment="center" valignment="top" width="0pt">
20382 <column alignment="center" valignment="top" width="0pt">
20384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20387 \begin_layout Plain Layout
20393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20396 \begin_layout Plain Layout
20404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20407 \begin_layout Plain Layout
20415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20418 \begin_layout Plain Layout
20419 \begin_inset Formula $\neg$
20429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20432 \begin_layout Plain Layout
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20443 \begin_layout Plain Layout
20444 \begin_inset Formula $\Im$
20454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20468 \begin_layout Plain Layout
20469 \begin_inset Formula $\Re$
20479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20482 \begin_layout Plain Layout
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20493 \begin_layout Plain Layout
20494 \begin_inset Formula $\aleph$
20504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20507 \begin_layout Plain Layout
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20518 \begin_layout Plain Layout
20519 \begin_inset Formula $\partial$
20529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20532 \begin_layout Plain Layout
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20543 \begin_layout Plain Layout
20544 \begin_inset Formula $\infty$
20554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20557 \begin_layout Plain Layout
20565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20568 \begin_layout Plain Layout
20569 \begin_inset Formula $\wp$
20579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20582 \begin_layout Plain Layout
20590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20593 \begin_layout Plain Layout
20594 \begin_inset Formula $\imath$
20604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20607 \begin_layout Plain Layout
20615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20618 \begin_layout Plain Layout
20619 \begin_inset Formula $\jmath$
20633 \begin_inset Space \hfill{}
20637 \begin_inset Tabular
20638 <lyxtabular version="3" rows="10" columns="2">
20640 <column alignment="center" valignment="top" width="0pt">
20641 <column alignment="center" valignment="top" width="0pt">
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20646 \begin_layout Plain Layout
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20655 \begin_layout Plain Layout
20657 \begin_inset Note Note
20660 \begin_layout Plain Layout
20667 is only used as spacer.
20679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20682 \begin_layout Plain Layout
20690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20693 \begin_layout Plain Layout
20694 \begin_inset Formula $\forall$
20704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20707 \begin_layout Plain Layout
20715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20718 \begin_layout Plain Layout
20719 \begin_inset Formula $\exists$
20729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20732 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20743 \begin_layout Plain Layout
20744 \begin_inset Formula $\nexists$
20754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20757 \begin_layout Plain Layout
20765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20768 \begin_layout Plain Layout
20769 \begin_inset Formula $\emptyset$
20779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20782 \begin_layout Plain Layout
20790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20793 \begin_layout Plain Layout
20794 \begin_inset Formula $\varnothing$
20804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20807 \begin_layout Plain Layout
20815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20818 \begin_layout Plain Layout
20819 \begin_inset Formula $\dag $
20829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20832 \begin_layout Plain Layout
20840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20843 \begin_layout Plain Layout
20844 \begin_inset Formula $\ddag $
20854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20857 \begin_layout Plain Layout
20865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20868 \begin_layout Plain Layout
20872 \begin_layout Plain Layout
20882 \begin_inset Formula $\complement$
20889 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20906 \begin_layout Plain Layout
20914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20917 \begin_layout Plain Layout
20918 \begin_inset Formula $\Bbbk$
20932 \begin_inset Space \hfill{}
20936 \begin_inset Tabular
20937 <lyxtabular version="3" rows="10" columns="2">
20939 <column alignment="center" valignment="top" width="0pt">
20940 <column alignment="center" valignment="top" width="0pt">
20942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20954 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20976 \begin_layout Plain Layout
20977 \begin_inset Formula $\prime$
20987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
20998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21001 \begin_layout Plain Layout
21002 \begin_inset Formula $\backprime$
21012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21015 \begin_layout Plain Layout
21023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21026 \begin_layout Plain Layout
21027 \begin_inset Formula $\mho$
21037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21040 \begin_layout Plain Layout
21048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21051 \begin_layout Plain Layout
21052 \begin_inset Formula $\triangle$
21062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21065 \begin_layout Plain Layout
21073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21076 \begin_layout Plain Layout
21077 \begin_inset Formula $\angle$
21087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21090 \begin_layout Plain Layout
21098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21101 \begin_layout Plain Layout
21102 \begin_inset Formula $\measuredangle$
21112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21126 \begin_layout Plain Layout
21127 \begin_inset Formula $\sphericalangle$
21137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21151 \begin_layout Plain Layout
21152 \begin_inset Formula $\top$
21162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21177 \begin_inset Formula $\bot$
21191 \begin_inset Space \hfill{}
21197 \begin_layout Standard
21198 \begin_inset Newpage newpage
21204 \begin_layout Subsection
21205 Miscellaneous Symbols
21206 \begin_inset CommandInset label
21208 name "sub:Miscellaneous-Symbols"
21216 \begin_layout Plain Layout
21217 Symbols ! miscellaneous
21225 \begin_layout Standard
21228 \begin_inset Tabular
21229 <lyxtabular version="3" rows="10" columns="2">
21231 <column alignment="center" valignment="top" width="0pt">
21232 <column alignment="center" valignment="top" width="0pt">
21234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21237 \begin_layout Plain Layout
21243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21246 \begin_layout Plain Layout
21254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21257 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\flat$
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\natural$
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\sharp$
21329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\surd$
21354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\checkmark$
21379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\yen$
21404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21407 \begin_layout Plain Layout
21415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21418 \begin_layout Plain Layout
21419 \begin_inset Formula $\pounds $
21429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21441 \begin_layout Plain Layout
21442 \begin_inset Formula $\$$
21452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21455 \begin_layout Plain Layout
21461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21464 \begin_layout Plain Layout
21465 \begin_inset Formula $§$
21479 \begin_inset Tabular
21480 <lyxtabular version="3" rows="10" columns="2">
21482 <column alignment="center" valignment="top" width="0">
21483 <column alignment="center" valignment="top" width="0">
21485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21488 \begin_layout Plain Layout
21494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21508 \begin_layout Plain Layout
21516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21519 \begin_layout Plain Layout
21520 \begin_inset Formula $\hbar$
21530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21533 \begin_layout Plain Layout
21541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21544 \begin_layout Plain Layout
21545 \begin_inset Formula $\hslash$
21555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21558 \begin_layout Plain Layout
21566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21569 \begin_layout Plain Layout
21570 \begin_inset Formula $\clubsuit$
21580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21583 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21595 \begin_inset Formula $\spadesuit$
21605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21608 \begin_layout Plain Layout
21616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21619 \begin_layout Plain Layout
21620 \begin_inset Formula $\bigstar$
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21633 \begin_layout Plain Layout
21641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21644 \begin_layout Plain Layout
21645 \begin_inset Formula $\blacklozenge$
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21658 \begin_layout Plain Layout
21666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21669 \begin_layout Plain Layout
21670 \begin_inset Formula $\blacktriangle$
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\blacktriangledown$
21705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\bullet$
21734 \begin_inset Tabular
21735 <lyxtabular version="3" rows="10" columns="2">
21737 <column alignment="center" valignment="top" width="0pt">
21738 <column alignment="center" valignment="top" width="0pt">
21740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21752 \begin_layout Plain Layout
21760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21763 \begin_layout Plain Layout
21771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21774 \begin_layout Plain Layout
21775 \begin_inset Formula $\diamondsuit$
21785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21788 \begin_layout Plain Layout
21796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21799 \begin_layout Plain Layout
21800 \begin_inset Formula $\Diamond$
21810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21824 \begin_layout Plain Layout
21825 \begin_inset Formula $\heartsuit$
21835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21838 \begin_layout Plain Layout
21846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21849 \begin_layout Plain Layout
21850 \begin_inset Formula $\P $
21860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21863 \begin_layout Plain Layout
21871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21874 \begin_layout Plain Layout
21875 \begin_inset Formula $\copyright $
21885 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21899 \begin_layout Plain Layout
21900 \begin_inset Formula $\circledR$
21910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21924 \begin_layout Plain Layout
21925 \begin_inset Formula $\maltese$
21935 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21949 \begin_layout Plain Layout
21950 \begin_inset Formula $\diagup$
21960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21974 \begin_layout Plain Layout
21975 \begin_inset Formula $\diagdown$
21991 \begin_layout Standard
21992 \begin_inset VSpace medskip
21995 More symbols are listed in
21996 \begin_inset CommandInset ref
21998 reference "sub:Miscellaneous-Special-Characters"
22005 \begin_layout Standard
22006 Some symbols can be displayed in different sizes, see
22007 \begin_inset CommandInset ref
22009 reference "sub:Font-Sizes"
22016 \begin_layout Subsection
22021 \begin_layout Plain Layout
22022 Symbols ! Euro-symbol
22031 \begin_layout Plain Layout
22035 \begin_layout Plain Layout
22052 \begin_layout Standard
22053 To use the Euro symbol in formulas, the LaTeX-package
22061 \begin_layout Plain Layout
22067 must be installed and loaded with the LaTeX-preamble line
22070 \begin_layout Standard
22075 usepackage[gennarrow]{eurosym}
22078 \begin_layout Standard
22079 The Euro symbol can now be inserted with the command
22089 \begin_layout Plain Layout
22100 \begin_layout Standard
22101 The Euro symbol can directly be inserted with the € key in mathematical
22102 text, without having
22117 can also be inserted in TeX-mode.
22118 The official currency symbol can then be inserted with the command
22128 \begin_layout Plain Layout
22136 , that is only available in TeX-mode.
22139 \begin_layout Standard
22143 \begin_layout Plain Layout
22153 \begin_inset Note Note
22156 \begin_layout Plain Layout
22157 The following table will only be displayed when the LaTeX-package
22169 \begin_layout Standard
22170 An overview about the different Euro symbols:
22173 \begin_layout Standard
22175 \begin_inset Tabular
22176 <lyxtabular version="3" rows="4" columns="3">
22178 <column alignment="center" valignment="top" width="0pt">
22179 <column alignment="center" valignment="top" width="0pt">
22180 <column alignment="center" valignment="top" width="0pt">
22182 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22185 \begin_layout Plain Layout
22191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22194 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22214 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22223 \begin_layout Plain Layout
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22234 \begin_layout Plain Layout
22235 \begin_inset Formula $\euro $
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" usebox="none">
22257 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22267 \begin_inset Formula $\mbox{€}$
22277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22280 \begin_layout Plain Layout
22286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22289 \begin_layout Plain Layout
22297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22300 \begin_layout Plain Layout
22304 \begin_layout Plain Layout
22326 \begin_layout Standard
22330 \begin_layout Plain Layout
22340 \begin_inset Note Note
22343 \begin_layout Plain Layout
22344 The following will be displayed when the LaTeX-package
22356 \begin_layout Standard
22357 You need to install the LaTeX-package
22361 to see the rest of this subsection in the output.
22364 \begin_layout Standard
22368 \begin_layout Plain Layout
22380 \begin_layout Section
22382 \begin_inset CommandInset label
22384 name "sec:Relations"
22392 \begin_layout Plain Layout
22402 \begin_layout Plain Layout
22407 \begin_layout Plain Layout
22418 \begin_layout Plain Layout
22433 \begin_layout Standard
22434 All relations can also be inserted via the toolbar button
22435 \begin_inset Graphics
22436 filename ../images/math/leq.png
22444 \begin_layout Standard
22445 \begin_inset Space \hfill{}
22449 \begin_inset Tabular
22450 <lyxtabular version="3" rows="17" columns="2">
22452 <column alignment="center" valignment="top" width="0pt">
22453 <column alignment="center" valignment="top" width="0pt">
22455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22458 \begin_layout Plain Layout
22464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22467 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22478 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $<$
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22512 \begin_layout Plain Layout
22513 \begin_inset Formula $\le$
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22526 \begin_layout Plain Layout
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22538 \begin_inset Formula $\ll$
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\prec$
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\preceq$
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\subset$
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\subseteq$
22648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\sqsubseteq$
22673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22688 \begin_inset Formula $\in$
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22701 \begin_layout Plain Layout
22709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22712 \begin_layout Plain Layout
22713 \begin_inset Formula $\vdash$
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22726 \begin_layout Plain Layout
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22737 \begin_layout Plain Layout
22738 \begin_inset Formula $\smile$
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22751 \begin_layout Plain Layout
22759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22762 \begin_layout Plain Layout
22763 \begin_inset Formula $\lhd$
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22776 \begin_layout Plain Layout
22784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22787 \begin_layout Plain Layout
22788 \begin_inset Formula $\unlhd$
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22801 \begin_layout Plain Layout
22809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22812 \begin_layout Plain Layout
22813 \begin_inset Formula $\gtrless$
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22826 \begin_layout Plain Layout
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22837 \begin_layout Plain Layout
22838 \begin_inset Formula $\mid$
22848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22851 \begin_layout Plain Layout
22859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22862 \begin_layout Plain Layout
22863 \begin_inset Formula $\nmid$
22877 \begin_inset Space \hfill{}
22881 \begin_inset Tabular
22882 <lyxtabular version="3" rows="17" columns="2">
22884 <column alignment="center" valignment="top" width="0pt">
22885 <column alignment="center" valignment="top" width="0pt">
22887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22919 \begin_layout Plain Layout
22920 \begin_inset Formula $=$
22930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22933 \begin_layout Plain Layout
22941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22944 \begin_layout Plain Layout
22945 \begin_inset Formula $\not=$
22955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22958 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22969 \begin_layout Plain Layout
22970 \begin_inset Formula $\equiv$
22980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22983 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22994 \begin_layout Plain Layout
22995 \begin_inset Formula $\sim$
23005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23020 \begin_inset Formula $\simeq$
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23044 \begin_layout Plain Layout
23045 \begin_inset Formula $\approx$
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23058 \begin_layout Plain Layout
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23069 \begin_layout Plain Layout
23070 \begin_inset Formula $\cong$
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23083 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23094 \begin_layout Plain Layout
23095 \begin_inset Formula $\bowtie$
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23108 \begin_layout Plain Layout
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23119 \begin_layout Plain Layout
23120 \begin_inset Formula $\notin$
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23144 \begin_layout Plain Layout
23145 \begin_inset Formula $\perp$
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23158 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23169 \begin_layout Plain Layout
23170 \begin_inset Formula $\propto$
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Plain Layout
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23194 \begin_layout Plain Layout
23195 \begin_inset Formula $\asymp$
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23219 \begin_layout Plain Layout
23220 \begin_inset Formula $\doteq$
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23233 \begin_layout Plain Layout
23241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23244 \begin_layout Plain Layout
23245 \begin_inset Formula $\circeq$
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23258 \begin_layout Plain Layout
23266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23269 \begin_layout Plain Layout
23270 \begin_inset Formula $\models$
23280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23283 \begin_layout Plain Layout
23291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23294 \begin_layout Plain Layout
23295 \begin_inset Formula $\widehat{=}$
23309 \begin_inset Space \hfill{}
23313 \begin_inset Tabular
23314 <lyxtabular version="3" rows="17" columns="2">
23316 <column alignment="center" valignment="top" width="0pt">
23317 <column alignment="center" valignment="top" width="0pt">
23319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23342 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $>$
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23376 \begin_layout Plain Layout
23377 \begin_inset Formula $\ge$
23387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23390 \begin_layout Plain Layout
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23401 \begin_layout Plain Layout
23402 \begin_inset Formula $\gg$
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $\succ$
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\succeq$
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\supset$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\supseteq$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\sqsupseteq$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\ni$
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\dashv$
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23590 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $\frown$
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\rhd$
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\unrhd$
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23665 \begin_layout Plain Layout
23673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23676 \begin_layout Plain Layout
23677 \begin_inset Formula $\lessgtr$
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23702 \begin_inset Formula $\parallel$
23712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23726 \begin_layout Plain Layout
23727 \begin_inset Formula $\nparallel$
23741 \begin_inset Space \hfill{}
23747 \begin_layout Standard
23748 \begin_inset VSpace medskip
23763 are bigger than the equal looking operators
23778 \begin_layout Standard
23779 Relations are, in contrary to symbols, always surrounded by space.
23782 \begin_layout Standard
23783 Relations with labels can be created with the command
23793 \begin_layout Plain Layout
23804 \begin_layout Standard
23806 \begin_inset Tabular
23807 <lyxtabular version="3" rows="2" columns="2">
23809 <column alignment="center" valignment="top" width="0">
23810 <column alignment="center" valignment="top" width="0">
23812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23824 \begin_layout Plain Layout
23826 \begin_inset Note Note
23829 \begin_layout Plain Layout
23836 is only used as spacer.
23848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23858 \begin_layout Plain Layout
23875 \begin_layout Plain Layout
23885 \begin_inset Formula $\downarrow$
23894 \begin_layout Plain Layout
23907 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\raisebox {5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23941 \begin_layout Section
23945 \begin_layout Subsection
23946 Predefined Functions
23947 \begin_inset CommandInset label
23949 name "sub:Predefined-Functions"
23957 \begin_layout Plain Layout
23958 Functions ! predefined
23966 \begin_layout Standard
23967 In general, variables are set
23971 in mathematical expressions, but not function names, because
23972 \begin_inset Formula $sin$
23975 could be misunderstood as
23976 \begin_inset Formula $s\cdot i\cdot n$
23980 Therefore there are predefined functions, that are additionally a bit separated
23982 They are inserted as commands starting with a backslash before their name.
23985 \begin_layout Standard
23987 \begin_inset Tabular
23988 <lyxtabular version="3" rows="2" columns="4">
23990 <column alignment="center" valignment="top" width="0pt">
23991 <column alignment="center" valignment="top" width="0pt">
23992 <column alignment="center" valignment="top" width="0pt">
23993 <column alignment="center" valignment="top" width="0pt">
23995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24007 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24025 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24036 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $Asin(x)+B$
24054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24068 \begin_layout Plain Layout
24069 \begin_inset Formula $A\sin(x)+B$
24083 \begin_inset Newpage pagebreak
24089 \begin_layout Standard
24090 The following functions are predefined:
24093 \begin_layout Standard
24094 \begin_inset VSpace -2mm
24100 \begin_layout Standard
24102 \begin_inset Tabular
24103 <lyxtabular version="3" rows="9" columns="4">
24105 <column alignment="center" valignment="top" width="0pt">
24106 <column alignment="center" valignment="top" width="0pt">
24107 <column alignment="center" valignment="top" width="0pt">
24108 <column alignment="center" valignment="top" width="0pt">
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" usebox="none">
24131 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24162 \begin_layout Plain Layout
24170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24184 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24243 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24276 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24289 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24335 \begin_layout Plain Layout
24343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24346 \begin_layout Plain Layout
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24392 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24414 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24438 \begin_layout Plain Layout
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24473 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24522 \begin_layout Standard
24523 They can also be inserted with the math toolbar button
24524 \begin_inset Graphics
24525 filename ../images/math/functions.png
24533 \begin_layout Subsection
24534 Self-defined Functions
24538 \begin_layout Plain Layout
24539 Functions ! self-defined
24547 \begin_layout Standard
24548 To use a function that is not predefined, like for example the sign function
24549 sgn(x), there are two possibilities:
24552 \begin_layout Itemize
24553 Define the function by inserting the following line to the LaTeX-preamble
24557 \begin_layout Plain Layout
24562 DeclareMathOperator
24565 \begin_inset CommandInset ref
24567 reference "sub:Self-defined-Operators"
24577 \begin_inset Newline newline
24581 \begin_inset VSpace -3mm
24585 \begin_inset Newline newline
24592 DeclareMathOperator{
24600 \begin_layout Plain Layout
24605 DeclareMathOperator
24611 \begin_inset Newline newline
24615 \begin_inset VSpace -2mm
24619 \begin_inset Newline newline
24622 Now the new defined function can be called with the command
24631 \begin_layout Itemize
24632 Write the the formula as usual, mark the formula name, in our example the
24637 , and change it to mathematical text.
24638 At last a space is inserted between prefactor and function.
24641 \begin_layout Standard
24642 The result is the same with both methods as with a predefined function
24646 \begin_layout Plain Layout
24647 In LyX self-defined functions are displayed red, predefined ones black.
24655 \begin_layout Standard
24657 \begin_inset Tabular
24658 <lyxtabular version="3" rows="3" columns="2">
24660 <column alignment="center" valignment="top" width="0pt">
24661 <column alignment="center" valignment="top" width="0pt">
24663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24666 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24675 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24686 \begin_layout Plain Layout
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24697 \begin_layout Plain Layout
24698 \begin_inset Formula $A\sgn (x)+B$
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24715 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24726 \begin_layout Plain Layout
24727 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24743 \begin_layout Standard
24744 The first method is more suitable when the self-defined function should
24745 be used several times.
24748 \begin_layout Subsection
24753 \begin_layout Plain Layout
24762 \begin_layout Standard
24763 For limits there are defined besides
24773 \begin_layout Plain Layout
24793 furthermore the following functions:
24796 \begin_layout Standard
24798 \begin_inset Tabular
24799 <lyxtabular version="3" rows="5" columns="2">
24801 <column alignment="center" valignment="top" width="0">
24802 <column alignment="center" valignment="top" width="0">
24804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24816 \begin_layout Plain Layout
24818 \begin_inset Note Note
24821 \begin_layout Plain Layout
24828 is only used as spacer.
24840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24843 \begin_layout Plain Layout
24851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24854 \begin_layout Plain Layout
24855 \begin_inset Formula $\varliminf $
24865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24868 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24880 \begin_inset Formula $\varlimsup $
24890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24893 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24904 \begin_layout Plain Layout
24905 \begin_inset Formula $\varprojlim $
24915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24929 \begin_layout Plain Layout
24930 \begin_inset Formula $\varinjlim $
24934 \begin_inset Formula $\raisebox {-2.5mm}{}$
24950 \begin_layout Standard
24951 \begin_inset VSpace medskip
24954 The limit is created by inserting a subscript.
24955 It is set right beside the function in an inline formula:
24958 \begin_layout Standard
24960 \begin_inset Tabular
24961 <lyxtabular version="3" rows="2" columns="2">
24963 <column alignment="center" valignment="top" width="0pt">
24964 <column alignment="center" valignment="top" width="0pt">
24966 <cell alignment="center" valignment="top" usebox="none">
24969 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" usebox="none">
24978 \begin_layout Plain Layout
24979 \begin_inset Space \hspace{}
24984 \begin_inset Note Note
24987 \begin_layout Plain Layout
25000 are used here as spacer.
25012 <cell alignment="center" valignment="top" usebox="none">
25015 \begin_layout Plain Layout
25024 \begin_layout Plain Layout
25037 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" usebox="none">
25054 \begin_layout Plain Layout
25055 \begin_inset Formula $\hspace {1cm}\raisebox {5mm}{}\lim_{x\to A}x=B$
25071 \begin_layout Standard
25072 In a displayed formula the limit is set below the formula, as usual:
25073 \begin_inset Formula \[
25081 \begin_layout Subsection
25086 \begin_layout Plain Layout
25087 Functions ! modulo-
25095 \begin_layout Standard
25096 The modulo-function is special, because it exists in four variants.
25099 \begin_layout Standard
25100 The variants in a displayed formula:
25101 \begin_inset Formula \begin{align*}
25102 \underline{\textrm{Command}\raisebox {-0.9mm}{}} & & \underline{\textrm{Result}}\\
25103 \mathrm{a\backslash mod\textrm{\spce }b} & & a\mod b\\
25104 \mathrm{a\backslash pmod\textrm{\spce }b} & & a\pmod b\\
25105 \mathrm{a\backslash bmod\textrm{\spce }b} & & a\bmod b\\
25106 \mathrm{a\backslash pod\textrm{\spce }b} & & a\pod b\end{align*}
25113 \begin_layout Standard
25114 In an inline formula less space is set before the function names for all
25118 \begin_layout Section
25123 \begin_layout Plain Layout
25132 \begin_layout Subsection
25133 Special Characters in Mathematical Text
25136 \begin_layout Standard
25137 The following commands can only be used in mathematical text or in TeX-mode:
25140 \begin_layout Standard
25141 \begin_inset Space \hfill{}
25145 \begin_inset Tabular
25146 <lyxtabular version="3" rows="8" columns="2">
25148 <column alignment="block" valignment="top" width="0">
25149 <column alignment="block" valignment="top" width="0">
25151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25163 \begin_layout Plain Layout
25171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25174 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25186 \begin_inset Formula $\textrm{\oe }$
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25211 \begin_inset Formula $\textrm{\OE }$
25221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25235 \begin_layout Plain Layout
25236 \begin_inset Formula $\textrm{\ae }$
25246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25261 \begin_inset Formula $\textrm{\AE }$
25271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25274 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25285 \begin_layout Plain Layout
25286 \begin_inset Formula $\textrm{\aa }$
25296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25306 \begin_layout Plain Layout
25310 \begin_layout Plain Layout
25318 \begin_layout Plain Layout
25329 \begin_layout Plain Layout
25345 \begin_layout Plain Layout
25353 \begin_layout Plain Layout
25364 \begin_layout Plain Layout
25380 \begin_layout Plain Layout
25391 \begin_layout Plain Layout
25399 \begin_layout Plain Layout
25410 \begin_layout Plain Layout
25426 \begin_layout Plain Layout
25443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25446 \begin_layout Plain Layout
25447 \begin_inset Formula $\textrm{\AA}$
25457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25460 \begin_layout Plain Layout
25468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25471 \begin_layout Plain Layout
25472 \begin_inset Formula $\textrm{\i }$
25486 \begin_inset Space \hfill{}
25490 \begin_inset Tabular
25491 <lyxtabular version="3" rows="8" columns="2">
25493 <column alignment="block" valignment="top" width="0">
25494 <column alignment="center" valignment="top" width="0">
25496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25499 \begin_layout Plain Layout
25501 \begin_inset Note Note
25504 \begin_layout Plain Layout
25511 is used for separation, because otherwise the output will be ¡ and ¿ respective
25522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25525 \begin_layout Plain Layout
25533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25536 \begin_layout Plain Layout
25544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25547 \begin_layout Plain Layout
25548 \begin_inset Formula $\textrm{\o }$
25558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25561 \begin_layout Plain Layout
25569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25572 \begin_layout Plain Layout
25573 \begin_inset Formula $\textrm{\O}$
25583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25586 \begin_layout Plain Layout
25594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25597 \begin_layout Plain Layout
25598 \begin_inset Formula $\textrm{\l }$
25608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25611 \begin_layout Plain Layout
25619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25622 \begin_layout Plain Layout
25623 \begin_inset Formula $\textrm{\L }$
25633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25636 \begin_layout Plain Layout
25638 \begin_inset Space \hspace{}
25646 \begin_layout Plain Layout
25660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25663 \begin_layout Plain Layout
25664 \begin_inset Formula $\textrm{!`}$
25674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25677 \begin_layout Plain Layout
25679 \begin_inset Space \hspace{}
25687 \begin_layout Plain Layout
25701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25704 \begin_layout Plain Layout
25705 \begin_inset Formula $\textrm{?`}$
25715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25718 \begin_layout Plain Layout
25726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25729 \begin_layout Plain Layout
25730 \begin_inset Formula $\textrm{\j }$
25744 \begin_inset Space \hfill{}
25750 \begin_layout Standard
25752 \begin_inset Formula $\textrm{\textrm{Å}}$
25756 \begin_inset Formula $\textrm{\textrm{Ø}}$
25759 can also be inserted via the math toolbar button
25760 \begin_inset Graphics
25761 filename ../images/math/digamma.png
25769 \begin_layout Standard
25770 An exception are the commands
25773 \begin_inset Space \hspace{}
25782 \begin_inset Space \hspace{}
25788 , because they can be inserted in LyX directly to text.
25791 \begin_layout Subsection
25793 \begin_inset CommandInset label
25795 name "sub:Accents-in-Text"
25803 \begin_layout Plain Layout
25812 \begin_layout Standard
25813 With the following commands all letters can be accented.
25814 The commands must be inserted in TeX-mode.
25817 \begin_layout Standard
25818 \begin_inset Space \hfill{}
25822 \begin_inset Tabular
25823 <lyxtabular version="3" rows="8" columns="2">
25825 <column alignment="block" valignment="top" width="0">
25826 <column alignment="block" valignment="top" width="0">
25828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25831 \begin_layout Plain Layout
25837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25840 \begin_layout Plain Layout
25848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25851 \begin_layout Plain Layout
25855 \begin_inset Quotes grd
25863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25866 \begin_layout Plain Layout
25870 \begin_layout Plain Layout
25886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25889 \begin_layout Plain Layout
25897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25900 \begin_layout Plain Layout
25904 \begin_layout Plain Layout
25920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25923 \begin_layout Plain Layout
25930 \begin_layout Plain Layout
25944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25947 \begin_layout Plain Layout
25951 \begin_layout Plain Layout
25967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25970 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25985 \begin_layout Plain Layout
26001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26004 \begin_layout Plain Layout
26011 \begin_layout Plain Layout
26025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26028 \begin_layout Plain Layout
26032 \begin_layout Plain Layout
26048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26051 \begin_layout Plain Layout
26058 \begin_layout Plain Layout
26072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26075 \begin_layout Plain Layout
26079 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26098 \begin_layout Plain Layout
26105 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26122 \begin_layout Plain Layout
26126 \begin_layout Plain Layout
26146 \begin_inset Space \hfill{}
26150 \begin_inset Tabular
26151 <lyxtabular version="3" rows="8" columns="2">
26153 <column alignment="block" valignment="top" width="0">
26154 <column alignment="center" valignment="top" width="0">
26156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26159 \begin_layout Plain Layout
26165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26168 \begin_layout Plain Layout
26176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26179 \begin_layout Plain Layout
26186 \begin_layout Plain Layout
26200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26203 \begin_layout Plain Layout
26207 \begin_layout Plain Layout
26223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26226 \begin_layout Plain Layout
26234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26237 \begin_layout Plain Layout
26241 \begin_layout Plain Layout
26257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26260 \begin_layout Plain Layout
26267 \begin_layout Plain Layout
26278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26281 \begin_layout Plain Layout
26285 \begin_layout Plain Layout
26301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26304 \begin_layout Plain Layout
26312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26315 \begin_layout Plain Layout
26319 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26338 \begin_layout Plain Layout
26345 \begin_layout Plain Layout
26359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26362 \begin_layout Plain Layout
26366 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26385 \begin_layout Plain Layout
26392 \begin_layout Plain Layout
26406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26409 \begin_layout Plain Layout
26413 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26432 \begin_layout Plain Layout
26439 \begin_layout Plain Layout
26453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26456 \begin_layout Plain Layout
26460 \begin_layout Plain Layout
26480 \begin_inset Space \hfill{}
26486 \begin_layout Standard
26487 \begin_inset VSpace medskip
26496 also two different characters can be accented.
26505 \begin_layout Plain Layout
26520 \begin_layout Plain Layout
26532 \begin_layout Standard
26545 can in combination with vowels directly be inserted with the keyboard without
26547 The same applies for the tilde
26551 \begin_layout Plain Layout
26552 This only applies for keyboards where the tilde is defined as accent.
26561 in combination with
26576 \begin_layout Standard
26619 , and accents inserted directly with the keyboard are also available in
26621 For the other accents there are special math commands to be used in formulas,
26623 \begin_inset CommandInset ref
26625 reference "sub:Accents-for-one"
26632 \begin_layout Standard
26633 \begin_inset VSpace bigskip
26636 Furthermore, with the command
26646 \begin_layout Plain Layout
26654 all numbers and letters can be set into a circle, quasi accented with a
26655 circle, similar to the the copyright symbol.
26658 \begin_layout Standard
26660 \begin_inset Tabular
26661 <lyxtabular version="3" rows="3" columns="2">
26663 <column alignment="center" valignment="top" width="0">
26664 <column alignment="center" valignment="top" width="0">
26666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26669 \begin_layout Plain Layout
26675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26678 \begin_layout Plain Layout
26680 \begin_inset Note Note
26683 \begin_layout Plain Layout
26690 is only used as spacer.
26702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26705 \begin_layout Plain Layout
26713 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26716 \begin_layout Plain Layout
26720 \begin_layout Plain Layout
26736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26739 \begin_layout Plain Layout
26750 raisebox{-1.5pt}{W}}
26755 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26758 \begin_layout Plain Layout
26759 \begin_inset Formula $\raisebox {4.5mm}{}$
26766 \begin_layout Plain Layout
26784 \begin_inset Formula $\raisebox {-2mm}{}$
26800 \begin_layout Standard
26801 One has to take care that the character fits in the circle.
26812 \begin_layout Plain Layout
26814 \begin_inset CommandInset ref
26816 reference "sub:Font-Sizes"
26825 specifies thereby the size of the circle.
26836 \begin_layout Plain Layout
26838 \begin_inset CommandInset ref
26840 reference "sub:Boxes-without-Frame"
26849 the character can be centered.
26852 \begin_layout Subsection
26857 \begin_layout Plain Layout
26866 \begin_layout Standard
26867 Minuscule numbers are created with the command
26877 \begin_layout Plain Layout
26886 The command can be used in formulas and in TeX-mode.
26887 The command scheme is:
26890 \begin_layout Standard
26895 oldstylenums{number}
26898 \begin_layout Standard
26903 oldstylenums{0123456789
26906 \begin_inset Formula $\oldstylenums {0123456789}$
26912 \begin_layout Subsection
26913 Miscellaneous Special Characters
26914 \begin_inset CommandInset label
26916 name "sub:Miscellaneous-Special-Characters"
26924 \begin_layout Plain Layout
26925 Special characters ! miscellaneous
26933 \begin_layout Standard
26934 The following characters can only be inserted to formulas by using commands:
26937 \begin_layout Standard
26939 \begin_inset Tabular
26940 <lyxtabular version="3" rows="4" columns="2">
26942 <column alignment="center" valignment="top" width="0">
26943 <column alignment="center" valignment="top" width="0">
26945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26948 \begin_layout Plain Layout
26954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26957 \begin_layout Plain Layout
26965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26968 \begin_layout Plain Layout
26975 \begin_layout Plain Layout
26989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26992 \begin_layout Plain Layout
26993 \begin_inset Formula $\mathcircumflex$
27003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27006 \begin_layout Plain Layout
27014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27017 \begin_layout Plain Layout
27018 \begin_inset Formula $\_{} {}{}{}{}{}{}{}{}$
27028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27031 \begin_layout Plain Layout
27036 \begin_layout Plain Layout
27051 \begin_layout Plain Layout
27062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27065 \begin_layout Plain Layout
27066 \begin_inset Formula $^{\circ}$
27082 \begin_layout Standard
27083 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27084 contains the following line
27088 \begin_layout Plain Layout
27089 More about this is described in
27090 \begin_inset CommandInset ref
27092 reference "sub:Text-Characters-in"
27104 \begin_layout Standard
27109 DeclareInputtext{176}{
27119 f\SpecialChar \textcompwordmark{}
27123 \begin_layout Section
27125 \begin_inset CommandInset label
27127 name "sec:Formula-Styles"
27135 \begin_layout Plain Layout
27144 \begin_layout Itemize
27145 There are two different alignment styles:
27149 \begin_layout Description
27150 Centered is the predefined standard
27153 \begin_layout Description
27154 Indented for this the option
27158 must be inserted in the menu
27160 Document\SpecialChar \menuseparator
27166 \begin_inset Space ~
27172 \begin_layout Standard
27177 is used, the indentation can be adjusted with the length
27187 \begin_layout Plain Layout
27196 Should the distance be 15
27197 \begin_inset Space \thinspace{}
27200 mm, the following command line is inserted in the LaTeX-preamble
27203 \begin_layout Standard
27213 \begin_layout Standard
27214 When no length is specified, the predefined value of 30
27215 \begin_inset Space \thinspace{}
27222 \begin_layout Itemize
27223 And two different numbering styles:
27227 \begin_layout Description
27228 Right is the predefined standard
27231 \begin_layout Description
27232 Left for this the option
27236 must be inserted in the menu
27238 Document\SpecialChar \menuseparator
27244 \begin_inset Space ~
27251 \begin_layout Standard
27260 can also be used together.
27261 In this case both options are inserted, separated by a comma.
27264 \begin_layout Standard
27265 The chosen styles are used for all displayed formulas of the document.
27266 When both, centered and indented formulas should be created in a document,
27272 The indented formulas are then set in a flalign environment, see
27273 \begin_inset CommandInset ref
27275 reference "sub:Flalign-Environment"
27282 \begin_layout Section
27284 \begin_inset CommandInset label
27286 name "sec:Multiline-Formulas"
27294 \begin_layout Plain Layout
27295 Formula ! multiline
27303 \begin_layout Subsection
27307 \begin_layout Standard
27308 In LyX multiline formulas are created by pressing
27319 that is described in
27320 \begin_inset CommandInset ref
27322 reference "sub:Standard-align-Environment"
27329 \begin_layout Standard
27330 There are other multiline formula environments that can be created via the
27333 Insert\SpecialChar \menuseparator
27337 These environments are described in the following sections.
27340 \begin_layout Standard
27341 In all multiline formula environments a new line is created by pressing
27347 To add or delete lines, the math toolbar buttons
27348 \begin_inset Graphics
27349 filename ../images/tabular-feature_append-row.png
27355 \begin_inset Graphics
27356 filename ../images/tabular-feature_delete-row.png
27361 , respectively, or the menu
27363 Edit\SpecialChar \menuseparator
27369 \begin_layout Subsubsection
27371 \begin_inset CommandInset label
27373 name "sub:Line-Separation"
27381 \begin_layout Plain Layout
27382 Formula ! multiline ! Line separation
27390 \begin_layout Standard
27391 There is sometimes not enough space in multiline formulas between the lines:
27392 \begin_inset Formula \begin{eqnarray*}
27393 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}\\
27394 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*}
27401 \begin_layout Standard
27402 In LaTeX additional line space is specified as optional argument of the
27404 This is not yet possible in LyX
27408 \begin_layout Plain Layout
27410 \begin_inset CommandInset href
27412 name "LyX-bug #1505"
27413 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27422 , therefore the whole formula must be inserted in TeX-mode.
27423 To add in our example space, the command
27431 is inserted at the end of the first line.
27436 \begin_layout Plain Layout
27443 \begin_layout Plain Layout
27445 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27448 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27455 \begin_layout Plain Layout
27459 left(B^{2}+x_{0}^{2}
27467 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27472 \begin_layout Plain Layout
27484 \begin_layout Standard
27485 \begin_inset VSpace bigskip
27488 To set the the line separation for all lines in a formula, the length
27498 \begin_layout Plain Layout
27508 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27519 \begin_inset Space \thinspace{}
27524 \begin_inset Space \thinspace{}
27527 mm additional line separation as in the previous example, the command
27530 \begin_layout Standard
27540 \begin_layout Standard
27541 is inserted in TeX-mode before the formula.
27542 This requires that the LaTeX-package
27550 \begin_layout Plain Layout
27555 is part of every LaTeX standard installation.
27564 \begin_layout Plain Layout
27570 was loaded in LaTeX-preamble with the line
27573 \begin_layout Standard
27581 \begin_layout Standard
27586 \begin_layout Plain Layout
27598 \begin_inset Formula \begin{eqnarray*}
27599 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}\\
27600 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*}
27607 \begin_layout Standard
27611 \begin_layout Plain Layout
27622 To get back to the predefined distance,
27628 is set to the value 3
27629 \begin_inset Space \thinspace{}
27635 \begin_layout Subsubsection
27637 \begin_inset CommandInset label
27639 name "sub:Column-Separation"
27647 \begin_layout Plain Layout
27648 Formula ! multiline ! Column separation
27656 \begin_layout Standard
27657 Multiline formulas form a matrix.
27658 A formula in the eqnarray environment is for example a matrix with three
27660 By changing the column separation in this environment, the space beside
27661 the relation sign can be changed.
27664 \begin_layout Standard
27665 The column separation is specified with the length
27675 \begin_layout Plain Layout
27684 \begin_inset Newline newline
27687 column separation = 2
27688 \begin_inset Space \thinspace{}
27698 \begin_inset Newline newline
27704 \begin_layout Standard
27714 \begin_layout Standard
27715 inserted in TeX-mode, sets for all following formulas a column separation
27717 \begin_inset Space \thinspace{}
27721 To get back to the predefined distance,
27728 \begin_inset Space \thinspace{}
27734 \begin_layout Standard
27736 \begin_inset Space \thinspace{}
27739 cm column separation:
27743 \begin_layout Plain Layout
27755 \begin_inset Formula \begin{eqnarray*}
27757 C & \ne & A\end{eqnarray*}
27761 A formula with the predefined column separation for matrices of 10
27762 \begin_inset Space \thinspace{}
27769 \begin_layout Plain Layout
27781 \begin_inset Formula \begin{eqnarray*}
27783 C & \ne & A\end{eqnarray*}
27790 \begin_layout Subsubsection
27795 \begin_layout Plain Layout
27804 \begin_layout Standard
27805 Long formulas can be typeset using these methods:
27808 \begin_layout Itemize
27809 When one side of the equation is much shorther than the line width, this
27810 one is chosen for the left side and the right side is typeset over two
27815 \begin_layout Plain Layout
27825 \begin_inset Formula \begin{eqnarray}
27826 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 \\
27827 & & -\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}
27835 \begin_layout Plain Layout
27845 \begin_inset Newline newline
27848 The minus sign at the beginning of the second line does normally not appear
27849 as operator because it is the first character of the line.
27850 Thus it would not be surrounded by space and could not be distinguished
27851 from the fraction bar.
27852 To avoid this, space was inserted behind the minus sign with the command
27863 \begin_layout Plain Layout
27871 \begin_inset CommandInset ref
27873 reference "sub:Variable-Space"
27886 \begin_layout Plain Layout
27897 \begin_layout Itemize
27898 When both sides of the equation are too long, the command
27908 \begin_layout Plain Layout
27917 It is inserted to the first column of the first line and effects that all
27918 further insertions overwrite the following columns:
27922 \begin_layout Plain Layout
27932 \begin_inset Formula \begin{eqnarray}
27933 \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 \\
27934 & & -\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 \\
27935 & & =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}
27943 \begin_layout Plain Layout
27953 \begin_inset Newline newline
27956 After the insertion of
27962 , the cursor is in a purple box that is a bit shifted to the left from the
27964 In this the formula is inserted.
27968 \begin_layout Plain Layout
27978 \begin_inset Newline newline
27981 The content of the further lines is inserted to the second or another formula
27983 The greater the column number where it was inserted, the larger the indentation.
27987 \begin_layout Plain Layout
27997 \begin_inset Newline newline
28001 \begin_inset Note Greyedout
28004 \begin_layout Plain Layout
28005 Note the following when using
28014 \begin_layout Itemize
28015 The formula doesn't use the full page width.
28017 \begin_inset Space \thinspace{}
28021 \begin_inset Space ~
28025 \begin_inset Formula $-B^{2}$
28028 is added to the first line in the above example, it would have been outside
28030 To better use the width, negative space can be inserted at the beginning
28034 \begin_layout Itemize
28035 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28040 \begin_layout Plain Layout
28041 \begin_inset CommandInset href
28043 name "LyX-bug #1429"
28044 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28053 One can only set the cursor at the beginning of the line and move it with
28062 \begin_layout Itemize
28063 Other methods to set long formulas are offered by the environments described
28065 \begin_inset CommandInset ref
28067 reference "sub:Multline-Environment"
28072 \begin_inset CommandInset ref
28074 reference "sub:Multiline-Formula-Parts"
28081 \begin_layout Subsubsection
28083 \begin_inset CommandInset label
28085 name "sub:Multiline-Brackets"
28093 \begin_layout Plain Layout
28094 Brackets ! for multiline expressions
28102 \begin_layout Standard
28103 For brackets spanning multiple lines the following problem occurs:
28104 \begin_inset Formula \begin{eqnarray*}
28105 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28106 & & \left.\cdots+B-D\right]\end{eqnarray*}
28113 \begin_layout Standard
28114 The closing bracket is smaller than the opening bracket because brackets
28115 with variable size may not span multiple lines.
28118 \begin_layout Standard
28119 To set the bracket size for the second line correctly, the first line is
28130 \begin_layout Plain Layout
28138 and the second line with
28146 \begin_layout Plain Layout
28160 \begin_inset CommandInset ref
28162 reference "sub:Automatic-Bracket-Size"
28177 \begin_layout Plain Layout
28203 \begin_layout Plain Layout
28222 \begin_layout Plain Layout
28241 \begin_layout Plain Layout
28253 \begin_inset Formula $\downarrow$
28262 \begin_layout Plain Layout
28270 is inserted, because the multiplication operator with its limits is the
28271 largest symbol in the first line and this should be the size for the bracket
28272 in the second line.
28275 \begin_layout Standard
28276 The result is this:
28277 \begin_inset Formula \begin{eqnarray*}
28278 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28279 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28286 \begin_layout Subsection
28290 \begin_layout Standard
28291 Align environments can be used for every kind of multiline formulas.
28292 They are specially useful to set several formulas side by side.
28295 \begin_layout Standard
28296 Align environments consist of columns.
28297 The odd columns are right aligned, the even ones left aligned.
28298 Every line in an Align environment can be numbered.
28301 \begin_layout Standard
28302 Align environments are created via the menu
28304 Insert\SpecialChar \menuseparator
28310 Edit\SpecialChar \menuseparator
28311 Math\SpecialChar \menuseparator
28312 Change Formula Type
28314 already existing formulas can be converted to Align environments.
28317 \begin_layout Standard
28318 To add or delete columns, the math toolbar buttons
28319 \begin_inset Graphics
28320 filename ../images/tabular-feature_append-column.png
28326 \begin_inset Graphics
28327 filename ../images/tabular-feature_delete-column.png
28332 , respectively, or the menu
28334 Edit\SpecialChar \menuseparator
28340 \begin_layout Subsubsection
28341 Standard align Environment
28342 \begin_inset CommandInset label
28344 name "sub:Standard-align-Environment"
28352 \begin_layout Plain Layout
28353 Formula ! multiline ! align environment
28361 \begin_layout Standard
28362 This Align environment is created by presssing
28366 in a formula or by the menu
28368 Insert\SpecialChar \menuseparator
28369 Math\SpecialChar \menuseparator
28370 AMS align Environment
28375 \begin_layout Standard
28376 An example for two formulas set side by side, that are created with a four
28377 column align environment:
28378 \begin_inset Formula \begin{align*}
28379 A & =\sin(B) & C & =D\\
28380 C & \ne A & B & \ne D\end{align*}
28384 As it can be seen, the formulas in this environment are placed so as if
28393 \begin_layout Plain Layout
28401 \begin_inset CommandInset ref
28403 reference "sub:Variable-Space"
28414 before the first and after every even column.
28415 When the formula style
28421 \begin_layout Plain Layout
28423 \begin_inset CommandInset ref
28425 reference "sec:Formula-Styles"
28436 is used, the formula is set without the
28442 before the first column.
28445 \begin_layout Subsubsection
28446 Alignat Environment
28450 \begin_layout Plain Layout
28451 Formula ! multiline ! alignat environment
28459 \begin_layout Standard
28460 The alignat environment has no predefined column separation.
28461 It can be inserted manually with the spaces that are described
28462 \begin_inset CommandInset ref
28464 reference "sub:Space"
28471 \begin_layout Standard
28472 The above example in the alignat environment where 1
28473 \begin_inset Space \thinspace{}
28476 cm space was inserted at the beginning of the second formula:
28477 \begin_inset Formula \begin{alignat*}{2}
28478 A & =\sin(B) & \hspace {1cm}C & =D\\
28479 C & \ne A & B & \ne D\end{alignat*}
28483 Because the column separation can be set separately for every column, this
28484 environment is especially suitable to set three and more formulas side
28488 \begin_layout Subsubsection
28489 Flalign Environment
28490 \begin_inset CommandInset label
28492 name "sub:Flalign-Environment"
28500 \begin_layout Plain Layout
28501 Formula ! multiline ! flalign environment
28509 \begin_layout Standard
28510 In this environment the first two columns are always set as much as possible
28511 to the left and the last two ones to the right.
28513 \begin_inset Formula \begin{flalign*}
28514 A & =1 & B & =2 & C & =3\\
28515 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28522 \begin_layout Standard
28523 By creating a flalign environment with an odd number of columns where an
28524 empty TeX-brace is inserted to the last column, several formulas in a document
28525 can be set to the left, although the formula style
28530 As example the indented formula
28531 \begin_inset CommandInset ref
28533 reference "eq:VolInt"
28538 \begin_inset Formula \begin{flalign}
28539 \hspace {30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28543 The first two columns contain the formula.
28544 To indent it as with the formula style
28549 \begin_inset Space \thinspace{}
28552 pt space was inserted at the beginning of the first column.
28555 \begin_layout Subsection
28556 Eqnarray Environment
28560 \begin_layout Plain Layout
28561 Formula ! multiline ! eqnarray environment
28569 \begin_layout Standard
28570 When this environment has been created, three blue boxes appear.
28571 The content of the first box is right aligned, the content of the last
28573 The content of the middle box appears centered and a bit smaller, because
28574 it is designed to insert there only relation characters.
28575 \begin_inset Formula \begin{eqnarray*}
28576 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28578 A & = & A\end{eqnarray*}
28585 \begin_layout Subsection
28590 \begin_layout Plain Layout
28591 Formula ! multiline ! gather environment
28599 \begin_layout Standard
28600 This environment consists of only one centered column.
28601 Every line can be numbered.
28602 \begin_inset Formula \begin{gather}
28604 X=\textrm{-}1\end{gather}
28611 \begin_layout Subsection
28612 Multline Environment
28613 \begin_inset CommandInset label
28615 name "sub:Multline-Environment"
28623 \begin_layout Plain Layout
28624 Formula ! multiline ! multline environment
28632 \begin_layout Standard
28633 The multline environment consists, like the gather environment, of only
28635 But the first line is left aligned, the last one right aligned.
28636 All other lines are centered.
28637 Therefore this environment is suitable for long formulas.
28639 \begin_inset CommandInset ref
28641 reference "eq:lefteqn"
28645 in the multline environment:
28646 \begin_inset Formula \begin{multline}
28647 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}\\
28648 -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}\\
28649 =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}
28656 \begin_layout Standard
28657 In the output only the last (first) line of a multline environment appears
28658 numbered when the document numbering is right (left).
28662 \begin_layout Plain Layout
28663 numbering styles see
28664 \begin_inset CommandInset ref
28666 reference "sec:Formula-Styles"
28678 \begin_layout Standard
28687 \begin_layout Plain Layout
28705 \begin_layout Plain Layout
28715 a centered line can be right or left aligned, respectively.
28716 The commands are used as follows:
28719 \begin_layout Standard
28724 shoveright{line content}
28730 shoveleft{line content}
28733 \begin_layout Standard
28734 \begin_inset VSpace medskip
28745 \begin_layout Plain Layout
28755 specifies the distance of the first line from the left page margin.
28756 Predefined is the length 0
28757 \begin_inset Space \thinspace{}
28763 \begin_layout Standard
28764 As example the above formula where the command
28767 \begin_layout Standard
28777 \begin_layout Standard
28778 was inserted in TeX-mode before:
28782 \begin_layout Plain Layout
28794 \begin_inset Formula \begin{multline}
28795 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}\\
28796 \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}}\\
28797 =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}
28805 \begin_layout Plain Layout
28816 The second line was left aligned using
28825 \begin_layout Subsection
28826 Multiline Formula Parts
28827 \begin_inset CommandInset label
28829 name "sub:Multiline-Formula-Parts"
28837 \begin_layout Plain Layout
28838 Formula ! multiline ! formula parts
28846 \begin_layout Standard
28847 To display only parts of a formula with multiple lines, one of the following
28848 environments are used:
28865 They can be inserted via the menu
28867 Insert\SpecialChar \menuseparator
28870 or by using the commands described in this section.
28873 \begin_layout Standard
28874 The first three have the same properties as the corresponding multiline
28875 formula environments, but it is possible to set further formula parts beside
28878 \begin_inset Formula \[
28879 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28880 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28881 \right\} \textrm{Uncertainty relations}\]
28888 \begin_layout Standard
28889 To get this formula, a displayed formula is created where the command
28897 \begin_layout Plain Layout
28908 A purple box appears around the blue formula box where now columns and
28909 lines can be added.
28910 Outside the multiline environment other formula parts can be set, like
28914 \begin_layout Standard
28915 The aligned environment is also suitable for long formulas whose lines are
28916 horizontally aligned.
28917 Using aligned in a displayed formula has the advantage that the formula
28918 number is vertically centered behind the lines.
28920 \begin_inset CommandInset ref
28922 reference "eq:kurzlang"
28926 in the aligned environment:
28927 \begin_inset Formula \begin{equation}
28928 \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}|}\\
28929 & -\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}
28937 \begin_layout Standard
28938 To use the environments
28960 \begin_layout Plain Layout
28978 \begin_layout Plain Layout
28996 \begin_layout Plain Layout
29004 are inserted, respectively.
29005 The split environment has the same properties as the aligned environment
29006 but it can only have two columns.
29009 \begin_layout Subsection
29010 Text in multiline Formulas
29011 \begin_inset CommandInset label
29013 name "sub:Text-in-multiline"
29021 \begin_layout Plain Layout
29031 \begin_layout Plain Layout
29032 Formula ! multiline ! text
29040 \begin_layout Standard
29041 In the Align environments, and the multline and gather environment, text
29042 can be inserted that will appear in a separate line and doesn't affect
29043 the column alignment.
29044 To do this, the command
29052 \begin_layout Plain Layout
29062 is used in the following scheme:
29065 \begin_layout Standard
29073 \begin_layout Standard
29074 The text should not be longer than a line because it cannot be hyphenated.
29075 As LyX doesn't yet support
29081 directly, the text is written as mathematical text.
29088 must hereby be at the beginning of a line and appears in the output above
29090 An example where the text was inserted at the beginning of the second line:
29091 \begin_inset Formula \begin{align}
29092 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29093 \intertext {\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29100 \begin_layout Section
29105 \begin_layout Plain Layout
29115 \begin_layout Plain Layout
29116 Formula ! numbering|see
29120 \begin_layout Plain Layout
29131 \begin_layout Plain Layout
29146 \begin_layout Subsection
29150 \begin_layout Standard
29151 Numbered formulas can be created with the menu
29153 Insert\SpecialChar \menuseparator
29154 Math\SpecialChar \menuseparator
29156 \begin_inset Space ~
29164 \begin_inset Space ~
29170 Existing formulas can be numbered with the menu
29172 Edit\SpecialChar \menuseparator
29173 Math\SpecialChar \menuseparator
29175 \begin_inset Space ~
29183 \begin_inset Space ~
29189 The formula number is displayed in LyX behind the formula as number sign
29191 The number sign is replaced in the output by the formula number.
29194 \begin_layout Standard
29195 When numbering is turned on in multiline formulas, all lines will be numbered.
29196 But the numbering can be controlled with the menu
29198 Edit\SpecialChar \menuseparator
29199 Math\SpecialChar \menuseparator
29201 \begin_inset Space ~
29205 \begin_inset Space ~
29209 \begin_inset Space ~
29217 \begin_inset Space ~
29225 \begin_layout Standard
29226 Except of inline formulas, all formulas can be numbered with two different
29228 \begin_inset CommandInset ref
29230 reference "sec:Formula-Styles"
29237 \begin_layout Subsection
29239 \begin_inset CommandInset label
29241 name "sub:Cross-References"
29249 \begin_layout Plain Layout
29250 Cross-references ! to formulas
29258 \begin_layout Standard
29259 All labeled formulas can be cross-referenced.
29260 A label is added by the menu
29262 Insert\SpecialChar \menuseparator
29265 or the toolbar button
29266 \begin_inset Graphics
29267 filename ../images/label-insert.png
29273 The cursor must hereby be inside a displayed formula.
29274 A dialog pops up displaying the prefix
29279 The label is inserted there behind the prefix.
29280 The predefined prefix means
29281 \begin_inset Quotes eld
29285 \begin_inset Quotes erd
29288 and makes it easier to find labels in large documents because it marks
29289 it as formula label to divide it from e.
29290 \begin_inset Space \thinspace{}
29294 \begin_inset Space ~
29298 To change a label, the menu
29300 Insert\SpecialChar \menuseparator
29306 \begin_layout Standard
29307 The name of the label is displayed in LyX within two parentheses behind
29309 A formula with a label is always numbered.
29312 \begin_layout Standard
29313 Cross-references are inserted via the menu
29315 Insert\SpecialChar \menuseparator
29318 or with the toolbar button
29319 \begin_inset Graphics
29320 filename ../images/dialog-show-new-inset_ref.png
29326 A formula cross-reference appears in the output as formula number.
29327 When in the cross-reference dialog window the format
29331 is chosen, the cross-reference appears in the output as formula number
29333 \begin_inset Newline newline
29336 By right-clicking on a cross-reference in LyX, one jumps to the formula
29337 that is referenced.
29340 \begin_layout Standard
29341 Here are as examples cross-references to formulas of the following subsections:
29342 \begin_inset Note Note
29345 \begin_layout Plain Layout
29346 Note the different cross-reference types.
29354 \begin_layout Standard
29356 \begin_inset CommandInset ref
29363 \begin_inset CommandInset ref
29371 \begin_inset CommandInset ref
29377 ) big Latin letters are used for the numbering in contrary to (
29378 \begin_inset CommandInset ref
29387 \begin_layout Standard
29388 \begin_inset VSpace medskip
29391 When the argument of
29399 \begin_layout Plain Layout
29407 \begin_inset CommandInset ref
29409 reference "sub:User-defined-Numbering"
29420 contains a box like in
29421 \begin_inset CommandInset ref
29423 reference "sub:Paragraph-Boxes"
29427 , the formula cannot be referenced.
29430 \begin_layout Subsection
29435 \begin_layout Plain Layout
29436 Formula numbering ! subnumbering
29444 \begin_layout Standard
29445 With the help of the commands
29449 begin{subequations}
29457 formulas can be subnumbered.
29458 Both commands are inserted in TeX-mode.
29461 \begin_layout Standard
29463 \begin_inset Formula \begin{equation}
29464 A=C-B\label{eq:a}\end{equation}
29472 \begin_layout Plain Layout
29476 addtocounter{equation}{-1}
29485 \begin_layout Plain Layout
29489 begin{subequations}
29495 \begin_inset VSpace -5mm
29499 \begin_inset Formula \begin{equation}
29500 B=C-A\label{eq:b}\end{equation}
29505 \begin_inset Formula \begin{equation}
29506 C=A+B\label{eq:c}\end{equation}
29513 \begin_layout Standard
29517 \begin_layout Plain Layout
29529 \begin_layout Standard
29530 To create the example, the following is done:
29533 \begin_layout Enumerate
29534 first formula is inserted
29537 \begin_layout Enumerate
29542 addtocounter{equation}{-1}
29544 begin{subequations}
29548 \begin_layout Plain Layout
29557 \begin_inset Newline newline
29562 is inserted after the first formula
29565 \begin_layout Enumerate
29566 second formula is inserted
29569 \begin_layout Enumerate
29570 third formula is inserted
29573 \begin_layout Enumerate
29580 is inserted after the third formula
29583 \begin_layout Standard
29584 Every formula between the commands
29596 is subnumbered as a, b,
29597 \begin_inset Newline linebreak
29600 c, \SpecialChar \ldots{}
29601 For multiline formulas every line will be subnumbered.
29602 All subnumbered formulas are treated as
29607 But as every numbered formula increases the counter
29611 by one, the command
29617 is needed to decrease it.
29618 Otherwise the formulas
29619 \begin_inset CommandInset ref
29626 \begin_inset CommandInset ref
29633 \begin_inset CommandInset ref
29639 would be numbered as
29640 \begin_inset CommandInset ref
29647 \begin_inset CommandInset ref
29654 \begin_inset CommandInset ref
29663 \begin_layout Standard
29664 By inserting the commands in TeX-mode, a space is created between the first
29667 \begin_inset Space \thinspace{}
29670 mm vertical space is inserted after the command
29674 begin{subequations}
29677 When the formula style
29683 \begin_layout Plain Layout
29685 \begin_inset CommandInset ref
29687 reference "sec:Formula-Styles"
29699 \begin_inset Space \thinspace{}
29702 mm space is inserted instead.
29705 \begin_layout Standard
29706 Here is an example for a multiline formula where the numbering was turned
29707 off for the second line:
29711 \begin_layout Plain Layout
29715 begin{subequations}
29721 \begin_inset Formula \begin{eqnarray}
29722 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29723 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29724 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29732 \begin_layout Plain Layout
29744 \begin_layout Subsection
29745 User-defined Numbering
29746 \begin_inset CommandInset label
29748 name "sub:User-defined-Numbering"
29756 \begin_layout Plain Layout
29757 Formula numbering ! user-defined
29765 \begin_layout Standard
29769 \begin_layout Plain Layout
29770 Formula numbering ! self-defined delimiters
29775 With the standard numbering parentheses are set around the formula number.
29776 To replace the parentheses for example by vertical bars, the following
29777 line is added to the LaTeX-preamble:
29780 \begin_layout Standard
29792 \begin_inset Note Note
29795 \begin_layout Plain Layout
29796 This macro is already declared in the LaTeX-preamble for testing.
29797 To activate it, remove the percent sign at the beginning.
29805 \begin_layout Standard
29806 To use other characters, the vertical bars besides the
29810 are replaced by one ore more characters.
29811 To get only the formula number the vertical bars are omitted.
29814 \begin_layout Standard
29815 \begin_inset VSpace bigskip
29818 When there should be an expression of your choice instead of the consecutive
29819 formula number in parentheses behind the formula, the command
29829 \begin_layout Plain Layout
29838 \begin_inset Formula \begin{equation}
29839 A+B=C\tag{something}\label{eq:tag}\end{equation}
29843 In this example the command
29851 \begin_layout Plain Layout
29862 was inserted to the formula.
29865 \begin_layout Standard
29874 \begin_layout Plain Layout
29885 is inserted instead, the star prevents the parentheses around the expression:
29886 \begin_inset Formula \[
29887 A+B=C\tag*{something}\]
29894 \begin_layout Standard
29895 \begin_inset VSpace bigskip
29898 To restart the formula numbering with new document parts or sections, the
29899 following command is used:
29902 \begin_layout Standard
29907 @addtoreset{equation}{part}
29913 \begin_layout Plain Layout
29918 \begin_layout Plain Layout
29929 \begin_layout Plain Layout
29942 \begin_layout Plain Layout
29953 \begin_layout Plain Layout
29966 \begin_inset Newline newline
29970 \begin_inset Newline newline
29977 @addtoreset{equation}{section}
29980 \begin_layout Standard
29981 To be able to use these commands in TeX-mode, the
29982 \begin_inset Quotes eld
29986 \begin_inset Quotes erd
29989 character has to be made
29990 \begin_inset Quotes eld
29994 \begin_inset Quotes erd
29997 for LaTeX using the command
30011 So the command sequence in TeX-mode is:
30014 \begin_layout Standard
30020 \begin_inset Newline newline
30025 @addtoreset{equation}{section}
30026 \begin_inset Newline newline
30034 \begin_layout Standard
30035 In the LaTeX-preamble
30047 can be omitted as they are automatically internally inserted by LyX.
30050 \begin_layout Standard
30065 \begin_layout Plain Layout
30070 is part of the LaTeX-package
30078 \begin_layout Plain Layout
30079 Packages ! carlisle
30084 that is part of every LaTeX standard installation.
30093 \begin_layout Plain Layout
30094 Packages ! remreset
30099 has to be loaded in the LaTeX-preamble with the line
30102 \begin_layout Standard
30107 usepackage{remreset}
30110 \begin_layout Standard
30121 \begin_layout Plain Layout
30126 \begin_layout Plain Layout
30137 \begin_layout Plain Layout
30150 \begin_layout Plain Layout
30161 \begin_layout Plain Layout
30173 can be used with the same scheme as
30182 \begin_layout Standard
30183 \begin_inset VSpace bigskip
30186 Sometimes formulas should be numbered in the following form:
30189 \begin_layout Standard
30192 (section number.formula number)
30195 \begin_layout Standard
30196 The formula number should start with every section with
30197 \begin_inset Quotes eld
30201 \begin_inset Quotes erd
30207 \begin_layout Standard
30208 For this case there is the command
30218 \begin_layout Plain Layout
30226 , which is used with the following scheme:
30229 \begin_layout Standard
30234 numberwithin{counter}{sectioning}
30237 \begin_layout Standard
30238 Counter denotes what kind of numbering is affected, sectioning denotes what
30239 number is before the dot.
30242 \begin_layout Standard
30243 Thus in our case the following LaTeX-preamble or ERT line is used:
30246 \begin_layout Standard
30251 numberwithin{equation}{section}
30254 \begin_layout Standard
30255 This is the result:
30259 \begin_layout Plain Layout
30263 numberwithin{equation}{section}
30269 \begin_inset Formula \begin{equation}
30270 A+B=C\end{equation}
30277 \begin_layout Standard
30279 \begin_inset Space \thinspace{}
30283 \begin_inset Space ~
30286 tables so that the number of the part is the sectioning,
30287 \begin_inset Newline newline
30294 numberwithin{table}{part}
30299 \begin_layout Standard
30300 To go back to the standard numbering or to prevent this kind of numbering
30301 when it is defined by the document class, the following command is inserted
30302 as ERT or to the LaTeX-preamble:
30305 \begin_layout Standard
30318 \begin_layout Plain Layout
30332 \begin_layout Plain Layout
30348 \begin_inset Newline newline
30356 \begin_inset Newline newline
30368 \begin_layout Standard
30375 uses internally the command
30381 , described above, that also needs to be reverted.
30385 \begin_layout Plain Layout
30392 \begin_layout Plain Layout
30396 @removefromreset{equation}{section}
30399 \begin_layout Plain Layout
30411 \begin_layout Subsection
30412 Numbering with Roman Numbers and Letters
30413 \begin_inset CommandInset label
30415 name "sub:Numbering-with-Roman"
30423 \begin_layout Plain Layout
30424 Formula numbering ! with letters
30433 \begin_layout Plain Layout
30434 Formula numbering ! with Roman numbers
30442 \begin_layout Standard
30443 Formulas can also be numbered with Roman numbers and Latin letters.
30444 To number for example with small Roman numbers, the command
30447 \begin_layout Standard
30459 \begin_layout Standard
30460 is inserted before the formula in TeX-mode.
30471 \begin_layout Plain Layout
30479 redefines the predefined command
30495 \begin_layout Plain Layout
30502 has the same scheme like the command
30508 that is described in
30509 \begin_inset CommandInset ref
30511 reference "sec:User-defined-commands"
30525 is the formula counter.
30532 is used as prefix for a counter, the value of the counter is output as
30534 When a formula is numbered, LaTeX sets internally the command
30540 behind the formula.
30549 \begin_layout Plain Layout
30559 outputs the counter as small Roman number.
30562 \begin_layout Standard
30563 All formulas behind the command
30573 are now numbered Roman.
30574 To switch to numbering with big Roman numbers, the command is inserted
30591 \begin_layout Plain Layout
30603 \begin_inset Quotes eld
30607 \begin_inset Quotes erd
30610 with small Latin letters there is the command
30620 \begin_layout Plain Layout
30628 , for big ones there is the command
30638 \begin_layout Plain Layout
30651 \begin_layout Standard
30652 \begin_inset Note Greyedout
30655 \begin_layout Plain Layout
30660 Only maximal 26 formulas can be numbered with Latin letters in one document.
30668 \begin_layout Standard
30672 \begin_layout Plain Layout
30688 \begin_layout Standard
30689 \begin_inset Formula \begin{equation}
30690 A=\textrm{small roman}\label{eq:rom}\end{equation}
30698 \begin_layout Plain Layout
30712 \begin_inset Formula \begin{equation}
30713 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30721 \begin_layout Plain Layout
30735 \begin_inset Formula \begin{equation}
30736 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30744 \begin_layout Plain Layout
30758 \begin_inset Formula \begin{equation}
30759 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30766 \begin_layout Standard
30767 To switch back to the default numbering, insert the command:
30770 \begin_layout Standard
30783 \begin_layout Plain Layout
30794 \begin_layout Standard
30798 \begin_layout Plain Layout
30812 \begin_inset Formula \begin{equation}
30813 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30820 \begin_layout Standard
30821 \begin_inset VSpace medskip
30824 As you see, formulas are numbered serially independent from the numbering
30826 When then numbering should start with
30827 \begin_inset Quotes eld
30831 \begin_inset Quotes erd
30834 when the style is changed, new equation counters have to be defined.
30835 A description about this can be found in the file
30836 \begin_inset CommandInset href
30838 target "Formula-numbering.lyx"
30845 \begin_layout Section
30846 User-defined commands
30847 \begin_inset CommandInset label
30849 name "sec:User-defined-commands"
30857 \begin_layout Plain Layout
30858 User-defined commands
30866 \begin_layout Standard
30867 Many LaTeX-commands are too long to be used frequently.
30868 But it is possible to define with the command
30878 \begin_layout Plain Layout
30886 new shorter commands.
30889 \begin_layout Standard
30890 The command scheme of
30899 \begin_layout Standard
30904 newcommand{new command name}[number of arguments][optional
30909 \begin_inset Newline newline
30916 \begin_layout Plain Layout
30931 \begin_layout Plain Layout
30938 {command definition}
30941 \begin_layout Standard
30942 \begin_inset Note Greyedout
30945 \begin_layout Plain Layout
30950 Assure that the name of the new command is not already used in your document
30951 or by LaTeX-packages that you use.
30952 When you for example define the command
30964 , you get an error message because
30970 is already defined as command for
30971 \begin_inset Quotes eld
30975 \begin_inset Formula $\le$
30979 \begin_inset Quotes erd
30990 \begin_layout Standard
30991 \begin_inset Note Greyedout
30994 \begin_layout Plain Layout
30999 The names of user-defined commands may only consist of Latin letters.
31007 \begin_layout Standard
31008 The number of arguments is an integer in the range 0
31009 \begin_inset Space \thinspace{}
31013 \begin_inset Space \thinspace{}
31016 9 and specifies how many arguments the new command should have.
31017 With the optional value a value for an optional argument can be predefined.
31018 When this is done, the
31026 rgument of the new command is automatically an optional one.
31029 \begin_layout Standard
31030 Here are some examples:
31033 \begin_layout Itemize
31034 To define the command
31046 , the LaTeX-preamble line is:
31050 \begin_layout Plain Layout
31062 \begin_inset Newline newline
31074 \begin_layout Itemize
31075 To define the command
31087 , the argument (that should be underlined) must be taken into account.
31088 For this the preamble line is:
31092 \begin_layout Plain Layout
31104 \begin_inset Newline newline
31119 \begin_layout Plain Layout
31131 \begin_inset Newline newline
31140 acts as argument placeholder, the
31144 behind it denotes that it is the placeholder for the first argument.
31147 \begin_layout Itemize
31155 \begin_inset Space \thinspace{}
31159 \begin_inset Space ~
31172 \begin_layout Plain Layout
31184 \begin_inset Newline newline
31193 framebox#1#2{$#3$}}
31199 \begin_layout Plain Layout
31211 \begin_inset Newline newline
31216 The two Dollar signs creates the extra formula needed for
31223 \begin_inset CommandInset ref
31225 reference "sub:Boxes-with-Frame"
31232 \begin_layout Itemize
31233 To create a new command for
31239 where the color for the box needn't to be specified, the argument for the
31240 color is defined optional:
31244 \begin_layout Plain Layout
31256 \begin_inset Newline newline
31265 fcolorbox{#2}{#1}{$#3$}}
31271 \begin_layout Plain Layout
31281 \begin_inset Newline newline
31284 When the color is not specified when using
31290 , the predefined color
31297 \begin_layout Standard
31298 A test of the new defined commands:
31301 \begin_layout Standard
31303 \begin_inset Tabular
31304 <lyxtabular version="3" rows="6" columns="2">
31306 <column alignment="center" valignment="top" width="0">
31307 <column alignment="center" valignment="top" width="0">
31309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31312 \begin_layout Plain Layout
31318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31321 \begin_layout Plain Layout
31323 \begin_inset Note Note
31326 \begin_layout Plain Layout
31333 is only used as spacer.
31345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31348 \begin_layout Plain Layout
31355 \begin_layout Plain Layout
31369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31372 \begin_layout Plain Layout
31373 \begin_inset Formula $A\gr B$
31383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31386 \begin_layout Plain Layout
31394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31397 \begin_layout Plain Layout
31398 \begin_inset Formula $\raisebox {4.5mm}{}\us {ABcd}\raisebox {-2mm}{}$
31408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31411 \begin_layout Plain Layout
31415 \begin_inset Formula $\to$
31421 \begin_inset Formula $\to$
31432 \begin_layout Plain Layout
31446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31449 \begin_layout Plain Layout
31450 \begin_inset Formula $\raisebox {6mm}{}\fb {[2cm]}{}{\int A=B}\raisebox {-4mm}{}$
31460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31463 \begin_layout Plain Layout
31467 \begin_inset Formula $\to$
31478 \begin_layout Plain Layout
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31495 \begin_layout Plain Layout
31496 \begin_inset Formula $\raisebox {6mm}{}\cb {red}{\int A=B}\raisebox {-4mm}{}$
31506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31509 \begin_layout Plain Layout
31515 \begin_inset Formula $\to$
31526 \begin_layout Plain Layout
31540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31543 \begin_layout Plain Layout
31544 \begin_inset Formula $\raisebox {6mm}{}\cb [green]{red}{\int A=B}\raisebox {-4mm}{}$
31560 \begin_layout Section
31565 \begin_layout Plain Layout
31574 \begin_layout Standard
31575 To create diagrams, the LaTeX-package
31581 \begin_layout Plain Layout
31586 is part of every LaTeX standard installation.
31597 \begin_layout Plain Layout
31604 It is loaded in the LaTeX-preamble with the line
31607 \begin_layout Standard
31615 \begin_layout Standard
31616 Diagrams visualize relations and look like this:
31617 \begin_inset Formula \[
31618 \begin{CD}A@>>>B@>>>C\\
31620 F@<<<E@<<<D\end{CD}\]
31627 \begin_layout Standard
31628 To get them, the command
31636 \begin_layout Plain Layout
31646 is inserted to a formula.
31647 A blue box appears with two dashed lines where further commands can be
31653 a new line is created.
31654 Horizontal relations are inserted in odd, vertical in even formula lines.
31657 \begin_layout Standard
31658 To create the relations there are the following commands:
31661 \begin_layout Itemize
31666 creates a left arrow,
31677 \begin_layout Itemize
31682 creates an up arrow,
31690 a vertical equal sign
31693 \begin_layout Itemize
31699 is a placeholder for non-existent relations
31702 \begin_layout Standard
31703 All arrows can be labeled as follows:
31706 \begin_layout Itemize
31707 Is text inserted between the first and second < or >, resp., it is placed
31709 When it is inserted between the second and third one, it appears under
31713 \begin_layout Itemize
31714 When text for vertical arrows is inserted between the first and second A
31715 or V, resp., it is placed left beside the arrow.
31716 When it is inserted between the second and third one, it appears right
31718 If the text contains an A or V, these letters must be set into a TeX-brace.
31721 \begin_layout Standard
31722 As example a diagram with all possible relations:
31725 \begin_layout Standard
31726 \begin_inset Formula \[
31727 \begin{CD}A@>j>>B@>>k>C@=F\\
31729 D@<<j<E@>k>>F@=C\end{CD}\]
31736 \begin_layout Standard
31737 The command for this is:
31738 \begin_inset Newline newline
31749 \begin_layout Plain Layout
31758 A@>j>>B@>>k>C@=F Ctrl-Enter
31759 \begin_inset Newline newline
31766 \begin_layout Plain Layout
31781 \begin_layout Plain Layout
31794 \begin_layout Plain Layout
31806 \begin_inset Formula $\to$
31812 \begin_inset Newline newline
31819 \begin_layout Plain Layout
31834 \begin_layout Plain Layout
31847 \begin_layout Plain Layout
31857 \begin_layout Standard
31858 \begin_inset Newpage newpage
31864 \begin_layout Section
31869 \begin_layout Plain Layout
31882 \begin_layout Plain Layout
31883 Other useful math tips can be found in
31884 \begin_inset CommandInset citation
31899 \begin_layout Plain Layout
31907 \begin_inset Note Note
31910 \begin_layout Plain Layout
31913 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31916 \begin_layout Plain Layout
31919 texorpdfstring is in section
31920 \begin_inset CommandInset ref
31922 reference "sub:Formulas-in-Section"
31935 \begin_layout Plain Layout
31945 \begin_layout Plain Layout
31950 \begin_layout Plain Layout
31957 Chemical characters
31961 \begin_layout Plain Layout
31976 \begin_layout Subsection
31977 Chemical Symbols and Equations
31978 \begin_inset CommandInset label
31980 name "sub:Chemical-Symbols-and"
31988 \begin_layout Plain Layout
31989 Chemical characters ! Symbols
31998 \begin_layout Plain Layout
32008 \begin_layout Plain Layout
32017 \begin_layout Standard
32018 An example text from chemistry:
32021 \begin_layout Quote
32023 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32026 -ion reacts with two
32027 \begin_inset Formula $\mathrm{Na^{+}}$
32030 -ions to sodium sulfate
32031 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32035 The chemical equation for this is:
32036 \begin_inset Formula \[
32037 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32044 \begin_layout Standard
32045 This chemical equation can directly be created as formula.
32046 To avoid that the symbols appear italic, everything is highlighted and
32047 changed by the shortcut
32050 \begin_inset Space ~
32055 to the upright font style.
32059 \begin_layout Plain Layout
32065 \begin_inset CommandInset ref
32067 reference "sub:Font-Styles"
32079 \begin_layout Subsection
32084 \begin_layout Plain Layout
32093 \begin_layout Standard
32094 Negative numbers often look ugly in formulas because the minus sign before
32095 the number is set with the same length as the minus operator sign.
32096 When writing the negative number in normal text, the minus sign appears
32100 \begin_layout Standard
32101 Thus, the problem disappears when converting the minus sign to mathematical
32105 \begin_layout Standard
32106 An example to visualize the problem:
32109 \begin_layout Standard
32111 \begin_inset Tabular
32112 <lyxtabular version="3" rows="3" columns="2">
32114 <column alignment="right" valignment="top" width="0">
32115 <column alignment="left" valignment="top" width="0">
32117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32120 \begin_layout Plain Layout
32126 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32129 \begin_layout Plain Layout
32137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32140 \begin_layout Plain Layout
32146 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32149 \begin_layout Plain Layout
32150 \begin_inset Formula $x=-2$
32160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32163 \begin_layout Plain Layout
32169 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32172 \begin_layout Plain Layout
32173 \begin_inset Formula $x=\textrm{-}2$
32189 \begin_layout Subsection
32190 Comma as Decimal Separator
32194 \begin_layout Plain Layout
32203 \begin_layout Standard
32204 In LaTeX a comma inside a formula is used, according to the English convention,
32205 as number group separator.
32206 So there will be space added behind all commas in formulas.
32209 \begin_layout Standard
32210 To avoid this, the comma is highlighted and changed to mathematical text
32214 \begin_inset Space ~
32222 \begin_layout Standard
32223 To use all formula commas in the document as decimal separator, the file
32232 \begin_layout Plain Layout
32237 is part of the LaTeX-package
32245 \begin_layout Plain Layout
32250 \begin_layout Plain Layout
32273 \begin_layout Plain Layout
32279 is loaded with the LaTeX-preamble line
32282 \begin_layout Standard
32290 \begin_layout Subsection
32292 \begin_inset CommandInset label
32294 name "sub:Physical-Vectors"
32302 \begin_layout Plain Layout
32311 \begin_layout Standard
32312 Predefined vectors are offered by the LaTeX-package
32320 \begin_layout Plain Layout
32325 should be part of every LaTeX standard installation.
32334 \begin_layout Plain Layout
32340 that is loaded with the LaTeX-preamble line
32343 \begin_layout Standard
32351 \begin_layout Standard
32355 \begin_layout Plain Layout
32365 \begin_inset Note Note
32368 \begin_layout Plain Layout
32369 The following table will only be displayed when the LaTeX-package
32378 The following commands are defined:
32381 \begin_layout Standard
32383 \begin_inset Tabular
32384 <lyxtabular version="3" rows="4" columns="2">
32386 <column alignment="center" valignment="top" width="0">
32387 <column alignment="center" valignment="top" width="0">
32389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32392 \begin_layout Plain Layout
32398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32401 \begin_layout Plain Layout
32409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32412 \begin_layout Plain Layout
32422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32425 \begin_layout Plain Layout
32426 \begin_inset Formula $\Bra {\psi}$
32436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32439 \begin_layout Plain Layout
32449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32452 \begin_layout Plain Layout
32453 \begin_inset Formula $\Ket {\psi}$
32463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32466 \begin_layout Plain Layout
32478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32481 \begin_layout Plain Layout
32482 \begin_inset Formula $\Braket {\psi|\phi}$
32498 \begin_layout Standard
32505 assures that all vertical bars are set in the size of the surrounding brackets:
32506 \begin_inset Formula \[
32507 \Braket {\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32515 \begin_layout Plain Layout
32525 \begin_inset Note Note
32528 \begin_layout Plain Layout
32529 The following will be displayed when the LaTeX-package
32541 \begin_layout Standard
32542 You need to install the LaTeX-package
32546 to see the rest of this subsection in the output.
32549 \begin_layout Standard
32553 \begin_layout Plain Layout
32565 \begin_layout Standard
32572 can also be achieved using the command
32578 , that is described in
32579 \begin_inset CommandInset ref
32581 reference "sub:Automatic-Bracket-Size"
32588 \begin_layout Subsection
32589 Self-defined Fractions
32590 \begin_inset CommandInset label
32592 name "sub:Self-defined-Fractions"
32600 \begin_layout Plain Layout
32601 Fractions ! self-defined
32609 \begin_layout Standard
32610 To define custom commands for fractions, the command
32620 \begin_layout Plain Layout
32628 is used in the following scheme:
32631 \begin_layout Standard
32644 bracket}{fraction bar thickness}{style}
32645 \begin_inset Newline newline
32652 \begin_layout Plain Layout
32667 \begin_layout Plain Layout
32674 {numerator}{denominator}
32677 \begin_layout Standard
32678 The style is a number in the range of 0
32679 \begin_inset Space \thinspace{}
32683 \begin_inset Space \thinspace{}
32689 \begin_layout Standard
32691 \begin_inset Tabular
32692 <lyxtabular version="3" rows="5" columns="2">
32694 <column alignment="center" valignment="top" width="0">
32695 <column alignment="center" valignment="top" width="0">
32697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32700 \begin_layout Plain Layout
32706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32709 \begin_layout Plain Layout
32717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32720 \begin_layout Plain Layout
32726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32729 \begin_layout Plain Layout
32730 display style formula
32737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32740 \begin_layout Plain Layout
32746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32749 \begin_layout Plain Layout
32757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32760 \begin_layout Plain Layout
32766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32769 \begin_layout Plain Layout
32777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32780 \begin_layout Plain Layout
32786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32789 \begin_layout Plain Layout
32803 \begin_layout Standard
32804 When no style is given, the size is adjusted to the surrounding environment
32805 like for the command
32814 \begin_layout Standard
32815 When no fraction bar thickness is given, the predefined value of 0.4
32816 \begin_inset Space \thinspace{}
32822 \begin_layout Standard
32823 \begin_inset VSpace medskip
32826 For example, the commands
32839 \begin_inset CommandInset ref
32841 reference "sub:Fractions"
32845 are defined with the commands
32848 \begin_layout Standard
32857 genfrac{}{}{}{0}{#1}{#2}}
32860 \begin_layout Standard
32864 \begin_layout Standard
32873 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32876 \begin_layout Standard
32877 \begin_inset VSpace medskip
32880 To define a fraction where the fraction bar thickness can be given as optional
32881 argument, the following line is inserted to the LaTeX-preamble:
32884 \begin_layout Standard
32893 genfrac{}{}{#1}{}{#2}{#3}}
32896 \begin_layout Standard
32898 \begin_inset Formula \begin{align*}
32899 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32900 \text{Result} & & \fracS [1mm]{A}{B} & & \fracS [5mm]{A}{B}\end{align*}
32904 As one can see, the distance of the numerator and the denominator to the
32905 fraction bar is round about three times the bar thickness.
32908 \begin_layout Subsection
32910 \begin_inset CommandInset label
32912 name "sub:Canceled-Formulas"
32920 \begin_layout Plain Layout
32929 \begin_layout Standard
32930 To cancel formulas or formula parts, the LaTeX-package
32938 \begin_layout Plain Layout
32943 is part of every LaTeX standard installation.
32952 \begin_layout Plain Layout
32958 has to be loaded with the LaTeX-preamble line
32961 \begin_layout Standard
32966 usepackage[samesize]{cancel}
32969 \begin_layout Standard
32970 There are four ways to cancel formulas:
32973 \begin_layout Standard
32975 \begin_inset Tabular
32976 <lyxtabular version="3" rows="5" columns="2">
32978 <column alignment="center" valignment="top" width="0">
32979 <column alignment="center" valignment="top" width="0">
32981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32984 \begin_layout Plain Layout
32990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32993 \begin_layout Plain Layout
32995 \begin_inset Note Note
32998 \begin_layout Plain Layout
33011 are used here as spacer.
33023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33026 \begin_layout Plain Layout
33035 \begin_layout Plain Layout
33049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33052 \begin_layout Plain Layout
33053 \begin_inset Formula $\raisebox {4.5mm}{}\cancel {\int A=B}\raisebox {-2.5mm}{}$
33063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33066 \begin_layout Plain Layout
33075 \begin_layout Plain Layout
33089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33092 \begin_layout Plain Layout
33093 \begin_inset Formula $\raisebox {4.5mm}{}\bcancel {\int A=B}\raisebox {-2.5mm}{}$
33103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33106 \begin_layout Plain Layout
33115 \begin_layout Plain Layout
33129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33132 \begin_layout Plain Layout
33133 \begin_inset Formula $\raisebox {4.5mm}{}\xcancel {\int A=B}\raisebox {-2.5mm}{}$
33143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33146 \begin_layout Plain Layout
33150 \begin_inset Formula $\to$
33161 \begin_layout Plain Layout
33175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33178 \begin_layout Plain Layout
33179 \begin_inset Formula $\raisebox {7mm}{}\cancelto {1}{\int A=B}\raisebox {-2.5mm}{}\hspace {3mm}$
33195 \begin_layout Standard
33202 is especially suitable to visualize the reduction of fractions within formulas:
33203 \begin_inset Formula \[
33204 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto {2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel {1+b^{2}}}\]
33211 \begin_layout Subsection
33212 Formulas in Section Headings
33213 \begin_inset CommandInset label
33215 name "sub:Formulas-in-Section"
33223 \begin_layout Plain Layout
33224 Formula ! in section headings
33232 \begin_layout Standard
33233 When formulas are used in section headings, the following has to be taken
33237 \begin_layout Standard
33238 \begin_inset Note Greyedout
33241 \begin_layout Plain Layout
33250 \begin_layout Plain Layout
33251 Packages ! hyperref
33256 support is enabled in the document settings dialog under
33259 \begin_inset Space ~
33264 , PDF-bookmarks are created for every section heading in the table of contents.
33265 If a section heading contains formulas, they are incorrectly displayed
33266 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33275 \begin_layout Standard
33276 Both problems can be solved by inserting at the end of the section heading
33277 a short title with the menu
33279 Insert\SpecialChar \menuseparator
33281 \begin_inset Space ~
33287 Short titles are used as alternative for multiline section headings to
33288 keep the table of contents clearly arranged.
33289 Only the short title appears in the table of contents and therefore also
33290 in the PDF-bookmark.
33293 \begin_layout Standard
33294 When formulas should be used in the table of contents but
33298 is used, one can use the following command in TeX-mode:
33301 \begin_layout Standard
33306 texorpdfstring{part}{alternative}
33310 \begin_layout Plain Layout
33321 \begin_layout Standard
33322 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33323 This can be characters, formulas, footnotes, but also cross-references.
33324 The alternative is used instead of the part for the bookmark.
33327 \begin_layout Standard
33328 Here are two example headings:
33329 \begin_inset VSpace -3mm
33336 \begin_layout Plain Layout
33348 \begin_layout Subsubsection
33349 Heading without formula in table of contents
33350 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33354 \begin_inset OptArg
33357 \begin_layout Plain Layout
33358 Heading without formula in table of contents
33366 \begin_layout Subsubsection
33367 Heading with formula in table of contents
33371 \begin_layout Plain Layout
33381 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33388 \begin_layout Plain Layout
33398 \begin_layout Standard
33402 \begin_layout Plain Layout
33411 In the first heading a short title was used, in the second one
33420 \begin_layout Standard
33421 To get the same formatting as for the other headings, the complete heading
33424 boldmath environment
33430 \begin_layout Plain Layout
33432 \begin_inset CommandInset ref
33434 reference "sub:Bold-Formulas"
33446 \begin_layout Subsection
33447 Formulas in multi-column Text
33451 \begin_layout Plain Layout
33452 Formula ! in multi-column text
33460 \begin_layout Standard
33461 Formulas in multi-column text are often too wide to fit into a column and
33462 thus need to be set over the whole page width.
33463 This is done by using the LaTeX-package
33471 \begin_layout Plain Layout
33476 is part of every LaTeX standard installation.
33485 \begin_layout Plain Layout
33486 Packages ! multicol
33491 , that is loaded with the LaTeX-preamble line
33494 \begin_layout Standard
33499 usepackage{multicol}
33502 \begin_layout Standard
33503 \begin_inset Note Greyedout
33506 \begin_layout Plain Layout
33507 Note herby that the setting
33510 \begin_inset Space ~
33517 Document\SpecialChar \menuseparator
33523 \begin_inset Space ~
33543 \begin_layout Standard
33544 Before the multi-column text the command
33547 \begin_layout Standard
33552 begin{multicols}{column number}
33555 \begin_layout Standard
33556 is written in TeX-mode.
33557 The column number is a number in the range of 2
33558 \begin_inset Space \thinspace{}
33562 \begin_inset Space \thinspace{}
33566 Before the formula the multi-column text is ended by inserting the command
33569 \begin_layout Standard
33577 \begin_layout Standard
33581 \begin_layout Standard
33582 Due to the command some space is automatically added before the formula.
33584 \begin_inset Space \thinspace{}
33587 mm vertical space is inserted before the formula.
33588 When the formula style
33594 \begin_layout Plain Layout
33596 \begin_inset CommandInset ref
33598 reference "sec:Formula-Styles"
33610 \begin_inset Space \thinspace{}
33613 mm space is inserted instead.
33616 \begin_layout Standard
33617 As example a multi-column text with a displayed formula:
33620 \begin_layout Standard
33624 \begin_layout Plain Layout
33628 begin{multicols}{2}
33633 Das Spektrum wird fouriertransformiert.
33634 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33635 , Lösungsmittel) zu trennen.
33636 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33637 nun das Aussehen des Ausgangssignals.
33638 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33639 über alle Phasen integrieren muss.
33641 \begin_inset Formula $S$
33644 unser normiertes Ausgangssignal and
33645 \begin_inset Formula $P$
33648 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33652 \begin_layout Plain Layout
33662 \begin_inset VSpace -6mm
33666 \begin_inset Formula \begin{equation}
33667 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33675 \begin_layout Plain Layout
33679 begin{multicols}{2}
33685 \begin_inset Formula $S_{0}$
33688 das Signal ohne Gradient ist and the Normierungsbedingung
33689 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33693 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33695 \begin_inset Formula $\nicefrac{\pi}{2}$
33699 \begin_inset Space \thinspace{}
33702 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33703 das Signal zusätzlich abschwächt.
33704 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33706 \begin_inset Formula $T_{2}$
33712 \begin_layout Standard
33716 \begin_layout Plain Layout
33728 \begin_layout Subsection
33729 Formulas with Description of Variables
33733 \begin_layout Plain Layout
33734 Formula ! with description of variables
33742 \begin_layout Standard
33743 To describe variables within a formula, like in formula
33744 \begin_inset CommandInset ref
33746 reference "eq:within"
33755 \begin_inset Formula $n$
33759 \begin_inset Space ~
33762 matrix is used with left aligned columns for the
33763 \begin_inset Formula $n$
33770 \begin_layout Plain Layout
33772 \begin_inset CommandInset ref
33774 reference "sec:Matrices"
33783 To set the description in a smaller size, before the matrix e.
33784 \begin_inset Space \thinspace{}
33788 \begin_inset Space ~
33801 \begin_layout Plain Layout
33803 \begin_inset CommandInset ref
33805 reference "sub:Font-Sizes"
33817 \begin_layout Standard
33818 When the formula style
33824 \begin_layout Plain Layout
33826 \begin_inset CommandInset ref
33828 reference "sec:Formula-Styles"
33849 \begin_layout Plain Layout
33856 only works in formulas with the style
33861 \begin_inset CommandInset ref
33863 reference "sub:Variable-Space"
33872 is inserted before and after the matrix to have the same separation of
33873 the matrix from the equation and the side margin.
33876 \begin_layout Standard
33877 When the formula style
33881 is used, the method described in
33882 \begin_inset CommandInset ref
33884 reference "sub:Flalign-Environment"
33888 is used to indent formulas.
33890 \begin_inset CommandInset ref
33892 reference "eq:within"
33896 consists of five columns whereas in the first two columns contain the equation,
33897 the third the matrix, and the last one an empty TeX-brace.
33898 \begin_inset Formula \begin{flalign}
33899 \hspace {30pt}F_{A} & =\rho·V·g & \footnotesize \begin{array}{ll}
33900 \rho & \textrm{density}\\
33901 V & \textrm{volume}\\
33902 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33909 \begin_layout Subsection
33910 Upright small Greek Letters
33911 \begin_inset CommandInset label
33913 name "sub:Upright-small-Greek"
33921 \begin_layout Plain Layout
33922 Greek letters ! upright
33930 \begin_layout Standard
33931 Most of the math fonts only provide italic small Greek letters.
33932 But for symbols of elementary particles like pions and neutrinos, upright
33933 Greek letters are needed.
33942 \begin_layout Plain Layout
33947 is part of the LaTeX-package
33955 \begin_layout Plain Layout
33960 \begin_layout Plain Layout
33983 \begin_layout Plain Layout
33989 that is loaded with the LaTeX-preamble line
33992 \begin_layout Standard
33997 usepackage{upgreek}
34000 \begin_layout Standard
34006 \begin_layout Plain Layout
34016 \begin_inset Note Note
34019 \begin_layout Plain Layout
34020 The following table will only be displayed when the LaTeX-package
34029 They are created when the command for a small Greek letters is started
34035 For example the command
34042 \begin_inset Formula $\uptau $
34048 \begin_layout Standard
34049 With these commands reactions of elementary particles can be typeset:
34050 \begin_inset Formula \[
34051 \uppi ^{+}\to\upmu ^{+}+\upnu _{\upmu }\]
34058 \begin_layout Standard
34059 The upright letters are more bold and wider than the italic ones.
34060 They should therefore not be used for units like
34061 \begin_inset Quotes eld
34065 \begin_inset Quotes erd
34071 \begin_layout Standard
34075 \begin_layout Plain Layout
34085 \begin_inset Note Note
34088 \begin_layout Plain Layout
34089 The following will be displayed when the LaTeX-package
34101 \begin_layout Standard
34102 You need to install the LaTeX-package
34106 to see the rest of this subsection in the output.
34109 \begin_layout Standard
34113 \begin_layout Plain Layout
34125 \begin_layout Subsection
34126 Text Characters in Formulas
34127 \begin_inset CommandInset label
34129 name "sub:Text-Characters-in"
34137 \begin_layout Plain Layout
34146 \begin_layout Standard
34147 In some cases you might want to insert text characters directly into formulas.
34148 When for example the centered dot · is often used in formulas like
34149 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34152 , one would have to insert the command
34162 \begin_layout Plain Layout
34164 \begin_inset CommandInset ref
34166 reference "sub:Binary-Operators"
34175 all the time, because this character is defined in all encodings as text
34177 But the encoding can be changed by this LaTeX-preamble line:
34180 \begin_layout Standard
34185 Declare Inputtext{183}{
34195 f\SpecialChar \textcompwordmark{}
34199 \begin_layout Standard
34200 The character encoding (menu
34202 Document\SpecialChar \menuseparator
34203 Settings\SpecialChar \menuseparator
34206 ) specifies what character appears when a keyboard key is pressed.
34207 When the key for the character '·' is pressed, internally the command
34214 But this command is not available in a formula so that you would get LaTeX-erro
34216 With the changed encoding the right command is chosen automatically, depending
34217 on if the character was inserted into a formula or not.
34220 \begin_layout Standard
34221 The encoding of several characters is saved in definition files.
34222 Fore example the encoding
34226 is defined in the file
34230 that is in the installation folder of LaTeX.
34231 Encodings should only be changed via the LaTeX-preamble and not in the
34233 Otherwise own documents could not be edited by other LyX users working
34234 on other computers.
34237 \begin_layout Standard
34238 \begin_inset VSpace medskip
34241 Besides the centered dot, in this document the degree sign ° is defined
34242 with the following LaTeX-preamble line so that it can directly be inserted
34246 \begin_layout Standard
34251 DeclareInputtext{176}{
34261 f\SpecialChar \textcompwordmark{}
34265 \begin_layout Standard
34266 \begin_inset Newpage newpage
34272 \begin_layout Section
34274 Typographic Advises
34278 \begin_layout Plain Layout
34279 Typographic Advises
34287 \begin_layout Standard
34288 This section is a summary of the most important typographic rules, listed
34293 \begin_layout Plain Layout
34294 This collection was partly taken from the German semi-official dictionary
34296 \begin_inset Quotes eld
34300 \begin_inset Quotes erd
34304 \begin_inset CommandInset citation
34310 that lists some of the ISO rules.
34318 \begin_layout Itemize
34327 \begin_layout Plain Layout
34328 done with font styles, see
34329 \begin_inset CommandInset ref
34331 reference "sub:Font-Styles"
34341 \begin_inset Space \thinspace{}
34345 \begin_inset Newline newline
34348 Between the value and the unit is the smallest space, see
34349 \begin_inset CommandInset ref
34351 reference "sub:Predefined-Space"
34358 \begin_layout Itemize
34359 Percent and perthousand signs are set like physical units:
34360 \begin_inset Newline newline
34364 \begin_inset Space \thinspace{}
34370 \begin_layout Itemize
34371 The degree sign follows directly on the value: 15°, but not when it is used
34373 \begin_inset Space \thinspace{}
34379 \begin_layout Itemize
34380 In numbers with more than four digits the smallest space is inserted before
34381 every third digit to group them:
34391 \begin_inset Space \thinspace{}
34395 \begin_inset Space \thinspace{}
34401 \begin_layout Itemize
34402 For dimensionings like 120×90×40
34403 \begin_inset Space \thinspace{}
34406 cm the multiplication sign
34407 \begin_inset Quotes eld
34411 \begin_inset Quotes erd
34415 It is available with the LaTeX-command
34421 , but can also directly be inserted with some keyboard definitions.
34424 \begin_layout Itemize
34425 Functions with names consisting of several letters are set upright to avoid
34427 \begin_inset CommandInset ref
34429 reference "sub:Predefined-Functions"
34436 \begin_layout Itemize
34437 Indices consisting of several letters, are set upright:
34438 \begin_inset Formula $E_{\mathrm{kin}}$
34442 \begin_inset Newline newline
34445 Components of matrices are set italic:
34446 \begin_inset Formula $\hat{H}_{kl}$
34452 \begin_layout Itemize
34453 The differentiation/integration operator 'd', the Euler's number 'e', and
34454 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34458 \begin_layout Standard
34459 \begin_inset Newpage newpage
34465 \begin_layout Section
34470 \begin_layout Plain Layout
34479 \begin_layout Standard
34480 Some characters and symbols can be created with several commands.
34481 Here is a list of the synonym commands:
34484 \begin_layout Standard
34485 \begin_inset VSpace bigskip
34489 \begin_inset Space \hfill{}
34493 \begin_inset Tabular
34494 <lyxtabular version="3" rows="12" columns="2">
34496 <column alignment="center" valignment="top" width="0pt">
34497 <column alignment="center" valignment="top" width="0pt">
34499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34502 \begin_layout Plain Layout
34508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34511 \begin_layout Plain Layout
34513 \begin_inset Note Note
34516 \begin_layout Plain Layout
34523 is only used as spacer.
34535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34538 \begin_layout Plain Layout
34546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34549 \begin_layout Plain Layout
34553 \begin_layout Plain Layout
34566 \begin_layout Plain Layout
34580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34583 \begin_layout Plain Layout
34591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34594 \begin_layout Plain Layout
34604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34607 \begin_layout Plain Layout
34615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34618 \begin_layout Plain Layout
34628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34631 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34642 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34653 \begin_layout Plain Layout
34661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34664 \begin_layout Plain Layout
34672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34675 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34686 \begin_layout Plain Layout
34696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34699 \begin_layout Plain Layout
34707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34710 \begin_layout Plain Layout
34720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34723 \begin_layout Plain Layout
34731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34734 \begin_layout Plain Layout
34744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34747 \begin_layout Plain Layout
34755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34758 \begin_layout Plain Layout
34768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34771 \begin_layout Plain Layout
34779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34782 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34793 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34804 \begin_layout Plain Layout
34816 \begin_inset Space \hfill{}
34820 \begin_inset Tabular
34821 <lyxtabular version="3" rows="12" columns="2">
34823 <column alignment="center" valignment="top" width="0pt">
34824 <column alignment="center" valignment="top" width="0pt">
34826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34829 \begin_layout Plain Layout
34835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34838 \begin_layout Plain Layout
34846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34849 \begin_layout Plain Layout
34857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34860 \begin_layout Plain Layout
34872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34875 \begin_layout Plain Layout
34883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34886 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34910 \begin_layout Plain Layout
34920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34923 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34934 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34945 \begin_layout Plain Layout
34953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34956 \begin_layout Plain Layout
34964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34967 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34978 \begin_layout Plain Layout
34988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34991 \begin_layout Plain Layout
34999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35002 \begin_layout Plain Layout
35012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35015 \begin_layout Plain Layout
35023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35026 \begin_layout Plain Layout
35036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35039 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35050 \begin_layout Plain Layout
35060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35063 \begin_layout Plain Layout
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35074 \begin_layout Plain Layout
35084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35087 \begin_layout Plain Layout
35095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35098 \begin_layout Plain Layout
35112 \begin_inset Space \hfill{}
35118 \begin_layout Standard
35119 \begin_inset Newpage newpage
35125 \begin_layout Bibliography
35126 \begin_inset CommandInset bibitem
35127 LatexCommand bibitem
35139 The LaTeX Companion
35142 Addison Wesley, 2004
35145 \begin_layout Bibliography
35146 \begin_inset CommandInset bibitem
35147 LatexCommand bibitem
35153 \begin_inset CommandInset href
35156 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35160 of LaTeX's math abilities
35163 \begin_layout Bibliography
35164 \begin_inset CommandInset bibitem
35165 LatexCommand bibitem
35170 LaTeX tips and tricks-
35171 \begin_inset CommandInset href
35174 target "http://tug.org/TeXnik/"
35181 \begin_layout Bibliography
35182 \begin_inset CommandInset bibitem
35183 LatexCommand bibitem
35189 \begin_inset CommandInset href
35192 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35200 \begin_layout Plain Layout
35212 \begin_layout Bibliography
35213 \begin_inset CommandInset bibitem
35214 LatexCommand bibitem
35220 \begin_inset CommandInset href
35223 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35227 of all symbols available with LaTeX-packages
35230 \begin_layout Bibliography
35231 \begin_inset CommandInset bibitem
35232 LatexCommand bibitem
35238 \begin_inset CommandInset href
35240 name "Documentation"
35241 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35245 of the LaTeX-package
35253 \begin_layout Plain Layout
35254 Packages ! hyperref
35262 \begin_layout Bibliography
35263 \begin_inset CommandInset bibitem
35264 LatexCommand bibitem
35270 \begin_inset CommandInset href
35273 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35284 \begin_inset CommandInset ref
35286 reference "sub:Operator-Limits"
35294 \begin_layout Plain Layout
35305 \begin_layout Bibliography
35306 \begin_inset CommandInset bibitem
35307 LatexCommand bibitem
35318 Auflage, Duden 2001
35321 \begin_layout Subsubsection*
35322 \begin_inset CommandInset index_print
35323 LatexCommand printindex