1 #LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
44 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
47 \settowidth{\abc}{\space}
48 \renewcommand{\equationautorefname}{\hspace{-\abc}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
76 \usepackage[samesize]{cancel}
78 % enables calculation of values,
81 % for multiple table row and column cells
91 % center multirows (e.g. in sec. 13.3)
92 \renewcommand{\multirowsetup}{\centering}
94 % define a color, used in sec.9.3
95 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
97 % declare operators (see sec. 10.4 and sec. 15.2)
98 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
99 \DeclareMathOperator{\sgn}{sgn}
101 \newcommand{\spce}{\textvisiblespace}
103 % example definitions for sec. 20.1
104 \newcommand{\gr}{\Longrightarrow}
105 \newcommand{\us}[1]{\underline{#1}}
106 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
107 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
108 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
110 % example macro from sec. 19.4
111 %\def\tagform@#1{\maketag@@@{|#1|}}
113 % macro from sec. 10.2
114 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
115 \def\mathclap {\mathpalette \mathclapinternal}
116 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
118 % redefine the greyed out note
119 \renewenvironment{lyxgreyedout}
120 {\textcolor{blue}\bgroup}{\egroup}
122 % ------------------------------------
123 % used to check for needed LaTeX packages
126 % check for package eurosym
127 % used for the Euro symbol
129 \IfFileExists{eurosym.sty}
130 {\usepackage[gennarrow]{eurosym}
131 \setboolean{eurosym}{true}}
132 {\setboolean{eurosym}{false}}
134 % needed in sec. 22.4
135 % check for package braket
137 \IfFileExists{braket.sty}
139 \setboolean{braket}{true}}
140 {\setboolean{braket}{false}}
142 % needed in sec. 22.10
143 % check for package upgreek
145 \IfFileExists{upgreek.sty}
146 {\usepackage{upgreek}
147 \setboolean{upgreek}{true}}
148 {\setboolean{upgreek}{false}}
150 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
155 \font_typewriter default
156 \font_default_family default
166 \pdf_title "LyX's Math Manual"
167 \pdf_author "LyX Team, Uwe Stöhr"
168 \pdf_subject "LyX-documentation about math"
169 \pdf_keywords "LyX, Mathed"
171 \pdf_bookmarksnumbered true
172 \pdf_bookmarksopen true
173 \pdf_bookmarksopenlevel 1
174 \pdf_breaklinks false
178 \pdf_pagebackref false
179 \pdf_pdfusetitle false
180 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
187 \paperorientation portrait
190 \paragraph_separation skip
192 \quotes_language english
195 \paperpagestyle plain
199 \tracking_changes false
200 \output_changes false
208 LyX's detailed Math manual
216 \begin_layout Plain Layout
218 If you have comments or error corrections, please send them to the LyX Documenta
222 \begin_inset CommandInset href
224 name "lyx-docs@lists.lyx.org"
225 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
236 \begin_inset Note Note
239 \begin_layout Plain Layout
246 \begin_inset Newline newline
250 \begin_inset Newline newline
258 \begin_layout Standard
259 \begin_inset CommandInset toc
260 LatexCommand tableofcontents
267 \begin_layout Standard
268 \begin_inset Note Note
271 \begin_layout Plain Layout
272 To export this document to PDF, PS, or DVI the LaTeX-packages
285 If they are not installed you can export the document anyway but the sections
286 where the packages are required won't appear in the output.
289 \begin_layout Plain Layout
290 The latest PDF-version of this document can be found here:
291 \begin_inset Newline newline
296 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
304 \begin_layout Standard
305 \begin_inset Newpage newpage
311 \begin_layout Section
313 \begin_inset CommandInset label
315 name "sec:Introduction"
322 \begin_layout Standard
323 This document explains LyX's math features and is furthermore a collection
324 of LaTeX-commands used for mathematical characters and constructs.
325 The explanations are designed for the usage of commands.
326 It is therefore required that you have read the section
337 \begin_layout Standard
338 Most of the characters and many constructs explained in this manual are
339 also accessible via the menu
343 \SpecialChar \menuseparator
359 But everybody who has to write lots of formulas will notice that it is
360 much faster to use commands instead of the math toolbar.
361 Therefore this manual is focused on commands but also mentions the correspondin
362 g toolbar buttons when available.
365 \begin_layout Standard
366 If not specially mentioned the commands are only available within formulas.
367 To be able to use all commands explained in this document, the option
371 must be used in the document settings (menu
373 Document\SpecialChar \menuseparator
374 Settings\SpecialChar \menuseparator
385 \begin_layout Plain Layout
388 Use AMS math package automatically
394 \begin_layout Plain Layout
403 -math when math constructs are found that are supported by LyX.
411 \begin_layout Standard
412 This document doesn't list all
416 \begin_layout Plain Layout
429 \begin_layout Plain Layout
434 \begin_layout Plain Layout
443 -math commands is in the file
446 \begin_inset CommandInset href
449 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
455 , which is part of every LaTeX standard installation.
460 for lucidity reasons.
463 \begin_layout Section
465 \begin_inset CommandInset label
467 name "sec:General-Instructions"
474 \begin_layout Standard
475 To create an inline formula
479 \begin_layout Plain Layout
485 that is embedded into a text line, press
489 or the toolbar button
490 \begin_inset Graphics
491 filename ../images/math-mode.png
497 \begin_inset Newline newline
500 To create a display style formula
504 \begin_layout Plain Layout
505 Formula ! display style
510 that will appear bigger and in an own paragraph, press
517 \begin_layout Standard
518 To change a display style formula to an inline formula, set the cursor into
519 the formula and press
525 Edit\SpecialChar \menuseparator
526 Math\SpecialChar \menuseparator
530 The same way is used to change an inline formula to a display style formula.
533 \begin_layout Standard
534 To display parts of an inline formula in the size of a display style formula,
543 \begin_layout Plain Layout
554 Then a new blue box appears in which the desired formula part is inserted.
557 \begin_layout Standard
558 Only inline formulas are allowed inside tables.
561 \begin_layout Standard
566 can be turned on in the menu
568 View\SpecialChar \menuseparator
572 When you click there on
573 \begin_inset Quotes eld
577 \begin_inset Quotes erd
580 the toolbar will be shown permanently at the bottom; this state is visualized
585 menu with a checkmark.
586 When you click in this state again on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
602 is only shown when the cursor is within a formula; this state is visualized
603 by the renaming of the menu entry from
604 \begin_inset Quotes eld
608 \begin_inset Quotes erd
612 \begin_inset Quotes eld
620 \begin_inset Quotes erd
626 \begin_layout Standard
631 \begin_layout Plain Layout
637 is invoked by pressing the toolbar button
638 \begin_inset Graphics
639 filename ../images/ert-insert.png
646 Insert\SpecialChar \menuseparator
651 \begin_layout Plain Layout
665 \begin_inset Note Note
668 \begin_layout Plain Layout
669 In LyX there are three
670 \begin_inset Quotes eld
674 \begin_inset Quotes erd
677 that appear in the output with sub- and superscript letters: TeX, LaTeX,
681 \begin_layout Plain Layout
682 To avoid that these names are recognized as proper names, a TeX-brace pair
691 \begin_layout Standard
692 To change the LaTeX-preamble
696 \begin_layout Plain Layout
704 Document\SpecialChar \menuseparator
705 Settings\SpecialChar \menuseparator
710 \begin_layout Plain Layout
726 \begin_layout Standard
727 To edit matrices, case differentiations, and multiline formulas subsequently,
730 Edit\SpecialChar \menuseparator
735 Edit\SpecialChar \menuseparator
737 \begin_inset space \thinspace{}
741 \begin_inset space \thinspace{}
751 When lines and columns are swapped via the menu, the column or line where
752 the cursor is in is exchanged with the column to the right or the line
754 Is the cursor in the last column or row, the exchange is done with the
755 column to the left or the line above.
758 \begin_layout Standard
759 To write text in formulas
763 \begin_layout Plain Layout
764 For multiline formulas the command
771 \begin_inset CommandInset ref
773 reference "sub:Text-in-multiline"
790 \begin_layout Plain Layout
800 \begin_layout Plain Layout
807 This mode is invoked with the the shortcut
815 or by the insertion of the command
823 \begin_layout Plain Layout
834 The text appears black in LyX and can therefore be distinguished from the
835 other formula parts that appear blue.
836 In the output mathematical text is set upright, in contrary to other formula
840 \begin_layout Subsection*
844 \begin_layout Standard
845 Most of the LaTeX-commands for math constructs have the following scheme:
848 \begin_layout Standard
864 \begin_layout Standard
865 A command starts always with a backslash
866 \begin_inset Quotes gld
876 \begin_inset Quotes grd
880 To omit optional arguments, also omit the associated brackets.
881 The braces around the required arguments are named in this document as
886 \begin_layout Plain Layout
893 If you add in a formula a left brace to a command name, LyX creates automatical
895 In all other cases TeX-braces are created in formulas with the command
903 TeX-braces appear red in LyX, in contrary to normal braces that appear
905 In TeX-mode no command is needed to get TeX-braces.
906 TeX-braces don't appear in the output.
909 \begin_layout Standard
910 When commands without arguments, like commands for symbols are entered in
911 TeX-mode, a space character must
915 be behind the command to end it.
916 This space doesn't appear in the output.
917 When the space should appear in the output, the space must be followed
918 by a protected space in normal text.
921 \begin_layout Standard
922 A protected space is inserted with
929 \begin_layout Subsection*
930 \begin_inset Newpage newpage
936 \begin_layout Itemize
941 \begin_layout Plain Layout
942 This visible space character can be created with the command
952 \begin_layout Plain Layout
960 , inserted in TeX-mode.
969 \begin_layout Plain Layout
982 denotes a space character to be input.
985 \begin_layout Itemize
987 \begin_inset Formula $\to$
990 denotes the usage of the corresponding arrow key on the keyboard.
993 \begin_layout Subsection*
997 \begin_layout Standard
999 \begin_inset Float table
1005 \begin_layout Plain Layout
1007 \begin_inset Caption
1009 \begin_layout Plain Layout
1010 \begin_inset CommandInset label
1012 name "tab:Used-units"
1024 \begin_layout Plain Layout
1026 \begin_inset Tabular
1027 <lyxtabular version="3" rows="13" columns="2">
1029 <column alignment="center" valignment="top" width="0">
1030 <column alignment="center" valignment="top" width="0">
1032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1035 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1044 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1055 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1064 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1075 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1084 \begin_layout Plain Layout
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1095 \begin_layout Plain Layout
1101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1104 \begin_layout Plain Layout
1106 \begin_inset space \thinspace{}
1110 \begin_inset space \thinspace{}
1120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1123 \begin_layout Plain Layout
1129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1132 \begin_layout Plain Layout
1134 \begin_inset space \thinspace{}
1138 \begin_inset space \thinspace{}
1148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1151 \begin_layout Plain Layout
1157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1160 \begin_layout Plain Layout
1162 \begin_inset space \thinspace{}
1166 \begin_inset space \thinspace{}
1176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1179 \begin_layout Plain Layout
1185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1188 \begin_layout Plain Layout
1190 \begin_inset space \thinspace{}
1194 \begin_inset space \thinspace{}
1204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1207 \begin_layout Plain Layout
1213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1216 \begin_layout Plain Layout
1218 \begin_inset space \thinspace{}
1222 \begin_inset space \thinspace{}
1232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1235 \begin_layout Plain Layout
1241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1244 \begin_layout Plain Layout
1246 \begin_inset space \thinspace{}
1250 \begin_inset Formula $\approx$
1254 \begin_inset space \thinspace{}
1264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1267 \begin_layout Plain Layout
1273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1276 \begin_layout Plain Layout
1278 \begin_inset space \thinspace{}
1282 \begin_inset space \thinspace{}
1292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1308 \begin_inset Quotes eld
1314 \begin_inset Quotes erd
1324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset Quotes eld
1346 \begin_inset Quotes erd
1356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1359 \begin_layout Plain Layout
1365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1368 \begin_layout Plain Layout
1370 \begin_inset space \thinspace{}
1374 \begin_inset Formula $\nicefrac{1}{18}$
1378 \begin_inset space \thinspace{}
1399 \begin_layout Standard
1400 \begin_inset Newpage newpage
1406 \begin_layout Section
1410 \begin_layout Subsection
1415 \begin_layout Plain Layout
1425 \begin_layout Plain Layout
1435 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1467 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1483 \begin_layout Plain Layout
1498 \begin_layout Standard
1499 Indices are created with an underscore
1500 \begin_inset Quotes eld
1504 \begin_inset Quotes erd
1507 or via the math toolbar button
1508 \begin_inset Graphics
1509 filename ../images/math-subscript.png
1514 , exponents with a caret
1515 \begin_inset Quotes eld
1519 \begin_inset Quotes erd
1522 or via the math toolbar button
1523 \begin_inset Graphics
1524 filename ../images/math-superscript.png
1532 \begin_layout Standard
1534 \begin_inset Tabular
1535 <lyxtabular version="3" rows="4" columns="2">
1537 <column alignment="center" valignment="top" width="0pt">
1538 <column alignment="center" valignment="top" width="0pt">
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1543 \begin_layout Plain Layout
1549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1552 \begin_layout Plain Layout
1554 \begin_inset Note Note
1557 \begin_layout Plain Layout
1564 is only used as spacer.
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1579 \begin_layout Plain Layout
1585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1588 \begin_layout Plain Layout
1589 \begin_inset Formula $B_{V}$
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1602 \begin_layout Plain Layout
1608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1611 \begin_layout Plain Layout
1612 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1625 \begin_layout Plain Layout
1630 \begin_layout Plain Layout
1644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1647 \begin_layout Plain Layout
1648 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1664 \begin_layout Standard
1665 As the caret is in some languages an accent, vowels will be accentuated
1666 in this case and not set as exponents
1670 \begin_layout Plain Layout
1671 Depending on the used keyboard settings this can also happen for other character
1678 To get in this case exponents, press
1682 after the caret as in the last example.
1685 \begin_layout Subsection
1687 \begin_inset CommandInset label
1689 name "sub:Fractions"
1697 \begin_layout Plain Layout
1706 \begin_layout Standard
1707 Fractions are generated with the command
1717 \begin_layout Plain Layout
1725 or via the math toolbar button
1726 \begin_inset Graphics
1727 filename ../images/math/frac.png
1733 The font size is adjusted automatically, depending on whether the fraction
1734 is in an inline or display style formula.
1735 With the math toolbar button
1736 \begin_inset Graphics
1737 filename ../images/math/frac-square.png
1742 you can select different fraction types.
1745 \begin_layout Standard
1754 \begin_layout Plain Layout
1764 a fraction can be created that has in any case the size of a display style
1774 \begin_layout Plain Layout
1784 the fraction appears always with the size of an inline formula.
1788 \begin_layout Standard
1789 A line with the fraction
1790 \begin_inset Formula $\frac{1}{2}$
1793 that was created with the command
1802 \begin_layout Standard
1803 A line with the fraction
1804 \begin_inset Formula $\dfrac{1}{2}$
1807 that was created with the command
1816 \begin_layout Standard
1818 \begin_inset Tabular
1819 <lyxtabular version="3" rows="4" columns="2">
1821 <column alignment="center" valignment="top" width="0pt">
1822 <column alignment="center" valignment="top" width="0pt">
1824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1827 \begin_layout Plain Layout
1833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1836 \begin_layout Plain Layout
1838 \begin_inset Note Note
1841 \begin_layout Plain Layout
1848 is only used as spacer.
1860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1863 \begin_layout Plain Layout
1870 \begin_layout Plain Layout
1880 \begin_inset Formula $\downarrow$
1888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1891 \begin_layout Plain Layout
1892 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1905 \begin_layout Plain Layout
1912 \begin_layout Plain Layout
1922 \begin_inset Formula $\downarrow$
1930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1933 \begin_layout Plain Layout
1934 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1947 \begin_layout Plain Layout
1954 \begin_layout Plain Layout
1967 \begin_layout Plain Layout
1982 \begin_layout Plain Layout
1992 \begin_inset Formula $\downarrow$
1996 \begin_inset Formula $\downarrow\downarrow$
2004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2007 \begin_layout Plain Layout
2008 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2024 \begin_layout Standard
2025 \begin_inset VSpace bigskip
2029 \begin_inset Newpage newpage
2032 For nested fractions the command
2042 \begin_layout Plain Layout
2052 \begin_inset VSpace -3mm
2058 \begin_layout Standard
2059 \begin_inset Formula \begin{align*}
2060 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2061 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2068 \begin_layout Standard
2069 The command for the example above is:
2072 \begin_layout Standard
2078 \begin_inset Formula $\to$
2088 \begin_inset Formula $\to$
2094 \begin_inset Formula $\to\to$
2102 \begin_layout Standard
2103 \begin_inset VSpace medskip
2109 \begin_layout Standard
2116 sets the fraction always in the size of a displayed formula, also when
2117 it is part of another fraction.
2124 has the following command scheme:
2127 \begin_layout Standard
2132 cfrac[numerator position]{numerator}{denominator}
2135 \begin_layout Standard
2136 The numerator position can be
2149 l or r aligns the numerator to the left or right, resp.
2150 \begin_inset space ~
2153 with the fraction stroke.
2158 or no position is given, the numerator appears centered.
2159 These fractions demonstrate the different alignments:
2160 \begin_inset Newline newline
2166 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2170 \begin_inset Formula $\cfrac{A}{B+C}$
2174 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2180 \begin_layout Standard
2181 \begin_inset VSpace medskip
2184 It is often advantageous to combine
2197 \begin_inset Formula \[
2198 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2205 \begin_layout Standard
2206 For inline fractions with a sloped fraction stroke you can use the command
2215 \begin_layout Plain Layout
2226 \begin_inset Formula $\nicefrac{5}{31}$
2232 \begin_layout Standard
2233 How to define own fractions where the fraction stroke can be changed, is
2235 \begin_inset CommandInset ref
2237 reference "sub:Self-defined-Fractions"
2244 \begin_layout Subsection
2249 \begin_layout Plain Layout
2258 \begin_layout Standard
2259 Square roots are created with
2269 \begin_layout Plain Layout
2277 or the math toolbar button
2278 \begin_inset Graphics
2279 filename ../images/math/sqrt.png
2284 , all other roots with the command
2294 \begin_layout Plain Layout
2302 or with the math toolbar button
2303 \begin_inset Graphics
2304 filename ../images/math/root.png
2312 \begin_layout Standard
2314 \begin_inset Tabular
2315 <lyxtabular version="3" rows="3" columns="2">
2317 <column alignment="center" valignment="top" width="0pt">
2318 <column alignment="center" valignment="top" width="0pt">
2320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2323 \begin_layout Plain Layout
2329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2332 \begin_layout Plain Layout
2334 \begin_inset Note Note
2337 \begin_layout Plain Layout
2344 is only used as spacer.
2356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2359 \begin_layout Plain Layout
2366 \begin_layout Plain Layout
2380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2383 \begin_layout Plain Layout
2384 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2397 \begin_layout Plain Layout
2404 \begin_layout Plain Layout
2414 \begin_inset Formula $\downarrow$
2422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2425 \begin_layout Plain Layout
2426 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2442 \begin_layout Standard
2443 A square root can also be created with
2449 when the root index field is left empty.
2452 \begin_layout Standard
2453 With certain indices the distance to the root is too small, like in this
2455 \begin_inset Formula $\sqrt[\beta]{B}$
2459 \begin_inset Newline newline
2463 \begin_inset Formula $\beta$
2467 To avoid this, the commands
2477 \begin_layout Plain Layout
2495 \begin_layout Plain Layout
2503 are used with the following scheme:
2506 \begin_layout Standard
2520 \begin_layout Standard
2521 Distance is the number of Big Points (unit bp;
2522 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2525 ), that the index should be moved to the left or top, resp..
2526 The commands are written to the index.
2527 This way the command
2528 \begin_inset Newline newline
2538 \begin_inset Formula $\to$
2544 \begin_inset Formula $\to$
2553 \begin_layout Plain Layout
2563 \begin_inset Formula $\to$
2567 \begin_inset Newline newline
2572 produces a correct typeset formula:
2573 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2579 \begin_layout Subsection
2580 Binomial coefficients
2584 \begin_layout Plain Layout
2585 Binomial coefficient s
2593 \begin_layout Standard
2594 Binomial coefficients are inserted with the command
2604 \begin_layout Plain Layout
2612 or with the submenu of the math toolbar button
2613 \begin_inset Graphics
2614 filename ../images/math/frac-square.png
2620 Analog to fractions (
2640 \begin_layout Plain Layout
2660 \begin_layout Plain Layout
2669 For other brackets around binomial coeficients there are the commands
2679 \begin_layout Plain Layout
2697 \begin_layout Plain Layout
2708 \begin_layout Standard
2710 \begin_inset Tabular
2711 <lyxtabular version="3" rows="6" columns="2">
2713 <column alignment="center" valignment="top" width="0pt">
2714 <column alignment="center" valignment="top" width="0pt">
2716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2719 \begin_layout Plain Layout
2725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2728 \begin_layout Plain Layout
2730 \begin_inset Note Note
2733 \begin_layout Plain Layout
2740 is only used as spacer.
2752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2755 \begin_layout Plain Layout
2762 \begin_layout Plain Layout
2772 \begin_inset Formula $\downarrow$
2780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2783 \begin_layout Plain Layout
2784 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2797 \begin_layout Plain Layout
2804 \begin_layout Plain Layout
2814 \begin_inset Formula $\downarrow$
2822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2825 \begin_layout Plain Layout
2826 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2839 \begin_layout Plain Layout
2846 \begin_layout Plain Layout
2856 \begin_inset Formula $\downarrow$
2864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2867 \begin_layout Plain Layout
2868 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2881 \begin_layout Plain Layout
2888 \begin_layout Plain Layout
2898 \begin_inset Formula $\downarrow$
2906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2909 \begin_layout Plain Layout
2910 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2923 \begin_layout Plain Layout
2930 \begin_layout Plain Layout
2940 \begin_inset Formula $\downarrow$
2948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2951 \begin_layout Plain Layout
2952 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2968 \begin_layout Subsection
2969 Case differentiations
2973 \begin_layout Plain Layout
2974 Case differentiations
2982 \begin_layout Standard
2984 \begin_inset Tabular
2985 <lyxtabular version="3" rows="3" columns="2">
2987 <column alignment="center" valignment="top" width="0pt">
2988 <column alignment="center" valignment="top" width="0pt">
2990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2993 \begin_layout Plain Layout
2999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3002 \begin_layout Plain Layout
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3020 \begin_layout Plain Layout
3030 \begin_inset Formula $\to$
3037 \begin_layout Plain Layout
3050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3053 \begin_layout Plain Layout
3054 \begin_inset Formula $\begin{cases}
3065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3068 \begin_layout Plain Layout
3075 \begin_layout Plain Layout
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3092 \begin_layout Plain Layout
3093 \begin_inset Formula $\begin{cases}
3094 A & \textrm{for }x>0\\
3095 B & \textrm{for }x=0\end{cases}$
3111 \begin_layout Standard
3118 or the usage of the math toolbar button
3119 \begin_inset Graphics
3120 filename ../images/math/cases.png
3125 you can create new lines with the shortcut
3129 or the table toolbar button
3130 \begin_inset Graphics
3131 filename ../images/tabular-feature_append-row.png
3139 \begin_layout Standard
3146 is also available via the menu
3148 Insert\SpecialChar \menuseparator
3149 Math\SpecialChar \menuseparator
3155 \begin_layout Subsection
3160 \begin_layout Plain Layout
3169 \begin_layout Standard
3180 \begin_layout Plain Layout
3188 every character can be displayed canceled.
3189 The characters are quasi accentuated by a slash.
3192 \begin_layout Standard
3194 \begin_inset Tabular
3195 <lyxtabular version="3" rows="4" columns="2">
3197 <column alignment="center" valignment="top" width="0pt">
3198 <column alignment="center" valignment="top" width="0pt">
3200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3203 \begin_layout Plain Layout
3209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3212 \begin_layout Plain Layout
3220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3223 \begin_layout Plain Layout
3231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3234 \begin_layout Plain Layout
3235 \begin_inset Formula $\not=$
3245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3248 \begin_layout Plain Layout
3258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3261 \begin_layout Plain Layout
3262 \begin_inset Formula $\not\le$
3272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3275 \begin_layout Plain Layout
3285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3288 \begin_layout Plain Layout
3289 \begin_inset Formula $\not\parallel$
3305 \begin_layout Standard
3306 The last example shows, that not all negations look good.
3307 Therefore there are for some negations special commands (see
3308 \begin_inset CommandInset ref
3310 reference "sub:Mathematical-Symbols"
3315 \begin_inset CommandInset ref
3317 reference "sec:Relations"
3324 \begin_layout Subsection
3326 \begin_inset CommandInset label
3328 name "sub:Placeholders"
3336 \begin_layout Plain Layout
3346 \begin_layout Plain Layout
3347 Chemical characters ! Isotopes
3356 \begin_layout Plain Layout
3361 \begin_layout Plain Layout
3372 \begin_layout Plain Layout
3387 \begin_layout Standard
3389 \begin_inset space \thinspace{}
3393 \begin_inset space ~
3400 \begin_layout Plain Layout
3401 More about chemical symbols is written in
3402 \begin_inset CommandInset ref
3404 reference "sub:Chemical-Symbols-and"
3413 the following problem occurs:
3416 \begin_layout Standard
3418 \begin_inset Tabular
3419 <lyxtabular version="3" rows="2" columns="2">
3421 <column alignment="center" valignment="top" width="0pt">
3422 <column alignment="center" valignment="top" width="0pt">
3424 <cell alignment="center" valignment="top" usebox="none">
3427 \begin_layout Plain Layout
3428 Indices created with sub- and superscripts:
3433 <cell alignment="center" valignment="top" usebox="none">
3436 \begin_layout Plain Layout
3437 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3447 <cell alignment="center" valignment="top" usebox="none">
3450 \begin_layout Plain Layout
3456 <cell alignment="center" valignment="top" usebox="none">
3459 \begin_layout Plain Layout
3460 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3474 \begin_inset Note Note
3477 \begin_layout Plain Layout
3484 is only used as spacer.
3492 \begin_layout Standard
3493 The shorter index is by default placed below or above the first character
3494 of the longer index.
3495 To avoid this there is the command
3505 \begin_layout Plain Layout
3513 or the math toolbar button
3514 \begin_inset space \thinspace{}
3521 \begin_layout Plain Layout
3522 can be found in the submenu of the toolbar button
3523 \begin_inset Graphics
3524 filename ../images/math/space.png
3535 \begin_inset Graphics
3536 filename ../images/math/phantom.png
3541 that creates one or more phantom characters.
3548 a small blue box appears that is superposed with two red arrows.
3549 The arrows indicate that the complete width and height of the box content
3550 will be created as placeholder.
3551 Phantom characters are accordingly placeholders with the size of the characters.
3554 \begin_layout Standard
3556 \begin_inset Tabular
3557 <lyxtabular version="3" rows="4" columns="2">
3559 <column alignment="center" valignment="top" width="0">
3560 <column alignment="center" valignment="top" width="0">
3562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3565 \begin_layout Plain Layout
3571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3574 \begin_layout Plain Layout
3576 \begin_inset Note Note
3579 \begin_layout Plain Layout
3586 is only used as spacer.
3598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3601 \begin_layout Plain Layout
3606 \begin_layout Plain Layout
3621 \begin_layout Plain Layout
3631 \begin_inset Formula $\to$
3638 \begin_layout Plain Layout
3652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3655 \begin_layout Plain Layout
3656 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3669 \begin_layout Plain Layout
3674 \begin_layout Plain Layout
3689 \begin_layout Plain Layout
3699 \begin_inset Formula $\to$
3706 \begin_layout Plain Layout
3720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3723 \begin_layout Plain Layout
3724 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3737 \begin_layout Plain Layout
3744 \begin_layout Plain Layout
3759 \begin_layout Plain Layout
3769 \begin_inset Formula $\to$
3776 \begin_layout Plain Layout
3790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3793 \begin_layout Plain Layout
3794 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3810 \begin_layout Standard
3811 Furthermore there are the commands
3821 \begin_layout Plain Layout
3830 \begin_inset space ~
3834 \begin_inset Graphics
3835 filename ../images/math/vphantom.png
3850 \begin_layout Plain Layout
3859 \begin_inset space ~
3863 \begin_inset Graphics
3864 filename ../images/math/hphantom.png
3876 creates only space for the maximal height of the characters in the box
3877 but not for its width.
3884 creates only space for the width of the box content.
3885 Therefore the boxes of both commands have only one red arrow.
3888 \begin_layout Standard
3899 \begin_layout Plain Layout
3914 space for the height of the integral sign,
3918 \begin_layout Plain Layout
3925 creates an integral sign, see
3926 \begin_inset CommandInset ref
3928 reference "sub:Big-Operators"
3937 because this is the larger character.
3938 An example application is in
3939 \begin_inset CommandInset ref
3941 reference "sub:Multiline-Brackets"
3948 \begin_layout Subsection
3953 \begin_layout Plain Layout
3963 \begin_layout Plain Layout
3964 Formula ! underlined
3972 \begin_layout Standard
3974 \begin_inset Tabular
3975 <lyxtabular version="3" rows="4" columns="2">
3977 <column alignment="center" valignment="top" width="0pt">
3978 <column alignment="center" valignment="top" width="0pt">
3980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3983 \begin_layout Plain Layout
3989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3992 \begin_layout Plain Layout
3994 \begin_inset Note Note
3997 \begin_layout Plain Layout
4004 is only used as spacer.
4016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4019 \begin_layout Plain Layout
4026 \begin_layout Plain Layout
4039 \begin_layout Plain Layout
4052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4055 \begin_layout Plain Layout
4056 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4069 \begin_layout Plain Layout
4076 \begin_layout Plain Layout
4089 \begin_layout Plain Layout
4102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4105 \begin_layout Plain Layout
4106 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4119 \begin_layout Plain Layout
4126 \begin_layout Plain Layout
4141 \begin_layout Plain Layout
4155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4158 \begin_layout Plain Layout
4159 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4175 \begin_layout Standard
4176 In the last example it doesn't matter if first
4191 \begin_layout Standard
4192 To double underline e.
4193 \begin_inset space \thinspace{}
4206 \begin_layout Standard
4207 It is possible to place up to 6 lines above or below characters.
4210 \begin_layout Subsection
4215 \begin_layout Plain Layout
4224 \begin_layout Standard
4225 There are different types of ellipses available.
4229 \begin_layout Plain Layout
4230 In the math toolbar in the submenu of the button
4231 \begin_inset Graphics
4232 filename ../images/math/ldots.png
4242 For listings dots at the baseline are used (
4252 \begin_layout Plain Layout
4260 ), while for operations dots are needed that are on the same height as the
4271 \begin_layout Plain Layout
4280 When using the command
4290 \begin_layout Plain Layout
4298 , LaTeX decides on the basis of the next character what type is used.
4301 \begin_layout Standard
4303 \begin_inset Tabular
4304 <lyxtabular version="3" rows="8" columns="2">
4306 <column alignment="center" valignment="top" width="0pt">
4307 <column alignment="center" valignment="top" width="0pt">
4309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4312 \begin_layout Plain Layout
4318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4321 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4332 \begin_layout Plain Layout
4337 \begin_layout Plain Layout
4352 \begin_layout Plain Layout
4366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4369 \begin_layout Plain Layout
4370 \begin_inset Formula $A_{1},\dots,A_{n}$
4380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4383 \begin_layout Plain Layout
4388 \begin_layout Plain Layout
4403 \begin_layout Plain Layout
4417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4420 \begin_layout Plain Layout
4421 \begin_inset Formula $A_{1}+\dots+A_{n}$
4431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4434 \begin_layout Plain Layout
4439 \begin_layout Plain Layout
4454 \begin_layout Plain Layout
4468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4471 \begin_layout Plain Layout
4472 \begin_inset Formula $A_{1},\ldots,A_{n}$
4482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4485 \begin_layout Plain Layout
4490 \begin_layout Plain Layout
4505 \begin_layout Plain Layout
4519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4522 \begin_layout Plain Layout
4523 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4536 \begin_layout Plain Layout
4544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4547 \begin_layout Plain Layout
4548 \begin_inset Formula $\vdots$
4558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4561 \begin_layout Plain Layout
4569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4572 \begin_layout Plain Layout
4573 \begin_inset Formula $\ddots$
4583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4586 \begin_layout Plain Layout
4588 \begin_inset space \thinspace{}
4591 matrix with the different dots
4596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4599 \begin_layout Plain Layout
4600 \begin_inset Formula $\begin{array}{ccc}
4601 A_{11} & \cdots & A_{1m}\\
4602 \vdots & \ddots & \vdots\\
4603 A_{n1} & \cdots & A_{nm}\end{array}$
4619 \begin_layout Standard
4620 The ellipses available in menu
4622 Insert\SpecialChar \menuseparator
4624 \begin_inset space ~
4638 \begin_layout Standard
4639 \begin_inset VSpace medskip
4642 Specially for matrices there are ellipses that span over several columns.
4643 They are created with the command
4653 \begin_layout Plain Layout
4661 , that has the following scheme:
4664 \begin_layout Standard
4669 hdotsfor[distance]{number of columns}
4672 \begin_layout Standard
4673 The number of columns specifies how many columns should be spanned.
4674 Distance is a factor for the distance between the dots.
4677 \begin_layout Standard
4678 In the following matrix the command
4684 was inserted in the first box of the second line, to get an ellipsis with
4685 a dot distance twice as long as with the command
4692 \begin_inset Formula \[
4693 \left(\begin{array}{cccc}
4696 q & w & e & r\end{array}\right)\]
4700 Note that the matrix fields that should be spanned must be empty, otherwise
4701 you get LaTeX-errors.
4704 \begin_layout Standard
4705 \begin_inset VSpace bigskip
4708 Furthermore you can fill with the command
4718 \begin_layout Plain Layout
4726 the rest of a line with dots.
4727 The effect of these commands is the same like with
4734 \begin_inset CommandInset ref
4736 reference "sub:Variable-Space"
4743 \begin_layout Standard
4744 For example the command
4752 \begin_layout Plain Layout
4766 \begin_layout Standard
4767 \begin_inset Formula $A\dotfill B$
4773 \begin_layout Standard
4780 there is for a line the command
4790 \begin_layout Plain Layout
4801 \begin_layout Standard
4802 \begin_inset Formula $A\hrulefill B$
4808 \begin_layout Standard
4809 To use the commands for text, they have to be inserted in TeX-mode.
4812 \begin_layout Section
4814 \begin_inset CommandInset label
4824 \begin_layout Plain Layout
4833 \begin_layout Standard
4834 Matrices can be inserted via the math toolbar button
4835 \begin_inset Graphics
4836 filename ../images/dialog-show_mathmatrix.png
4843 Insert\SpecialChar \menuseparator
4844 Math\SpecialChar \menuseparator
4848 You will be asked for the number of matrix columns and rows, and the alignment.
4849 The vertical alignment is hereby only of importance for matrices in inline
4853 \begin_layout Standard
4854 The first matrix is top
4855 \begin_inset Formula $\begin{array}[t]{cccc}
4858 C & F & I & L\end{array}$
4862 \begin_inset Formula $\begin{array}{cccc}
4865 C & F & I & L\end{array}$
4868 , and the third bottom
4869 \begin_inset Formula $\begin{array}[b]{cccc}
4872 C & F & I & L\end{array}$
4878 \begin_layout Standard
4879 The horizontal alignment specifies how the column entries should be aligned.
4880 It is set by entering a letter for every column.
4885 denotes left aligned,
4894 To create for example a 4
4899 \begin_inset space ~
4902 matrix where the first column is left aligned, the second and third are
4903 centered, and the last one is right aligned, one enters for the horizontal
4909 Normally are in a matrix all columns centered, therefore the default is
4910 for every column is a
4917 \begin_layout Standard
4918 Horizontal alignment:
4921 \begin_layout Standard
4927 \begin_inset Formula $\begin{array}{lll}
4930 C & F & 10000\end{array}$
4938 \begin_inset Formula $\begin{array}{ccc}
4941 C & F & 10000\end{array}$
4949 \begin_inset Formula $\begin{array}{rrr}
4952 C & F & 10000\end{array}$
4958 \begin_layout Standard
4959 To add or delete rows and columns subsequently, the math toolbar buttons
4961 \begin_inset Graphics
4962 filename ../images/tabular-feature_append-row.png
4968 \begin_inset Graphics
4969 filename ../images/tabular-feature_delete-row.png
4975 \begin_inset space \thinspace{}
4980 Edit\SpecialChar \menuseparator
4984 New rows can also be created with
4991 \begin_layout Standard
4992 \begin_inset VSpace bigskip
4995 Parentheses around a matrix can can either be created with the commands
5006 \begin_layout Plain Layout
5024 \begin_layout Plain Layout
5035 \begin_inset space ~
5041 \begin_inset CommandInset ref
5043 reference "sub:Automatic-Bracket-Size"
5047 , or by using the following commands:
5048 \begin_inset VSpace medskip
5054 \begin_layout Standard
5055 \begin_inset space \hfill{}
5059 \begin_inset Tabular
5060 <lyxtabular version="3" rows="4" columns="2">
5062 <column alignment="center" valignment="top" width="0">
5063 <column alignment="center" valignment="top" width="0">
5065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5068 \begin_layout Plain Layout
5074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5077 \begin_layout Plain Layout
5079 \begin_inset Note Note
5082 \begin_layout Plain Layout
5089 is only used as spacer.
5101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5104 \begin_layout Plain Layout
5111 \begin_layout Plain Layout
5125 \begin_inset space \thinspace{}
5133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5136 \begin_layout Plain Layout
5137 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5138 0 & \textrm{-}\mathrm{i}\\
5139 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5152 \begin_layout Plain Layout
5159 \begin_layout Plain Layout
5173 \begin_inset space \thinspace{}
5181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5184 \begin_layout Plain Layout
5185 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5186 0 & \textrm{-}\mathrm{i}\\
5187 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5200 \begin_layout Plain Layout
5207 \begin_layout Plain Layout
5221 \begin_inset space \thinspace{}
5229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5232 \begin_layout Plain Layout
5233 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5234 0 & \textrm{-}\mathrm{i}\\
5235 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5249 \begin_inset space \hfill{}
5253 \begin_inset Tabular
5254 <lyxtabular version="3" rows="4" columns="2">
5256 <column alignment="center" valignment="top" width="0">
5257 <column alignment="center" valignment="top" width="0">
5259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5262 \begin_layout Plain Layout
5268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5271 \begin_layout Plain Layout
5279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5282 \begin_layout Plain Layout
5289 \begin_layout Plain Layout
5303 \begin_inset space \thinspace{}
5311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5314 \begin_layout Plain Layout
5315 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5316 0 & \textrm{-}\mathrm{i}\\
5317 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5330 \begin_layout Plain Layout
5337 \begin_layout Plain Layout
5351 \begin_inset space \thinspace{}
5359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5362 \begin_layout Plain Layout
5363 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5364 0 & \textrm{-}\mathrm{i}\\
5365 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5378 \begin_layout Plain Layout
5385 \begin_layout Plain Layout
5399 \begin_inset space \thinspace{}
5407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5410 \begin_layout Plain Layout
5411 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5412 0 & \textrm{-}\mathrm{i}\\
5413 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5427 \begin_inset space \hfill{}
5433 \begin_layout Standard
5434 \begin_inset VSpace medskip
5438 \begin_inset space \thinspace{}
5442 \begin_inset space ~
5451 is inserted, a blue box appears between two vertical lines where the matrix
5455 \begin_layout Standard
5456 \begin_inset VSpace bigskip
5459 As all multiline formulas are matrices, the length
5469 \begin_layout Plain Layout
5477 that is described in
5478 \begin_inset CommandInset ref
5480 reference "sub:Column-Separation"
5484 can also be used to change the column separation of matrices.
5487 \begin_layout Standard
5488 To change the row separation, the command
5498 \begin_layout Plain Layout
5507 It is used as follows:
5510 \begin_layout Standard
5517 arraystretch}{stretch factor}
5521 \begin_layout Plain Layout
5532 \begin_layout Standard
5539 assigns the stretch factor to the predefined command
5547 \begin_inset space \thinspace{}
5551 \begin_inset space ~
5554 the row separation, use the factor 2.
5555 This is then used for all following matrices.
5556 To go back to the original separation, assign the factor 1 to
5565 \begin_layout Standard
5566 To set matrices into a text line, the command
5576 \begin_layout Plain Layout
5585 When it is inserted a blue box with two dashed lines appears.
5586 In this box the matrix is inserted.
5589 \begin_layout Standard
5591 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5592 C & D\end{smallmatrix}\right)$
5598 \begin_layout Section
5599 Brackets and Delimiters
5603 \begin_layout Plain Layout
5613 \begin_layout Plain Layout
5622 \begin_layout Subsection
5623 Vertical Brackets and Delimiters
5627 \begin_layout Plain Layout
5636 \begin_layout Standard
5637 \begin_inset space \hfill{}
5641 \begin_inset Tabular
5642 <lyxtabular version="3" rows="9" columns="2">
5644 <column alignment="center" valignment="top" width="0pt">
5645 <column alignment="center" valignment="top" width="0pt">
5647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5650 \begin_layout Plain Layout
5656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5659 \begin_layout Plain Layout
5667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5670 \begin_layout Plain Layout
5676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5679 \begin_layout Plain Layout
5680 \begin_inset Formula $($
5690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5693 \begin_layout Plain Layout
5699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5702 \begin_layout Plain Layout
5703 \begin_inset Formula $\{$
5713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5716 \begin_layout Plain Layout
5722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5725 \begin_layout Plain Layout
5726 \begin_inset Formula $[$
5736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5739 \begin_layout Plain Layout
5747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5750 \begin_layout Plain Layout
5751 \begin_inset Formula $\langle$
5761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5764 \begin_layout Plain Layout
5772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5775 \begin_layout Plain Layout
5776 \begin_inset Formula $\lceil$
5786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5789 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5801 \begin_inset Formula $\lfloor$
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5814 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $/$
5834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5837 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $|$
5861 \begin_inset space \hfill{}
5865 \begin_inset Tabular
5866 <lyxtabular version="3" rows="9" columns="2">
5868 <column alignment="center" valignment="top" width="0pt">
5869 <column alignment="center" valignment="top" width="0pt">
5871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5874 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5883 \begin_layout Plain Layout
5891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5894 \begin_layout Plain Layout
5900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5903 \begin_layout Plain Layout
5904 \begin_inset Formula $)$
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5917 \begin_layout Plain Layout
5923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5926 \begin_layout Plain Layout
5927 \begin_inset Formula $\}$
5937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5940 \begin_layout Plain Layout
5946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5949 \begin_layout Plain Layout
5950 \begin_inset Formula $]$
5960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5963 \begin_layout Plain Layout
5971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5974 \begin_layout Plain Layout
5975 \begin_inset Formula $\rangle$
5985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5988 \begin_layout Plain Layout
5996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5999 \begin_layout Plain Layout
6000 \begin_inset Formula $\rceil$
6010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6013 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6024 \begin_layout Plain Layout
6025 \begin_inset Formula $\rfloor$
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6038 \begin_layout Plain Layout
6048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6051 \begin_layout Plain Layout
6052 \begin_inset Formula $\backslash$
6062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6065 \begin_layout Plain Layout
6073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6076 \begin_layout Plain Layout
6077 \begin_inset Formula $\|$
6091 \begin_inset space \hfill{}
6097 \begin_layout Standard
6100 \begin_inset Note Greyedout
6103 \begin_layout Plain Layout
6108 In TeX-mode the command
6118 \begin_layout Plain Layout
6126 must be used for the backslash, because the command
6134 produces there a line break.
6142 \begin_layout Standard
6143 For all characters listed above the size can be adjusted with the commands
6144 described in the following two subsections.
6145 When using these commands, the characters < and > can directly be used
6146 instead of the commands
6161 \begin_layout Subsubsection
6163 \begin_inset CommandInset label
6165 name "sub:Manual-Bracket-Size"
6173 \begin_layout Plain Layout
6174 Bracket size ! manual
6182 \begin_layout Standard
6183 The bracket size can be specified manually by the LaTeX-commands
6193 \begin_layout Plain Layout
6226 denotes the smallest and
6232 the largest bracket size.
6235 \begin_layout Standard
6236 These commands are used to emphasize levels of brackets:
6239 \begin_layout Standard
6241 \begin_inset Tabular
6242 <lyxtabular version="3" rows="2" columns="2">
6244 <column alignment="center" valignment="top" width="0pt">
6245 <column alignment="center" valignment="top" width="0pt">
6247 <cell alignment="center" valignment="top" usebox="none">
6250 \begin_layout Plain Layout
6251 all brackets in the same size:
6256 <cell alignment="center" valignment="top" usebox="none">
6259 \begin_layout Plain Layout
6260 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6270 <cell alignment="center" valignment="top" usebox="none">
6273 \begin_layout Plain Layout
6279 <cell alignment="center" valignment="top" usebox="none">
6282 \begin_layout Plain Layout
6283 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6297 \begin_inset Note Note
6300 \begin_layout Plain Layout
6307 is only used as spacer.
6315 \begin_layout Standard
6316 For the second formula the command
6326 \begin_layout Plain Layout
6340 \begin_layout Standard
6341 Here is an overview about all bracket sizes:
6344 \begin_layout Standard
6364 \begin_layout Plain Layout
6381 \begin_layout Plain Layout
6394 \begin_layout Plain Layout
6410 \begin_layout Standard
6412 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6418 \begin_layout Standard
6419 \begin_inset Newpage newpage
6428 -commands there is the variant
6438 \begin_layout Plain Layout
6446 that adds a bit more space between the bracket and its content, and the
6463 \begin_layout Plain Layout
6473 , that don't add additional space.
6478 at the end of the command
6484 is for a left bracket; for a right bracket this will be replaced by an
6490 A left or right bracket can each be an opening or closing bracket.
6493 \begin_layout Standard
6494 In the following table is a comparison of the variants:
6497 \begin_layout Standard
6499 \begin_inset Tabular
6500 <lyxtabular version="3" rows="5" columns="2">
6502 <column alignment="center" valignment="middle" width="0">
6503 <column alignment="center" valignment="middle" width="0">
6505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6508 \begin_layout Plain Layout
6514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6517 \begin_layout Plain Layout
6519 \begin_inset Note Note
6522 \begin_layout Plain Layout
6529 is only used as spacer.
6541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6544 \begin_layout Plain Layout
6559 \begin_layout Plain Layout
6577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6580 \begin_layout Plain Layout
6581 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6594 \begin_layout Plain Layout
6609 \begin_layout Plain Layout
6627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6630 \begin_layout Plain Layout
6631 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6644 \begin_layout Plain Layout
6659 \begin_layout Plain Layout
6677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6680 \begin_layout Plain Layout
6681 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6694 \begin_layout Plain Layout
6706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6709 \begin_layout Plain Layout
6710 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6726 \begin_layout Subsubsection
6727 Automatic Bracket Size
6728 \begin_inset CommandInset label
6730 name "sub:Automatic-Bracket-Size"
6738 \begin_layout Plain Layout
6739 Bracket size ! automatic
6747 \begin_layout Standard
6748 Brackets with variable size can be inserted with the commands
6758 \begin_layout Plain Layout
6776 \begin_layout Plain Layout
6784 or via the math toolbar button
6785 \begin_inset Graphics
6786 filename ../images/dialog-show_mathdelimiter.png
6804 the wanted bracket must be inserted.
6805 The bracket size will then automatically be calculated for the output.
6808 \begin_layout Standard
6810 normal bracket: The command
6820 \begin_layout Plain Layout
6830 \begin_inset Formula $\downarrow$
6837 \begin_layout Plain Layout
6849 \begin_inset Formula \[
6857 \begin_layout Standard
6859 multiline bracket: The command
6871 \begin_layout Plain Layout
6881 \begin_inset Formula $\downarrow$
6888 \begin_layout Plain Layout
6902 \begin_inset Formula \[
6903 \ln\left(\frac{A}{C}\right)\]
6910 \begin_layout Standard
6926 \begin_inset space ~
6932 This has the advantage that you can see in LyX immediately the real bracket
6933 size and that the matching right bracket will be created too.
6934 \begin_inset Newline newline
6937 The command for the last example would then be:
6951 \begin_layout Plain Layout
6961 \begin_inset Formula $\downarrow$
6967 \begin_layout Standard
6968 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6969 For example the command
6979 \begin_layout Plain Layout
6989 \begin_inset Formula $\downarrow$
6996 \begin_layout Plain Layout
7012 \begin_inset Formula \[
7013 \left.\frac{A}{B}\right\} \]
7031 will be converted by LyX to brackets in the right size when the document
7032 is reloaded and an omitted bracket will appear as dashed line.
7035 \begin_layout Standard
7036 \begin_inset VSpace bigskip
7039 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7050 \begin_layout Plain Layout
7058 is additionally available for all brackets and limits.
7059 With this command the height of the following character is adapted to the
7060 one of the surrounding brackets, what is e.
7061 \begin_inset space \thinspace{}
7065 \begin_inset space ~
7068 needed for physical vectors:
7069 \begin_inset Formula \[
7070 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7074 For physical vectors there is a special LaTeX-package, described in
7075 \begin_inset CommandInset ref
7077 reference "sub:Physical-Vectors"
7084 \begin_layout Subsection
7089 \begin_layout Plain Layout
7090 Brackets ! horizontal
7098 \begin_layout Standard
7100 \begin_inset Tabular
7101 <lyxtabular version="3" rows="4" columns="2">
7103 <column alignment="center" valignment="top" width="0pt">
7104 <column alignment="center" valignment="top" width="0pt">
7106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7109 \begin_layout Plain Layout
7111 \begin_inset Note Note
7114 \begin_layout Plain Layout
7121 is only used as spacer.
7131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7134 \begin_layout Plain Layout
7142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7145 \begin_layout Plain Layout
7149 \begin_layout Plain Layout
7164 \begin_layout Plain Layout
7177 \begin_layout Plain Layout
7190 \begin_layout Plain Layout
7203 \begin_layout Plain Layout
7214 \begin_layout Plain Layout
7227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7230 \begin_layout Plain Layout
7231 \begin_inset Formula $\overbrace{A+B}^{3}$
7241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7244 \begin_layout Plain Layout
7248 \begin_layout Plain Layout
7263 \begin_layout Plain Layout
7276 \begin_layout Plain Layout
7289 \begin_layout Plain Layout
7300 \begin_layout Plain Layout
7313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7316 \begin_layout Plain Layout
7317 \begin_inset Formula $\underbrace{A+B}_{5}$
7327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7330 \begin_layout Plain Layout
7337 \begin_layout Plain Layout
7352 \begin_layout Plain Layout
7365 \begin_layout Plain Layout
7378 \begin_layout Plain Layout
7391 \begin_layout Plain Layout
7404 \begin_layout Plain Layout
7417 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7435 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7451 \begin_layout Standard
7452 In the last example it doesn't matter if
7464 is inserted at first.
7467 \begin_layout Standard
7468 \begin_inset VSpace bigskip
7471 When brackets are needed that overlap each other, multiline formulas, as
7473 \begin_inset CommandInset ref
7475 reference "sec:Multiline-Formulas"
7480 \begin_inset Formula \begin{eqnarray*}
7481 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7482 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7486 In the first row the formula is inserted together with the first brace.
7487 It is hereby important that the space command
7491 \begin_layout Plain Layout
7492 Space commands are explained in
7493 \begin_inset CommandInset ref
7495 reference "sub:Predefined-Space"
7510 is inserted before the first
7511 \begin_inset Formula $d$
7514 , because the brace that ends behind the
7515 \begin_inset Formula $q$
7518 prevents that the following
7519 \begin_inset Quotes eld
7523 \begin_inset Quotes erd
7526 is surrounded by space.
7530 \begin_layout Plain Layout
7531 because a bracket is not handled as character, see
7532 \begin_inset CommandInset ref
7534 reference "sub:Binary-Operators"
7543 In the second row the second brace is inserted.
7544 As it should begin before the
7545 \begin_inset Formula $b$
7560 \begin_layout Plain Layout
7568 \begin_inset CommandInset ref
7570 reference "sub:Placeholders"
7579 This space is needed because the
7580 \begin_inset Quotes eld
7584 \begin_inset Quotes erd
7587 is also surrounded by space in the formula.
7588 The brace is placed under the command
7597 \begin_layout Standard
7598 It gets more complicated when brackets overlap each other, like in the following
7603 \begin_layout Plain Layout
7615 \begin_inset Formula \begin{eqnarray*}
7616 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7617 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7625 \begin_layout Plain Layout
7636 The first formula row is the same as the second row of the previous example,
7637 with the difference that the brace is above.
7638 The second row contains the formula together with the second brace.
7639 To avoid that there is space between the upper brace in the first row and
7640 the formula, the row spacing need to be reduced.
7641 This is not easily possible due to a bug in LyX
7645 \begin_layout Plain Layout
7646 \begin_inset CommandInset href
7648 name "LyX-bug #1505"
7649 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7659 As solution for the problem, the global formula row separation
7669 \begin_layout Plain Layout
7677 must be changed to -6
7678 \begin_inset space \thinspace{}
7681 pt before the formula with the command
7696 is set back after the formula to the standard value of 3
7697 \begin_inset space \thinspace{}
7700 pt using the same command.
7701 More about the row separation in formulas is explained in
7702 \begin_inset CommandInset ref
7704 reference "sub:Line-Separation"
7711 \begin_layout Section
7716 \begin_layout Plain Layout
7725 \begin_layout Standard
7726 Arrows can be inserted via the math toolbar button
7727 \begin_inset Graphics
7728 filename ../images/math/leftarrow.png
7733 or the commands listed in the following subsections.
7736 \begin_layout Subsection
7741 \begin_layout Plain Layout
7750 \begin_layout Standard
7751 \begin_inset space \hfill{}
7755 \begin_inset Tabular
7756 <lyxtabular version="3" rows="8" columns="2">
7758 <column alignment="center" valignment="top" width="0pt">
7759 <column alignment="center" valignment="top" width="0pt">
7761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7764 \begin_layout Plain Layout
7770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7773 \begin_layout Plain Layout
7781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7784 \begin_layout Plain Layout
7792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7795 \begin_layout Plain Layout
7796 \begin_inset Formula $\gets$
7806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7809 \begin_layout Plain Layout
7817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7820 \begin_layout Plain Layout
7821 \begin_inset Formula $\Leftarrow$
7831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7834 \begin_layout Plain Layout
7842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7845 \begin_layout Plain Layout
7846 \begin_inset Formula $\longleftarrow$
7856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7859 \begin_layout Plain Layout
7867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7870 \begin_layout Plain Layout
7871 \begin_inset Formula $\Longleftarrow$
7881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7884 \begin_layout Plain Layout
7892 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7895 \begin_layout Plain Layout
7896 \begin_inset Formula $\leftharpoonup$
7906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7921 \begin_inset Formula $\leftharpoondown$
7931 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7934 \begin_layout Plain Layout
7942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7945 \begin_layout Plain Layout
7946 \begin_inset Formula $\hookleftarrow$
7960 \begin_inset space \hfill{}
7964 \begin_inset Tabular
7965 <lyxtabular version="3" rows="8" columns="2">
7967 <column alignment="center" valignment="top" width="0pt">
7968 <column alignment="center" valignment="top" width="0pt">
7970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7982 \begin_layout Plain Layout
7990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7993 \begin_layout Plain Layout
8001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8004 \begin_layout Plain Layout
8005 \begin_inset Formula $\to$
8015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8018 \begin_layout Plain Layout
8026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8029 \begin_layout Plain Layout
8030 \begin_inset Formula $\Rightarrow$
8040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8043 \begin_layout Plain Layout
8051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8054 \begin_layout Plain Layout
8055 \begin_inset Formula $\longrightarrow$
8065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8068 \begin_layout Plain Layout
8076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8079 \begin_layout Plain Layout
8080 \begin_inset Formula $\Longrightarrow$
8090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8093 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8104 \begin_layout Plain Layout
8105 \begin_inset Formula $\rightharpoonup$
8115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\rightharpoondown$
8140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\hookrightarrow$
8169 \begin_inset space \hfill{}
8175 \begin_layout Standard
8176 \begin_inset space \hfill{}
8180 \begin_inset Tabular
8181 <lyxtabular version="3" rows="6" columns="2">
8183 <column alignment="center" valignment="top" width="0pt">
8184 <column alignment="center" valignment="top" width="0pt">
8186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8189 \begin_layout Plain Layout
8195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8198 \begin_layout Plain Layout
8206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8209 \begin_layout Plain Layout
8217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8220 \begin_layout Plain Layout
8221 \begin_inset Formula $\leftrightarrow$
8231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8234 \begin_layout Plain Layout
8242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8245 \begin_layout Plain Layout
8246 \begin_inset Formula $\Leftrightarrow$
8256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8259 \begin_layout Plain Layout
8267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8270 \begin_layout Plain Layout
8271 \begin_inset Formula $\longleftrightarrow$
8281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8284 \begin_layout Plain Layout
8292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8295 \begin_layout Plain Layout
8296 \begin_inset Formula $\Longleftrightarrow$
8306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8309 \begin_layout Plain Layout
8317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8320 \begin_layout Plain Layout
8321 \begin_inset Formula $\rightleftharpoons$
8335 \begin_inset space \hspace{}
8340 \begin_inset space \hfill{}
8344 \begin_inset Tabular
8345 <lyxtabular version="3" rows="5" columns="2">
8347 <column alignment="center" valignment="top" width="0pt">
8348 <column alignment="center" valignment="top" width="0pt">
8350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8353 \begin_layout Plain Layout
8359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8362 \begin_layout Plain Layout
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 $\mapsto$
8395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8398 \begin_layout Plain Layout
8406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8409 \begin_layout Plain Layout
8410 \begin_inset Formula $\longmapsto$
8420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8423 \begin_layout Plain Layout
8431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8434 \begin_layout Plain Layout
8435 \begin_inset Formula $\leadsto$
8445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8448 \begin_layout Plain Layout
8456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8459 \begin_layout Plain Layout
8460 \begin_inset Formula $\dasharrow$
8474 \begin_inset space \hfill{}
8480 \begin_layout Standard
8481 \begin_inset VSpace medskip
8484 Arrows used as accent like e.
8485 \begin_inset space \thinspace{}
8489 \begin_inset space ~
8492 vector arrows are listed in
8493 \begin_inset CommandInset ref
8495 reference "sec:Accents"
8502 \begin_layout Standard
8503 \begin_inset VSpace bigskip
8506 Furthermore there are the labeled arrows
8510 \begin_layout Plain Layout
8526 \begin_layout Plain Layout
8544 \begin_layout Plain Layout
8551 \begin_layout Plain Layout
8566 When inserting one of these commands in a formula, an arrow with two blue
8567 boxes appear where the label can be inserted.
8568 The length of the arrow adapts to the label width.
8571 \begin_layout Standard
8573 \begin_inset Tabular
8574 <lyxtabular version="3" rows="3" columns="2">
8576 <column alignment="center" valignment="top" width="0pt">
8577 <column alignment="center" valignment="top" width="0pt">
8579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8582 \begin_layout Plain Layout
8588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8591 \begin_layout Plain Layout
8593 \begin_inset Note Note
8596 \begin_layout Plain Layout
8603 is only used as spacer.
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8618 \begin_layout Plain Layout
8625 \begin_layout Plain Layout
8635 \begin_inset Formula $\downarrow$
8639 \begin_inset Formula $\to$
8647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8650 \begin_layout Plain Layout
8651 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8664 \begin_layout Plain Layout
8671 \begin_layout Plain Layout
8681 \begin_inset Formula $\downarrow$
8685 \begin_inset Formula $\to$
8693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8696 \begin_layout Plain Layout
8697 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8713 \begin_layout Subsection
8714 Vertical and diagonal Arrows
8718 \begin_layout Plain Layout
8728 \begin_layout Plain Layout
8737 \begin_layout Standard
8738 \begin_inset space \hfill{}
8742 \begin_inset Tabular
8743 <lyxtabular version="3" rows="7" columns="2">
8745 <column alignment="center" valignment="top" width="0pt">
8746 <column alignment="center" valignment="top" width="0pt">
8748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8751 \begin_layout Plain Layout
8757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8760 \begin_layout Plain Layout
8768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8771 \begin_layout Plain Layout
8779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8782 \begin_layout Plain Layout
8783 \begin_inset Formula $\uparrow$
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8796 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\Uparrow$
8818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8821 \begin_layout Plain Layout
8829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8832 \begin_layout Plain Layout
8833 \begin_inset Formula $\updownarrow$
8843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8846 \begin_layout Plain Layout
8854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8857 \begin_layout Plain Layout
8858 \begin_inset Formula $\Updownarrow$
8868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8871 \begin_layout Plain Layout
8879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8882 \begin_layout Plain Layout
8883 \begin_inset Formula $\Downarrow$
8893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8896 \begin_layout Plain Layout
8904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8908 \begin_inset Formula $\downarrow$
8922 \begin_inset space \hfill{}
8926 \begin_inset Tabular
8927 <lyxtabular version="3" rows="5" columns="2">
8929 <column alignment="center" valignment="top" width="0pt">
8930 <column alignment="center" valignment="top" width="0pt">
8932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8935 \begin_layout Plain Layout
8941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8944 \begin_layout Plain Layout
8952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8955 \begin_layout Plain Layout
8963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8966 \begin_layout Plain Layout
8967 \begin_inset Formula $\nearrow$
8977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8980 \begin_layout Plain Layout
8988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8991 \begin_layout Plain Layout
8992 \begin_inset Formula $\searrow$
9002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9005 \begin_layout Plain Layout
9013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9016 \begin_layout Plain Layout
9017 \begin_inset Formula $\swarrow$
9027 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9030 \begin_layout Plain Layout
9038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9041 \begin_layout Plain Layout
9042 \begin_inset Formula $\nwarrow$
9056 \begin_inset space \hfill{}
9062 \begin_layout Standard
9063 \begin_inset VSpace medskip
9066 Vertical arrows can be used also as delimiter together with the commands
9068 \begin_inset CommandInset ref
9070 reference "sub:Manual-Bracket-Size"
9075 \begin_inset CommandInset ref
9077 reference "sub:Automatic-Bracket-Size"
9084 \begin_layout Standard
9085 \begin_inset Newpage newpage
9091 \begin_layout Section
9093 \begin_inset CommandInset label
9103 \begin_layout Plain Layout
9112 \begin_layout Standard
9113 Accents can be inserted via the math toolbar button
9114 \begin_inset Graphics
9115 filename ../images/math/hat.png
9120 or the commands listed in the following subsections.
9123 \begin_layout Subsection
9124 Accents for one Character
9128 \begin_layout Plain Layout
9141 \begin_layout Plain Layout
9143 \begin_inset CommandInset ref
9145 reference "sub:Accents-in-Text"
9158 \begin_layout Plain Layout
9166 \begin_inset Note Note
9169 \begin_layout Plain Layout
9172 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9175 \begin_layout Plain Layout
9178 texorpdfstring is in section
9179 \begin_inset CommandInset ref
9181 reference "sub:Formulas-in-Section"
9191 \begin_inset CommandInset label
9193 name "sub:Accents-for-one"
9201 \begin_layout Plain Layout
9202 Accents ! for one character
9210 \begin_layout Standard
9211 \begin_inset space \hfill{}
9215 \begin_inset Tabular
9216 <lyxtabular version="3" rows="8" columns="2">
9218 <column alignment="center" valignment="top" width="0pt">
9219 <column alignment="center" valignment="top" width="0pt">
9221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9224 \begin_layout Plain Layout
9230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9233 \begin_layout Plain Layout
9235 \begin_inset Note Note
9238 \begin_layout Plain Layout
9245 is only used as spacer.
9257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9260 \begin_layout Plain Layout
9267 \begin_layout Plain Layout
9281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9284 \begin_layout Plain Layout
9285 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9298 \begin_layout Plain Layout
9305 \begin_layout Plain Layout
9319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9322 \begin_layout Plain Layout
9323 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9336 \begin_layout Plain Layout
9343 \begin_layout Plain Layout
9357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9360 \begin_layout Plain Layout
9361 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9374 \begin_layout Plain Layout
9382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9385 \begin_layout Plain Layout
9386 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9399 \begin_layout Plain Layout
9406 \begin_layout Plain Layout
9419 \begin_layout Plain Layout
9430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9433 \begin_layout Plain Layout
9434 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9447 \begin_layout Plain Layout
9454 \begin_layout Plain Layout
9468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9471 \begin_layout Plain Layout
9472 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9485 \begin_layout Plain Layout
9492 \begin_layout Plain Layout
9506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9509 \begin_layout Plain Layout
9510 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9524 \begin_inset space \hfill{}
9528 \begin_inset Tabular
9529 <lyxtabular version="3" rows="7" columns="2">
9531 <column alignment="center" valignment="top" width="0pt">
9532 <column alignment="center" valignment="top" width="0pt">
9534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9537 \begin_layout Plain Layout
9543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9546 \begin_layout Plain Layout
9554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9557 \begin_layout Plain Layout
9564 \begin_layout Plain Layout
9578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9581 \begin_layout Plain Layout
9582 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9595 \begin_layout Plain Layout
9602 \begin_layout Plain Layout
9616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9619 \begin_layout Plain Layout
9620 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9633 \begin_layout Plain Layout
9640 \begin_layout Plain Layout
9654 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9657 \begin_layout Plain Layout
9658 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9671 \begin_layout Plain Layout
9678 \begin_layout Plain Layout
9692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9695 \begin_layout Plain Layout
9696 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9709 \begin_layout Plain Layout
9716 \begin_layout Plain Layout
9730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9733 \begin_layout Plain Layout
9734 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9747 \begin_layout Plain Layout
9754 \begin_layout Plain Layout
9768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9771 \begin_layout Plain Layout
9772 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9786 \begin_inset space \hfill{}
9792 \begin_layout Standard
9793 \begin_inset VSpace bigskip
9800 \begin_layout Plain Layout
9806 in formulas, a quotation mark is inserted before the vowel.
9807 These two characters are then treated by LaTeX as
9811 character when the formula part with the umlaut is marked as German.
9819 \begin_inset Quotes eld
9823 \begin_inset Quotes erd
9826 umlauts are created as demonstrated in the following example:
9829 \begin_layout Standard
9830 \begin_inset VSpace -2mm
9836 \begin_layout Standard
9838 \begin_inset Tabular
9839 <lyxtabular version="3" rows="3" columns="2">
9841 <column alignment="center" valignment="top" width="0">
9842 <column alignment="center" valignment="top" width="0">
9844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9847 \begin_layout Plain Layout
9853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9856 \begin_layout Plain Layout
9858 \begin_inset Note Note
9861 \begin_layout Plain Layout
9868 is only used as spacer.
9880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9883 \begin_layout Plain Layout
9886 \begin_inset Quotes grd
9894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9897 \begin_layout Plain Layout
9900 \begin_inset Formula $"i$
9910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9913 \begin_layout Plain Layout
9920 \begin_layout Plain Layout
9934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9937 \begin_layout Plain Layout
9938 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9954 \begin_layout Standard
9955 Another advantage to
9961 is that umlauts can directly be converted to mathematical text because
9962 the accent commands above are
9968 in mathematical text
9971 To convert an accented character to mathematical text, only the character
9972 under the accent may be converted.
9973 This applies also for all other conversions, e.
9974 \begin_inset space \thinspace{}
9978 \begin_inset space ~
9984 \begin_layout Standard
9985 In mathematical text, umlauts and other accented characters can directly
9989 \begin_layout Subsection
9990 Accents for Operators
9994 \begin_layout Plain Layout
9995 Accents ! for operators
10003 \begin_layout Standard
10014 \begin_layout Plain Layout
10032 \begin_layout Plain Layout
10040 characters can be placed above or below an operator, respectively, to accent
10052 \begin_layout Plain Layout
10060 characters can be set before and behind an operator.
10061 The command scheme is:
10064 \begin_layout Standard
10080 \begin_layout Standard
10087 must always be before the operator that should be accented.
10088 You can accent with several characters and even with other operators and
10096 for example only characters behind an operator, write nothing between the
10097 first braces but don't omit the braces.
10100 \begin_layout Standard
10101 For example the command
10106 \begin_inset Formula $\to$
10116 \begin_inset Formula $\to$
10125 \begin_layout Plain Layout
10141 \begin_inset Formula \[
10142 \sideset{}{'}\sum_{k=1}^{n}\]
10149 \begin_layout Standard
10158 \begin_layout Plain Layout
10173 \begin_layout Plain Layout
10185 \begin_inset Formula $\uparrow$
10193 \begin_inset Formula \[
10194 \overset{a}{\maltese}\]
10198 As seen in the last example, with
10210 also symbols and characters can be accented; with
10216 this is not possible.
10219 \begin_layout Subsection
10220 Accents for several Characters
10221 \begin_inset CommandInset label
10223 name "sub:Accents-for-several"
10231 \begin_layout Plain Layout
10232 Accents ! for several characters
10240 \begin_layout Standard
10241 \begin_inset space \hfill{}
10245 \begin_inset Tabular
10246 <lyxtabular version="3" rows="5" columns="2">
10248 <column alignment="center" valignment="top" width="0pt">
10249 <column alignment="center" valignment="top" width="0pt">
10251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10254 \begin_layout Plain Layout
10260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10263 \begin_layout Plain Layout
10265 \begin_inset Note Note
10268 \begin_layout Plain Layout
10275 is only used as spacer.
10287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10290 \begin_layout Plain Layout
10297 \begin_layout Plain Layout
10311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10314 \begin_layout Plain Layout
10315 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10328 \begin_layout Plain Layout
10335 \begin_layout Plain Layout
10349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10352 \begin_layout Plain Layout
10353 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10366 \begin_layout Plain Layout
10373 \begin_layout Plain Layout
10387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10390 \begin_layout Plain Layout
10391 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10404 \begin_layout Plain Layout
10407 underleftrightarrow
10411 \begin_layout Plain Layout
10425 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10428 \begin_layout Plain Layout
10429 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10443 \begin_inset space \hfill{}
10447 \begin_inset Tabular
10448 <lyxtabular version="3" rows="5" columns="2">
10450 <column alignment="center" valignment="top" width="0pt">
10451 <column alignment="center" valignment="top" width="0pt">
10453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10456 \begin_layout Plain Layout
10462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10465 \begin_layout Plain Layout
10473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10476 \begin_layout Plain Layout
10483 \begin_layout Plain Layout
10497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10500 \begin_layout Plain Layout
10501 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10514 \begin_layout Plain Layout
10521 \begin_layout Plain Layout
10535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10538 \begin_layout Plain Layout
10539 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10552 \begin_layout Plain Layout
10559 \begin_layout Plain Layout
10573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10576 \begin_layout Plain Layout
10577 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10590 \begin_layout Plain Layout
10597 \begin_layout Plain Layout
10611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10614 \begin_layout Plain Layout
10615 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10629 \begin_inset space \hfill{}
10635 \begin_layout Standard
10636 \begin_inset VSpace medskip
10639 With these commands as many characters as you like can be accented.
10652 will only be set in the output with a length of three characters, as shown
10653 in the following example:
10654 \begin_inset Formula \[
10655 \widetilde{A+B=C-D}\]
10662 \begin_layout Standard
10673 \begin_layout Plain Layout
10691 \begin_layout Plain Layout
10699 described in the previous subsection it is also possible to accent several
10709 \begin_layout Plain Layout
10719 \begin_inset Formula $\downarrow$
10725 \begin_inset Formula \[
10726 \underset{***}{A=B}\]
10733 \begin_layout Section
10735 \begin_inset CommandInset label
10745 \begin_layout Plain Layout
10754 \begin_layout Subsection
10756 \begin_inset CommandInset label
10758 name "sub:Predefined-Space"
10766 \begin_layout Plain Layout
10767 Space ! horizontal ! predefined
10775 \begin_layout Standard
10776 Sometimes it is necessary to insert horizontal space to a formula.
10777 This is done by inserting a protected space (shortcut
10783 \begin_inset Quotes eld
10793 \begin_layout Plain Layout
10806 \begin_inset Quotes erd
10809 appears and by pressing
10813 several times one can select one of eight different space sizes.
10814 The spaces can also be inserted using the math toolbar button
10815 \begin_inset Graphics
10816 filename ../images/math/space.png
10821 or special commands.
10822 Independent from the inserted command, one can select the size again by
10830 \begin_layout Standard
10833 \begin_inset VSpace -5mm
10837 \begin_inset Tabular
10838 <lyxtabular version="3" rows="3" columns="7">
10840 <column alignment="center" valignment="middle" width="6.8cm">
10841 <column alignment="center" valignment="top" width="0">
10842 <column alignment="center" valignment="top" width="0">
10843 <column alignment="center" valignment="top" width="0">
10844 <column alignment="center" valignment="top" width="0">
10845 <column alignment="center" valignment="top" width="0">
10846 <column alignment="center" valignment="top" width="0">
10848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10851 \begin_layout Plain Layout
10857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10860 \begin_layout Plain Layout
10868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10871 \begin_layout Plain Layout
10879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10882 \begin_layout Plain Layout
10890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10893 \begin_layout Plain Layout
10901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10904 \begin_layout Plain Layout
10912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10915 \begin_layout Plain Layout
10925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10928 \begin_layout Plain Layout
10933 keystrokes after inserting the protected space
10938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10941 \begin_layout Plain Layout
10947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10950 \begin_layout Plain Layout
10956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10959 \begin_layout Plain Layout
10965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10968 \begin_layout Plain Layout
10974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10977 \begin_layout Plain Layout
10983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10986 \begin_layout Plain Layout
10994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10997 \begin_layout Plain Layout
11003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11006 \begin_layout Plain Layout
11007 \begin_inset Formula $A\, B$
11015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11018 \begin_layout Plain Layout
11019 \begin_inset Formula $A\: B$
11027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11030 \begin_layout Plain Layout
11031 \begin_inset Formula $A\; B$
11039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11042 \begin_layout Plain Layout
11043 \begin_inset Formula $A\quad B$
11051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11054 \begin_layout Plain Layout
11055 \begin_inset Formula $A\qquad B$
11063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11066 \begin_layout Plain Layout
11067 \begin_inset Formula $A\! B$
11083 \begin_layout Standard
11084 The last size seem to produce no space.
11085 It is displayed red in LyX contrary to the other sizes, because it is a
11087 There are two more negative spaces:
11090 \begin_layout Standard
11092 \begin_inset Tabular
11093 <lyxtabular version="3" rows="3" columns="3">
11095 <column alignment="center" valignment="middle" width="6.8cm">
11096 <column alignment="center" valignment="top" width="0pt">
11097 <column alignment="center" valignment="top" width="0pt">
11099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11111 \begin_layout Plain Layout
11119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11122 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11140 keystrokes after inserting the protected space
11145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11148 \begin_layout Plain Layout
11154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11157 \begin_layout Plain Layout
11165 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11177 \begin_layout Plain Layout
11178 \begin_inset Formula $A\negmedspace B$
11186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11189 \begin_layout Plain Layout
11190 \begin_inset Formula $A\negthickspace B$
11206 \begin_layout Standard
11207 Negative spaces can lead to characters overlapping each other.
11208 Thus they can be used to enforce ligatures, what is e.
11209 \begin_inset space \thinspace{}
11213 \begin_inset space ~
11216 useful for summation operators:
11219 \begin_layout Standard
11221 \begin_inset Tabular
11222 <lyxtabular version="3" rows="3" columns="2">
11224 <column alignment="center" valignment="top" width="0">
11225 <column alignment="center" valignment="top" width="0">
11227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11230 \begin_layout Plain Layout
11236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11239 \begin_layout Plain Layout
11241 \begin_inset Note Note
11244 \begin_layout Plain Layout
11251 is only used as spacer.
11263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11275 \begin_layout Plain Layout
11289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11292 \begin_layout Plain Layout
11293 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11317 \begin_layout Plain Layout
11331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11334 \begin_layout Plain Layout
11335 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11351 \begin_layout Standard
11352 Relations like for example equal signs, are always surrounded by space.
11353 To suppress this, the equal sign is placed into a TeX-brace.
11354 The following example demonstrates this:
11357 \begin_layout Standard
11359 \begin_inset Tabular
11360 <lyxtabular version="3" rows="2" columns="2">
11362 <column alignment="center" valignment="top" width="0pt">
11363 <column alignment="center" valignment="top" width="0pt">
11365 <cell alignment="center" valignment="top" usebox="none">
11368 \begin_layout Plain Layout
11374 <cell alignment="center" valignment="top" usebox="none">
11377 \begin_layout Plain Layout
11378 \begin_inset Formula $A=B$
11388 <cell alignment="center" valignment="top" usebox="none">
11391 \begin_layout Plain Layout
11392 \begin_inset Note Note
11395 \begin_layout Plain Layout
11402 is only used as spacer.
11408 \begin_inset Formula $\raisebox{5mm}{}$
11411 equation without space
11416 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11419 \begin_layout Plain Layout
11420 \begin_inset Formula $A{=}B$
11436 \begin_layout Standard
11438 The command for the last formula is:
11443 \begin_inset Formula $\to$
11449 \begin_layout Standard
11450 \begin_inset VSpace bigskip
11453 Spaces are needed for physical units, because the space between the value
11454 and the unit is the smallest one and not a normal space.
11455 For units in text, the smallest space is inserted via the menu
11457 Insert\SpecialChar \menuseparator
11458 Formatting\SpecialChar \menuseparator
11460 \begin_inset space ~
11472 \begin_layout Standard
11473 An example to visualize the difference:
11476 \begin_layout Standard
11477 \begin_inset Tabular
11478 <lyxtabular version="3" rows="2" columns="2">
11480 <column alignment="left" valignment="top" width="0">
11481 <column alignment="left" valignment="top" width="0">
11483 <cell alignment="center" valignment="top" usebox="none">
11486 \begin_layout Plain Layout
11488 \begin_inset Formula $\cdot$
11496 <cell alignment="center" valignment="top" usebox="none">
11499 \begin_layout Plain Layout
11500 space between value and unit
11507 <cell alignment="center" valignment="top" usebox="none">
11510 \begin_layout Plain Layout
11512 \begin_inset space \thinspace{}
11516 \begin_inset Formula $\cdot$
11524 <cell alignment="center" valignment="top" usebox="none">
11527 \begin_layout Plain Layout
11528 smallest space between value and unit
11541 \begin_layout Subsection
11546 \begin_layout Plain Layout
11559 \begin_layout Plain Layout
11560 for vertical space in formulas see
11561 \begin_inset CommandInset ref
11563 reference "sub:Line-Separation"
11576 \begin_layout Plain Layout
11584 \begin_inset Note Note
11587 \begin_layout Plain Layout
11590 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11593 \begin_layout Plain Layout
11596 texorpdfstring is in section
11597 \begin_inset CommandInset ref
11599 reference "sub:Formulas-in-Section"
11609 \begin_inset CommandInset label
11611 name "sub:Variable-Space"
11619 \begin_layout Plain Layout
11620 Space ! horizontal ! variable
11628 \begin_layout Standard
11629 Space with a defined length can be inserted in LyX with the command
11630 \begin_inset Newline newline
11643 \begin_layout Plain Layout
11652 For the length all units listed in
11653 \begin_inset CommandInset ref
11655 reference "tab:Used-units"
11659 are allowed, except of the unit
11660 \begin_inset Quotes eld
11664 \begin_inset Quotes erd
11668 The length may also be negative.
11669 To insert so many space that the formula uses all available space, the
11680 \begin_layout Plain Layout
11691 \begin_layout Standard
11692 \begin_inset VSpace -1mm
11698 \begin_layout Standard
11700 \begin_inset Tabular
11701 <lyxtabular version="3" rows="4" columns="2">
11703 <column alignment="center" valignment="top" width="0">
11704 <column alignment="center" valignment="top" width="0">
11706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11709 \begin_layout Plain Layout
11715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11718 \begin_layout Plain Layout
11726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11729 \begin_layout Plain Layout
11733 \begin_inset Formula $\to$
11743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11746 \begin_layout Plain Layout
11747 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11760 \begin_layout Plain Layout
11764 \begin_inset Formula $\to$
11774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11777 \begin_layout Plain Layout
11778 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11791 \begin_layout Plain Layout
11798 \begin_layout Plain Layout
11812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11815 \begin_layout Plain Layout
11816 \begin_inset Formula $A=A\hfill B=B$
11832 \begin_layout Standard
11833 In the last example the available space is given by the longest column entry
11835 In an inline formula the space depends on the length of the line in which
11843 Thus, when the line uses the full width, no space will be created.
11850 only has an effect on displayed formulas when the formula style
11855 (Formula styles are explained in
11856 \begin_inset CommandInset ref
11858 reference "sec:Formula-Styles"
11865 \begin_layout Standard
11866 For text, variable space can be inserted via the menu
11868 Insert\SpecialChar \menuseparator
11869 Formatting\SpecialChar \menuseparator
11871 \begin_inset space ~
11876 , what is not possible in formulas:
11879 \begin_layout Standard
11880 This is a line with
11881 \begin_inset space \hspace{}
11886 \begin_inset space \thinspace{}
11892 \begin_layout Standard
11893 This is a line with
11894 \begin_inset space \hfill{}
11900 \begin_layout Subsection
11901 Space besides inline Formulas
11905 \begin_layout Plain Layout
11906 Space ! besides inline formulas
11914 \begin_layout Standard
11915 The space that surrounds inline formulas can be adjusted with the length
11924 \begin_layout Plain Layout
11935 The value of a length is set with the command
11943 \begin_layout Plain Layout
11953 that has the following scheme:
11956 \begin_layout Standard
11961 setlength{length name}{value}
11964 \begin_layout Standard
11972 \begin_inset space \thinspace{}
11978 \begin_layout Standard
11988 \begin_layout Standard
11989 is inserted in TeX-mode.
11991 \begin_inset space \thinspace{}
11994 mm space will now be set around all inline formulas:
11998 \begin_layout Plain Layout
12012 \begin_layout Standard
12013 This is a line with an inline formula
12014 \begin_inset Formula $A=B$
12018 \begin_inset space \thinspace{}
12021 mm surrounding space.
12025 \begin_layout Plain Layout
12039 \begin_layout Standard
12040 To return to the predefined value,
12046 is set to the value 0
12047 \begin_inset space \thinspace{}
12053 \begin_layout Section
12058 \begin_layout Plain Layout
12068 \begin_layout Plain Layout
12073 \begin_layout Plain Layout
12084 \begin_layout Plain Layout
12099 \begin_layout Standard
12100 Boxes for text are described in chapter
12107 \begin_inset space ~
12115 \begin_layout Subsection
12117 \begin_inset CommandInset label
12119 name "sub:Boxes-with-Frame"
12127 \begin_layout Plain Layout
12136 \begin_layout Standard
12137 It is possible to frame formulas or parts of it with the commands
12147 \begin_layout Plain Layout
12165 \begin_layout Plain Layout
12176 \begin_layout Standard
12177 When one of these commands is inserted to a formula, a blue box appears
12178 within a frame to enter formula parts.
12185 an additional formula has to be created by
12193 \begin_layout Plain Layout
12194 Due to a bug in LyX it is not possible to create a new formula with
12199 \begin_inset CommandInset href
12201 name "LyX-bug #1435"
12202 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12211 , because the box content will otherwise be treated as mathematical text.
12218 is used, a new formula is automatically created inside the frame.
12221 \begin_layout Standard
12228 is not suitable to frame displayed formulas, because the formula will always
12229 be set in the size of the text.
12236 is in contrary not suitable to frame inline formulas, because the formula
12237 will always be set in the size of a displayed formula.
12240 \begin_layout Standard
12247 there is the command
12257 \begin_layout Plain Layout
12265 where additionally the frame width and the alignment can be specified.
12272 is used in the following scheme:
12275 \begin_layout Standard
12280 framebox[frame width][position]{box content}
12283 \begin_layout Standard
12284 The position can either be
12301 right aligns the formula in the box.
12302 When no position is given, the formula will be centered.
12303 \begin_inset Newline newline
12306 Is no width given, also no position can be given.
12307 In this case the frame width is adjusted to the box content like for
12316 \begin_layout Standard
12323 is inserted, a box appears containing three blue boxes.
12324 The first two boxes are surrounded by brackets and denote the two optional
12326 The third box is for formula parts like for
12335 \begin_layout Standard
12337 \begin_inset Note Note
12340 \begin_layout Plain Layout
12341 The table has been set into a minipage to make the footnote appearing.
12342 Otherwise the footnote text would not be displayed.
12348 \begin_inset Box Frameless
12357 height_special "totalheight"
12360 \begin_layout Plain Layout
12362 \begin_inset Tabular
12363 <lyxtabular version="3" rows="5" columns="2">
12365 <column alignment="center" valignment="top" width="0">
12366 <column alignment="center" valignment="top" width="0">
12368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12371 \begin_layout Plain Layout
12376 \begin_layout Plain Layout
12377 Due to a bug in LyX it is not possible to create a new formula with
12382 \begin_inset CommandInset href
12384 name "LyX-bug #1435"
12385 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12402 \begin_layout Plain Layout
12404 \begin_inset Note Note
12407 \begin_layout Plain Layout
12414 is only used as spacer.
12426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12429 \begin_layout Plain Layout
12436 \begin_layout Plain Layout
12455 \begin_layout Plain Layout
12469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12472 \begin_layout Plain Layout
12473 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12487 \begin_layout Plain Layout
12494 \begin_layout Plain Layout
12509 \begin_layout Plain Layout
12523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12526 \begin_layout Plain Layout
12527 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12540 \begin_layout Plain Layout
12547 \begin_layout Plain Layout
12561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12564 \begin_layout Plain Layout
12565 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12578 \begin_layout Plain Layout
12585 \begin_layout Plain Layout
12595 \begin_inset Formula $\to$
12599 \begin_inset Formula $\to$
12612 \begin_layout Plain Layout
12622 \begin_inset Formula $\downarrow$
12630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12633 \begin_layout Plain Layout
12634 \begin_inset Formula $\raisebox{6mm}{}$
12638 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12642 \begin_inset Formula $\raisebox{-4mm}{}$
12663 \begin_layout Standard
12664 The frame thickness can also be adjusted.
12665 To do this the following commands have to be inserted in TeX-mode before
12669 \begin_layout Standard
12679 \begin_inset Quotes eld
12683 \begin_inset Quotes erd
12697 \begin_inset Quotes eld
12701 \begin_inset Quotes erd
12707 \begin_layout Standard
12708 \begin_inset Quotes eld
12712 \begin_inset Quotes erd
12715 specifies the minimal distance between the frame and the first character
12717 An example for this is the following framed formula:
12721 \begin_layout Plain Layout
12733 \begin_inset Formula \[
12738 Before this formula the commands
12741 \begin_layout Standard
12763 \begin_layout Standard
12764 were inserted in TeX-mode.
12765 The given values are used for all following boxes.
12768 \begin_layout Standard
12769 To return to the standard frame size, the command
12772 \begin_layout Standard
12797 \begin_layout Plain Layout
12811 \begin_layout Standard
12812 is inserted in TeX-mode before the next formula.
12815 \begin_layout Subsection
12816 Boxes without Frame
12817 \begin_inset CommandInset label
12819 name "sub:Boxes-without-Frame"
12827 \begin_layout Plain Layout
12828 Boxes ! without frame
12836 \begin_layout Standard
12837 For boxes without a frame there are the following box commands:
12847 \begin_layout Plain Layout
12865 \begin_layout Plain Layout
12883 \begin_layout Plain Layout
12894 \begin_layout Standard
12901 a box can be super- or subscripted.
12902 But in contrary to normal super- and subscripting, the characters in the
12903 box keep their font size.
12910 is used in the following scheme:
12913 \begin_layout Standard
12918 raisebox{height}{box content}
12921 \begin_layout Standard
12922 When the box should contain a formula, an extra formula is needed like for
12932 \begin_layout Standard
12934 \begin_inset Tabular
12935 <lyxtabular version="3" rows="4" columns="2">
12937 <column alignment="center" valignment="top" width="0">
12938 <column alignment="center" valignment="top" width="0">
12940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12943 \begin_layout Plain Layout
12949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12952 \begin_layout Plain Layout
12960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12963 \begin_layout Plain Layout
12967 \begin_inset Formula $\to$
12973 \begin_inset Formula $\to$
12981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12984 \begin_layout Plain Layout
12985 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12998 \begin_layout Plain Layout
13002 \begin_inset Formula $\to$
13008 \begin_inset Formula $\to$
13016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13019 \begin_layout Plain Layout
13020 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13033 \begin_layout Plain Layout
13037 \begin_inset Formula $\to$
13052 \begin_layout Plain Layout
13066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13069 \begin_layout Plain Layout
13073 \begin_layout Plain Layout
13097 \begin_layout Standard
13098 The last formula can currently only be created using TeX-mode because LyX
13099 inserts a box instead of the needed extra formula.
13103 \begin_layout Plain Layout
13105 \begin_inset CommandInset href
13107 name "LyX-bug #1435"
13108 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13120 \begin_layout Standard
13145 , with the difference that there is no frame.
13148 \begin_layout Subsection
13150 \begin_inset CommandInset label
13152 name "sub:Colored-Boxes"
13160 \begin_layout Plain Layout
13169 \begin_layout Standard
13170 To be able to use all commands explained in this section, the LaTeX-package
13179 \begin_layout Plain Layout
13184 is part of every LaTeX standard installation.
13193 \begin_layout Plain Layout
13199 has to be loaded in the LaTeX-preamble with the line
13203 \begin_layout Plain Layout
13204 When text is colored somewhere in the document with a predefined color,
13205 LyX loads the LaTeX-package
13210 Thus it is possible that the package is loaded twice, but this doesn't
13217 \begin_inset Note Note
13220 \begin_layout Plain Layout
13221 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13230 \begin_layout Standard
13238 \begin_layout Standard
13239 \begin_inset VSpace medskip
13242 To color boxes, the command
13252 \begin_layout Plain Layout
13260 is used in the following scheme:
13263 \begin_layout Standard
13268 colorbox{color}{box content}
13271 \begin_layout Standard
13272 The box content can also be a box and a
13278 can also be part of another box (see the 2nd and 3rd example).
13279 When the box should contain a formula, an extra formula has to be created,
13290 \begin_layout Plain Layout
13291 This also applies for the command
13299 \begin_inset CommandInset href
13301 name "LyX-bug #1435"
13302 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13314 \begin_layout Standard
13315 One of the following predefined colors can be chosen:
13318 \begin_layout Standard
13352 \begin_layout Standard
13354 \begin_inset Tabular
13355 <lyxtabular version="3" rows="4" columns="2">
13357 <column alignment="center" valignment="top" width="0">
13358 <column alignment="center" valignment="top" width="0">
13360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13363 \begin_layout Plain Layout
13369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13372 \begin_layout Plain Layout
13374 \begin_inset Note Note
13377 \begin_layout Plain Layout
13384 is only used as spacer.
13396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13399 \begin_layout Plain Layout
13403 \begin_inset Formula $\to$
13413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13416 \begin_layout Plain Layout
13417 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13430 \begin_layout Plain Layout
13434 \begin_inset Formula $\to$
13445 \begin_layout Plain Layout
13459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13462 \begin_layout Plain Layout
13463 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13476 \begin_layout Plain Layout
13483 \begin_layout Plain Layout
13495 \begin_inset Formula $\to$
13505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13508 \begin_layout Plain Layout
13509 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13525 \begin_layout Standard
13532 only colors the box but not the characters in the box.
13533 To color all characters, the whole formula is highlighted and the wanted
13534 color is chosen in the
13537 \begin_inset space ~
13543 The dialog can be called with the toolbar button
13544 \begin_inset Graphics
13545 filename ../images/dialog-show_character.png
13552 Edit\SpecialChar \menuseparator
13554 \begin_inset space ~
13557 Style\SpecialChar \menuseparator
13561 The formula number has then the same color as the formula.
13562 When the formula number should get another color than the formula characters,
13563 the color must be changed within the formula.
13566 \begin_layout Standard
13570 \begin_layout Standard
13573 \begin_inset Formula \begin{equation}
13574 \int A=B\label{eq:red}\end{equation}
13581 \begin_inset Formula \begin{equation}
13582 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13589 \begin_layout Standard
13591 \begin_inset CommandInset ref
13597 is completely colored red.
13598 \begin_inset Newline newline
13602 \begin_inset CommandInset ref
13604 reference "eq:redgreen"
13608 was first completely colored green to set the color for the formula number.
13609 Subsequently the formula characters were colored red.
13612 \begin_layout Standard
13613 \begin_inset VSpace bigskip
13616 To color the frame different than the rest of the box, the command
13626 \begin_layout Plain Layout
13634 is used in the following scheme:
13637 \begin_layout Standard
13642 fcolorbox{frame color}{color}{box content}
13645 \begin_layout Standard
13652 is an extension of the command
13659 The frame width is set, like for
13682 \begin_layout Plain Layout
13694 \begin_inset Formula \[
13695 \fcolorbox{cyan}{magenta}{A=B}\]
13703 \begin_layout Plain Layout
13717 \begin_layout Standard
13718 This formula was created with the command
13719 \begin_inset Newline newline
13727 \begin_inset Formula $\to$
13733 \begin_inset Formula $\to$
13743 \begin_layout Standard
13744 \begin_inset VSpace bigskip
13747 To use other colors than the predefined ones, they have to be defined first.
13750 \begin_layout Standard
13751 One can for example define the color
13752 \begin_inset Quotes eld
13760 \begin_inset Quotes erd
13763 with the LaTeX-preamble line:
13766 \begin_layout Standard
13771 definecolor{darkgreen}{cmyk}{0.5,
13789 \begin_layout Plain Layout
13800 \begin_layout Standard
13805 is the color space that denotes the colors
13822 The four comma separated numbers are the portion factor for the corresponding
13823 colors of the color space.
13824 The factors can be in the range of 0
13825 \begin_inset space \thinspace{}
13829 \begin_inset space \thinspace{}
13837 also the color space
13841 can be used for definitions.
13858 , so that there are in this case three portion factors for the corresponding
13860 Furthermore there is the color space
13864 with one portion factor for the gray value.
13867 \begin_layout Standard
13868 As example a framed box with the new defined color
13872 where the characters have been colored
13877 \begin_inset Formula \begin{equation}
13878 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13885 \begin_layout Standard
13886 Self-defined colors can also be used for text with the help of the command
13897 \begin_layout Plain Layout
13906 \begin_layout Standard
13910 \begin_layout Plain Layout
13914 textcolor{darkgreen}{
13920 \begin_inset Quotes eld
13924 \begin_inset Quotes erd
13931 \begin_layout Plain Layout
13941 \begin_layout Standard
13952 \begin_layout Plain Layout
13960 is used in the scheme
13964 textcolor{color}{characters to color}
13969 \begin_layout Subsection
13971 \begin_inset CommandInset label
13973 name "sub:Paragraph-Boxes"
13981 \begin_layout Plain Layout
13982 Boxes ! as paragraph
13990 \begin_layout Standard
13991 A box that can contain several lines and paragraphs, a so called paragraph
13992 box (parbox), can be created with the menu
13994 Insert\SpecialChar \menuseparator
13997 or the toolbar button
13998 \begin_inset Graphics
13999 filename ../images/box-insert.png
14007 \begin_layout Standard
14008 The following example shows a framed parbox in a line:
14011 \begin_layout Standard
14012 \begin_inset VSpace medskip
14016 \begin_inset Box Boxed
14025 height_special "totalheight"
14028 \begin_layout Plain Layout
14029 This is a paragraph box.
14031 \begin_inset space \thinspace{}
14034 cm long and can also contain formulas:
14035 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14046 \begin_layout Standard
14047 \begin_inset VSpace medskip
14053 \begin_layout Standard
14054 Such a box is created by right-clicking on the gray box inset.
14055 A dialog pops up showing the box properties.
14069 \begin_inset space \thinspace{}
14074 Vertical Box Alignment
14079 \begin_layout Standard
14080 \begin_inset VSpace medskip
14083 In LaTeX a parbox is created with the command
14093 \begin_layout Plain Layout
14101 that has the following scheme:
14104 \begin_layout Standard
14109 parbox[position]{width}{box content}
14112 \begin_layout Standard
14126 for bottom means that the box is aligned within the surrounding text with
14132 for top this is done with the first line.
14133 When no position is given, the box will be vertically centered, see section
14141 \begin_inset space ~
14146 manual for examples.
14149 \begin_layout Standard
14150 \begin_inset VSpace bigskip
14153 To frame formulas completely, including the formula number, the formula
14154 must be set into a parbox.
14155 To do this, the command
14169 is inserted in TeX-mode before the formula.
14178 \begin_layout Plain Layout
14188 is hereby the line width set for the document.
14189 Because the frame is outside the parbox, 2
14190 \begin_inset space \thinspace{}
14193 times the frame separation and the frame thickness must be subtracted from
14195 As this is not automatically done by LyX due to a bug
14199 \begin_layout Plain Layout
14200 \begin_inset CommandInset href
14202 name "LyX-bug #4483"
14203 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14212 , TeX-mode has to be used.
14213 To be able to multiply and subtract in arguments, the LaTeX-package
14221 \begin_layout Plain Layout
14226 is part of every LaTeX standard installation.
14235 \begin_layout Plain Layout
14241 must be loaded in the LaTeX-preamble with the line
14244 \begin_layout Standard
14252 \begin_layout Standard
14253 Behind the formula both boxes are closed by entering
14258 Here is an example:
14262 \begin_layout Plain Layout
14276 \begin_layout Standard
14280 \begin_layout Plain Layout
14298 \begin_inset Formula \begin{equation}
14299 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14307 \begin_layout Plain Layout
14318 \begin_layout Plain Layout
14332 \begin_layout Standard
14333 \begin_inset VSpace medskip
14336 As a parbox is used as argument of
14342 , there is in this case no difference between
14357 \begin_layout Standard
14358 \begin_inset VSpace bigskip
14361 Paragraph boxes are very useful to comment formulas directly.
14368 is used in combination with the command
14382 \begin_inset CommandInset ref
14384 reference "sub:User-defined-Numbering"
14391 \begin_layout Standard
14392 An example of a formula commented with
14401 \begin_layout Standard
14405 \begin_layout Plain Layout
14418 This is a description.
14419 It is distinctly separated from the formula and multiline.
14423 \begin_layout Plain Layout
14435 \begin_layout Standard
14436 Such a formula must be inserted completely in TeX-mode because LyX does
14437 not yet support the command
14444 The formula is created with the following command sequence:
14447 \begin_layout Standard
14460 is inserted in TeX-mode.
14464 \begin_layout Plain Layout
14465 When the formula style
14477 can also be replaced by
14484 (formula styles see
14485 \begin_inset CommandInset ref
14487 reference "sec:Formula-Styles"
14496 Then the description follows as normal text, and finally
14502 is inserted in TeX-mode.
14515 hereby create a displayed formula.
14518 \begin_layout Standard
14525 can be seen in this example that was
14526 \begin_inset Quotes eld
14530 \begin_inset Quotes erd
14533 using the mathematical textmode:
14534 \begin_inset Formula \[
14535 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14542 \begin_layout Section
14547 \begin_layout Plain Layout
14556 \begin_layout Subsection
14558 \begin_inset CommandInset label
14560 name "sub:Big-Operators"
14568 \begin_layout Plain Layout
14578 \begin_layout Plain Layout
14588 \begin_layout Plain Layout
14597 \begin_layout Standard
14598 To be able to use all integral operators listed here, the option
14600 Use esint package automatically
14602 must be set in the document settings under
14605 \begin_inset space ~
14613 \begin_layout Standard
14614 \begin_inset space \hfill{}
14618 \begin_inset Tabular
14619 <lyxtabular version="3" rows="11" columns="2">
14621 <column alignment="center" valignment="top" width="0pt">
14622 <column alignment="center" valignment="top" width="0pt">
14624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14627 \begin_layout Plain Layout
14633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14636 \begin_layout Plain Layout
14644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14647 \begin_layout Plain Layout
14654 \begin_layout Plain Layout
14667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14670 \begin_layout Plain Layout
14671 \begin_inset Formula $\sum$
14681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14684 \begin_layout Plain Layout
14691 \begin_layout Plain Layout
14704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14707 \begin_layout Plain Layout
14708 \begin_inset Formula $\int$
14718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14721 \begin_layout Plain Layout
14729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14732 \begin_layout Plain Layout
14733 \begin_inset Formula $\intop$
14743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14746 \begin_layout Plain Layout
14754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14757 \begin_layout Plain Layout
14758 \begin_inset Formula $\oint$
14768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14771 \begin_layout Plain Layout
14779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14782 \begin_layout Plain Layout
14783 \begin_inset Formula $\ointop$
14793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14796 \begin_layout Plain Layout
14804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14807 \begin_layout Plain Layout
14808 \begin_inset Formula $\ointctrclockwise$
14818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14821 \begin_layout Plain Layout
14829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14832 \begin_layout Plain Layout
14833 \begin_inset Formula $\ointclockwise$
14843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14846 \begin_layout Plain Layout
14854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14857 \begin_layout Plain Layout
14858 \begin_inset Formula $\sqint$
14868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14871 \begin_layout Plain Layout
14879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14882 \begin_layout Plain Layout
14883 \begin_inset Formula $\bigcap$
14893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14896 \begin_layout Plain Layout
14904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14907 \begin_layout Plain Layout
14908 \begin_inset Formula $\bigcup$
14922 \begin_inset space \hfill{}
14926 \begin_inset Tabular
14927 <lyxtabular version="3" rows="10" columns="2">
14929 <column alignment="center" valignment="top" width="0pt">
14930 <column alignment="center" valignment="top" width="0pt">
14932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14935 \begin_layout Plain Layout
14941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14944 \begin_layout Plain Layout
14952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14955 \begin_layout Plain Layout
14962 \begin_layout Plain Layout
14975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14978 \begin_layout Plain Layout
14979 \begin_inset Formula $\prod$
14989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14992 \begin_layout Plain Layout
15000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15003 \begin_layout Plain Layout
15004 \begin_inset Formula $\coprod$
15014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15017 \begin_layout Plain Layout
15025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15028 \begin_layout Plain Layout
15029 \begin_inset Formula $\bigodot$
15039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15042 \begin_layout Plain Layout
15050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15053 \begin_layout Plain Layout
15054 \begin_inset Formula $\bigotimes$
15064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15067 \begin_layout Plain Layout
15075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15078 \begin_layout Plain Layout
15079 \begin_inset Formula $\bigoplus$
15089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15092 \begin_layout Plain Layout
15100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15103 \begin_layout Plain Layout
15104 \begin_inset Formula $\bigwedge$
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15117 \begin_layout Plain Layout
15125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15128 \begin_layout Plain Layout
15129 \begin_inset Formula $\bigvee$
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15142 \begin_layout Plain Layout
15150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15153 \begin_layout Plain Layout
15154 \begin_inset Formula $\bigsqcup$
15164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15167 \begin_layout Plain Layout
15175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15178 \begin_layout Plain Layout
15179 \begin_inset Formula $\biguplus$
15193 \begin_inset space \hfill{}
15199 \begin_layout Standard
15200 All big operators can also be inserted via the math toolbar button
15201 \begin_inset Graphics
15202 filename ../images/math/intop.png
15210 \begin_layout Standard
15211 The operators are called big because they are bigger than the sometimes
15212 equal looking binary operators.
15213 All big operators can have limits as described in the next subsection.
15216 \begin_layout Standard
15242 \begin_inset space ~
15245 in the style the operator limits are displayed, see
15246 \begin_inset CommandInset ref
15248 reference "sub:Operator-Limits"
15256 \begin_layout Subsubsection*
15257 Advices for Integrals
15260 \begin_layout Standard
15265 in an integral is an operator, that therefore has to be set upright.
15266 This is done by highlighting the
15270 and using the keyboard shortcut
15273 \begin_inset space ~
15282 \begin_layout Plain Layout
15288 \begin_inset CommandInset ref
15290 reference "sub:Font-Styles"
15300 Finally the smallest space is inserted before the
15304 , as this is usual for operators.
15308 \begin_layout Standard
15310 \begin_inset Formula $\int A(x)dx$
15314 \begin_inset Newline newline
15321 \begin_layout Plain Layout
15331 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15337 \begin_layout Standard
15338 For multiple integrals there are the following commands:
15339 \begin_inset VSpace medskip
15345 \begin_layout Standard
15346 \begin_inset space \hfill{}
15350 \begin_inset Tabular
15351 <lyxtabular version="3" rows="4" columns="2">
15353 <column alignment="center" valignment="top" width="0">
15354 <column alignment="center" valignment="top" width="0">
15356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15359 \begin_layout Plain Layout
15365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15368 \begin_layout Plain Layout
15370 \begin_inset Note Note
15373 \begin_layout Plain Layout
15380 is only used as spacer.
15392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15395 \begin_layout Plain Layout
15403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15406 \begin_layout Plain Layout
15407 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15420 \begin_layout Plain Layout
15428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15431 \begin_layout Plain Layout
15432 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15445 \begin_layout Plain Layout
15453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15456 \begin_layout Plain Layout
15457 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15471 \begin_inset space \hfill{}
15475 \begin_inset Tabular
15476 <lyxtabular version="3" rows="4" columns="2">
15478 <column alignment="center" valignment="top" width="0">
15479 <column alignment="center" valignment="top" width="0">
15481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15484 \begin_layout Plain Layout
15490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15493 \begin_layout Plain Layout
15501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15504 \begin_layout Plain Layout
15512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15515 \begin_layout Plain Layout
15516 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15529 \begin_layout Plain Layout
15537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15540 \begin_layout Plain Layout
15541 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15554 \begin_layout Plain Layout
15562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15565 \begin_layout Plain Layout
15566 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15580 \begin_inset space \hfill{}
15586 \begin_layout Subsection
15588 \begin_inset CommandInset label
15590 name "sub:Operator-Limits"
15598 \begin_layout Plain Layout
15607 \begin_layout Standard
15608 Limits are created by super- and subscripts:
15611 \begin_layout Standard
15613 \begin_inset Tabular
15614 <lyxtabular version="3" rows="2" columns="2">
15616 <column alignment="center" valignment="top" width="0pt">
15617 <column alignment="center" valignment="top" width="0pt">
15619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15622 \begin_layout Plain Layout
15628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15631 \begin_layout Plain Layout
15633 \begin_inset Note Note
15636 \begin_layout Plain Layout
15643 is only used as spacer.
15655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15658 \begin_layout Plain Layout
15667 \begin_layout Plain Layout
15677 \begin_inset Formula $\to$
15681 \begin_inset Formula $\to$
15689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15692 \begin_layout Plain Layout
15693 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15709 \begin_layout Standard
15710 Limits of inline formulas are set right beside the operator.
15711 Limits in displayed formulas are set above or below the operator, except
15712 of integral limits.
15715 \begin_layout Standard
15716 To force that the limits are set beside the operator, the cursor is set
15717 directly behind the operator and the limits type is changed with the menu
15720 Edit\SpecialChar \menuseparator
15721 Math\SpecialChar \menuseparator
15733 \begin_inset space ~
15742 \begin_layout Standard
15743 The default limits type is this:
15744 \begin_inset Formula \[
15745 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15749 This is how it looks when the limits type was changed to
15756 \begin_inset Formula \[
15757 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15761 For integrals, except of
15773 , the limits are by default set beside the operator.
15774 But for multiple integrals the limits are often set below the operator.
15775 In the following example the limits type was therefore set to
15779 and so set below the integrals:
15780 \begin_inset Formula \begin{equation}
15781 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15788 \begin_layout Standard
15789 \begin_inset VSpace medskip
15792 To specify conditions for limits, the commands
15802 \begin_layout Plain Layout
15820 \begin_layout Plain Layout
15829 To create for example this expression
15830 \begin_inset Formula \begin{equation}
15831 \sum_{\begin{subarray}{c}
15833 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15840 \begin_layout Standard
15841 the following has to be done:
15842 \begin_inset Newline newline
15857 \begin_layout Plain Layout
15869 One is now in a blue box under the summation operator and insert there
15878 \begin_layout Plain Layout
15890 The blue box is now within a purple box and now several lines can be written
15892 A new line is created by inserting a line break (
15898 \begin_inset Newline newline
15903 0<k<1000 Ctrl-Return
15904 \begin_inset Newline newline
15909 is typed in, a new box appears below for the new line.
15912 \begin_layout Standard
15913 The alignment of the lines can be changed to left aligned with the
15923 Edit\SpecialChar \menuseparator
15927 To get right alignment,
15935 \begin_layout Plain Layout
15946 is inserted at the beginning of the line.
15949 \begin_layout Standard
15962 with the difference that the lines are always centered.
15965 \begin_layout Standard
15966 \begin_inset VSpace bigskip
15970 \begin_inset CommandInset ref
15972 reference "eq:substack"
15976 there can be too much space beside an operator, because the characters
15977 following the operator are set beside the limits.
15980 \begin_layout Standard
15981 To avoid this, the following macro can be used in the LaTeX-preamble:
15984 \begin_layout Standard
15998 \begin_inset Newline newline
16010 \begin_inset Newline newline
16017 mathclapinternal #1#2{
16021 mathsurround =0pt #1{#2}$}}
16024 \begin_layout Standard
16025 This defines the command
16035 \begin_layout Plain Layout
16043 that sets the width of the limit to 0
16044 \begin_inset space \thinspace{}
16048 The command scheme is
16051 \begin_layout Standard
16059 \begin_layout Standard
16060 where the limit can consist of several conditions.
16063 \begin_layout Standard
16065 \begin_inset CommandInset ref
16067 reference "eq:substack"
16071 , one uses the command
16074 \begin_layout Standard
16087 \begin_layout Plain Layout
16096 0<k<1000 Ctrl-Enter
16099 \begin_layout Standard
16100 to create the lower limit.
16101 The summand is now directly behind the summation operator:
16102 \begin_inset Formula \[
16103 \sum_{\mathclap{\substack{0<k<1000\\
16104 \\k\,\in\,\mathbb{N}}
16112 \begin_layout Standard
16113 \begin_inset VSpace bigskip
16116 How to use one limit for several operators is described in
16117 \begin_inset CommandInset ref
16119 reference "sub:Self-defined-Operators"
16126 \begin_layout Subsection
16128 \begin_inset CommandInset label
16130 name "sub:Binary-Operators"
16138 \begin_layout Plain Layout
16147 \begin_layout Standard
16148 Binary operators are surrounded by space when there is a character before
16150 \begin_inset VSpace medskip
16156 \begin_layout Standard
16157 \begin_inset space \hfill{}
16161 \begin_inset Tabular
16162 <lyxtabular version="3" rows="13" columns="2">
16164 <column alignment="center" valignment="top" width="0pt">
16165 <column alignment="center" valignment="top" width="0pt">
16167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16170 \begin_layout Plain Layout
16172 \begin_inset Note Note
16175 \begin_layout Plain Layout
16182 is only used as spacer.
16192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16195 \begin_layout Plain Layout
16203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16206 \begin_layout Plain Layout
16212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16215 \begin_layout Plain Layout
16216 \begin_inset Formula $+$
16226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16229 \begin_layout Plain Layout
16235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16238 \begin_layout Plain Layout
16239 \begin_inset Formula $-$
16249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16252 \begin_layout Plain Layout
16260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16263 \begin_layout Plain Layout
16264 \begin_inset Formula $\pm$
16274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16277 \begin_layout Plain Layout
16285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16288 \begin_layout Plain Layout
16289 \begin_inset Formula $\mp$
16299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16302 \begin_layout Plain Layout
16310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16313 \begin_layout Plain Layout
16314 \begin_inset Formula $\cdot$
16324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16327 \begin_layout Plain Layout
16335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16338 \begin_layout Plain Layout
16339 \begin_inset Formula $\times$
16349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16352 \begin_layout Plain Layout
16360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16363 \begin_layout Plain Layout
16364 \begin_inset Formula $\div$
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16377 \begin_layout Plain Layout
16381 \begin_layout Plain Layout
16394 \begin_layout Plain Layout
16406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16409 \begin_layout Plain Layout
16410 \begin_inset Formula $*$
16420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16423 \begin_layout Plain Layout
16431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16434 \begin_layout Plain Layout
16435 \begin_inset Formula $\star$
16445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16448 \begin_layout Plain Layout
16456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16459 \begin_layout Plain Layout
16460 \begin_inset Formula $\circ$
16470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16473 \begin_layout Plain Layout
16481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16484 \begin_layout Plain Layout
16485 \begin_inset Formula $\diamond$
16495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16498 \begin_layout Plain Layout
16506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16509 \begin_layout Plain Layout
16510 \begin_inset Formula $\bullet$
16524 \begin_inset space \hfill{}
16528 \begin_inset Tabular
16529 <lyxtabular version="3" rows="13" columns="2">
16531 <column alignment="center" valignment="top" width="0pt">
16532 <column alignment="center" valignment="top" width="0pt">
16534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16537 \begin_layout Plain Layout
16543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16546 \begin_layout Plain Layout
16554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16557 \begin_layout Plain Layout
16565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16568 \begin_layout Plain Layout
16569 \begin_inset Formula $\nabla$
16579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16582 \begin_layout Plain Layout
16590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16593 \begin_layout Plain Layout
16594 \begin_inset Formula $\bigtriangledown$
16604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16607 \begin_layout Plain Layout
16615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16618 \begin_layout Plain Layout
16619 \begin_inset Formula $\bigtriangleup$
16629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16632 \begin_layout Plain Layout
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16643 \begin_layout Plain Layout
16644 \begin_inset Formula $\Box$
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16657 \begin_layout Plain Layout
16665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16668 \begin_layout Plain Layout
16669 \begin_inset Formula $\cap$
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16682 \begin_layout Plain Layout
16690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16693 \begin_layout Plain Layout
16694 \begin_inset Formula $\cup$
16704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16707 \begin_layout Plain Layout
16715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16718 \begin_layout Plain Layout
16719 \begin_inset Formula $\dagger$
16729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16732 \begin_layout Plain Layout
16740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16743 \begin_layout Plain Layout
16744 \begin_inset Formula $\ddagger$
16754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16757 \begin_layout Plain Layout
16765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16768 \begin_layout Plain Layout
16769 \begin_inset Formula $\wr$
16779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16782 \begin_layout Plain Layout
16790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16793 \begin_layout Plain Layout
16794 \begin_inset Formula $\bigcirc$
16804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16807 \begin_layout Plain Layout
16815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16818 \begin_layout Plain Layout
16819 \begin_inset Formula $\wedge$
16829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16832 \begin_layout Plain Layout
16840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16843 \begin_layout Plain Layout
16844 \begin_inset Formula $\vee$
16858 \begin_inset space \hfill{}
16862 \begin_inset Tabular
16863 <lyxtabular version="3" rows="13" columns="2">
16865 <column alignment="center" valignment="top" width="0pt">
16866 <column alignment="center" valignment="top" width="0pt">
16868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16891 \begin_layout Plain Layout
16899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16902 \begin_layout Plain Layout
16903 \begin_inset Formula $\oplus$
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16916 \begin_layout Plain Layout
16924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16927 \begin_layout Plain Layout
16928 \begin_inset Formula $\ominus$
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16941 \begin_layout Plain Layout
16949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16952 \begin_layout Plain Layout
16953 \begin_inset Formula $\otimes$
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16966 \begin_layout Plain Layout
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16977 \begin_layout Plain Layout
16978 \begin_inset Formula $\oslash$
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16991 \begin_layout Plain Layout
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17002 \begin_layout Plain Layout
17003 \begin_inset Formula $\odot$
17013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17016 \begin_layout Plain Layout
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17027 \begin_layout Plain Layout
17028 \begin_inset Formula $\amalg$
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17041 \begin_layout Plain Layout
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17052 \begin_layout Plain Layout
17053 \begin_inset Formula $\uplus$
17063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17066 \begin_layout Plain Layout
17074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17077 \begin_layout Plain Layout
17078 \begin_inset Formula $\setminus$
17088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17091 \begin_layout Plain Layout
17099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17102 \begin_layout Plain Layout
17103 \begin_inset Formula $\sqcap$
17113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17116 \begin_layout Plain Layout
17124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17127 \begin_layout Plain Layout
17128 \begin_inset Formula $\sqcup$
17138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17141 \begin_layout Plain Layout
17149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17152 \begin_layout Plain Layout
17153 \begin_inset Formula $\triangleleft$
17163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17166 \begin_layout Plain Layout
17174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17177 \begin_layout Plain Layout
17178 \begin_inset Formula $\triangleright$
17192 \begin_inset space \hfill{}
17198 \begin_layout Standard
17199 All binary operators can also be inserted via the math toolbar button
17200 \begin_inset Graphics
17201 filename ../images/math/pm.png
17209 \begin_layout Standard
17210 To typeset the Laplace operator also
17227 \begin_inset Formula $\nabla^{2}$
17230 ) can be used instead of
17239 \begin_layout Standard
17246 Insert\SpecialChar \menuseparator
17258 \begin_layout Subsection
17259 Self-defined Operators
17260 \begin_inset CommandInset label
17262 name "sub:Self-defined-Operators"
17270 \begin_layout Plain Layout
17271 Operators ! self-defined
17279 \begin_layout Standard
17280 With the help of the command
17284 DeclareMathOperator
17290 \begin_layout Plain Layout
17295 DeclareMathOperator
17300 custom operators can be defined in the LaTeX-preamble.
17301 Its command scheme is:
17304 \begin_layout Standard
17309 DeclareMathOperator{new command}{display}
17312 \begin_layout Standard
17313 Display can be characters or symbols that define how the operator looks
17315 To define a big operator a * is set behind the command.
17316 All self-defined big operators can have limits as described in
17317 \begin_inset CommandInset ref
17319 reference "sub:Operator-Limits"
17326 \begin_layout Standard
17327 For example the LaTeX-preamble line
17330 \begin_layout Standard
17335 DeclareMathOperator*{
17342 \begin_layout Standard
17343 defines the command
17349 , that inserts a big operator consisting of the lozenge symbol from
17350 \begin_inset CommandInset ref
17352 reference "sub:Miscellaneous-Symbols"
17357 \begin_inset Formula \[
17358 \Lozenge_{n=1}^{\infty}\]
17362 The command for this formula is:
17373 \begin_inset Formula $\to$
17379 \begin_layout Standard
17380 \begin_inset VSpace bigskip
17383 When self-defined operators are not used several times in the document,
17384 they can also be defined with the commands
17394 \begin_layout Plain Layout
17412 \begin_layout Plain Layout
17420 , which have the following scheme:
17423 \begin_layout Standard
17437 \begin_layout Standard
17444 defines big operators,
17453 \begin_layout Standard
17461 \begin_inset space \thinspace{}
17465 \begin_inset space ~
17468 be used to use one limit for several operators:
17471 \begin_layout Standard
17472 \begin_inset Formula \[
17473 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17480 \begin_layout Standard
17481 The command for the formula above is:
17482 \begin_inset Newline newline
17501 \begin_layout Plain Layout
17513 \begin_inset Formula $\to$
17522 \begin_layout Plain Layout
17536 \begin_layout Section
17541 \begin_layout Plain Layout
17550 \begin_layout Subsection
17552 \begin_inset CommandInset label
17554 name "sub:Font-Styles"
17562 \begin_layout Plain Layout
17571 \begin_layout Standard
17572 Latin letters in formulas can be set in one of the following font styles:
17573 \begin_inset VSpace -2mm
17579 \begin_layout Standard
17581 \begin_inset Tabular
17582 <lyxtabular version="3" rows="6" columns="3">
17584 <column alignment="center" valignment="top" width="0">
17585 <column alignment="center" valignment="top" width="0">
17586 <column alignment="center" valignment="top" width="0">
17588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17591 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17600 \begin_layout Plain Layout
17606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17609 \begin_layout Plain Layout
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17629 \begin_layout Plain Layout
17645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17648 \begin_layout Plain Layout
17649 \begin_inset Formula $\mathbb{ABC}$
17657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17660 \begin_layout Plain Layout
17668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17671 \begin_layout Plain Layout
17680 \begin_layout Plain Layout
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17699 \begin_layout Plain Layout
17700 \begin_inset Formula $\mathbf{AbC}$
17708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17711 \begin_layout Plain Layout
17719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17722 \begin_layout Plain Layout
17731 \begin_layout Plain Layout
17747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17750 \begin_layout Plain Layout
17751 \begin_inset Formula $\boldsymbol{AbC}$
17759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17762 \begin_layout Plain Layout
17770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17773 \begin_layout Plain Layout
17782 \begin_layout Plain Layout
17798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17801 \begin_layout Plain Layout
17802 \begin_inset Formula $\mathcal{ABC}$
17810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17813 \begin_layout Plain Layout
17821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17824 \begin_layout Plain Layout
17833 \begin_layout Plain Layout
17849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17852 \begin_layout Plain Layout
17853 \begin_inset Formula $\mathfrak{AbC}$
17861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17864 \begin_layout Plain Layout
17878 \begin_layout Standard
17880 \begin_inset Tabular
17881 <lyxtabular version="3" rows="5" columns="3">
17883 <column alignment="center" valignment="top" width="0">
17884 <column alignment="center" valignment="top" width="0">
17885 <column alignment="center" valignment="top" width="0">
17887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17899 \begin_layout Plain Layout
17905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17908 \begin_layout Plain Layout
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17919 \begin_layout Plain Layout
17928 \begin_layout Plain Layout
17944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17947 \begin_layout Plain Layout
17948 \begin_inset Formula $\mathit{AbC}$
17956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17959 \begin_layout Plain Layout
17967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17970 \begin_layout Plain Layout
17979 \begin_layout Plain Layout
17995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17998 \begin_layout Plain Layout
17999 \begin_inset Formula $\mathrm{AbC}$
18007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18010 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18021 \begin_layout Plain Layout
18030 \begin_layout Plain Layout
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18049 \begin_layout Plain Layout
18050 \begin_inset Formula $\mathsf{AbC}$
18058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18061 \begin_layout Plain Layout
18069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18072 \begin_layout Plain Layout
18081 \begin_layout Plain Layout
18097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18100 \begin_layout Plain Layout
18101 \begin_inset Formula $\mathtt{AbC}$
18109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18112 \begin_layout Plain Layout
18126 \begin_layout Standard
18127 \begin_inset Note Greyedout
18130 \begin_layout Plain Layout
18147 can only be used for big letters.
18155 \begin_layout Standard
18156 Predefined is the style
18165 \begin_layout Standard
18166 The style commands work also for letters in mathematical constructs:
18167 \begin_inset Formula \[
18168 \mathfrak{A=\frac{b}{C}}\]
18175 \begin_layout Standard
18176 Characters in mathematical text don't appear in a math font style but in
18177 the text font style
18184 That their style can't be set correctly via the text style dialog is a
18189 \begin_layout Plain Layout
18190 \begin_inset CommandInset href
18192 name "LyX-bug #4091"
18193 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18205 \begin_layout Standard
18206 Instead of the style commands the dialog
18208 Edit\SpecialChar \menuseparator
18209 Math\SpecialChar \menuseparator
18212 or the toolbar button
18213 \begin_inset Graphics
18214 filename ../images/math/font.png
18222 \begin_layout Subsection
18224 \begin_inset CommandInset label
18226 name "sub:Bold-Formulas"
18234 \begin_layout Plain Layout
18243 \begin_layout Standard
18244 To make a complete formula bold, the command
18250 from the previous subsection cannot be used, because it doesn't work for
18251 small Greek letters.
18252 Furthermore it prints Latin letters always upright, like in the following
18256 \begin_layout Standard
18257 \begin_inset Formula \[
18258 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18265 \begin_layout Standard
18266 To display the formula correctly, the command
18273 \begin_inset Formula \[
18274 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18278 It is also possible to set the formula in a
18280 boldmath environment
18283 This environment is created by inserting the command
18291 \begin_layout Plain Layout
18302 To end the environment, the command
18310 \begin_layout Plain Layout
18320 is inserted in TeX-mode.
18324 \begin_layout Plain Layout
18334 \begin_inset Formula \[
18335 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18343 \begin_layout Plain Layout
18355 \begin_layout Subsection
18357 \begin_inset CommandInset label
18359 name "sub:Font-Sizes"
18367 \begin_layout Plain Layout
18376 \begin_layout Standard
18377 For characters in formulas there are, analog to characters in text, the
18378 following size commands:
18381 \begin_layout Standard
18425 \begin_inset Newline newline
18447 \begin_layout Standard
18448 The size produced by the commands depends on the document font size, that
18449 corresponds with the command
18456 The other commands produce smaller or larger sizes than
18463 The font size can however not exceed a certain value.
18464 Is for example the document font size 12
18465 \begin_inset space \thinspace{}
18474 switches to the same size as
18484 \begin_layout Standard
18485 A size command is inserted in TeX-mode before the formula and sets the size
18486 for all following formula and text characters.
18487 To switch back to the initial size, the command
18493 is inserted behind the formula in TeX-mode.
18496 \begin_layout Standard
18497 Within a formula the size can only be changed for symbols or letters in
18499 To do this, the size command is inserted in mathematical text.
18500 All following characters until the end of the mathematical text or until
18501 another size command will have the selected size.
18503 \begin_inset VSpace -2mm
18509 \begin_layout Standard
18513 \begin_layout Plain Layout
18523 \begin_inset Formula \[
18524 A=\frac{B}{c}\cdot\maltese\]
18529 \begin_inset Formula \[
18530 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18538 \begin_layout Plain Layout
18550 \begin_layout Standard
18551 \begin_inset VSpace medskip
18554 Before both formulas the command
18561 The command for the second formula is:
18562 \begin_inset Newline newline
18573 \begin_layout Plain Layout
18588 \begin_layout Plain Layout
18603 \begin_layout Plain Layout
18618 \begin_layout Plain Layout
18628 \begin_inset Formula $\to$
18632 \begin_inset Formula $\to$
18636 \begin_inset Newline newline
18640 \begin_inset space \hspace*{}
18654 \begin_layout Plain Layout
18669 \begin_layout Plain Layout
18684 \begin_layout Plain Layout
18696 \begin_layout Standard
18697 If a symbol cannot be displayed in different sizes, it will always be displayed
18698 in the default size.
18701 \begin_layout Section
18706 \begin_layout Plain Layout
18715 \begin_layout Standard
18716 All Greek letters can also be inserted via the toolbar button
18717 \begin_inset Graphics
18718 filename ../images/math/alpha.png
18726 \begin_layout Subsection
18728 \begin_inset CommandInset label
18730 name "sub:Small-Letters"
18738 \begin_layout Plain Layout
18739 Greek letters ! small
18747 \begin_layout Standard
18748 \begin_inset space \hfill{}
18752 \begin_inset Tabular
18753 <lyxtabular version="3" rows="11" columns="2">
18755 <column alignment="center" valignment="top" width="0pt">
18756 <column alignment="center" valignment="top" width="0pt">
18758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18761 \begin_layout Plain Layout
18767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18770 \begin_layout Plain Layout
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18781 \begin_layout Plain Layout
18789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18792 \begin_layout Plain Layout
18793 \begin_inset Formula $\alpha$
18803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18806 \begin_layout Plain Layout
18814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18817 \begin_layout Plain Layout
18818 \begin_inset Formula $\beta$
18828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18831 \begin_layout Plain Layout
18839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18842 \begin_layout Plain Layout
18843 \begin_inset Formula $\gamma$
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18856 \begin_layout Plain Layout
18864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18867 \begin_layout Plain Layout
18868 \begin_inset Formula $\delta$
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18881 \begin_layout Plain Layout
18889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18892 \begin_layout Plain Layout
18893 \begin_inset Formula $\epsilon$
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18906 \begin_layout Plain Layout
18914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18917 \begin_layout Plain Layout
18918 \begin_inset Formula $\varepsilon$
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18931 \begin_layout Plain Layout
18939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18942 \begin_layout Plain Layout
18943 \begin_inset Formula $\zeta$
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18956 \begin_layout Plain Layout
18964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18967 \begin_layout Plain Layout
18968 \begin_inset Formula $\eta$
18978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18981 \begin_layout Plain Layout
18989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18992 \begin_layout Plain Layout
18993 \begin_inset Formula $\theta$
19003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19006 \begin_layout Plain Layout
19014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19017 \begin_layout Plain Layout
19018 \begin_inset Formula $\vartheta$
19032 \begin_inset space \hfill{}
19036 \begin_inset Tabular
19037 <lyxtabular version="3" rows="12" columns="2">
19039 <column alignment="center" valignment="top" width="0pt">
19040 <column alignment="center" valignment="top" width="0pt">
19042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19045 \begin_layout Plain Layout
19051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19054 \begin_layout Plain Layout
19062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19065 \begin_layout Plain Layout
19073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19076 \begin_layout Plain Layout
19077 \begin_inset Formula $\iota$
19087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19090 \begin_layout Plain Layout
19098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19101 \begin_layout Plain Layout
19102 \begin_inset Formula $\kappa$
19112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19115 \begin_layout Plain Layout
19123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19126 \begin_layout Plain Layout
19127 \begin_inset Formula $\varkappa$
19137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19140 \begin_layout Plain Layout
19148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19151 \begin_layout Plain Layout
19152 \begin_inset Formula $\lambda$
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19165 \begin_layout Plain Layout
19173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19176 \begin_layout Plain Layout
19177 \begin_inset Formula $\mu$
19187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19190 \begin_layout Plain Layout
19198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19201 \begin_layout Plain Layout
19202 \begin_inset Formula $\nu$
19212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19215 \begin_layout Plain Layout
19223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19226 \begin_layout Plain Layout
19227 \begin_inset Formula $\xi$
19237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19240 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula $o$
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula $\pi$
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\varpi$
19310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $\rho$
19339 \begin_inset space \hfill{}
19343 \begin_inset Tabular
19344 <lyxtabular version="3" rows="11" columns="2">
19346 <column alignment="center" valignment="top" width="0pt">
19347 <column alignment="center" valignment="top" width="0pt">
19349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19372 \begin_layout Plain Layout
19380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19383 \begin_layout Plain Layout
19384 \begin_inset Formula $\varrho$
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19397 \begin_layout Plain Layout
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19408 \begin_layout Plain Layout
19409 \begin_inset Formula $\sigma$
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19422 \begin_layout Plain Layout
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19433 \begin_layout Plain Layout
19434 \begin_inset Formula $\varsigma$
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19447 \begin_layout Plain Layout
19455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19458 \begin_layout Plain Layout
19459 \begin_inset Formula $\tau$
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19472 \begin_layout Plain Layout
19480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19483 \begin_layout Plain Layout
19484 \begin_inset Formula $\upsilon$
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19497 \begin_layout Plain Layout
19505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19508 \begin_layout Plain Layout
19509 \begin_inset Formula $\phi$
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19522 \begin_layout Plain Layout
19530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19533 \begin_layout Plain Layout
19534 \begin_inset Formula $\varphi$
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19547 \begin_layout Plain Layout
19555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19558 \begin_layout Plain Layout
19559 \begin_inset Formula $\chi$
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19572 \begin_layout Plain Layout
19580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19583 \begin_layout Plain Layout
19584 \begin_inset Formula $\psi$
19594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19597 \begin_layout Plain Layout
19605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19608 \begin_layout Plain Layout
19609 \begin_inset Formula $\omega$
19623 \begin_inset space \hfill{}
19629 \begin_layout Standard
19630 \begin_inset VSpace medskip
19636 \begin_layout Standard
19637 How to create upright Greek letters is explained in
19638 \begin_inset CommandInset ref
19640 reference "sub:Upright-small-Greek"
19647 \begin_layout Subsection
19652 \begin_layout Plain Layout
19653 Greek letters ! big
19661 \begin_layout Standard
19662 \begin_inset space \hfill{}
19666 \begin_inset Tabular
19667 <lyxtabular version="3" rows="7" columns="2">
19669 <column alignment="center" valignment="top" width="0pt">
19670 <column alignment="center" valignment="top" width="0pt">
19672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19675 \begin_layout Plain Layout
19681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19684 \begin_layout Plain Layout
19692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19695 \begin_layout Plain Layout
19703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19706 \begin_layout Plain Layout
19707 \begin_inset Formula $\Gamma$
19717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19720 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19732 \begin_inset Formula $\Delta$
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $\Theta$
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\Lambda$
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19795 \begin_layout Plain Layout
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19806 \begin_layout Plain Layout
19807 \begin_inset Formula $\Xi$
19817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19820 \begin_layout Plain Layout
19828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19831 \begin_layout Plain Layout
19832 \begin_inset Formula $\Pi$
19846 \begin_inset space \hfill{}
19850 \begin_inset Tabular
19851 <lyxtabular version="3" rows="6" columns="2">
19853 <column alignment="center" valignment="top" width="0pt">
19854 <column alignment="center" valignment="top" width="0pt">
19856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19859 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\Sigma$
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19904 \begin_layout Plain Layout
19912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19915 \begin_layout Plain Layout
19916 \begin_inset Formula $\Upsilon$
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19929 \begin_layout Plain Layout
19937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19940 \begin_layout Plain Layout
19941 \begin_inset Formula $\Phi$
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19965 \begin_layout Plain Layout
19966 \begin_inset Formula $\Psi$
19976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19979 \begin_layout Plain Layout
19987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19990 \begin_layout Plain Layout
19991 \begin_inset Formula $\Omega$
20005 \begin_inset space \hfill{}
20011 \begin_layout Standard
20012 \begin_inset VSpace medskip
20015 That the big Greek letters appear upright is caused by a design bug when
20017 To get correct italic big letters, begin every command with
20022 For example the command
20029 \begin_inset Formula $\varGamma$
20035 \begin_layout Subsection
20040 \begin_layout Plain Layout
20041 Greek letters ! bold
20049 \begin_layout Standard
20050 Greek letters cannot be set with different font styles like Latin letters.
20051 They can only be made bold with the command
20061 \begin_layout Plain Layout
20072 \begin_layout Standard
20074 \begin_inset Tabular
20075 <lyxtabular version="3" rows="3" columns="2">
20077 <column alignment="center" valignment="top" width="0">
20078 <column alignment="center" valignment="top" width="0">
20080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20083 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20103 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Plain Layout
20119 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20132 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20148 \begin_inset Formula $\theta\boldsymbol{\theta}$
20164 \begin_layout Section
20169 \begin_layout Plain Layout
20182 \begin_layout Plain Layout
20183 A list with all symbols of most of the LaTeX-packages can be found in
20184 \begin_inset CommandInset citation
20199 \begin_layout Plain Layout
20207 \begin_inset Note Note
20210 \begin_layout Plain Layout
20213 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20216 \begin_layout Plain Layout
20219 texorpdfstring is in section
20220 \begin_inset CommandInset ref
20222 reference "sub:Formulas-in-Section"
20235 \begin_layout Plain Layout
20244 \begin_layout Standard
20245 Many of the symbols listed in this section can also be inserted via the
20247 \begin_inset Graphics
20248 filename ../images/math/nabla.png
20254 \begin_inset Graphics
20255 filename ../images/math/digamma.png
20263 \begin_layout Subsection
20264 Mathematical Symbols
20265 \begin_inset CommandInset label
20267 name "sub:Mathematical-Symbols"
20275 \begin_layout Plain Layout
20276 Symbols ! mathematical
20284 \begin_layout Standard
20285 \begin_inset space \hfill{}
20289 \begin_inset Tabular
20290 <lyxtabular version="3" rows="10" columns="2">
20292 <column alignment="center" valignment="top" width="0pt">
20293 <column alignment="center" valignment="top" width="0pt">
20295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20298 \begin_layout Plain Layout
20304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20307 \begin_layout Plain Layout
20315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20329 \begin_layout Plain Layout
20330 \begin_inset Formula $\neg$
20340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $\Im$
20365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20368 \begin_layout Plain Layout
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20379 \begin_layout Plain Layout
20380 \begin_inset Formula $\Re$
20390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20404 \begin_layout Plain Layout
20405 \begin_inset Formula $\aleph$
20415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20418 \begin_layout Plain Layout
20426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20429 \begin_layout Plain Layout
20430 \begin_inset Formula $\partial$
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20443 \begin_layout Plain Layout
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20454 \begin_layout Plain Layout
20455 \begin_inset Formula $\infty$
20465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20468 \begin_layout Plain Layout
20476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20479 \begin_layout Plain Layout
20480 \begin_inset Formula $\wp$
20490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20493 \begin_layout Plain Layout
20501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20504 \begin_layout Plain Layout
20505 \begin_inset Formula $\imath$
20515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20518 \begin_layout Plain Layout
20526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20529 \begin_layout Plain Layout
20530 \begin_inset Formula $\jmath$
20544 \begin_inset space \hfill{}
20548 \begin_inset Tabular
20549 <lyxtabular version="3" rows="10" columns="2">
20551 <column alignment="center" valignment="top" width="0pt">
20552 <column alignment="center" valignment="top" width="0pt">
20554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20557 \begin_layout Plain Layout
20563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20566 \begin_layout Plain Layout
20568 \begin_inset Note Note
20571 \begin_layout Plain Layout
20578 is only used as spacer.
20590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20593 \begin_layout Plain Layout
20601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20604 \begin_layout Plain Layout
20605 \begin_inset Formula $\forall$
20615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20618 \begin_layout Plain Layout
20626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20629 \begin_layout Plain Layout
20630 \begin_inset Formula $\exists$
20640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20643 \begin_layout Plain Layout
20651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20654 \begin_layout Plain Layout
20655 \begin_inset Formula $\nexists$
20665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20668 \begin_layout Plain Layout
20676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20679 \begin_layout Plain Layout
20680 \begin_inset Formula $\emptyset$
20690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20693 \begin_layout Plain Layout
20701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20704 \begin_layout Plain Layout
20705 \begin_inset Formula $\varnothing$
20715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20718 \begin_layout Plain Layout
20726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20729 \begin_layout Plain Layout
20730 \begin_inset Formula $\dag$
20740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20743 \begin_layout Plain Layout
20751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20754 \begin_layout Plain Layout
20755 \begin_inset Formula $\ddag$
20765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20768 \begin_layout Plain Layout
20776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20779 \begin_layout Plain Layout
20783 \begin_layout Plain Layout
20793 \begin_inset Formula $\complement$
20800 \begin_layout Plain Layout
20814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20817 \begin_layout Plain Layout
20825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20828 \begin_layout Plain Layout
20829 \begin_inset Formula $\Bbbk$
20843 \begin_inset space \hfill{}
20847 \begin_inset Tabular
20848 <lyxtabular version="3" rows="10" columns="2">
20850 <column alignment="center" valignment="top" width="0pt">
20851 <column alignment="center" valignment="top" width="0pt">
20853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20856 \begin_layout Plain Layout
20862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20865 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20876 \begin_layout Plain Layout
20884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20887 \begin_layout Plain Layout
20888 \begin_inset Formula $\prime$
20898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20901 \begin_layout Plain Layout
20909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20912 \begin_layout Plain Layout
20913 \begin_inset Formula $\backprime$
20923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20926 \begin_layout Plain Layout
20934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20937 \begin_layout Plain Layout
20938 \begin_inset Formula $\mho$
20948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20951 \begin_layout Plain Layout
20959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20962 \begin_layout Plain Layout
20963 \begin_inset Formula $\triangle$
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20976 \begin_layout Plain Layout
20984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20987 \begin_layout Plain Layout
20988 \begin_inset Formula $\angle$
20998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21012 \begin_layout Plain Layout
21013 \begin_inset Formula $\measuredangle$
21023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21026 \begin_layout Plain Layout
21034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21037 \begin_layout Plain Layout
21038 \begin_inset Formula $\sphericalangle$
21048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21051 \begin_layout Plain Layout
21059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21062 \begin_layout Plain Layout
21063 \begin_inset Formula $\top$
21073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21076 \begin_layout Plain Layout
21084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21087 \begin_layout Plain Layout
21088 \begin_inset Formula $\bot$
21102 \begin_inset space \hfill{}
21108 \begin_layout Standard
21109 \begin_inset Newpage newpage
21115 \begin_layout Subsection
21116 Miscellaneous Symbols
21117 \begin_inset CommandInset label
21119 name "sub:Miscellaneous-Symbols"
21127 \begin_layout Plain Layout
21128 Symbols ! miscellaneous
21136 \begin_layout Standard
21139 \begin_inset Tabular
21140 <lyxtabular version="3" rows="10" columns="2">
21142 <column alignment="center" valignment="top" width="0pt">
21143 <column alignment="center" valignment="top" width="0pt">
21145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21148 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21157 \begin_layout Plain Layout
21165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21168 \begin_layout Plain Layout
21176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21179 \begin_layout Plain Layout
21180 \begin_inset Formula $\flat$
21190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21193 \begin_layout Plain Layout
21201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21204 \begin_layout Plain Layout
21205 \begin_inset Formula $\natural$
21215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21218 \begin_layout Plain Layout
21226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21229 \begin_layout Plain Layout
21230 \begin_inset Formula $\sharp$
21240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21243 \begin_layout Plain Layout
21251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21254 \begin_layout Plain Layout
21255 \begin_inset Formula $\surd$
21265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21268 \begin_layout Plain Layout
21276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21279 \begin_layout Plain Layout
21280 \begin_inset Formula $\checkmark$
21290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21293 \begin_layout Plain Layout
21301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21304 \begin_layout Plain Layout
21305 \begin_inset Formula $\yen$
21315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21318 \begin_layout Plain Layout
21326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21329 \begin_layout Plain Layout
21330 \begin_inset Formula $\pounds$
21340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21343 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\$$
21363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21376 \begin_inset Formula $§$
21390 \begin_inset Tabular
21391 <lyxtabular version="3" rows="10" columns="2">
21393 <column alignment="center" valignment="top" width="0">
21394 <column alignment="center" valignment="top" width="0">
21396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21399 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21419 \begin_layout Plain Layout
21427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Plain Layout
21431 \begin_inset Formula $\hbar$
21441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21444 \begin_layout Plain Layout
21452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21455 \begin_layout Plain Layout
21456 \begin_inset Formula $\hslash$
21466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21469 \begin_layout Plain Layout
21477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21480 \begin_layout Plain Layout
21481 \begin_inset Formula $\clubsuit$
21491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21494 \begin_layout Plain Layout
21502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21505 \begin_layout Plain Layout
21506 \begin_inset Formula $\spadesuit$
21516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21519 \begin_layout Plain Layout
21527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21530 \begin_layout Plain Layout
21531 \begin_inset Formula $\bigstar$
21541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21544 \begin_layout Plain Layout
21552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21555 \begin_layout Plain Layout
21556 \begin_inset Formula $\blacklozenge$
21566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21569 \begin_layout Plain Layout
21577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21580 \begin_layout Plain Layout
21581 \begin_inset Formula $\blacktriangle$
21591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21594 \begin_layout Plain Layout
21602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21605 \begin_layout Plain Layout
21606 \begin_inset Formula $\blacktriangledown$
21616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21619 \begin_layout Plain Layout
21627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21630 \begin_layout Plain Layout
21631 \begin_inset Formula $\bullet$
21645 \begin_inset Tabular
21646 <lyxtabular version="3" rows="10" columns="2">
21648 <column alignment="center" valignment="top" width="0pt">
21649 <column alignment="center" valignment="top" width="0pt">
21651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21654 \begin_layout Plain Layout
21660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21663 \begin_layout Plain Layout
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\diamondsuit$
21696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Plain Layout
21711 \begin_inset Formula $\Diamond$
21721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Plain Layout
21736 \begin_inset Formula $\heartsuit$
21746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\P$
21771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\copyright$
21796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Plain Layout
21811 \begin_inset Formula $\circledR$
21821 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\maltese$
21846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\diagup$
21871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\diagdown$
21902 \begin_layout Standard
21903 \begin_inset VSpace medskip
21906 More symbols are listed in
21907 \begin_inset CommandInset ref
21909 reference "sub:Miscellaneous-Special-Characters"
21916 \begin_layout Standard
21917 Some symbols can be displayed in different sizes, see
21918 \begin_inset CommandInset ref
21920 reference "sub:Font-Sizes"
21927 \begin_layout Subsection
21932 \begin_layout Plain Layout
21933 Symbols ! Euro-symbol
21942 \begin_layout Plain Layout
21946 \begin_layout Plain Layout
21963 \begin_layout Standard
21964 To use the Euro symbol in formulas, the LaTeX-package
21972 \begin_layout Plain Layout
21978 must be installed and loaded with the LaTeX-preamble line
21981 \begin_layout Standard
21986 usepackage[gennarrow]{eurosym}
21989 \begin_layout Standard
21990 The Euro symbol can now be inserted with the command
22000 \begin_layout Plain Layout
22011 \begin_layout Standard
22012 The Euro symbol can directly be inserted with the € key in mathematical
22013 text, without having
22028 can also be inserted in TeX-mode.
22029 The official currency symbol can then be inserted with the command
22039 \begin_layout Plain Layout
22047 , that is only available in TeX-mode.
22050 \begin_layout Standard
22054 \begin_layout Plain Layout
22064 \begin_inset Note Note
22067 \begin_layout Plain Layout
22068 The following table will only be displayed when the LaTeX-package
22080 \begin_layout Standard
22081 An overview about the different Euro symbols:
22084 \begin_layout Standard
22086 \begin_inset Tabular
22087 <lyxtabular version="3" rows="4" columns="3">
22089 <column alignment="center" valignment="top" width="0pt">
22090 <column alignment="center" valignment="top" width="0pt">
22091 <column alignment="center" valignment="top" width="0pt">
22093 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22096 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22105 \begin_layout Plain Layout
22111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22114 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22125 \begin_layout Plain Layout
22131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22134 \begin_layout Plain Layout
22142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22145 \begin_layout Plain Layout
22146 \begin_inset Formula $\euro$
22156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22168 \begin_layout Plain Layout
22174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22178 \begin_inset Formula $\mbox{€}$
22188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22191 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22200 \begin_layout Plain Layout
22208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22211 \begin_layout Plain Layout
22215 \begin_layout Plain Layout
22237 \begin_layout Standard
22241 \begin_layout Plain Layout
22251 \begin_inset Note Note
22254 \begin_layout Plain Layout
22255 The following will be displayed when the LaTeX-package
22267 \begin_layout Standard
22268 You need to install the LaTeX-package
22272 to see the rest of this subsection in the output.
22275 \begin_layout Standard
22279 \begin_layout Plain Layout
22291 \begin_layout Section
22293 \begin_inset CommandInset label
22295 name "sec:Relations"
22303 \begin_layout Plain Layout
22313 \begin_layout Plain Layout
22318 \begin_layout Plain Layout
22329 \begin_layout Plain Layout
22344 \begin_layout Standard
22345 All relations can also be inserted via the toolbar button
22346 \begin_inset Graphics
22347 filename ../images/math/leq.png
22355 \begin_layout Standard
22356 \begin_inset space \hfill{}
22360 \begin_inset Tabular
22361 <lyxtabular version="3" rows="17" columns="2">
22363 <column alignment="center" valignment="top" width="0pt">
22364 <column alignment="center" valignment="top" width="0pt">
22366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22389 \begin_layout Plain Layout
22395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22398 \begin_layout Plain Layout
22399 \begin_inset Formula $<$
22409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22412 \begin_layout Plain Layout
22420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22423 \begin_layout Plain Layout
22424 \begin_inset Formula $\le$
22434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22437 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22448 \begin_layout Plain Layout
22449 \begin_inset Formula $\ll$
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22473 \begin_layout Plain Layout
22474 \begin_inset Formula $\prec$
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22487 \begin_layout Plain Layout
22495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22498 \begin_layout Plain Layout
22499 \begin_inset Formula $\preceq$
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22512 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22524 \begin_inset Formula $\subset$
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22537 \begin_layout Plain Layout
22545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22548 \begin_layout Plain Layout
22549 \begin_inset Formula $\subseteq$
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22562 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22573 \begin_layout Plain Layout
22574 \begin_inset Formula $\sqsubseteq$
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22587 \begin_layout Plain Layout
22595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22598 \begin_layout Plain Layout
22599 \begin_inset Formula $\in$
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22612 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22624 \begin_inset Formula $\vdash$
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22648 \begin_layout Plain Layout
22649 \begin_inset Formula $\smile$
22659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22662 \begin_layout Plain Layout
22670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22673 \begin_layout Plain Layout
22674 \begin_inset Formula $\lhd$
22684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22687 \begin_layout Plain Layout
22695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22698 \begin_layout Plain Layout
22699 \begin_inset Formula $\unlhd$
22709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22712 \begin_layout Plain Layout
22720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22723 \begin_layout Plain Layout
22724 \begin_inset Formula $\gtrless$
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22737 \begin_layout Plain Layout
22745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22748 \begin_layout Plain Layout
22749 \begin_inset Formula $\mid$
22759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22762 \begin_layout Plain Layout
22770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22773 \begin_layout Plain Layout
22774 \begin_inset Formula $\nmid$
22788 \begin_inset space \hfill{}
22792 \begin_inset Tabular
22793 <lyxtabular version="3" rows="17" columns="2">
22795 <column alignment="center" valignment="top" width="0pt">
22796 <column alignment="center" valignment="top" width="0pt">
22798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22801 \begin_layout Plain Layout
22807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22810 \begin_layout Plain Layout
22818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22821 \begin_layout Plain Layout
22827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22830 \begin_layout Plain Layout
22831 \begin_inset Formula $=$
22841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22844 \begin_layout Plain Layout
22852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22855 \begin_layout Plain Layout
22856 \begin_inset Formula $\not=$
22866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22869 \begin_layout Plain Layout
22877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22880 \begin_layout Plain Layout
22881 \begin_inset Formula $\equiv$
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22894 \begin_layout Plain Layout
22902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22905 \begin_layout Plain Layout
22906 \begin_inset Formula $\sim$
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22919 \begin_layout Plain Layout
22927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22930 \begin_layout Plain Layout
22931 \begin_inset Formula $\simeq$
22941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22944 \begin_layout Plain Layout
22952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22955 \begin_layout Plain Layout
22956 \begin_inset Formula $\approx$
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22969 \begin_layout Plain Layout
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22980 \begin_layout Plain Layout
22981 \begin_inset Formula $\cong$
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23005 \begin_layout Plain Layout
23006 \begin_inset Formula $\bowtie$
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23019 \begin_layout Plain Layout
23027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23030 \begin_layout Plain Layout
23031 \begin_inset Formula $\notin$
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23044 \begin_layout Plain Layout
23052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23055 \begin_layout Plain Layout
23056 \begin_inset Formula $\perp$
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23069 \begin_layout Plain Layout
23077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23080 \begin_layout Plain Layout
23081 \begin_inset Formula $\propto$
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23094 \begin_layout Plain Layout
23102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23105 \begin_layout Plain Layout
23106 \begin_inset Formula $\asymp$
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23119 \begin_layout Plain Layout
23127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23130 \begin_layout Plain Layout
23131 \begin_inset Formula $\doteq$
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23144 \begin_layout Plain Layout
23152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23155 \begin_layout Plain Layout
23156 \begin_inset Formula $\circeq$
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23169 \begin_layout Plain Layout
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23180 \begin_layout Plain Layout
23181 \begin_inset Formula $\models$
23191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23194 \begin_layout Plain Layout
23202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23205 \begin_layout Plain Layout
23206 \begin_inset Formula $\widehat{=}$
23220 \begin_inset space \hfill{}
23224 \begin_inset Tabular
23225 <lyxtabular version="3" rows="17" columns="2">
23227 <column alignment="center" valignment="top" width="0pt">
23228 <column alignment="center" valignment="top" width="0pt">
23230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23233 \begin_layout Plain Layout
23239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23242 \begin_layout Plain Layout
23250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23253 \begin_layout Plain Layout
23259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23262 \begin_layout Plain Layout
23263 \begin_inset Formula $>$
23273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23276 \begin_layout Plain Layout
23284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23287 \begin_layout Plain Layout
23288 \begin_inset Formula $\ge$
23298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23301 \begin_layout Plain Layout
23309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23312 \begin_layout Plain Layout
23313 \begin_inset Formula $\gg$
23323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23326 \begin_layout Plain Layout
23334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23337 \begin_layout Plain Layout
23338 \begin_inset Formula $\succ$
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23351 \begin_layout Plain Layout
23359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23362 \begin_layout Plain Layout
23363 \begin_inset Formula $\succeq$
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23376 \begin_layout Plain Layout
23384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23387 \begin_layout Plain Layout
23388 \begin_inset Formula $\supset$
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23401 \begin_layout Plain Layout
23409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23412 \begin_layout Plain Layout
23413 \begin_inset Formula $\supseteq$
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23426 \begin_layout Plain Layout
23434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23437 \begin_layout Plain Layout
23438 \begin_inset Formula $\sqsupseteq$
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23451 \begin_layout Plain Layout
23459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23462 \begin_layout Plain Layout
23463 \begin_inset Formula $\ni$
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23476 \begin_layout Plain Layout
23484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23487 \begin_layout Plain Layout
23488 \begin_inset Formula $\dashv$
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23501 \begin_layout Plain Layout
23509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23512 \begin_layout Plain Layout
23513 \begin_inset Formula $\frown$
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23526 \begin_layout Plain Layout
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23537 \begin_layout Plain Layout
23538 \begin_inset Formula $\rhd$
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23551 \begin_layout Plain Layout
23559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23562 \begin_layout Plain Layout
23563 \begin_inset Formula $\unrhd$
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23576 \begin_layout Plain Layout
23584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23587 \begin_layout Plain Layout
23588 \begin_inset Formula $\lessgtr$
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23601 \begin_layout Plain Layout
23609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23612 \begin_layout Plain Layout
23613 \begin_inset Formula $\parallel$
23623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23626 \begin_layout Plain Layout
23634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23637 \begin_layout Plain Layout
23638 \begin_inset Formula $\nparallel$
23652 \begin_inset space \hfill{}
23658 \begin_layout Standard
23659 \begin_inset VSpace medskip
23674 are bigger than the equal looking operators
23689 \begin_layout Standard
23690 Relations are, in contrary to symbols, always surrounded by space.
23693 \begin_layout Standard
23694 Relations with labels can be created with the command
23704 \begin_layout Plain Layout
23715 \begin_layout Standard
23717 \begin_inset Tabular
23718 <lyxtabular version="3" rows="2" columns="2">
23720 <column alignment="center" valignment="top" width="0">
23721 <column alignment="center" valignment="top" width="0">
23723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23726 \begin_layout Plain Layout
23732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23735 \begin_layout Plain Layout
23737 \begin_inset Note Note
23740 \begin_layout Plain Layout
23747 is only used as spacer.
23759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23769 \begin_layout Plain Layout
23786 \begin_layout Plain Layout
23796 \begin_inset Formula $\downarrow$
23805 \begin_layout Plain Layout
23818 \begin_layout Plain Layout
23832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23835 \begin_layout Plain Layout
23836 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23852 \begin_layout Section
23856 \begin_layout Subsection
23857 Predefined Functions
23858 \begin_inset CommandInset label
23860 name "sub:Predefined-Functions"
23868 \begin_layout Plain Layout
23869 Functions ! predefined
23877 \begin_layout Standard
23878 In general, variables are set
23882 in mathematical expressions, but not function names, because
23883 \begin_inset Formula $sin$
23886 could be misunderstood as
23887 \begin_inset Formula $s\cdot i\cdot n$
23891 Therefore there are predefined functions, that are additionally a bit separated
23893 They are inserted as commands starting with a backslash before their name.
23896 \begin_layout Standard
23898 \begin_inset Tabular
23899 <lyxtabular version="3" rows="2" columns="4">
23901 <column alignment="center" valignment="top" width="0pt">
23902 <column alignment="center" valignment="top" width="0pt">
23903 <column alignment="center" valignment="top" width="0pt">
23904 <column alignment="center" valignment="top" width="0pt">
23906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23909 \begin_layout Plain Layout
23915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23918 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23927 \begin_layout Plain Layout
23933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23936 \begin_layout Plain Layout
23944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23956 \begin_layout Plain Layout
23957 \begin_inset Formula $Asin(x)+B$
23965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23968 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23980 \begin_inset Formula $A\sin(x)+B$
23994 \begin_inset Newpage pagebreak
24000 \begin_layout Standard
24001 The following functions are predefined:
24004 \begin_layout Standard
24005 \begin_inset VSpace -2mm
24011 \begin_layout Standard
24013 \begin_inset Tabular
24014 <lyxtabular version="3" rows="9" columns="4">
24016 <column alignment="center" valignment="top" width="0pt">
24017 <column alignment="center" valignment="top" width="0pt">
24018 <column alignment="center" valignment="top" width="0pt">
24019 <column alignment="center" valignment="top" width="0pt">
24021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24033 \begin_layout Plain Layout
24039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24062 \begin_layout Plain Layout
24070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24073 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24095 \begin_layout Plain Layout
24105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24108 \begin_layout Plain Layout
24116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24130 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24141 \begin_layout Plain Layout
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24154 \begin_layout Plain Layout
24162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24165 \begin_layout Plain Layout
24173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24176 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24187 \begin_layout Plain Layout
24197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24200 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24233 \begin_layout Plain Layout
24243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24246 \begin_layout Plain Layout
24254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24257 \begin_layout Plain Layout
24265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24268 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24279 \begin_layout Plain Layout
24289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24292 \begin_layout Plain Layout
24300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24303 \begin_layout Plain Layout
24311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24314 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24325 \begin_layout Plain Layout
24335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24338 \begin_layout Plain Layout
24346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24360 \begin_layout Plain Layout
24368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24371 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24384 \begin_layout Plain Layout
24392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24406 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24417 \begin_layout Plain Layout
24433 \begin_layout Standard
24434 They can also be inserted with the math toolbar button
24435 \begin_inset Graphics
24436 filename ../images/math/functions.png
24444 \begin_layout Subsection
24445 Self-defined Functions
24449 \begin_layout Plain Layout
24450 Functions ! self-defined
24458 \begin_layout Standard
24459 To use a function that is not predefined, like for example the sign function
24460 sgn(x), there are two possibilities:
24463 \begin_layout Itemize
24464 Define the function by inserting the following line to the LaTeX-preamble
24468 \begin_layout Plain Layout
24473 DeclareMathOperator
24476 \begin_inset CommandInset ref
24478 reference "sub:Self-defined-Operators"
24488 \begin_inset Newline newline
24492 \begin_inset VSpace -3mm
24496 \begin_inset Newline newline
24503 DeclareMathOperator{
24511 \begin_layout Plain Layout
24516 DeclareMathOperator
24522 \begin_inset Newline newline
24526 \begin_inset VSpace -2mm
24530 \begin_inset Newline newline
24533 Now the new defined function can be called with the command
24542 \begin_layout Itemize
24543 Write the the formula as usual, mark the formula name, in our example the
24548 , and change it to mathematical text.
24549 At last a space is inserted between prefactor and function.
24552 \begin_layout Standard
24553 The result is the same with both methods as with a predefined function
24557 \begin_layout Plain Layout
24558 In LyX self-defined functions are displayed red, predefined ones black.
24566 \begin_layout Standard
24568 \begin_inset Tabular
24569 <lyxtabular version="3" rows="3" columns="2">
24571 <column alignment="center" valignment="top" width="0pt">
24572 <column alignment="center" valignment="top" width="0pt">
24574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24577 \begin_layout Plain Layout
24583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24586 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24608 \begin_layout Plain Layout
24609 \begin_inset Formula $A\sgn(x)+B$
24619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24626 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24638 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24654 \begin_layout Standard
24655 The first method is more suitable when the self-defined function should
24656 be used several times.
24659 \begin_layout Subsection
24664 \begin_layout Plain Layout
24673 \begin_layout Standard
24674 For limits there are defined besides
24684 \begin_layout Plain Layout
24704 furthermore the following functions:
24707 \begin_layout Standard
24709 \begin_inset Tabular
24710 <lyxtabular version="3" rows="5" columns="2">
24712 <column alignment="center" valignment="top" width="0">
24713 <column alignment="center" valignment="top" width="0">
24715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24718 \begin_layout Plain Layout
24724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24727 \begin_layout Plain Layout
24729 \begin_inset Note Note
24732 \begin_layout Plain Layout
24739 is only used as spacer.
24751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24765 \begin_layout Plain Layout
24766 \begin_inset Formula $\varliminf$
24776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24779 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24791 \begin_inset Formula $\varlimsup$
24801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24804 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24816 \begin_inset Formula $\varprojlim$
24826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24829 \begin_layout Plain Layout
24837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24840 \begin_layout Plain Layout
24841 \begin_inset Formula $\varinjlim$
24845 \begin_inset Formula $\raisebox{-2.5mm}{}$
24861 \begin_layout Standard
24862 \begin_inset VSpace medskip
24865 The limit is created by inserting a subscript.
24866 It is set right beside the function in an inline formula:
24869 \begin_layout Standard
24871 \begin_inset Tabular
24872 <lyxtabular version="3" rows="2" columns="2">
24874 <column alignment="center" valignment="top" width="0pt">
24875 <column alignment="center" valignment="top" width="0pt">
24877 <cell alignment="center" valignment="top" usebox="none">
24880 \begin_layout Plain Layout
24886 <cell alignment="center" valignment="top" usebox="none">
24889 \begin_layout Plain Layout
24890 \begin_inset space \hspace{}
24895 \begin_inset Note Note
24898 \begin_layout Plain Layout
24911 are used here as spacer.
24923 <cell alignment="center" valignment="top" usebox="none">
24926 \begin_layout Plain Layout
24935 \begin_layout Plain Layout
24948 \begin_layout Plain Layout
24962 <cell alignment="center" valignment="top" usebox="none">
24965 \begin_layout Plain Layout
24966 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24982 \begin_layout Standard
24983 In a displayed formula the limit is set below the formula, as usual:
24984 \begin_inset Formula \[
24992 \begin_layout Subsection
24997 \begin_layout Plain Layout
24998 Functions ! modulo-
25006 \begin_layout Standard
25007 The modulo-function is special, because it exists in four variants.
25010 \begin_layout Standard
25011 The variants in a displayed formula:
25012 \begin_inset Formula \begin{align*}
25013 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25014 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25015 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25016 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25017 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25024 \begin_layout Standard
25025 In an inline formula less space is set before the function names for all
25029 \begin_layout Section
25034 \begin_layout Plain Layout
25043 \begin_layout Subsection
25044 Special Characters in Mathematical Text
25047 \begin_layout Standard
25048 The following commands can only be used in mathematical text or in TeX-mode:
25051 \begin_layout Standard
25052 \begin_inset space \hfill{}
25056 \begin_inset Tabular
25057 <lyxtabular version="3" rows="8" columns="2">
25059 <column alignment="block" valignment="top" width="0">
25060 <column alignment="block" valignment="top" width="0">
25062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25074 \begin_layout Plain Layout
25082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25085 \begin_layout Plain Layout
25093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25096 \begin_layout Plain Layout
25097 \begin_inset Formula $\textrm{œ}$
25107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25110 \begin_layout Plain Layout
25118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25121 \begin_layout Plain Layout
25122 \begin_inset Formula $\textrm{Œ}$
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25146 \begin_layout Plain Layout
25147 \begin_inset Formula $\textrm{æ}$
25157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25160 \begin_layout Plain Layout
25168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25171 \begin_layout Plain Layout
25172 \begin_inset Formula $\textrm{Æ}$
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25185 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25196 \begin_layout Plain Layout
25197 \begin_inset Formula $\textrm{\aa}$
25207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25210 \begin_layout Plain Layout
25217 \begin_layout Plain Layout
25221 \begin_layout Plain Layout
25229 \begin_layout Plain Layout
25240 \begin_layout Plain Layout
25256 \begin_layout Plain Layout
25264 \begin_layout Plain Layout
25275 \begin_layout Plain Layout
25291 \begin_layout Plain Layout
25302 \begin_layout Plain Layout
25310 \begin_layout Plain Layout
25321 \begin_layout Plain Layout
25337 \begin_layout Plain Layout
25354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25357 \begin_layout Plain Layout
25358 \begin_inset Formula $\textrm{Å}$
25368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25371 \begin_layout Plain Layout
25379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25382 \begin_layout Plain Layout
25383 \begin_inset Formula $\textrm{ı}$
25397 \begin_inset space \hfill{}
25401 \begin_inset Tabular
25402 <lyxtabular version="3" rows="8" columns="2">
25404 <column alignment="block" valignment="top" width="0">
25405 <column alignment="center" valignment="top" width="0">
25407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25410 \begin_layout Plain Layout
25412 \begin_inset Note Note
25415 \begin_layout Plain Layout
25422 is used for separation, because otherwise the output will be ¡ and ¿ respective
25433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25436 \begin_layout Plain Layout
25444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25447 \begin_layout Plain Layout
25455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25458 \begin_layout Plain Layout
25459 \begin_inset Formula $\textrm{ø}$
25469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25472 \begin_layout Plain Layout
25480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25483 \begin_layout Plain Layout
25484 \begin_inset Formula $\textrm{Ø}$
25494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25497 \begin_layout Plain Layout
25505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25508 \begin_layout Plain Layout
25509 \begin_inset Formula $\textrm{ł}$
25519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25533 \begin_layout Plain Layout
25534 \begin_inset Formula $\textrm{Ł}$
25544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25547 \begin_layout Plain Layout
25549 \begin_inset space \hspace{}
25557 \begin_layout Plain Layout
25571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25574 \begin_layout Plain Layout
25575 \begin_inset Formula $\textrm{!`}$
25585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25588 \begin_layout Plain Layout
25590 \begin_inset space \hspace{}
25598 \begin_layout Plain Layout
25612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25615 \begin_layout Plain Layout
25616 \begin_inset Formula $\textrm{?`}$
25626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25629 \begin_layout Plain Layout
25637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25640 \begin_layout Plain Layout
25641 \begin_inset Formula $\textrm{ȷ}$
25655 \begin_inset space \hfill{}
25661 \begin_layout Standard
25663 \begin_inset Formula $\textrm{\textrm{Å}}$
25667 \begin_inset Formula $\textrm{\textrm{Ø}}$
25670 can also be inserted via the math toolbar button
25671 \begin_inset Graphics
25672 filename ../images/math/digamma.png
25680 \begin_layout Standard
25681 An exception are the commands
25684 \begin_inset space \hspace{}
25693 \begin_inset space \hspace{}
25699 , because they can be inserted in LyX directly to text.
25702 \begin_layout Subsection
25704 \begin_inset CommandInset label
25706 name "sub:Accents-in-Text"
25714 \begin_layout Plain Layout
25723 \begin_layout Standard
25724 With the following commands all letters can be accented.
25725 The commands must be inserted in TeX-mode.
25728 \begin_layout Standard
25729 \begin_inset space \hfill{}
25733 \begin_inset Tabular
25734 <lyxtabular version="3" rows="8" columns="2">
25736 <column alignment="block" valignment="top" width="0">
25737 <column alignment="block" valignment="top" width="0">
25739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25742 \begin_layout Plain Layout
25748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25751 \begin_layout Plain Layout
25759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25762 \begin_layout Plain Layout
25766 \begin_inset Quotes grd
25774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25777 \begin_layout Plain Layout
25781 \begin_layout Plain Layout
25797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25800 \begin_layout Plain Layout
25808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25811 \begin_layout Plain Layout
25815 \begin_layout Plain Layout
25831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25834 \begin_layout Plain Layout
25841 \begin_layout Plain Layout
25855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25858 \begin_layout Plain Layout
25862 \begin_layout Plain Layout
25878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25881 \begin_layout Plain Layout
25889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25892 \begin_layout Plain Layout
25896 \begin_layout Plain Layout
25912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25915 \begin_layout Plain Layout
25922 \begin_layout Plain Layout
25936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25939 \begin_layout Plain Layout
25943 \begin_layout Plain Layout
25959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25962 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25986 \begin_layout Plain Layout
25990 \begin_layout Plain Layout
26006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26009 \begin_layout Plain Layout
26016 \begin_layout Plain Layout
26030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26033 \begin_layout Plain Layout
26037 \begin_layout Plain Layout
26057 \begin_inset space \hfill{}
26061 \begin_inset Tabular
26062 <lyxtabular version="3" rows="8" columns="2">
26064 <column alignment="block" valignment="top" width="0">
26065 <column alignment="center" valignment="top" width="0">
26067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26070 \begin_layout Plain Layout
26076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26079 \begin_layout Plain Layout
26087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26090 \begin_layout Plain Layout
26097 \begin_layout Plain Layout
26111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26114 \begin_layout Plain Layout
26118 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26137 \begin_layout Plain Layout
26145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26148 \begin_layout Plain Layout
26152 \begin_layout Plain Layout
26168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26171 \begin_layout Plain Layout
26178 \begin_layout Plain Layout
26189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26192 \begin_layout Plain Layout
26196 \begin_layout Plain Layout
26212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26215 \begin_layout Plain Layout
26223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26226 \begin_layout Plain Layout
26230 \begin_layout Plain Layout
26246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26249 \begin_layout Plain Layout
26256 \begin_layout Plain Layout
26270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26273 \begin_layout Plain Layout
26277 \begin_layout Plain Layout
26293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26296 \begin_layout Plain Layout
26303 \begin_layout Plain Layout
26317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26320 \begin_layout Plain Layout
26324 \begin_layout Plain Layout
26340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26343 \begin_layout Plain Layout
26350 \begin_layout Plain Layout
26364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26367 \begin_layout Plain Layout
26371 \begin_layout Plain Layout
26391 \begin_inset space \hfill{}
26397 \begin_layout Standard
26398 \begin_inset VSpace medskip
26407 also two different characters can be accented.
26416 \begin_layout Plain Layout
26431 \begin_layout Plain Layout
26443 \begin_layout Standard
26456 can in combination with vowels directly be inserted with the keyboard without
26458 The same applies for the tilde
26462 \begin_layout Plain Layout
26463 This only applies for keyboards where the tilde is defined as accent.
26472 in combination with
26487 \begin_layout Standard
26530 , and accents inserted directly with the keyboard are also available in
26532 For the other accents there are special math commands to be used in formulas,
26534 \begin_inset CommandInset ref
26536 reference "sub:Accents-for-one"
26543 \begin_layout Standard
26544 \begin_inset VSpace bigskip
26547 Furthermore, with the command
26557 \begin_layout Plain Layout
26565 all numbers and letters can be set into a circle, quasi accented with a
26566 circle, similar to the the copyright symbol.
26569 \begin_layout Standard
26571 \begin_inset Tabular
26572 <lyxtabular version="3" rows="3" columns="2">
26574 <column alignment="center" valignment="top" width="0">
26575 <column alignment="center" valignment="top" width="0">
26577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26580 \begin_layout Plain Layout
26586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26589 \begin_layout Plain Layout
26591 \begin_inset Note Note
26594 \begin_layout Plain Layout
26601 is only used as spacer.
26613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26616 \begin_layout Plain Layout
26624 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26627 \begin_layout Plain Layout
26631 \begin_layout Plain Layout
26647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26650 \begin_layout Plain Layout
26661 raisebox{-1.5pt}{W}}
26666 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26670 \begin_inset Formula $\raisebox{4.5mm}{}$
26677 \begin_layout Plain Layout
26695 \begin_inset Formula $\raisebox{-2mm}{}$
26711 \begin_layout Standard
26712 One has to take care that the character fits in the circle.
26723 \begin_layout Plain Layout
26725 \begin_inset CommandInset ref
26727 reference "sub:Font-Sizes"
26736 specifies thereby the size of the circle.
26747 \begin_layout Plain Layout
26749 \begin_inset CommandInset ref
26751 reference "sub:Boxes-without-Frame"
26760 the character can be centered.
26763 \begin_layout Subsection
26768 \begin_layout Plain Layout
26777 \begin_layout Standard
26778 Minuscule numbers are created with the command
26788 \begin_layout Plain Layout
26797 The command can be used in formulas and in TeX-mode.
26798 The command scheme is:
26801 \begin_layout Standard
26806 oldstylenums{number}
26809 \begin_layout Standard
26814 oldstylenums{0123456789
26817 \begin_inset Formula $\oldstylenums{0123456789}$
26823 \begin_layout Subsection
26824 Miscellaneous Special Characters
26825 \begin_inset CommandInset label
26827 name "sub:Miscellaneous-Special-Characters"
26835 \begin_layout Plain Layout
26836 Special characters ! miscellaneous
26844 \begin_layout Standard
26845 The following characters can only be inserted to formulas by using commands:
26848 \begin_layout Standard
26850 \begin_inset Tabular
26851 <lyxtabular version="3" rows="4" columns="2">
26853 <column alignment="center" valignment="top" width="0">
26854 <column alignment="center" valignment="top" width="0">
26856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26859 \begin_layout Plain Layout
26865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26868 \begin_layout Plain Layout
26876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26879 \begin_layout Plain Layout
26886 \begin_layout Plain Layout
26900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26903 \begin_layout Plain Layout
26904 \begin_inset Formula $\mathcircumflex$
26914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26917 \begin_layout Plain Layout
26925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26928 \begin_layout Plain Layout
26929 \begin_inset Formula $\_$
26939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26942 \begin_layout Plain Layout
26947 \begin_layout Plain Layout
26962 \begin_layout Plain Layout
26973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26976 \begin_layout Plain Layout
26977 \begin_inset Formula $^{\circ}$
26993 \begin_layout Standard
26994 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
26995 contains the following line
26999 \begin_layout Plain Layout
27000 More about this is described in
27001 \begin_inset CommandInset ref
27003 reference "sub:Text-Characters-in"
27015 \begin_layout Standard
27020 DeclareInputtext{176}{
27033 \begin_layout Section
27035 \begin_inset CommandInset label
27037 name "sec:Formula-Styles"
27045 \begin_layout Plain Layout
27054 \begin_layout Itemize
27055 There are two different alignment styles:
27059 \begin_layout Description
27060 Centered is the predefined standard
27063 \begin_layout Description
27064 Indented for this the option
27068 must be inserted in the menu
27070 Document\SpecialChar \menuseparator
27076 \begin_inset space ~
27082 \begin_layout Standard
27087 is used, the indentation can be adjusted with the length
27097 \begin_layout Plain Layout
27106 Should the distance be 15
27107 \begin_inset space \thinspace{}
27110 mm, the following command line is inserted in the LaTeX-preamble
27113 \begin_layout Standard
27123 \begin_layout Standard
27124 When no length is specified, the predefined value of 30
27125 \begin_inset space \thinspace{}
27132 \begin_layout Itemize
27133 And two different numbering styles:
27137 \begin_layout Description
27138 Right is the predefined standard
27141 \begin_layout Description
27142 Left for this the option
27146 must be inserted in the menu
27148 Document\SpecialChar \menuseparator
27154 \begin_inset space ~
27161 \begin_layout Standard
27170 can also be used together.
27171 In this case both options are inserted, separated by a comma.
27174 \begin_layout Standard
27175 The chosen styles are used for all displayed formulas of the document.
27176 When both, centered and indented formulas should be created in a document,
27182 The indented formulas are then set in a flalign environment, see
27183 \begin_inset CommandInset ref
27185 reference "sub:Flalign-Environment"
27192 \begin_layout Section
27194 \begin_inset CommandInset label
27196 name "sec:Multiline-Formulas"
27204 \begin_layout Plain Layout
27205 Formula ! multiline
27213 \begin_layout Subsection
27217 \begin_layout Standard
27218 In LyX multiline formulas are created by pressing
27229 that is described in
27230 \begin_inset CommandInset ref
27232 reference "sub:Standard-align-Environment"
27239 \begin_layout Standard
27240 There are other multiline formula environments that can be created via the
27243 Insert\SpecialChar \menuseparator
27247 These environments are described in the following sections.
27250 \begin_layout Standard
27251 In all multiline formula environments a new line is created by pressing
27257 To add or delete lines, the math toolbar buttons
27258 \begin_inset Graphics
27259 filename ../images/tabular-feature_append-row.png
27265 \begin_inset Graphics
27266 filename ../images/tabular-feature_delete-row.png
27271 , respectively, or the menu
27273 Edit\SpecialChar \menuseparator
27279 \begin_layout Subsubsection
27281 \begin_inset CommandInset label
27283 name "sub:Line-Separation"
27291 \begin_layout Plain Layout
27292 Formula ! multiline ! Line separation
27300 \begin_layout Standard
27301 There is sometimes not enough space in multiline formulas between the lines:
27302 \begin_inset Formula \begin{eqnarray*}
27303 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}\\
27304 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*}
27311 \begin_layout Standard
27312 In LaTeX additional line space is specified as optional argument of the
27314 This is not yet possible in LyX
27318 \begin_layout Plain Layout
27320 \begin_inset CommandInset href
27322 name "LyX-bug #1505"
27323 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27332 , therefore the whole formula must be inserted in TeX-mode.
27333 To add in our example space, the command
27341 is inserted at the end of the first line.
27346 \begin_layout Plain Layout
27353 \begin_layout Plain Layout
27355 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27358 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27365 \begin_layout Plain Layout
27369 left(B^{2}+x_{0}^{2}
27377 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27382 \begin_layout Plain Layout
27394 \begin_layout Standard
27395 \begin_inset VSpace bigskip
27398 To set the the line separation for all lines in a formula, the length
27408 \begin_layout Plain Layout
27418 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27429 \begin_inset space \thinspace{}
27434 \begin_inset space \thinspace{}
27437 mm additional line separation as in the previous example, the command
27440 \begin_layout Standard
27450 \begin_layout Standard
27451 is inserted in TeX-mode before the formula.
27452 This requires that the LaTeX-package
27460 \begin_layout Plain Layout
27465 is part of every LaTeX standard installation.
27474 \begin_layout Plain Layout
27480 was loaded in LaTeX-preamble with the line
27483 \begin_layout Standard
27491 \begin_layout Standard
27496 \begin_layout Plain Layout
27508 \begin_inset Formula \begin{eqnarray*}
27509 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}\\
27510 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*}
27517 \begin_layout Standard
27521 \begin_layout Plain Layout
27532 To get back to the predefined distance,
27538 is set to the value 3
27539 \begin_inset space \thinspace{}
27545 \begin_layout Subsubsection
27547 \begin_inset CommandInset label
27549 name "sub:Column-Separation"
27557 \begin_layout Plain Layout
27558 Formula ! multiline ! Column separation
27566 \begin_layout Standard
27567 Multiline formulas form a matrix.
27568 A formula in the eqnarray environment is for example a matrix with three
27570 By changing the column separation in this environment, the space beside
27571 the relation sign can be changed.
27574 \begin_layout Standard
27575 The column separation is specified with the length
27585 \begin_layout Plain Layout
27594 \begin_inset Newline newline
27597 column separation = 2
27598 \begin_inset space \thinspace{}
27608 \begin_inset Newline newline
27614 \begin_layout Standard
27624 \begin_layout Standard
27625 inserted in TeX-mode, sets for all following formulas a column separation
27627 \begin_inset space \thinspace{}
27631 To get back to the predefined distance,
27638 \begin_inset space \thinspace{}
27644 \begin_layout Standard
27646 \begin_inset space \thinspace{}
27649 cm column separation:
27653 \begin_layout Plain Layout
27665 \begin_inset Formula \begin{eqnarray*}
27667 C & \ne & A\end{eqnarray*}
27671 A formula with the predefined column separation for matrices of 10
27672 \begin_inset space \thinspace{}
27679 \begin_layout Plain Layout
27691 \begin_inset Formula \begin{eqnarray*}
27693 C & \ne & A\end{eqnarray*}
27700 \begin_layout Subsubsection
27705 \begin_layout Plain Layout
27714 \begin_layout Standard
27715 Long formulas can be typeset using these methods:
27718 \begin_layout Itemize
27719 When one side of the equation is much shorther than the line width, this
27720 one is chosen for the left side and the right side is typeset over two
27725 \begin_layout Plain Layout
27735 \begin_inset Formula \begin{eqnarray}
27736 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 \\
27737 & & -\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}
27745 \begin_layout Plain Layout
27755 \begin_inset Newline newline
27758 The minus sign at the beginning of the second line does normally not appear
27759 as operator because it is the first character of the line.
27760 Thus it would not be surrounded by space and could not be distinguished
27761 from the fraction bar.
27762 To avoid this, space was inserted behind the minus sign with the command
27773 \begin_layout Plain Layout
27781 \begin_inset CommandInset ref
27783 reference "sub:Variable-Space"
27796 \begin_layout Plain Layout
27807 \begin_layout Itemize
27808 When both sides of the equation are too long, the command
27818 \begin_layout Plain Layout
27827 It is inserted to the first column of the first line and effects that all
27828 further insertions overwrite the following columns:
27832 \begin_layout Plain Layout
27842 \begin_inset Formula \begin{eqnarray}
27843 \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 \\
27844 & & -\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 \\
27845 & & =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}
27853 \begin_layout Plain Layout
27863 \begin_inset Newline newline
27866 After the insertion of
27872 , the cursor is in a purple box that is a bit shifted to the left from the
27874 In this the formula is inserted.
27878 \begin_layout Plain Layout
27888 \begin_inset Newline newline
27891 The content of the further lines is inserted to the second or another formula
27893 The greater the column number where it was inserted, the larger the indentation.
27897 \begin_layout Plain Layout
27907 \begin_inset Newline newline
27911 \begin_inset Note Greyedout
27914 \begin_layout Plain Layout
27915 Note the following when using
27924 \begin_layout Itemize
27925 The formula doesn't use the full page width.
27927 \begin_inset space \thinspace{}
27931 \begin_inset space ~
27935 \begin_inset Formula $-B^{2}$
27938 is added to the first line in the above example, it would have been outside
27940 To better use the width, negative space can be inserted at the beginning
27944 \begin_layout Itemize
27945 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27950 \begin_layout Plain Layout
27951 \begin_inset CommandInset href
27953 name "LyX-bug #1429"
27954 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
27963 One can only set the cursor at the beginning of the line and move it with
27972 \begin_layout Itemize
27973 Other methods to set long formulas are offered by the environments described
27975 \begin_inset CommandInset ref
27977 reference "sub:Multline-Environment"
27982 \begin_inset CommandInset ref
27984 reference "sub:Multiline-Formula-Parts"
27991 \begin_layout Subsubsection
27993 \begin_inset CommandInset label
27995 name "sub:Multiline-Brackets"
28003 \begin_layout Plain Layout
28004 Brackets ! for multiline expressions
28012 \begin_layout Standard
28013 For brackets spanning multiple lines the following problem occurs:
28014 \begin_inset Formula \begin{eqnarray*}
28015 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28016 & & \left.\cdots+B-D\right]\end{eqnarray*}
28023 \begin_layout Standard
28024 The closing bracket is smaller than the opening bracket because brackets
28025 with variable size may not span multiple lines.
28028 \begin_layout Standard
28029 To set the bracket size for the second line correctly, the first line is
28040 \begin_layout Plain Layout
28048 and the second line with
28056 \begin_layout Plain Layout
28070 \begin_inset CommandInset ref
28072 reference "sub:Automatic-Bracket-Size"
28087 \begin_layout Plain Layout
28113 \begin_layout Plain Layout
28132 \begin_layout Plain Layout
28151 \begin_layout Plain Layout
28163 \begin_inset Formula $\downarrow$
28172 \begin_layout Plain Layout
28180 is inserted, because the multiplication operator with its limits is the
28181 largest symbol in the first line and this should be the size for the bracket
28182 in the second line.
28185 \begin_layout Standard
28186 The result is this:
28187 \begin_inset Formula \begin{eqnarray*}
28188 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28189 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28196 \begin_layout Subsection
28200 \begin_layout Standard
28201 Align environments can be used for every kind of multiline formulas.
28202 They are specially useful to set several formulas side by side.
28205 \begin_layout Standard
28206 Align environments consist of columns.
28207 The odd columns are right aligned, the even ones left aligned.
28208 Every line in an Align environment can be numbered.
28211 \begin_layout Standard
28212 Align environments are created via the menu
28214 Insert\SpecialChar \menuseparator
28220 Edit\SpecialChar \menuseparator
28221 Math\SpecialChar \menuseparator
28222 Change Formula Type
28224 already existing formulas can be converted to Align environments.
28227 \begin_layout Standard
28228 To add or delete columns, the math toolbar buttons
28229 \begin_inset Graphics
28230 filename ../images/tabular-feature_append-column.png
28236 \begin_inset Graphics
28237 filename ../images/tabular-feature_delete-column.png
28242 , respectively, or the menu
28244 Edit\SpecialChar \menuseparator
28250 \begin_layout Subsubsection
28251 Standard align Environment
28252 \begin_inset CommandInset label
28254 name "sub:Standard-align-Environment"
28262 \begin_layout Plain Layout
28263 Formula ! multiline ! align environment
28271 \begin_layout Standard
28272 This Align environment is created by presssing
28276 in a formula or by the menu
28278 Insert\SpecialChar \menuseparator
28279 Math\SpecialChar \menuseparator
28280 AMS align Environment
28285 \begin_layout Standard
28286 An example for two formulas set side by side, that are created with a four
28287 column align environment:
28288 \begin_inset Formula \begin{align*}
28289 A & =\sin(B) & C & =D\\
28290 C & \ne A & B & \ne D\end{align*}
28294 As it can be seen, the formulas in this environment are placed so as if
28303 \begin_layout Plain Layout
28311 \begin_inset CommandInset ref
28313 reference "sub:Variable-Space"
28324 before the first and after every even column.
28325 When the formula style
28331 \begin_layout Plain Layout
28333 \begin_inset CommandInset ref
28335 reference "sec:Formula-Styles"
28346 is used, the formula is set without the
28352 before the first column.
28355 \begin_layout Subsubsection
28356 Alignat Environment
28360 \begin_layout Plain Layout
28361 Formula ! multiline ! alignat environment
28369 \begin_layout Standard
28370 The alignat environment has no predefined column separation.
28371 It can be inserted manually with the spaces that are described
28372 \begin_inset CommandInset ref
28374 reference "sub:Space"
28381 \begin_layout Standard
28382 The above example in the alignat environment where 1
28383 \begin_inset space \thinspace{}
28386 cm space was inserted at the beginning of the second formula:
28387 \begin_inset Formula \begin{alignat*}{2}
28388 A & =\sin(B) & \hspace{1cm}C & =D\\
28389 C & \ne A & B & \ne D\end{alignat*}
28393 Because the column separation can be set separately for every column, this
28394 environment is especially suitable to set three and more formulas side
28398 \begin_layout Subsubsection
28399 Flalign Environment
28400 \begin_inset CommandInset label
28402 name "sub:Flalign-Environment"
28410 \begin_layout Plain Layout
28411 Formula ! multiline ! flalign environment
28419 \begin_layout Standard
28420 In this environment the first two columns are always set as much as possible
28421 to the left and the last two ones to the right.
28423 \begin_inset Formula \begin{flalign*}
28424 A & =1 & B & =2 & C & =3\\
28425 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28432 \begin_layout Standard
28433 By creating a flalign environment with an odd number of columns where an
28434 empty TeX-brace is inserted to the last column, several formulas in a document
28435 can be set to the left, although the formula style
28440 As example the indented formula
28441 \begin_inset CommandInset ref
28443 reference "eq:VolInt"
28448 \begin_inset Formula \begin{flalign}
28449 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28453 The first two columns contain the formula.
28454 To indent it as with the formula style
28459 \begin_inset space \thinspace{}
28462 pt space was inserted at the beginning of the first column.
28465 \begin_layout Subsection
28466 Eqnarray Environment
28470 \begin_layout Plain Layout
28471 Formula ! multiline ! eqnarray environment
28479 \begin_layout Standard
28480 When this environment has been created, three blue boxes appear.
28481 The content of the first box is right aligned, the content of the last
28483 The content of the middle box appears centered and a bit smaller, because
28484 it is designed to insert there only relation characters.
28485 \begin_inset Formula \begin{eqnarray*}
28486 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28488 A & = & A\end{eqnarray*}
28495 \begin_layout Subsection
28500 \begin_layout Plain Layout
28501 Formula ! multiline ! gather environment
28509 \begin_layout Standard
28510 This environment consists of only one centered column.
28511 Every line can be numbered.
28512 \begin_inset Formula \begin{gather}
28514 X=\textrm{-}1\end{gather}
28521 \begin_layout Subsection
28522 Multline Environment
28523 \begin_inset CommandInset label
28525 name "sub:Multline-Environment"
28533 \begin_layout Plain Layout
28534 Formula ! multiline ! multline environment
28542 \begin_layout Standard
28543 The multline environment consists, like the gather environment, of only
28545 But the first line is left aligned, the last one right aligned.
28546 All other lines are centered.
28547 Therefore this environment is suitable for long formulas.
28549 \begin_inset CommandInset ref
28551 reference "eq:lefteqn"
28555 in the multline environment:
28556 \begin_inset Formula \begin{multline}
28557 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}\\
28558 -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}\\
28559 =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}
28566 \begin_layout Standard
28567 In the output only the last (first) line of a multline environment appears
28568 numbered when the document numbering is right (left).
28572 \begin_layout Plain Layout
28573 numbering styles see
28574 \begin_inset CommandInset ref
28576 reference "sec:Formula-Styles"
28588 \begin_layout Standard
28597 \begin_layout Plain Layout
28615 \begin_layout Plain Layout
28625 a centered line can be right or left aligned, respectively.
28626 The commands are used as follows:
28629 \begin_layout Standard
28634 shoveright{line content}
28640 shoveleft{line content}
28643 \begin_layout Standard
28644 \begin_inset VSpace medskip
28655 \begin_layout Plain Layout
28665 specifies the distance of the first line from the left page margin.
28666 Predefined is the length 0
28667 \begin_inset space \thinspace{}
28673 \begin_layout Standard
28674 As example the above formula where the command
28677 \begin_layout Standard
28687 \begin_layout Standard
28688 was inserted in TeX-mode before:
28692 \begin_layout Plain Layout
28704 \begin_inset Formula \begin{multline}
28705 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}\\
28706 \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}}\\
28707 =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}
28715 \begin_layout Plain Layout
28726 The second line was left aligned using
28735 \begin_layout Subsection
28736 Multiline Formula Parts
28737 \begin_inset CommandInset label
28739 name "sub:Multiline-Formula-Parts"
28747 \begin_layout Plain Layout
28748 Formula ! multiline ! formula parts
28756 \begin_layout Standard
28757 To display only parts of a formula with multiple lines, one of the following
28758 environments are used:
28775 They can be inserted via the menu
28777 Insert\SpecialChar \menuseparator
28780 or by using the commands described in this section.
28783 \begin_layout Standard
28784 The first three have the same properties as the corresponding multiline
28785 formula environments, but it is possible to set further formula parts beside
28788 \begin_inset Formula \[
28789 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28790 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28791 \right\} \textrm{Uncertainty relations}\]
28798 \begin_layout Standard
28799 To get this formula, a displayed formula is created where the command
28807 \begin_layout Plain Layout
28818 A purple box appears around the blue formula box where now columns and
28819 lines can be added.
28820 Outside the multiline environment other formula parts can be set, like
28824 \begin_layout Standard
28825 The aligned environment is also suitable for long formulas whose lines are
28826 horizontally aligned.
28827 Using aligned in a displayed formula has the advantage that the formula
28828 number is vertically centered behind the lines.
28830 \begin_inset CommandInset ref
28832 reference "eq:kurzlang"
28836 in the aligned environment:
28837 \begin_inset Formula \begin{equation}
28838 \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}|}\\
28839 & -\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}
28847 \begin_layout Standard
28848 To use the environments
28870 \begin_layout Plain Layout
28888 \begin_layout Plain Layout
28906 \begin_layout Plain Layout
28914 are inserted, respectively.
28915 The split environment has the same properties as the aligned environment
28916 but it can only have two columns.
28919 \begin_layout Subsection
28920 Text in multiline Formulas
28921 \begin_inset CommandInset label
28923 name "sub:Text-in-multiline"
28931 \begin_layout Plain Layout
28941 \begin_layout Plain Layout
28942 Formula ! multiline ! text
28950 \begin_layout Standard
28951 In the Align environments, and the multline and gather environment, text
28952 can be inserted that will appear in a separate line and doesn't affect
28953 the column alignment.
28954 To do this, the command
28962 \begin_layout Plain Layout
28972 is used in the following scheme:
28975 \begin_layout Standard
28983 \begin_layout Standard
28984 The text should not be longer than a line because it cannot be hyphenated.
28985 As LyX doesn't yet support
28991 directly, the text is written as mathematical text.
28998 must hereby be at the beginning of a line and appears in the output above
29000 An example where the text was inserted at the beginning of the second line:
29001 \begin_inset Formula \begin{align}
29002 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29003 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29010 \begin_layout Section
29015 \begin_layout Plain Layout
29025 \begin_layout Plain Layout
29026 Formula ! numbering|see
29030 \begin_layout Plain Layout
29041 \begin_layout Plain Layout
29056 \begin_layout Subsection
29060 \begin_layout Standard
29061 Numbered formulas can be created with the menu
29063 Insert\SpecialChar \menuseparator
29064 Math\SpecialChar \menuseparator
29066 \begin_inset space ~
29074 \begin_inset space ~
29080 Existing formulas can be numbered with the menu
29082 Edit\SpecialChar \menuseparator
29083 Math\SpecialChar \menuseparator
29085 \begin_inset space ~
29093 \begin_inset space ~
29099 The formula number is displayed in LyX behind the formula as number sign
29101 The number sign is replaced in the output by the formula number.
29104 \begin_layout Standard
29105 When numbering is turned on in multiline formulas, all lines will be numbered.
29106 But the numbering can be controlled with the menu
29108 Edit\SpecialChar \menuseparator
29109 Math\SpecialChar \menuseparator
29111 \begin_inset space ~
29115 \begin_inset space ~
29119 \begin_inset space ~
29127 \begin_inset space ~
29135 \begin_layout Standard
29136 Except of inline formulas, all formulas can be numbered with two different
29138 \begin_inset CommandInset ref
29140 reference "sec:Formula-Styles"
29147 \begin_layout Subsection
29149 \begin_inset CommandInset label
29151 name "sub:Cross-References"
29159 \begin_layout Plain Layout
29160 Cross-references ! to formulas
29168 \begin_layout Standard
29169 All labeled formulas can be cross-referenced.
29170 A label is added by the menu
29172 Insert\SpecialChar \menuseparator
29175 or the toolbar button
29176 \begin_inset Graphics
29177 filename ../images/label-insert.png
29183 The cursor must hereby be inside a displayed formula.
29184 A dialog pops up displaying the prefix
29189 The label is inserted there behind the prefix.
29190 The predefined prefix means
29191 \begin_inset Quotes eld
29195 \begin_inset Quotes erd
29198 and makes it easier to find labels in large documents because it marks
29199 it as formula label to divide it from e.
29200 \begin_inset space \thinspace{}
29204 \begin_inset space ~
29208 To change a label, the menu
29210 Insert\SpecialChar \menuseparator
29216 \begin_layout Standard
29217 The name of the label is displayed in LyX within two parentheses behind
29219 A formula with a label is always numbered.
29222 \begin_layout Standard
29223 Cross-references are inserted via the menu
29225 Insert\SpecialChar \menuseparator
29228 or with the toolbar button
29229 \begin_inset Graphics
29230 filename ../images/dialog-show-new-inset_ref.png
29236 A formula cross-reference appears in the output as formula number.
29237 When in the cross-reference dialog window the format
29241 is chosen, the cross-reference appears in the output as formula number
29243 \begin_inset Newline newline
29246 By right-clicking on a cross-reference in LyX, one jumps to the formula
29247 that is referenced.
29250 \begin_layout Standard
29251 Here are as examples cross-references to formulas of the following subsections:
29252 \begin_inset Note Note
29255 \begin_layout Plain Layout
29256 Note the different cross-reference types.
29264 \begin_layout Standard
29266 \begin_inset CommandInset ref
29273 \begin_inset CommandInset ref
29281 \begin_inset CommandInset ref
29287 ) big Latin letters are used for the numbering in contrary to (
29288 \begin_inset CommandInset ref
29297 \begin_layout Standard
29298 \begin_inset VSpace medskip
29301 When the argument of
29309 \begin_layout Plain Layout
29317 \begin_inset CommandInset ref
29319 reference "sub:User-defined-Numbering"
29330 contains a box like in
29331 \begin_inset CommandInset ref
29333 reference "sub:Paragraph-Boxes"
29337 , the formula cannot be referenced.
29340 \begin_layout Subsection
29345 \begin_layout Plain Layout
29346 Formula numbering ! subnumbering
29354 \begin_layout Standard
29355 With the help of the commands
29359 begin{subequations}
29367 formulas can be subnumbered.
29368 Both commands are inserted in TeX-mode.
29371 \begin_layout Standard
29373 \begin_inset Formula \begin{equation}
29374 A=C-B\label{eq:a}\end{equation}
29382 \begin_layout Plain Layout
29386 addtocounter{equation}{-1}
29395 \begin_layout Plain Layout
29399 begin{subequations}
29405 \begin_inset VSpace -5mm
29409 \begin_inset Formula \begin{equation}
29410 B=C-A\label{eq:b}\end{equation}
29415 \begin_inset Formula \begin{equation}
29416 C=A+B\label{eq:c}\end{equation}
29423 \begin_layout Standard
29427 \begin_layout Plain Layout
29439 \begin_layout Standard
29440 To create the example, the following is done:
29443 \begin_layout Enumerate
29444 first formula is inserted
29447 \begin_layout Enumerate
29452 addtocounter{equation}{-1}
29454 begin{subequations}
29458 \begin_layout Plain Layout
29467 \begin_inset Newline newline
29472 is inserted after the first formula
29475 \begin_layout Enumerate
29476 second formula is inserted
29479 \begin_layout Enumerate
29480 third formula is inserted
29483 \begin_layout Enumerate
29490 is inserted after the third formula
29493 \begin_layout Standard
29494 Every formula between the commands
29506 is subnumbered as a, b,
29507 \begin_inset Newline linebreak
29510 c, \SpecialChar \ldots{}
29511 For multiline formulas every line will be subnumbered.
29512 All subnumbered formulas are treated as
29517 But as every numbered formula increases the counter
29521 by one, the command
29527 is needed to decrease it.
29528 Otherwise the formulas
29529 \begin_inset CommandInset ref
29536 \begin_inset CommandInset ref
29543 \begin_inset CommandInset ref
29549 would be numbered as
29550 \begin_inset CommandInset ref
29557 \begin_inset CommandInset ref
29564 \begin_inset CommandInset ref
29573 \begin_layout Standard
29574 By inserting the commands in TeX-mode, a space is created between the first
29577 \begin_inset space \thinspace{}
29580 mm vertical space is inserted after the command
29584 begin{subequations}
29587 When the formula style
29593 \begin_layout Plain Layout
29595 \begin_inset CommandInset ref
29597 reference "sec:Formula-Styles"
29609 \begin_inset space \thinspace{}
29612 mm space is inserted instead.
29615 \begin_layout Standard
29616 Here is an example for a multiline formula where the numbering was turned
29617 off for the second line:
29621 \begin_layout Plain Layout
29625 begin{subequations}
29631 \begin_inset Formula \begin{eqnarray}
29632 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29633 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29634 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29642 \begin_layout Plain Layout
29654 \begin_layout Subsection
29655 User-defined Numbering
29656 \begin_inset CommandInset label
29658 name "sub:User-defined-Numbering"
29666 \begin_layout Plain Layout
29667 Formula numbering ! user-defined
29675 \begin_layout Standard
29679 \begin_layout Plain Layout
29680 Formula numbering ! self-defined delimiters
29685 With the standard numbering parentheses are set around the formula number.
29686 To replace the parentheses for example by vertical bars, the following
29687 line is added to the LaTeX-preamble:
29690 \begin_layout Standard
29702 \begin_inset Note Note
29705 \begin_layout Plain Layout
29706 This macro is already declared in the LaTeX-preamble for testing.
29707 To activate it, remove the percent sign at the beginning.
29715 \begin_layout Standard
29716 To use other characters, the vertical bars besides the
29720 are replaced by one ore more characters.
29721 To get only the formula number the vertical bars are omitted.
29724 \begin_layout Standard
29725 \begin_inset VSpace bigskip
29728 When there should be an expression of your choice instead of the consecutive
29729 formula number in parentheses behind the formula, the command
29739 \begin_layout Plain Layout
29748 \begin_inset Formula \begin{equation}
29749 A+B=C\tag{something}\label{eq:tag}\end{equation}
29753 In this example the command
29761 \begin_layout Plain Layout
29772 was inserted to the formula.
29775 \begin_layout Standard
29784 \begin_layout Plain Layout
29795 is inserted instead, the star prevents the parentheses around the expression:
29796 \begin_inset Formula \[
29797 A+B=C\tag*{something}\]
29804 \begin_layout Standard
29805 \begin_inset VSpace bigskip
29808 To restart the formula numbering with new document parts or sections, the
29809 following command is used:
29812 \begin_layout Standard
29817 @addtoreset{equation}{part}
29823 \begin_layout Plain Layout
29828 \begin_layout Plain Layout
29839 \begin_layout Plain Layout
29852 \begin_layout Plain Layout
29863 \begin_layout Plain Layout
29876 \begin_inset Newline newline
29880 \begin_inset Newline newline
29887 @addtoreset{equation}{section}
29890 \begin_layout Standard
29891 To be able to use these commands in TeX-mode, the
29892 \begin_inset Quotes eld
29896 \begin_inset Quotes erd
29899 character has to be made
29900 \begin_inset Quotes eld
29904 \begin_inset Quotes erd
29907 for LaTeX using the command
29921 So the command sequence in TeX-mode is:
29924 \begin_layout Standard
29930 \begin_inset Newline newline
29935 @addtoreset{equation}{section}
29936 \begin_inset Newline newline
29944 \begin_layout Standard
29945 In the LaTeX-preamble
29957 can be omitted as they are automatically internally inserted by LyX.
29960 \begin_layout Standard
29975 \begin_layout Plain Layout
29980 is part of the LaTeX-package
29988 \begin_layout Plain Layout
29989 Packages ! carlisle
29994 that is part of every LaTeX standard installation.
30003 \begin_layout Plain Layout
30004 Packages ! remreset
30009 has to be loaded in the LaTeX-preamble with the line
30012 \begin_layout Standard
30017 usepackage{remreset}
30020 \begin_layout Standard
30031 \begin_layout Plain Layout
30036 \begin_layout Plain Layout
30047 \begin_layout Plain Layout
30060 \begin_layout Plain Layout
30071 \begin_layout Plain Layout
30083 can be used with the same scheme as
30092 \begin_layout Standard
30093 \begin_inset VSpace bigskip
30096 Sometimes formulas should be numbered in the following form:
30099 \begin_layout Standard
30102 (section number.formula number)
30105 \begin_layout Standard
30106 The formula number should start with every section with
30107 \begin_inset Quotes eld
30111 \begin_inset Quotes erd
30117 \begin_layout Standard
30118 For this case there is the command
30128 \begin_layout Plain Layout
30136 , which is used with the following scheme:
30139 \begin_layout Standard
30144 numberwithin{counter}{sectioning}
30147 \begin_layout Standard
30148 Counter denotes what kind of numbering is affected, sectioning denotes what
30149 number is before the dot.
30152 \begin_layout Standard
30153 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30156 \begin_layout Standard
30161 numberwithin{equation}{section}
30164 \begin_layout Standard
30165 This is the result:
30169 \begin_layout Plain Layout
30173 numberwithin{equation}{section}
30179 \begin_inset Formula \begin{equation}
30180 A+B=C\end{equation}
30187 \begin_layout Standard
30189 \begin_inset space \thinspace{}
30193 \begin_inset space ~
30196 tables so that the number of the part is the sectioning,
30197 \begin_inset Newline newline
30204 numberwithin{table}{part}
30209 \begin_layout Standard
30210 To go back to the standard numbering or to prevent this kind of numbering
30211 when it is defined by the document class, the following command is inserted
30212 as TeX-Code or to the LaTeX-preamble:
30215 \begin_layout Standard
30228 \begin_layout Plain Layout
30242 \begin_layout Plain Layout
30258 \begin_inset Newline newline
30266 \begin_inset Newline newline
30278 \begin_layout Standard
30285 uses internally the command
30291 , described above, that also needs to be reverted.
30295 \begin_layout Plain Layout
30302 \begin_layout Plain Layout
30306 @removefromreset{equation}{section}
30309 \begin_layout Plain Layout
30321 \begin_layout Subsection
30322 Numbering with Roman Numbers and Letters
30323 \begin_inset CommandInset label
30325 name "sub:Numbering-with-Roman"
30333 \begin_layout Plain Layout
30334 Formula numbering ! with letters
30343 \begin_layout Plain Layout
30344 Formula numbering ! with Roman numbers
30352 \begin_layout Standard
30353 Formulas can also be numbered with Roman numbers and Latin letters.
30354 To number for example with small Roman numbers, the command
30357 \begin_layout Standard
30369 \begin_layout Standard
30370 is inserted before the formula in TeX-mode.
30381 \begin_layout Plain Layout
30389 redefines the predefined command
30405 \begin_layout Plain Layout
30412 has the same scheme like the command
30418 that is described in
30419 \begin_inset CommandInset ref
30421 reference "sec:User-defined-commands"
30435 is the formula counter.
30442 is used as prefix for a counter, the value of the counter is output as
30444 When a formula is numbered, LaTeX sets internally the command
30450 behind the formula.
30459 \begin_layout Plain Layout
30469 outputs the counter as small Roman number.
30472 \begin_layout Standard
30473 All formulas behind the command
30483 are now numbered Roman.
30484 To switch to numbering with big Roman numbers, the command is inserted
30501 \begin_layout Plain Layout
30513 \begin_inset Quotes eld
30517 \begin_inset Quotes erd
30520 with small Latin letters there is the command
30530 \begin_layout Plain Layout
30538 , for big ones there is the command
30548 \begin_layout Plain Layout
30561 \begin_layout Standard
30562 \begin_inset Note Greyedout
30565 \begin_layout Plain Layout
30570 Only maximal 26 formulas can be numbered with Latin letters in one document.
30578 \begin_layout Standard
30582 \begin_layout Plain Layout
30598 \begin_layout Standard
30599 \begin_inset Formula \begin{equation}
30600 A=\textrm{small roman}\label{eq:rom}\end{equation}
30608 \begin_layout Plain Layout
30622 \begin_inset Formula \begin{equation}
30623 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30631 \begin_layout Plain Layout
30645 \begin_inset Formula \begin{equation}
30646 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30654 \begin_layout Plain Layout
30668 \begin_inset Formula \begin{equation}
30669 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30676 \begin_layout Standard
30677 To switch back to the default numbering, insert the command:
30680 \begin_layout Standard
30693 \begin_layout Plain Layout
30704 \begin_layout Standard
30708 \begin_layout Plain Layout
30722 \begin_inset Formula \begin{equation}
30723 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30730 \begin_layout Standard
30731 \begin_inset VSpace medskip
30734 As you see, formulas are numbered serially independent from the numbering
30736 When then numbering should start with
30737 \begin_inset Quotes eld
30741 \begin_inset Quotes erd
30744 when the style is changed, new equation counters have to be defined.
30745 A description about this can be found in the file
30746 \begin_inset CommandInset href
30748 target "Formula-numbering.lyx"
30755 \begin_layout Section
30756 User-defined commands
30757 \begin_inset CommandInset label
30759 name "sec:User-defined-commands"
30767 \begin_layout Plain Layout
30768 User-defined commands
30776 \begin_layout Standard
30777 Many LaTeX-commands are too long to be used frequently.
30778 But it is possible to define with the command
30788 \begin_layout Plain Layout
30796 new shorter commands.
30799 \begin_layout Standard
30800 The command scheme of
30809 \begin_layout Standard
30814 newcommand{new command name}[number of arguments][optional
30819 \begin_inset Newline newline
30826 \begin_layout Plain Layout
30841 \begin_layout Plain Layout
30848 {command definition}
30851 \begin_layout Standard
30852 \begin_inset Note Greyedout
30855 \begin_layout Plain Layout
30860 Assure that the name of the new command is not already used in your document
30861 or by LaTeX-packages that you use.
30862 When you for example define the command
30874 , you get an error message because
30880 is already defined as command for
30881 \begin_inset Quotes eld
30885 \begin_inset Formula $\le$
30889 \begin_inset Quotes erd
30900 \begin_layout Standard
30901 \begin_inset Note Greyedout
30904 \begin_layout Plain Layout
30909 The names of user-defined commands may only consist of Latin letters.
30917 \begin_layout Standard
30918 The number of arguments is an integer in the range 0
30919 \begin_inset space \thinspace{}
30923 \begin_inset space \thinspace{}
30926 9 and specifies how many arguments the new command should have.
30927 With the optional value a value for an optional argument can be predefined.
30928 When this is done, the
30936 rgument of the new command is automatically an optional one.
30939 \begin_layout Standard
30940 Here are some examples:
30943 \begin_layout Itemize
30944 To define the command
30956 , the LaTeX-preamble line is:
30960 \begin_layout Plain Layout
30972 \begin_inset Newline newline
30984 \begin_layout Itemize
30985 To define the command
30997 , the argument (that should be underlined) must be taken into account.
30998 For this the preamble line is:
31002 \begin_layout Plain Layout
31014 \begin_inset Newline newline
31029 \begin_layout Plain Layout
31041 \begin_inset Newline newline
31050 acts as argument placeholder, the
31054 behind it denotes that it is the placeholder for the first argument.
31057 \begin_layout Itemize
31065 \begin_inset space \thinspace{}
31069 \begin_inset space ~
31082 \begin_layout Plain Layout
31094 \begin_inset Newline newline
31103 framebox#1#2{$#3$}}
31109 \begin_layout Plain Layout
31121 \begin_inset Newline newline
31126 The two Dollar signs creates the extra formula needed for
31133 \begin_inset CommandInset ref
31135 reference "sub:Boxes-with-Frame"
31142 \begin_layout Itemize
31143 To create a new command for
31149 where the color for the box needn't to be specified, the argument for the
31150 color is defined optional:
31154 \begin_layout Plain Layout
31166 \begin_inset Newline newline
31175 fcolorbox{#2}{#1}{$#3$}}
31181 \begin_layout Plain Layout
31191 \begin_inset Newline newline
31194 When the color is not specified when using
31200 , the predefined color
31207 \begin_layout Standard
31208 A test of the new defined commands:
31211 \begin_layout Standard
31213 \begin_inset Tabular
31214 <lyxtabular version="3" rows="6" columns="2">
31216 <column alignment="center" valignment="top" width="0">
31217 <column alignment="center" valignment="top" width="0">
31219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31222 \begin_layout Plain Layout
31228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31231 \begin_layout Plain Layout
31233 \begin_inset Note Note
31236 \begin_layout Plain Layout
31243 is only used as spacer.
31255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31258 \begin_layout Plain Layout
31265 \begin_layout Plain Layout
31279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31282 \begin_layout Plain Layout
31283 \begin_inset Formula $A\gr B$
31293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31296 \begin_layout Plain Layout
31304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31307 \begin_layout Plain Layout
31308 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31321 \begin_layout Plain Layout
31325 \begin_inset Formula $\to$
31331 \begin_inset Formula $\to$
31342 \begin_layout Plain Layout
31356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31359 \begin_layout Plain Layout
31360 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31373 \begin_layout Plain Layout
31377 \begin_inset Formula $\to$
31388 \begin_layout Plain Layout
31402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31405 \begin_layout Plain Layout
31406 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31419 \begin_layout Plain Layout
31425 \begin_inset Formula $\to$
31436 \begin_layout Plain Layout
31450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31453 \begin_layout Plain Layout
31454 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31470 \begin_layout Section
31475 \begin_layout Plain Layout
31484 \begin_layout Standard
31485 To create diagrams, the LaTeX-package
31491 \begin_layout Plain Layout
31496 is part of every LaTeX standard installation.
31507 \begin_layout Plain Layout
31514 It is loaded in the LaTeX-preamble with the line
31517 \begin_layout Standard
31525 \begin_layout Standard
31526 Diagrams visualize relations and look like this:
31527 \begin_inset Formula \[
31528 \begin{CD}A@>>>B@>>>C\\
31530 F@<<<E@<<<D\end{CD}\]
31537 \begin_layout Standard
31538 To get them, the command
31546 \begin_layout Plain Layout
31556 is inserted to a formula.
31557 A blue box appears with two dashed lines where further commands can be
31563 a new line is created.
31564 Horizontal relations are inserted in odd, vertical in even formula lines.
31567 \begin_layout Standard
31568 To create the relations there are the following commands:
31571 \begin_layout Itemize
31576 creates a left arrow,
31587 \begin_layout Itemize
31592 creates an up arrow,
31600 a vertical equal sign
31603 \begin_layout Itemize
31609 is a placeholder for non-existent relations
31612 \begin_layout Standard
31613 All arrows can be labeled as follows:
31616 \begin_layout Itemize
31617 Is text inserted between the first and second < or >, resp., it is placed
31619 When it is inserted between the second and third one, it appears under
31623 \begin_layout Itemize
31624 When text for vertical arrows is inserted between the first and second A
31625 or V, resp., it is placed left beside the arrow.
31626 When it is inserted between the second and third one, it appears right
31628 If the text contains an A or V, these letters must be set into a TeX-brace.
31631 \begin_layout Standard
31632 As example a diagram with all possible relations:
31635 \begin_layout Standard
31636 \begin_inset Formula \[
31637 \begin{CD}A@>j>>B@>>k>C@=F\\
31639 D@<<j<E@>k>>F@=C\end{CD}\]
31646 \begin_layout Standard
31647 The command for this is:
31648 \begin_inset Newline newline
31659 \begin_layout Plain Layout
31668 A@>j>>B@>>k>C@=F Ctrl-Enter
31669 \begin_inset Newline newline
31676 \begin_layout Plain Layout
31691 \begin_layout Plain Layout
31704 \begin_layout Plain Layout
31716 \begin_inset Formula $\to$
31722 \begin_inset Newline newline
31729 \begin_layout Plain Layout
31744 \begin_layout Plain Layout
31757 \begin_layout Plain Layout
31767 \begin_layout Standard
31768 \begin_inset Newpage newpage
31774 \begin_layout Section
31779 \begin_layout Plain Layout
31792 \begin_layout Plain Layout
31793 Other useful math tips can be found in
31794 \begin_inset CommandInset citation
31809 \begin_layout Plain Layout
31817 \begin_inset Note Note
31820 \begin_layout Plain Layout
31823 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31826 \begin_layout Plain Layout
31829 texorpdfstring is in section
31830 \begin_inset CommandInset ref
31832 reference "sub:Formulas-in-Section"
31845 \begin_layout Plain Layout
31855 \begin_layout Plain Layout
31860 \begin_layout Plain Layout
31867 Chemical characters
31871 \begin_layout Plain Layout
31886 \begin_layout Subsection
31887 Chemical Symbols and Equations
31888 \begin_inset CommandInset label
31890 name "sub:Chemical-Symbols-and"
31898 \begin_layout Plain Layout
31899 Chemical characters ! Symbols
31908 \begin_layout Plain Layout
31918 \begin_layout Plain Layout
31927 \begin_layout Standard
31928 An example text from chemistry:
31931 \begin_layout Quote
31933 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31936 -ion reacts with two
31937 \begin_inset Formula $\mathrm{Na^{+}}$
31940 -ions to sodium sulfate
31941 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31945 The chemical equation for this is:
31946 \begin_inset Formula \[
31947 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
31954 \begin_layout Standard
31955 This chemical equation can directly be created as formula.
31956 To avoid that the symbols appear italic, everything is highlighted and
31957 changed by the shortcut
31960 \begin_inset space ~
31965 to the upright font style.
31969 \begin_layout Plain Layout
31975 \begin_inset CommandInset ref
31977 reference "sub:Font-Styles"
31989 \begin_layout Subsection
31994 \begin_layout Plain Layout
32003 \begin_layout Standard
32004 Negative numbers often look ugly in formulas because the minus sign before
32005 the number is set with the same length as the minus operator sign.
32006 When writing the negative number in normal text, the minus sign appears
32010 \begin_layout Standard
32011 Thus, the problem disappears when converting the minus sign to mathematical
32015 \begin_layout Standard
32016 An example to visualize the problem:
32019 \begin_layout Standard
32021 \begin_inset Tabular
32022 <lyxtabular version="3" rows="3" columns="2">
32024 <column alignment="right" valignment="top" width="0">
32025 <column alignment="left" valignment="top" width="0">
32027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32030 \begin_layout Plain Layout
32036 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32039 \begin_layout Plain Layout
32047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32050 \begin_layout Plain Layout
32056 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32059 \begin_layout Plain Layout
32060 \begin_inset Formula $x=-2$
32070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32073 \begin_layout Plain Layout
32079 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32082 \begin_layout Plain Layout
32083 \begin_inset Formula $x=\textrm{-}2$
32099 \begin_layout Subsection
32100 Comma as Decimal Separator
32104 \begin_layout Plain Layout
32113 \begin_layout Standard
32114 In LaTeX a comma inside a formula is used, according to the English convention,
32115 as number group separator.
32116 So there will be space added behind all commas in formulas.
32119 \begin_layout Standard
32120 To avoid this, the comma is highlighted and changed to mathematical text
32124 \begin_inset space ~
32132 \begin_layout Standard
32133 To use all formula commas in the document as decimal separator, the file
32142 \begin_layout Plain Layout
32147 is part of the LaTeX-package
32155 \begin_layout Plain Layout
32160 \begin_layout Plain Layout
32183 \begin_layout Plain Layout
32189 is loaded with the LaTeX-preamble line
32192 \begin_layout Standard
32200 \begin_layout Subsection
32202 \begin_inset CommandInset label
32204 name "sub:Physical-Vectors"
32212 \begin_layout Plain Layout
32221 \begin_layout Standard
32222 Predefined vectors are offered by the LaTeX-package
32230 \begin_layout Plain Layout
32235 should be part of every LaTeX standard installation.
32244 \begin_layout Plain Layout
32250 that is loaded with the LaTeX-preamble line
32253 \begin_layout Standard
32261 \begin_layout Standard
32265 \begin_layout Plain Layout
32275 \begin_inset Note Note
32278 \begin_layout Plain Layout
32279 The following table will only be displayed when the LaTeX-package
32288 The following commands are defined:
32291 \begin_layout Standard
32293 \begin_inset Tabular
32294 <lyxtabular version="3" rows="4" columns="2">
32296 <column alignment="center" valignment="top" width="0">
32297 <column alignment="center" valignment="top" width="0">
32299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32302 \begin_layout Plain Layout
32308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32311 \begin_layout Plain Layout
32319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32322 \begin_layout Plain Layout
32332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32335 \begin_layout Plain Layout
32336 \begin_inset Formula $\Bra{\psi}$
32346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32349 \begin_layout Plain Layout
32359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32362 \begin_layout Plain Layout
32363 \begin_inset Formula $\Ket{\psi}$
32373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32376 \begin_layout Plain Layout
32388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32391 \begin_layout Plain Layout
32392 \begin_inset Formula $\Braket{\psi|\phi}$
32408 \begin_layout Standard
32415 assures that all vertical bars are set in the size of the surrounding brackets:
32416 \begin_inset Formula \[
32417 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32425 \begin_layout Plain Layout
32435 \begin_inset Note Note
32438 \begin_layout Plain Layout
32439 The following will be displayed when the LaTeX-package
32451 \begin_layout Standard
32452 You need to install the LaTeX-package
32456 to see the rest of this subsection in the output.
32459 \begin_layout Standard
32463 \begin_layout Plain Layout
32475 \begin_layout Standard
32482 can also be achieved using the command
32488 , that is described in
32489 \begin_inset CommandInset ref
32491 reference "sub:Automatic-Bracket-Size"
32498 \begin_layout Subsection
32499 Self-defined Fractions
32500 \begin_inset CommandInset label
32502 name "sub:Self-defined-Fractions"
32510 \begin_layout Plain Layout
32511 Fractions ! self-defined
32519 \begin_layout Standard
32520 To define custom commands for fractions, the command
32530 \begin_layout Plain Layout
32538 is used in the following scheme:
32541 \begin_layout Standard
32554 bracket}{fraction bar thickness}{style}
32555 \begin_inset Newline newline
32562 \begin_layout Plain Layout
32577 \begin_layout Plain Layout
32584 {numerator}{denominator}
32587 \begin_layout Standard
32588 The style is a number in the range of 0
32589 \begin_inset space \thinspace{}
32593 \begin_inset space \thinspace{}
32599 \begin_layout Standard
32601 \begin_inset Tabular
32602 <lyxtabular version="3" rows="5" columns="2">
32604 <column alignment="center" valignment="top" width="0">
32605 <column alignment="center" valignment="top" width="0">
32607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32610 \begin_layout Plain Layout
32616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32619 \begin_layout Plain Layout
32627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32630 \begin_layout Plain Layout
32636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32639 \begin_layout Plain Layout
32640 display style formula
32647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32650 \begin_layout Plain Layout
32656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32659 \begin_layout Plain Layout
32667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32670 \begin_layout Plain Layout
32676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32679 \begin_layout Plain Layout
32687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32690 \begin_layout Plain Layout
32696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32699 \begin_layout Plain Layout
32713 \begin_layout Standard
32714 When no style is given, the size is adjusted to the surrounding environment
32715 like for the command
32724 \begin_layout Standard
32725 When no fraction bar thickness is given, the predefined value of 0.4
32726 \begin_inset space \thinspace{}
32732 \begin_layout Standard
32733 \begin_inset VSpace medskip
32736 For example, the commands
32749 \begin_inset CommandInset ref
32751 reference "sub:Fractions"
32755 are defined with the commands
32758 \begin_layout Standard
32767 genfrac{}{}{}{0}{#1}{#2}}
32770 \begin_layout Standard
32774 \begin_layout Standard
32783 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32786 \begin_layout Standard
32787 \begin_inset VSpace medskip
32790 To define a fraction where the fraction bar thickness can be given as optional
32791 argument, the following line is inserted to the LaTeX-preamble:
32794 \begin_layout Standard
32803 genfrac{}{}{#1}{}{#2}{#3}}
32806 \begin_layout Standard
32808 \begin_inset Formula \begin{align*}
32809 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32810 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32814 As one can see, the distance of the numerator and the denominator to the
32815 fraction bar is round about three times the bar thickness.
32818 \begin_layout Subsection
32820 \begin_inset CommandInset label
32822 name "sub:Canceled-Formulas"
32830 \begin_layout Plain Layout
32839 \begin_layout Standard
32840 To cancel formulas or formula parts, the LaTeX-package
32848 \begin_layout Plain Layout
32853 is part of every LaTeX standard installation.
32862 \begin_layout Plain Layout
32868 has to be loaded with the LaTeX-preamble line
32871 \begin_layout Standard
32876 usepackage[samesize]{cancel}
32879 \begin_layout Standard
32880 There are four ways to cancel formulas:
32883 \begin_layout Standard
32885 \begin_inset Tabular
32886 <lyxtabular version="3" rows="5" columns="2">
32888 <column alignment="center" valignment="top" width="0">
32889 <column alignment="center" valignment="top" width="0">
32891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32894 \begin_layout Plain Layout
32900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32903 \begin_layout Plain Layout
32905 \begin_inset Note Note
32908 \begin_layout Plain Layout
32921 are used here as spacer.
32933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32936 \begin_layout Plain Layout
32945 \begin_layout Plain Layout
32959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32962 \begin_layout Plain Layout
32963 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
32973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32976 \begin_layout Plain Layout
32985 \begin_layout Plain Layout
32999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33002 \begin_layout Plain Layout
33003 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33016 \begin_layout Plain Layout
33025 \begin_layout Plain Layout
33039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33042 \begin_layout Plain Layout
33043 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33056 \begin_layout Plain Layout
33060 \begin_inset Formula $\to$
33071 \begin_layout Plain Layout
33085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33088 \begin_layout Plain Layout
33089 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33105 \begin_layout Standard
33112 is especially suitable to visualize the reduction of fractions within formulas:
33113 \begin_inset Formula \[
33114 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33121 \begin_layout Subsection
33122 Formulas in Section Headings
33123 \begin_inset CommandInset label
33125 name "sub:Formulas-in-Section"
33133 \begin_layout Plain Layout
33134 Formula ! in section headings
33142 \begin_layout Standard
33143 When formulas are used in section headings, the following has to be taken
33147 \begin_layout Standard
33148 \begin_inset Note Greyedout
33151 \begin_layout Plain Layout
33160 \begin_layout Plain Layout
33161 Packages ! hyperref
33166 support is enabled in the document settings dialog under
33169 \begin_inset space ~
33174 , PDF-bookmarks are created for every section heading in the table of contents.
33175 If a section heading contains formulas, they are incorrectly displayed
33176 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33185 \begin_layout Standard
33186 Both problems can be solved by inserting at the end of the section heading
33187 a short title with the menu
33189 Insert\SpecialChar \menuseparator
33191 \begin_inset space ~
33197 Short titles are used as alternative for multiline section headings to
33198 keep the table of contents clearly arranged.
33199 Only the short title appears in the table of contents and therefore also
33200 in the PDF-bookmark.
33203 \begin_layout Standard
33204 When formulas should be used in the table of contents but
33208 is used, one can use the following command in TeX-mode:
33211 \begin_layout Standard
33216 texorpdfstring{part}{alternative}
33220 \begin_layout Plain Layout
33231 \begin_layout Standard
33232 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33233 This can be characters, formulas, footnotes, but also cross-references.
33234 The alternative is used instead of the part for the bookmark.
33237 \begin_layout Standard
33238 Here are two example headings:
33239 \begin_inset VSpace -3mm
33246 \begin_layout Plain Layout
33258 \begin_layout Subsubsection
33259 Heading without formula in table of contents
33260 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33264 \begin_inset OptArg
33267 \begin_layout Plain Layout
33268 Heading without formula in table of contents
33276 \begin_layout Subsubsection
33277 Heading with formula in table of contents
33281 \begin_layout Plain Layout
33291 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33298 \begin_layout Plain Layout
33308 \begin_layout Standard
33312 \begin_layout Plain Layout
33321 In the first heading a short title was used, in the second one
33330 \begin_layout Standard
33331 To get the same formatting as for the other headings, the complete heading
33334 boldmath environment
33340 \begin_layout Plain Layout
33342 \begin_inset CommandInset ref
33344 reference "sub:Bold-Formulas"
33356 \begin_layout Subsection
33357 Formulas in multi-column Text
33361 \begin_layout Plain Layout
33362 Formula ! in multi-column text
33370 \begin_layout Standard
33371 Formulas in multi-column text are often too wide to fit into a column and
33372 thus need to be set over the whole page width.
33373 This is done by using the LaTeX-package
33381 \begin_layout Plain Layout
33386 is part of every LaTeX standard installation.
33395 \begin_layout Plain Layout
33396 Packages ! multicol
33401 , that is loaded with the LaTeX-preamble line
33404 \begin_layout Standard
33409 usepackage{multicol}
33412 \begin_layout Standard
33413 \begin_inset Note Greyedout
33416 \begin_layout Plain Layout
33417 Note herby that the setting
33420 \begin_inset space ~
33427 Document\SpecialChar \menuseparator
33433 \begin_inset space ~
33453 \begin_layout Standard
33454 Before the multi-column text the command
33457 \begin_layout Standard
33462 begin{multicols}{column number}
33465 \begin_layout Standard
33466 is written in TeX-mode.
33467 The column number is a number in the range of 2
33468 \begin_inset space \thinspace{}
33472 \begin_inset space \thinspace{}
33476 Before the formula the multi-column text is ended by inserting the command
33479 \begin_layout Standard
33487 \begin_layout Standard
33491 \begin_layout Standard
33492 Due to the command some space is automatically added before the formula.
33494 \begin_inset space \thinspace{}
33497 mm vertical space is inserted before the formula.
33498 When the formula style
33504 \begin_layout Plain Layout
33506 \begin_inset CommandInset ref
33508 reference "sec:Formula-Styles"
33520 \begin_inset space \thinspace{}
33523 mm space is inserted instead.
33526 \begin_layout Standard
33527 As example a multi-column text with a displayed formula:
33530 \begin_layout Standard
33534 \begin_layout Plain Layout
33538 begin{multicols}{2}
33543 Das Spektrum wird fouriertransformiert.
33544 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33545 , Lösungsmittel) zu trennen.
33546 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33547 nun das Aussehen des Ausgangssignals.
33548 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33549 über alle Phasen integrieren muss.
33551 \begin_inset Formula $S$
33554 unser normiertes Ausgangssignal and
33555 \begin_inset Formula $P$
33558 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33562 \begin_layout Plain Layout
33572 \begin_inset VSpace -6mm
33576 \begin_inset Formula \begin{equation}
33577 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33585 \begin_layout Plain Layout
33589 begin{multicols}{2}
33595 \begin_inset Formula $S_{0}$
33598 das Signal ohne Gradient ist and the Normierungsbedingung
33599 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33603 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33605 \begin_inset Formula $\nicefrac{\pi}{2}$
33609 \begin_inset space \thinspace{}
33612 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33613 das Signal zusätzlich abschwächt.
33614 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33616 \begin_inset Formula $T_{2}$
33622 \begin_layout Standard
33626 \begin_layout Plain Layout
33638 \begin_layout Subsection
33639 Formulas with Description of Variables
33643 \begin_layout Plain Layout
33644 Formula ! with description of variables
33652 \begin_layout Standard
33653 To describe variables within a formula, like in formula
33654 \begin_inset CommandInset ref
33656 reference "eq:within"
33665 \begin_inset Formula $n$
33669 \begin_inset space ~
33672 matrix is used with left aligned columns for the
33673 \begin_inset Formula $n$
33680 \begin_layout Plain Layout
33682 \begin_inset CommandInset ref
33684 reference "sec:Matrices"
33693 To set the description in a smaller size, before the matrix e.
33694 \begin_inset space \thinspace{}
33698 \begin_inset space ~
33711 \begin_layout Plain Layout
33713 \begin_inset CommandInset ref
33715 reference "sub:Font-Sizes"
33727 \begin_layout Standard
33728 When the formula style
33734 \begin_layout Plain Layout
33736 \begin_inset CommandInset ref
33738 reference "sec:Formula-Styles"
33759 \begin_layout Plain Layout
33766 only works in formulas with the style
33771 \begin_inset CommandInset ref
33773 reference "sub:Variable-Space"
33782 is inserted before and after the matrix to have the same separation of
33783 the matrix from the equation and the side margin.
33786 \begin_layout Standard
33787 When the formula style
33791 is used, the method described in
33792 \begin_inset CommandInset ref
33794 reference "sub:Flalign-Environment"
33798 is used to indent formulas.
33800 \begin_inset CommandInset ref
33802 reference "eq:within"
33806 consists of five columns whereas in the first two columns contain the equation,
33807 the third the matrix, and the last one an empty TeX-brace.
33808 \begin_inset Formula \begin{flalign}
33809 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33810 \rho & \textrm{density}\\
33811 V & \textrm{volume}\\
33812 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33819 \begin_layout Subsection
33820 Upright small Greek Letters
33821 \begin_inset CommandInset label
33823 name "sub:Upright-small-Greek"
33831 \begin_layout Plain Layout
33832 Greek letters ! upright
33840 \begin_layout Standard
33841 Most of the math fonts only provide italic small Greek letters.
33842 But for symbols of elementary particles like pions and neutrinos, upright
33843 Greek letters are needed.
33852 \begin_layout Plain Layout
33857 is part of the LaTeX-package
33865 \begin_layout Plain Layout
33870 \begin_layout Plain Layout
33893 \begin_layout Plain Layout
33899 that is loaded with the LaTeX-preamble line
33902 \begin_layout Standard
33907 usepackage{upgreek}
33910 \begin_layout Standard
33916 \begin_layout Plain Layout
33926 \begin_inset Note Note
33929 \begin_layout Plain Layout
33930 The following table will only be displayed when the LaTeX-package
33939 They are created when the command for a small Greek letters is started
33945 For example the command
33952 \begin_inset Formula $\uptau$
33958 \begin_layout Standard
33959 With these commands reactions of elementary particles can be typeset:
33960 \begin_inset Formula \[
33961 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
33968 \begin_layout Standard
33969 The upright letters are more bold and wider than the italic ones.
33970 They should therefore not be used for units like
33971 \begin_inset Quotes eld
33975 \begin_inset Quotes erd
33981 \begin_layout Standard
33985 \begin_layout Plain Layout
33995 \begin_inset Note Note
33998 \begin_layout Plain Layout
33999 The following will be displayed when the LaTeX-package
34011 \begin_layout Standard
34012 You need to install the LaTeX-package
34016 to see the rest of this subsection in the output.
34019 \begin_layout Standard
34023 \begin_layout Plain Layout
34035 \begin_layout Subsection
34036 Text Characters in Formulas
34037 \begin_inset CommandInset label
34039 name "sub:Text-Characters-in"
34047 \begin_layout Plain Layout
34056 \begin_layout Standard
34057 In some cases you might want to insert text characters directly into formulas.
34058 When for example the centered dot · is often used in formulas like
34059 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34062 , one would have to insert the command
34072 \begin_layout Plain Layout
34074 \begin_inset CommandInset ref
34076 reference "sub:Binary-Operators"
34085 all the time, because this character is defined in all encodings as text
34087 But the encoding can be changed by this LaTeX-preamble line:
34090 \begin_layout Standard
34095 Declare Inputtext{183}{
34105 f\SpecialChar \textcompwordmark{}
34109 \begin_layout Standard
34110 The character encoding (menu
34112 Document\SpecialChar \menuseparator
34113 Settings\SpecialChar \menuseparator
34116 ) specifies what character appears when a keyboard key is pressed.
34117 When the key for the character '·' is pressed, internally the command
34124 But this command is not available in a formula so that you would get LaTeX-erro
34126 With the changed encoding the right command is chosen automatically, depending
34127 on if the character was inserted into a formula or not.
34130 \begin_layout Standard
34131 The encoding of several characters is saved in definition files.
34132 Fore example the encoding
34136 is defined in the file
34140 that is in the installation folder of LaTeX.
34141 Encodings should only be changed via the LaTeX-preamble and not in the
34143 Otherwise own documents could not be edited by other LyX users working
34144 on other computers.
34147 \begin_layout Standard
34148 \begin_inset VSpace medskip
34151 Besides the centered dot, in this document the degree sign ° is defined
34152 with the following LaTeX-preamble line so that it can directly be inserted
34156 \begin_layout Standard
34161 DeclareInputtext{176}{
34171 f\SpecialChar \textcompwordmark{}
34175 \begin_layout Standard
34176 \begin_inset Newpage newpage
34182 \begin_layout Section
34184 Typographic Advises
34188 \begin_layout Plain Layout
34189 Typographic Advises
34197 \begin_layout Standard
34198 This section is a summary of the most important typographic rules, listed
34203 \begin_layout Plain Layout
34204 This collection was partly taken from the German semi-official dictionary
34206 \begin_inset Quotes eld
34210 \begin_inset Quotes erd
34214 \begin_inset CommandInset citation
34220 that lists some of the ISO rules.
34228 \begin_layout Itemize
34237 \begin_layout Plain Layout
34238 done with font styles, see
34239 \begin_inset CommandInset ref
34241 reference "sub:Font-Styles"
34251 \begin_inset space \thinspace{}
34255 \begin_inset Newline newline
34258 Between the value and the unit is the smallest space, see
34259 \begin_inset CommandInset ref
34261 reference "sub:Predefined-Space"
34268 \begin_layout Itemize
34269 Percent and perthousand signs are set like physical units:
34270 \begin_inset Newline newline
34274 \begin_inset space \thinspace{}
34280 \begin_layout Itemize
34281 The degree sign follows directly on the value: 15°, but not when it is used
34283 \begin_inset space \thinspace{}
34289 \begin_layout Itemize
34290 In numbers with more than four digits the smallest space is inserted before
34291 every third digit to group them:
34301 \begin_inset space \thinspace{}
34305 \begin_inset space \thinspace{}
34311 \begin_layout Itemize
34312 For dimensionings like 120×90×40
34313 \begin_inset space \thinspace{}
34316 cm the multiplication sign
34317 \begin_inset Quotes eld
34321 \begin_inset Quotes erd
34325 It is available with the LaTeX-command
34331 , but can also directly be inserted with some keyboard definitions.
34334 \begin_layout Itemize
34335 Functions with names consisting of several letters are set upright to avoid
34337 \begin_inset CommandInset ref
34339 reference "sub:Predefined-Functions"
34346 \begin_layout Itemize
34347 Indices consisting of several letters, are set upright:
34348 \begin_inset Formula $E_{\mathrm{kin}}$
34352 \begin_inset Newline newline
34355 Components of matrices are set italic:
34356 \begin_inset Formula $\hat{H}_{kl}$
34362 \begin_layout Itemize
34363 The differentiation/integration operator 'd', the Euler's number 'e', and
34364 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34368 \begin_layout Standard
34369 \begin_inset Newpage newpage
34375 \begin_layout Section
34380 \begin_layout Plain Layout
34389 \begin_layout Standard
34390 Some characters and symbols can be created with several commands.
34391 Here is a list of the synonym commands:
34394 \begin_layout Standard
34395 \begin_inset VSpace bigskip
34399 \begin_inset space \hfill{}
34403 \begin_inset Tabular
34404 <lyxtabular version="3" rows="12" columns="2">
34406 <column alignment="center" valignment="top" width="0pt">
34407 <column alignment="center" valignment="top" width="0pt">
34409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34412 \begin_layout Plain Layout
34418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34421 \begin_layout Plain Layout
34423 \begin_inset Note Note
34426 \begin_layout Plain Layout
34433 is only used as spacer.
34445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34448 \begin_layout Plain Layout
34456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34459 \begin_layout Plain Layout
34463 \begin_layout Plain Layout
34476 \begin_layout Plain Layout
34490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34493 \begin_layout Plain Layout
34501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34504 \begin_layout Plain Layout
34514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34517 \begin_layout Plain Layout
34525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34528 \begin_layout Plain Layout
34538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34541 \begin_layout Plain Layout
34549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34552 \begin_layout Plain Layout
34560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34563 \begin_layout Plain Layout
34571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34574 \begin_layout Plain Layout
34582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34585 \begin_layout Plain Layout
34593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34596 \begin_layout Plain Layout
34606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34609 \begin_layout Plain Layout
34617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34620 \begin_layout Plain Layout
34630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34633 \begin_layout Plain Layout
34641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34644 \begin_layout Plain Layout
34654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34657 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34668 \begin_layout Plain Layout
34678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34681 \begin_layout Plain Layout
34689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34692 \begin_layout Plain Layout
34700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34703 \begin_layout Plain Layout
34711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34714 \begin_layout Plain Layout
34726 \begin_inset space \hfill{}
34730 \begin_inset Tabular
34731 <lyxtabular version="3" rows="12" columns="2">
34733 <column alignment="center" valignment="top" width="0pt">
34734 <column alignment="center" valignment="top" width="0pt">
34736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34739 \begin_layout Plain Layout
34745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34748 \begin_layout Plain Layout
34756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34759 \begin_layout Plain Layout
34767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34770 \begin_layout Plain Layout
34782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34785 \begin_layout Plain Layout
34793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34796 \begin_layout Plain Layout
34806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34809 \begin_layout Plain Layout
34817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34820 \begin_layout Plain Layout
34830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34833 \begin_layout Plain Layout
34841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34844 \begin_layout Plain Layout
34852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34855 \begin_layout Plain Layout
34863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34866 \begin_layout Plain Layout
34874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34877 \begin_layout Plain Layout
34885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34888 \begin_layout Plain Layout
34898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34901 \begin_layout Plain Layout
34909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34912 \begin_layout Plain Layout
34922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34925 \begin_layout Plain Layout
34933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34936 \begin_layout Plain Layout
34946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34949 \begin_layout Plain Layout
34957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34960 \begin_layout Plain Layout
34970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34973 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34984 \begin_layout Plain Layout
34994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34997 \begin_layout Plain Layout
35005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35008 \begin_layout Plain Layout
35022 \begin_inset space \hfill{}
35028 \begin_layout Standard
35029 \begin_inset Newpage newpage
35035 \begin_layout Bibliography
35036 \begin_inset CommandInset bibitem
35037 LatexCommand bibitem
35049 The LaTeX Companion
35052 Addison Wesley, 2004
35055 \begin_layout Bibliography
35056 \begin_inset CommandInset bibitem
35057 LatexCommand bibitem
35063 \begin_inset CommandInset href
35066 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35070 of LaTeX's math abilities
35073 \begin_layout Bibliography
35074 \begin_inset CommandInset bibitem
35075 LatexCommand bibitem
35080 LaTeX tips and tricks-
35081 \begin_inset CommandInset href
35084 target "http://tug.org/TeXnik/"
35091 \begin_layout Bibliography
35092 \begin_inset CommandInset bibitem
35093 LatexCommand bibitem
35099 \begin_inset CommandInset href
35102 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35110 \begin_layout Plain Layout
35122 \begin_layout Bibliography
35123 \begin_inset CommandInset bibitem
35124 LatexCommand bibitem
35130 \begin_inset CommandInset href
35133 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35137 of all symbols available with LaTeX-packages
35140 \begin_layout Bibliography
35141 \begin_inset CommandInset bibitem
35142 LatexCommand bibitem
35148 \begin_inset CommandInset href
35150 name "Documentation"
35151 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35155 of the LaTeX-package
35163 \begin_layout Plain Layout
35164 Packages ! hyperref
35172 \begin_layout Bibliography
35173 \begin_inset CommandInset bibitem
35174 LatexCommand bibitem
35180 \begin_inset CommandInset href
35183 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35194 \begin_inset CommandInset ref
35196 reference "sub:Operator-Limits"
35204 \begin_layout Plain Layout
35215 \begin_layout Bibliography
35216 \begin_inset CommandInset bibitem
35217 LatexCommand bibitem
35228 Auflage, Duden 2001
35231 \begin_layout Subsubsection*
35232 \begin_inset CommandInset index_print
35233 LatexCommand printindex