1 #LyX 1.5.4svn 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 % link all cross references and URLs
27 \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
28 bookmarksopen, bookmarksopenlevel=1,
29 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
30 pdfpagelayout=OneColumn, pdfnewwindow=true,
31 pdfstartview=XYZ, plainpages=false, pdfpagelabels,
32 pdfauthor={LyX Team}, pdftex,
33 pdftitle={LyX's Math Manual},
34 pdfsubject={LyX-documentation about math},
35 pdfkeywords={LyX, Mathed}]{hyperref}
37 \else % if dvi or ps is produced
39 % link all cross references and URLs in DVI output
40 \usepackage[ps2pdf, colorlinks=true,
41 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
43 \fi % end if pdflatex is used
45 % Folgendes Problem lösen:
46 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
47 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
48 % die Kapitelnummer geschrieben.
49 % Als Lösung wird mehr Platz zwischen Nummer und
50 % Überschrift eingefügt.
51 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
52 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
54 % To be able to enter the character ° and · directly in LyX,
56 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
57 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
59 % increase link area for cross-references and autoname them,
61 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
62 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
63 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
64 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
66 \settowidth{\abc}{\space}
67 \renewcommand{\equationautorefname}{\hspace{-\abc}}
69 % don't load packages twice
70 % see first footnote in sec. 9.3
71 \@ifundefined{textcolor}{\usepackage{color}}{}
73 % the pages of the TOC are numbered roman
74 % and a PDF-bookmark for the TOC is added
76 \let\myTOC\tableofcontents
77 \renewcommand{\tableofcontents}{%
79 \pdfbookmark[1]{Contents}{}
82 \pagenumbering{arabic}}
84 % insert additional vertical space of 1.5 mm between footnotes,
87 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
89 % provides caption formatting
90 \setkomafont{captionlabel}{\bfseries}
96 \usepackage[samesize]{cancel}
98 % enables calculation of values,
101 % for multiple table row and column cells
102 \usepackage{multirow}
103 \usepackage{multicol}
105 % needed for diagrams
108 % needed in sec. 19.4
109 \usepackage{remreset}
111 % center multirows (e.g. in sec. 13.3)
112 \renewcommand{\multirowsetup}{\centering}
114 % define a color, used in sec.9.3
115 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
117 % declare operators (see sec. 10.4 and sec. 15.2)
118 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
119 \DeclareMathOperator{\sgn}{sgn}
121 \newcommand{\spce}{\textvisiblespace}
123 % example definitions for sec. 20.1
124 \newcommand{\gr}{\Longrightarrow}
125 \newcommand{\us}[1]{\underline{#1}}
126 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
127 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
128 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
130 % example macro from sec. 19.4
131 %\def\tagform@#1{\maketag@@@{|#1|}}
133 % macro from sec. 10.2
134 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
135 \def\mathclap {\mathpalette \mathclapinternal}
136 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
138 % redefine the greyed out note
139 \renewenvironment{lyxgreyedout}
140 {\textcolor{blue}\bgroup}{\egroup}
142 % check for package eurosym
143 % used for the Euro symbol
145 \IfFileExists{eurosym.sty}
146 {\usepackage[gennarrow]{eurosym}
147 \setboolean{eurosym}{true}}
148 {\setboolean{eurosym}{false}}
150 % needed in sec. 22.4
151 % check for package braket
153 \IfFileExists{braket.sty}
155 \setboolean{braket}{true}}
156 {\setboolean{braket}{false}}
158 % needed in sec. 22.10
159 % check for package upgreek
161 \IfFileExists{upgreek.sty}
162 {\usepackage{upgreek}
163 \setboolean{upgreek}{true}}
164 {\setboolean{upgreek}{false}}
166 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
171 \font_typewriter default
172 \font_default_family default
186 \paperorientation portrait
189 \paragraph_separation skip
191 \quotes_language english
194 \paperpagestyle plain
198 \tracking_changes false
199 \output_changes false
207 LyX's detailed Math manual
215 \begin_layout Standard
217 If you have comments or error corrections, please send them to the LyX Documenta
224 \begin_layout Standard
228 href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
233 lyx-docs@lists.lyx.org
237 \begin_layout Standard
250 \begin_inset Note Note
253 \begin_layout Standard
270 \begin_layout Standard
271 \begin_inset LatexCommand tableofcontents
278 \begin_layout Standard
279 \begin_inset Note Note
282 \begin_layout Standard
283 To export this document to PDF, PS, or DVI the LaTeX-packages
296 If they are not installed you can export the document anyway but the sections
297 where the packages are required won't appear in the output.
305 \begin_layout Standard
311 \begin_layout Section
313 \begin_inset LatexCommand label
314 name "sec:Introduction"
321 \begin_layout Standard
322 This document explains LyX's math features and is furthermore a collection
323 of LaTeX-commands used for mathematical characters and constructs.
324 The explanations are designed for the usage of commands.
325 It is therefore required that you have read the section
327 Mathematical\InsetSpace ~
333 \begin_layout Standard
334 Most of the characters and many constructs explained in this manual are
335 also accessible via the menu
339 \SpecialChar \menuseparator
355 But everybody who has to write lots of formulas will notice that it is
356 much faster to use commands instead of the math toolbar.
357 Therefore this manual is focused on commands but also mentions the correspondin
358 g toolbar buttons when available.
361 \begin_layout Standard
362 If not specially mentioned the commands are only available within formulas.
363 To be able to use all commands explained in this document, the option
367 must be used in the document settings (menu
369 Document\SpecialChar \menuseparator
370 Settings\SpecialChar \menuseparator
378 \begin_layout Standard
381 Use AMS math package automatically
387 \begin_layout Standard
396 -math when math constructs are found that are supported by LyX.
404 \begin_layout Standard
405 This document doesn't list all
409 \begin_layout Standard
422 \begin_layout Standard
427 \begin_layout Standard
436 -math commands is in the file
440 \begin_layout Standard
444 href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
457 \begin_layout Standard
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
474 \begin_inset LatexCommand label
475 name "sec:General-Instructions"
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset LatexCommand index
485 name "Formula ! inline"
489 that is embedded into a text line, press
493 or the toolbar button
494 \begin_inset Graphics
495 filename ../images/math-mode.png
502 To create a display style formula
503 \begin_inset LatexCommand index
504 name "Formula ! display style"
508 that will appear bigger and in an own paragraph, press
515 \begin_layout Standard
516 To change a display style formula to an inline formula, set the cursor into
517 the formula and press
523 Edit\SpecialChar \menuseparator
524 Math\SpecialChar \menuseparator
528 The same way is used to change an inline formula to a display style formula.
531 \begin_layout Standard
532 To display parts of an inline formula in the size of a display style formula,
538 \begin_inset LatexCommand index
539 name "Commands ! D ! \\textbackslash displaystyle"
546 Then a new blue box appears in which the desired formula part is inserted.
549 \begin_layout Standard
550 Only inline formulas are allowed inside tables.
553 \begin_layout Standard
558 can be turned on in the menu
560 View\SpecialChar \menuseparator
564 When you click there on
565 \begin_inset Quotes eld
569 \begin_inset Quotes erd
572 the toolbar will be shown permanently at the bottom; this state is visualized
577 menu with a checkmark.
578 When you click in this state again on
579 \begin_inset Quotes eld
583 \begin_inset Quotes erd
594 is only shown when the cursor is within a formula; this state is visualized
595 by the renaming of the menu entry from
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
604 \begin_inset Quotes eld
609 \begin_inset Quotes erd
615 \begin_layout Standard
617 \begin_inset LatexCommand index
622 is invoked by pressing the toolbar button
623 \begin_inset Graphics
624 filename ../images/ert-insert.png
631 Insert\SpecialChar \menuseparator
636 \begin_layout Standard
647 \begin_layout Standard
661 \begin_inset Note Note
664 \begin_layout Standard
665 In LyX there are three
666 \begin_inset Quotes eld
670 \begin_inset Quotes erd
673 that appear in the output with sub- and superscript letters: TeX, LaTeX,
677 \begin_layout Standard
678 To avoid that these names are recognized as proper names, TeX-braces are
679 set around one of the letters of the name.
687 \begin_layout Standard
688 To change the LaTeX-preamble
689 \begin_inset LatexCommand index
690 name "L@\\LaTeX-preamble"
696 Document\SpecialChar \menuseparator
697 Settings\SpecialChar \menuseparator
702 \begin_layout Standard
713 \begin_layout Standard
729 \begin_layout Standard
730 To edit matrices, case differentiations, and multiline formulas subsequently,
733 Edit\SpecialChar \menuseparator
738 Edit\SpecialChar \menuseparator
739 Rows\InsetSpace \thinspace{}
740 &\InsetSpace \thinspace{}
748 When lines and columns are swapped via the menu, the column or line where
749 the cursor is in is exchanged with the column to the right or the line
751 Is the cursor in the last column or row, the exchange is done with the
752 column to the left or the line above.
755 \begin_layout Standard
756 To write text in formulas
760 \begin_layout Standard
761 For multiline formulas the command
768 \begin_inset LatexCommand ref
769 reference "sub:Text-in-multiline"
783 \begin_inset LatexCommand index
784 name "Text ! in formulas"
789 \begin_inset LatexCommand index
790 name "Mathematical text"
795 This mode is invoked with the the shortcut
800 or by the insertion of the command
805 \begin_inset LatexCommand index
806 name "Commands ! T ! \\textbackslash text"
813 The text appears black in LyX and can therefore be distinguished from the
814 other formula parts that appear blue.
815 In the output mathematical text is set upright, in contrary to other formula
819 \begin_layout Subsection*
823 \begin_layout Standard
824 Most of the LaTeX-commands for math constructs have the following scheme:
827 \begin_layout Standard
843 \begin_layout Standard
844 A command starts always with a backslash
845 \begin_inset Quotes gld
855 \begin_inset Quotes grd
859 To omit optional arguments, also omit the associated brackets.
860 The braces around the required arguments are named in this document as
862 \begin_inset LatexCommand index
863 name "T@\\TeX-braces"
868 If you add in a formula a left brace to a command name, LyX creates automatical
870 In all other cases TeX-braces are created in formulas with the command
878 TeX-braces appear red in LyX, in contrary to normal braces that appear
880 In TeX-mode no command is needed to get TeX-braces.
881 TeX-braces don't appear in the output.
884 \begin_layout Standard
885 When commands without arguments, like commands for symbols are entered in
886 TeX-mode, a space character must
890 be behind the command to end it.
891 This space doesn't appear in the output.
892 When the space should appear in the output, the space must be followed
893 by a protected space in normal text.
896 \begin_layout Standard
897 A protected space is inserted with
904 \begin_layout Subsection*
910 \begin_layout Itemize
915 \begin_layout Standard
916 This visible space character can be created with the command
923 \begin_inset LatexCommand index
924 name "Commands ! T ! \\textbackslash textvisiblespace"
928 , inserted in TeX-mode.
937 \begin_layout Standard
947 denotes a space character to be input.
950 \begin_layout Itemize
952 \begin_inset Formula $\to$
955 denotes the usage of the corresponding arrow key on the keyboard.
958 \begin_layout Subsection*
962 \begin_layout Standard
964 \begin_inset Float table
970 \begin_layout Standard
974 \begin_layout Standard
975 \begin_inset LatexCommand label
976 name "tab:Used-units"
988 \begin_layout Standard
991 <lyxtabular version="3" rows="13" columns="2">
993 <column alignment="center" valignment="top" leftline="true" width="0">
994 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
995 <row topline="true" bottomline="true">
996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
999 \begin_layout Standard
1005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1008 \begin_layout Standard
1015 <row topline="true">
1016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1019 \begin_layout Standard
1025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1028 \begin_layout Standard
1035 <row topline="true">
1036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1039 \begin_layout Standard
1045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1048 \begin_layout Standard
1055 <row topline="true">
1056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1059 \begin_layout Standard
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1068 \begin_layout Standard
1069 Inch (1\InsetSpace \thinspace{}
1070 in = 2,54\InsetSpace \thinspace{}
1077 <row topline="true">
1078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1081 \begin_layout Standard
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1090 \begin_layout Standard
1091 Point (72.27\InsetSpace \thinspace{}
1092 pt = 1\InsetSpace \thinspace{}
1099 <row topline="true">
1100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1103 \begin_layout Standard
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1112 \begin_layout Standard
1113 Pica (1\InsetSpace \thinspace{}
1114 pc = 12\InsetSpace \thinspace{}
1121 <row topline="true">
1122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1125 \begin_layout Standard
1131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1134 \begin_layout Standard
1135 scaled point (65536\InsetSpace \thinspace{}
1136 sp = 1\InsetSpace \thinspace{}
1143 <row topline="true">
1144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1147 \begin_layout Standard
1153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1156 \begin_layout Standard
1157 big point (72\InsetSpace \thinspace{}
1158 bp = 1\InsetSpace \thinspace{}
1165 <row topline="true">
1166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1169 \begin_layout Standard
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1178 \begin_layout Standard
1179 Didot (1\InsetSpace \thinspace{}
1181 \begin_inset Formula $\approx$
1184 0.376\InsetSpace \thinspace{}
1191 <row topline="true">
1192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1195 \begin_layout Standard
1201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1204 \begin_layout Standard
1205 Cicero (1\InsetSpace \thinspace{}
1206 cc = 12\InsetSpace \thinspace{}
1213 <row topline="true">
1214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1217 \begin_layout Standard
1223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1226 \begin_layout Standard
1230 \begin_inset Quotes eld
1236 \begin_inset Quotes erd
1245 <row topline="true">
1246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1249 \begin_layout Standard
1255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1258 \begin_layout Standard
1260 \begin_inset Quotes eld
1268 \begin_inset Quotes erd
1277 <row topline="true" bottomline="true">
1278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1281 \begin_layout Standard
1287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1290 \begin_layout Standard
1291 math unit (1\InsetSpace \thinspace{}
1293 \begin_inset Formula $\nicefrac{1}{18}$
1296 \InsetSpace \thinspace{}
1298 \begin_inset Note Note
1301 \begin_layout Standard
1308 is explained in sec.\InsetSpace \thinspace{}
1310 \begin_inset LatexCommand ref
1311 reference "sub:Self-defined-Fractions"
1338 \begin_layout Standard
1344 \begin_layout Section
1348 \begin_layout Subsection
1350 \begin_inset LatexCommand index
1356 \begin_inset LatexCommand index
1362 \begin_inset LatexCommand index
1363 name "Superscripts|see{Exponents}"
1368 \begin_inset LatexCommand index
1369 name "Subscripts|see{Indices}"
1376 \begin_layout Standard
1377 Indices are created with an underscore
1378 \begin_inset Quotes eld
1382 \begin_inset Quotes erd
1385 or via the math toolbar button
1386 \begin_inset Graphics
1387 filename ../images/math-subscript.png
1392 , exponents with a caret
1393 \begin_inset Quotes eld
1397 \begin_inset Quotes erd
1400 or via the math toolbar button
1401 \begin_inset Graphics
1402 filename ../images/math-superscript.png
1410 \begin_layout Standard
1412 \begin_inset Tabular
1413 <lyxtabular version="3" rows="4" columns="2">
1415 <column alignment="center" valignment="top" leftline="true" width="0pt">
1416 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1417 <row topline="true" bottomline="true">
1418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1421 \begin_layout Standard
1427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1430 \begin_layout Standard
1432 \begin_inset Note Note
1435 \begin_layout Standard
1442 is only used as spacer.
1453 <row topline="true">
1454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1457 \begin_layout Standard
1463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1466 \begin_layout Standard
1467 \begin_inset Formula $B_{V}$
1476 <row topline="true" bottomline="true">
1477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1480 \begin_layout Standard
1486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1489 \begin_layout Standard
1490 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1499 <row topline="true" bottomline="true">
1500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1503 \begin_layout Standard
1508 \begin_layout Standard
1522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1525 \begin_layout Standard
1526 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1542 \begin_layout Standard
1543 As the caret is in some languages an accent, vowels will be accentuated
1544 in this case and not set as exponents
1548 \begin_layout Standard
1549 Depending on the used keyboard settings this can also happen for other character
1556 To get in this case exponents, press
1560 after the caret as in the last example.
1563 \begin_layout Subsection
1565 \begin_inset LatexCommand label
1566 name "sub:Fractions"
1571 \begin_inset LatexCommand index
1579 \begin_layout Standard
1580 Fractions are generated with the command
1587 \begin_inset LatexCommand index
1588 name "Commands ! F ! \\textbackslash frac"
1592 or via the math toolbar button
1593 \begin_inset Graphics
1594 filename ../images/math/frac.png
1600 The font size is adjusted automatically, depending on whether the fraction
1601 is in an inline or display style formula.
1602 With the math toolbar button
1603 \begin_inset Graphics
1604 filename ../images/math/frac-square.png
1609 you can select different fraction types.
1612 \begin_layout Standard
1618 \begin_inset LatexCommand index
1619 name "Commands ! D ! \\textbackslash dfrac"
1625 a fraction can be created that has in any case the size of a display style
1632 \begin_inset LatexCommand index
1633 name "Commands ! T ! \\textbackslash tfrac"
1639 the fraction appears always with the size of an inline formula.
1643 \begin_layout Standard
1644 A line with the fraction
1645 \begin_inset Formula $\frac{1}{2}$
1648 that was created with the command
1657 \begin_layout Standard
1658 A line with the fraction
1659 \begin_inset Formula $\dfrac{1}{2}$
1662 that was created with the command
1671 \begin_layout Standard
1673 \begin_inset Tabular
1674 <lyxtabular version="3" rows="4" columns="2">
1676 <column alignment="center" valignment="top" leftline="true" width="0pt">
1677 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1678 <row topline="true" bottomline="true">
1679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1682 \begin_layout Standard
1688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1691 \begin_layout Standard
1693 \begin_inset Note Note
1696 \begin_layout Standard
1703 is only used as spacer.
1714 <row topline="true">
1715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1718 \begin_layout Standard
1725 \begin_layout Standard
1735 \begin_inset Formula $\downarrow$
1743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1746 \begin_layout Standard
1747 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1756 <row topline="true">
1757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1760 \begin_layout Standard
1767 \begin_layout Standard
1777 \begin_inset Formula $\downarrow$
1785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1788 \begin_layout Standard
1789 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1798 <row topline="true" bottomline="true">
1799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1802 \begin_layout Standard
1809 \begin_layout Standard
1822 \begin_layout Standard
1837 \begin_layout Standard
1847 \begin_inset Formula $\downarrow$
1851 \begin_inset Formula $\downarrow\downarrow$
1859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1862 \begin_layout Standard
1863 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1879 \begin_layout Standard
1880 \begin_inset VSpace bigskip
1885 For nested fractions the command
1892 \begin_inset LatexCommand index
1893 name "Commands ! C ! \\textbackslash cfrac"
1899 \begin_inset VSpace -3mm
1905 \begin_layout Standard
1906 \begin_inset Formula \begin{align*}
1907 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1908 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
1915 \begin_layout Standard
1916 The command for the example above is:
1919 \begin_layout Standard
1925 \begin_inset Formula $\to$
1935 \begin_inset Formula $\to$
1941 \begin_inset Formula $\to\to$
1949 \begin_layout Standard
1950 \begin_inset VSpace medskip
1956 \begin_layout Standard
1963 sets the fraction always in the size of a displayed formula, also when
1964 it is part of another fraction.
1971 has the following command scheme:
1974 \begin_layout Standard
1979 cfrac[numerator position]{numerator}{denominator}
1982 \begin_layout Standard
1983 The numerator position can be
1996 l or r aligns the numerator to the left or right, resp.\InsetSpace ~
2003 or no position is given, the numerator appears centered.
2004 These fractions demonstrate the different alignments:
2009 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2013 \begin_inset Formula $\cfrac{A}{B+C}$
2017 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2023 \begin_layout Standard
2024 \begin_inset VSpace medskip
2027 It is often advantageous to combine
2040 \begin_inset Formula \[
2041 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2048 \begin_layout Standard
2049 For inline fractions with a sloped fraction stroke you can use the command
2055 \begin_inset LatexCommand index
2056 name "Commands ! N ! \\textbackslash nicefrac"
2063 \begin_inset Formula $\nicefrac{5}{31}$
2069 \begin_layout Standard
2070 How to define own fractions where the fraction stroke can be changed, is
2072 \begin_inset LatexCommand ref
2073 reference "sub:Self-defined-Fractions"
2080 \begin_layout Subsection
2082 \begin_inset LatexCommand index
2090 \begin_layout Standard
2091 Square roots are created with
2098 \begin_inset LatexCommand index
2099 name "Commands ! S ! \\textbackslash sqrt"
2103 or the math toolbar button
2104 \begin_inset Graphics
2105 filename ../images/math/sqrt.png
2110 , all other roots with the command
2117 \begin_inset LatexCommand index
2118 name "Commands ! R ! \\textbackslash root"
2122 or with the math toolbar button
2123 \begin_inset Graphics
2124 filename ../images/math/root.png
2132 \begin_layout Standard
2134 \begin_inset Tabular
2135 <lyxtabular version="3" rows="3" columns="2">
2137 <column alignment="center" valignment="top" leftline="true" width="0pt">
2138 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2139 <row topline="true" bottomline="true">
2140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2143 \begin_layout Standard
2149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2152 \begin_layout Standard
2154 \begin_inset Note Note
2157 \begin_layout Standard
2164 is only used as spacer.
2175 <row topline="true" bottomline="true">
2176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2179 \begin_layout Standard
2186 \begin_layout Standard
2200 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
2203 \begin_layout Standard
2204 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2213 <row bottomline="true">
2214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2217 \begin_layout Standard
2224 \begin_layout Standard
2234 \begin_inset Formula $\downarrow$
2242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2245 \begin_layout Standard
2246 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2262 \begin_layout Standard
2263 A square root can also be created with
2269 when the root index field is left empty.
2272 \begin_layout Standard
2273 With certain indices the distance to the root is too small, like in this
2275 \begin_inset Formula $\sqrt[\beta]{B}$
2281 \begin_inset Formula $\beta$
2285 To avoid this, the commands
2292 \begin_inset LatexCommand index
2293 name "Commands ! L ! \\textbackslash leftroot"
2304 \begin_inset LatexCommand index
2305 name "Commands ! U ! \\textbackslash uproot"
2309 are used with the following scheme:
2312 \begin_layout Standard
2326 \begin_layout Standard
2327 Distance is the number of Big Points (unit bp;
2328 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2331 ), that the index should be moved to the left or top, resp..
2332 The commands are written to the index.
2333 This way the command
2342 \begin_inset Formula $\to$
2348 \begin_inset Formula $\to$
2357 \begin_layout Standard
2367 \begin_inset Formula $\to$
2374 produces a correct typeset formula:
2375 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2381 \begin_layout Subsection
2382 Binomial coefficients
2383 \begin_inset LatexCommand index
2384 name "Binomial coefficient s"
2391 \begin_layout Standard
2392 Binomial coefficients are inserted with the command
2399 \begin_inset LatexCommand index
2400 name "Commands ! B ! \\textbackslash binom"
2404 or with the submenu of the math toolbar button
2405 \begin_inset Graphics
2406 filename ../images/math/frac-square.png
2414 \begin_layout Standard
2416 \begin_inset Tabular
2417 <lyxtabular version="3" rows="3" columns="2">
2419 <column alignment="center" valignment="top" leftline="true" width="0pt">
2420 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2421 <row topline="true" bottomline="true">
2422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2425 \begin_layout Standard
2431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2434 \begin_layout Standard
2436 \begin_inset Note Note
2439 \begin_layout Standard
2446 is only used as spacer.
2457 <row topline="true">
2458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2461 \begin_layout Standard
2468 \begin_layout Standard
2478 \begin_inset Formula $\downarrow$
2486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2489 \begin_layout Standard
2490 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2499 <row topline="true" bottomline="true">
2500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2503 \begin_layout Standard
2507 \begin_inset Formula $\to$
2517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2520 \begin_layout Standard
2521 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2537 \begin_layout Standard
2538 Analog to fractions (
2555 \begin_inset LatexCommand index
2556 name "Commands ! D ! \\textbackslash dbinom"
2569 \begin_inset LatexCommand index
2570 name "Commands ! T ! \\textbackslash tbinom"
2574 with the following command scheme:
2577 \begin_layout Standard
2582 dbinom{numerator}{denominator}
2590 tbinom{numerator}{denominator}
2593 \begin_layout Subsection
2594 Case differentiations
2595 \begin_inset LatexCommand index
2596 name "Case differentiations "
2603 \begin_layout Standard
2605 \begin_inset Tabular
2606 <lyxtabular version="3" rows="3" columns="2">
2608 <column alignment="center" valignment="top" leftline="true" width="0pt">
2609 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2610 <row topline="true" bottomline="true">
2611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2614 \begin_layout Standard
2620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2623 \begin_layout Standard
2630 <row topline="true">
2631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2634 \begin_layout Standard
2641 \begin_layout Standard
2651 \begin_inset Formula $\to$
2655 \begin_inset LatexCommand index
2656 name "Commands ! C ! \\textbackslash cases"
2665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2668 \begin_layout Standard
2669 \begin_inset Formula $\begin{cases}
2679 <row topline="true" bottomline="true">
2680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2683 \begin_layout Standard
2690 \begin_layout Standard
2704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2707 \begin_layout Standard
2708 \begin_inset Formula $\begin{cases}
2709 A & \textrm{for }x>0\\
2710 B & \textrm{for }x=0\end{cases}$
2726 \begin_layout Standard
2733 or the usage of the math toolbar button
2734 \begin_inset Graphics
2735 filename ../images/math/cases.png
2740 you can create new lines with the shortcut
2744 or the table toolbar button
2745 \begin_inset Graphics
2746 filename ../images/tabular-feature_append-row.png
2754 \begin_layout Standard
2761 is also available via the menu
2763 Insert\SpecialChar \menuseparator
2764 Math\SpecialChar \menuseparator
2770 \begin_layout Subsection
2772 \begin_inset LatexCommand index
2780 \begin_layout Standard
2788 \begin_inset LatexCommand index
2789 name "Commands ! N ! \\textbackslash not"
2793 every character can be displayed canceled.
2794 The characters are quasi accentuated by a slash.
2797 \begin_layout Standard
2799 \begin_inset Tabular
2800 <lyxtabular version="3" rows="4" columns="2">
2802 <column alignment="center" valignment="top" leftline="true" width="0pt">
2803 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2804 <row topline="true" bottomline="true">
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2808 \begin_layout Standard
2814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2817 \begin_layout Standard
2824 <row topline="true">
2825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2828 \begin_layout Standard
2836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2839 \begin_layout Standard
2840 \begin_inset Formula $\not=$
2849 <row topline="true" bottomline="true">
2850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2853 \begin_layout Standard
2863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2866 \begin_layout Standard
2867 \begin_inset Formula $\not\le$
2876 <row topline="true" bottomline="true">
2877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2880 \begin_layout Standard
2890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2893 \begin_layout Standard
2894 \begin_inset Formula $\not\parallel$
2910 \begin_layout Standard
2911 The last example shows, that not all negations look good.
2912 Therefore there are for some negations special commands (see
2913 \begin_inset LatexCommand ref
2914 reference "sub:Mathematical-Symbols"
2919 \begin_inset LatexCommand ref
2920 reference "sec:Relations"
2927 \begin_layout Subsection
2929 \begin_inset LatexCommand label
2930 name "sub:Placeholders"
2935 \begin_inset LatexCommand index
2941 \begin_inset LatexCommand index
2942 name "Chemical characters ! Isotopes"
2947 \begin_inset LatexCommand index
2948 name "Isotopes|see{Chemical characters}"
2955 \begin_layout Standard
2956 When displaying e.\InsetSpace \thinspace{}
2962 \begin_layout Standard
2963 More about chemical symbols is written in
2964 \begin_inset LatexCommand ref
2965 reference "sub:Chemical-Symbols-and"
2974 the following problem occurs:
2977 \begin_layout Standard
2979 \begin_inset Tabular
2980 <lyxtabular version="3" rows="2" columns="2">
2982 <column alignment="center" valignment="top" width="0pt">
2983 <column alignment="center" valignment="top" width="0pt">
2985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2988 \begin_layout Standard
2989 Indices created with sub- and superscripts:
2994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2997 \begin_layout Standard
2998 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3011 \begin_layout Standard
3017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3020 \begin_layout Standard
3021 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3035 \begin_inset Note Note
3038 \begin_layout Standard
3045 is only used as spacer.
3053 \begin_layout Standard
3054 The shorter index is by default placed below or above the first character
3055 of the longer index.
3056 To avoid this there is the command
3063 \begin_inset LatexCommand index
3064 name "Commands ! P ! \\textbackslash phantom"
3068 or the math toolbar button\InsetSpace \thinspace{}
3073 \begin_layout Standard
3074 can be found in the submenu of the toolbar button
3075 \begin_inset Graphics
3076 filename ../images/math/space.png
3087 \begin_inset Graphics
3088 filename ../images/math/phantom.png
3093 that creates one or more phantom characters.
3100 a small blue box appears that is superposed with two red arrows.
3101 The arrows indicate that the complete width and height of the box content
3102 will be created as placeholder.
3103 Phantom characters are accordingly placeholders with the size of the characters.
3106 \begin_layout Standard
3108 \begin_inset Tabular
3109 <lyxtabular version="3" rows="4" columns="2">
3111 <column alignment="center" valignment="top" leftline="true" width="0">
3112 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3113 <row topline="true" bottomline="true">
3114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3117 \begin_layout Standard
3123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3126 \begin_layout Standard
3128 \begin_inset Note Note
3131 \begin_layout Standard
3138 is only used as spacer.
3149 <row topline="true">
3150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3153 \begin_layout Standard
3158 \begin_layout Standard
3173 \begin_layout Standard
3183 \begin_inset Formula $\to$
3190 \begin_layout Standard
3204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3207 \begin_layout Standard
3208 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3217 <row topline="true" bottomline="true">
3218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3221 \begin_layout Standard
3226 \begin_layout Standard
3241 \begin_layout Standard
3251 \begin_inset Formula $\to$
3258 \begin_layout Standard
3272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3275 \begin_layout Standard
3276 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3285 <row topline="true" bottomline="true">
3286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3289 \begin_layout Standard
3296 \begin_layout Standard
3311 \begin_layout Standard
3321 \begin_inset Formula $\to$
3328 \begin_layout Standard
3342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3345 \begin_layout Standard
3346 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3362 \begin_layout Standard
3363 Furthermore there are the commands
3370 \begin_inset LatexCommand index
3371 name "Commands ! V ! \\textbackslash vphantom"
3375 (toolbar button \InsetSpace ~
3377 \begin_inset Graphics
3378 filename ../images/math/vphantom.png
3390 \begin_inset LatexCommand index
3391 name "Commands ! H ! \\textbackslash hphantom"
3395 (toolbar button \InsetSpace ~
3397 \begin_inset Graphics
3398 filename ../images/math/hphantom.png
3410 creates only space for the maximal height of the characters in the box
3411 but not for its width.
3418 creates only space for the width of the box content.
3419 Therefore the boxes of both commands have only one red arrow.
3422 \begin_layout Standard
3433 \begin_layout Standard
3448 space for the height of the integral sign,
3452 \begin_layout Standard
3459 creates an integral sign, see
3460 \begin_inset LatexCommand ref
3461 reference "sub:Big-Operators"
3470 because this is the larger character.
3471 An example application is in
3472 \begin_inset LatexCommand ref
3473 reference "sub:Multiline-Brackets"
3480 \begin_layout Subsection
3482 \begin_inset LatexCommand index
3488 \begin_inset LatexCommand index
3489 name "Formula ! underlined"
3496 \begin_layout Standard
3498 \begin_inset Tabular
3499 <lyxtabular version="3" rows="4" columns="2">
3501 <column alignment="center" valignment="top" leftline="true" width="0pt">
3502 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3503 <row topline="true" bottomline="true">
3504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3507 \begin_layout Standard
3513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3516 \begin_layout Standard
3518 \begin_inset Note Note
3521 \begin_layout Standard
3528 is only used as spacer.
3539 <row topline="true" bottomline="true">
3540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3543 \begin_layout Standard
3550 \begin_layout Standard
3560 \begin_inset LatexCommand index
3561 name "Commands ! O ! \\textbackslash overline"
3570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3573 \begin_layout Standard
3574 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3583 <row bottomline="true">
3584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3587 \begin_layout Standard
3594 \begin_layout Standard
3604 \begin_inset LatexCommand index
3605 name "Commands ! U ! \\textbackslash underline"
3614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3617 \begin_layout Standard
3618 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3627 <row topline="true" bottomline="true">
3628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3631 \begin_layout Standard
3638 \begin_layout Standard
3653 \begin_layout Standard
3667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3670 \begin_layout Standard
3671 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3687 \begin_layout Standard
3688 In the last example it doesn't matter if first
3703 \begin_layout Standard
3704 To double underline e.\InsetSpace \thinspace{}
3715 \begin_layout Standard
3716 It is possible to place up to 6 lines above or below characters.
3719 \begin_layout Subsection
3721 \begin_inset LatexCommand index
3729 \begin_layout Standard
3730 There are different types of ellipses available.
3734 \begin_layout Standard
3735 In the math toolbar in the submenu of the button
3736 \begin_inset Graphics
3737 filename ../images/math/ldots.png
3747 For listings dots at the baseline are used (
3754 \begin_inset LatexCommand index
3755 name "Commands ! L ! \\textbackslash ldots"
3759 ), while for operations dots are needed that are on the same height as the
3767 \begin_inset LatexCommand index
3768 name "Commands ! C ! \\textbackslash cdots"
3773 When using the command
3780 \begin_inset LatexCommand index
3781 name "Commands ! D ! \\textbackslash dots"
3785 , LaTeX decides on the basis of the next character what type is used.
3788 \begin_layout Standard
3790 \begin_inset Tabular
3791 <lyxtabular version="3" rows="8" columns="2">
3793 <column alignment="center" valignment="top" leftline="true" width="0pt">
3794 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3795 <row topline="true" bottomline="true">
3796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3799 \begin_layout Standard
3805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3808 \begin_layout Standard
3815 <row topline="true">
3816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3819 \begin_layout Standard
3824 \begin_layout Standard
3839 \begin_layout Standard
3853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3856 \begin_layout Standard
3857 \begin_inset Formula $A_{1},\dots,A_{n}$
3866 <row topline="true">
3867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3870 \begin_layout Standard
3875 \begin_layout Standard
3890 \begin_layout Standard
3904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3907 \begin_layout Standard
3908 \begin_inset Formula $A_{1}+\dots+A_{n}$
3917 <row topline="true">
3918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3921 \begin_layout Standard
3926 \begin_layout Standard
3941 \begin_layout Standard
3955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3958 \begin_layout Standard
3959 \begin_inset Formula $A_{1},\ldots,A_{n}$
3968 <row topline="true" bottomline="true">
3969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3972 \begin_layout Standard
3977 \begin_layout Standard
3992 \begin_layout Standard
4006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4009 \begin_layout Standard
4010 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4019 <row topline="true">
4020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4023 \begin_layout Standard
4031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4034 \begin_layout Standard
4035 \begin_inset Formula $\vdots$
4044 <row topline="true" bottomline="true">
4045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4048 \begin_layout Standard
4056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4059 \begin_layout Standard
4060 \begin_inset Formula $\ddots$
4069 <row topline="true" bottomline="true">
4070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4073 \begin_layout Standard
4074 3×3\InsetSpace \thinspace{}
4075 matrix with the different dots
4080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4083 \begin_layout Standard
4084 \begin_inset Formula $\begin{array}{ccc}
4085 A_{11} & \cdots & A_{1m}\\
4086 \vdots & \ddots & \vdots\\
4087 A_{n1} & \cdots & A_{nm}\end{array}$
4103 \begin_layout Standard
4104 The ellipses available in menu
4106 Insert\SpecialChar \menuseparator
4107 Special\InsetSpace ~
4119 \begin_layout Standard
4120 \begin_inset VSpace medskip
4123 Specially for matrices there are ellipses that span over several columns.
4124 They are created with the command
4131 \begin_inset LatexCommand index
4132 name "Commands ! H ! \\textbackslash hdotsfor"
4136 , that has the following scheme:
4139 \begin_layout Standard
4144 hdotsfor[distance]{number of columns}
4147 \begin_layout Standard
4148 The number of columns specifies how many columns should be spanned.
4149 Distance is a factor for the distance between the dots.
4152 \begin_layout Standard
4153 In the following matrix the command
4159 was inserted in the first box of the second line, to get an ellipsis with
4160 a dot distance twice as long as with the command
4167 \begin_inset Formula \[
4168 \left(\begin{array}{cccc}
4171 q & w & e & r\end{array}\right)\]
4175 Note that the matrix fields that should be spanned must be empty, otherwise
4176 you get LaTeX-errors.
4179 \begin_layout Standard
4180 \begin_inset VSpace bigskip
4183 Furthermore you can fill with the command
4190 \begin_inset LatexCommand index
4191 name "Commands ! D ! \\textbackslash dotfill"
4195 the rest of a line with dots.
4196 The effect of these commands is the same like with
4203 \begin_inset LatexCommand ref
4204 reference "sub:Variable-Space"
4211 \begin_layout Standard
4212 For example the command
4220 \begin_layout Standard
4234 \begin_layout Standard
4235 \begin_inset Formula $A\dotfill B$
4241 \begin_layout Standard
4248 there is for a line the command
4255 \begin_inset LatexCommand index
4256 name "Commands ! H ! \\textbackslash hrulefill"
4263 \begin_layout Standard
4264 \begin_inset Formula $A\hrulefill B$
4270 \begin_layout Standard
4271 To use the commands for text, they have to be inserted in TeX-mode.
4274 \begin_layout Section
4276 \begin_inset LatexCommand label
4282 \begin_inset LatexCommand index
4290 \begin_layout Standard
4291 Matrices can be inserted via the math toolbar button
4292 \begin_inset Graphics
4293 filename ../images/dialog-show_mathmatrix.png
4300 Insert\SpecialChar \menuseparator
4301 Math\SpecialChar \menuseparator
4305 You will be asked for the number of matrix columns and rows, and the alignment.
4306 The vertical alignment is hereby only of importance for matrices in inline
4310 \begin_layout Standard
4311 The first matrix is top
4312 \begin_inset Formula $\begin{array}[t]{cccc}
4315 C & F & I & L\end{array}$
4319 \begin_inset Formula $\begin{array}{cccc}
4322 C & F & I & L\end{array}$
4325 , and the third bottom
4326 \begin_inset Formula $\begin{array}[b]{cccc}
4329 C & F & I & L\end{array}$
4335 \begin_layout Standard
4336 The horizontal alignment specifies how the column entries should be aligned.
4337 It is set by entering a letter for every column.
4342 denotes left aligned,
4351 To create for example a 4
4356 matrix where the first column is left aligned, the second and third are
4357 centered, and the last one is right aligned, one enters for the horizontal
4363 Normally are in a matrix all columns centered, therefore the default is
4364 for every column is a
4371 \begin_layout Standard
4372 Horizontal alignment:
4375 \begin_layout Standard
4381 \begin_inset Formula $\begin{array}{lll}
4384 C & F & 10000\end{array}$
4392 \begin_inset Formula $\begin{array}{ccc}
4395 C & F & 10000\end{array}$
4403 \begin_inset Formula $\begin{array}{rrr}
4406 C & F & 10000\end{array}$
4412 \begin_layout Standard
4413 To add or delete rows and columns subsequently, the math toolbar buttons
4415 \begin_inset Graphics
4416 filename ../images/tabular-feature_append-row.png
4422 \begin_inset Graphics
4423 filename ../images/tabular-feature_delete-row.png
4428 , etc.\InsetSpace \thinspace{}
4431 Edit\SpecialChar \menuseparator
4435 New rows can also be created with
4442 \begin_layout Standard
4443 \begin_inset VSpace bigskip
4446 Parentheses around a matrix can can either be created with the commands
4454 \begin_inset LatexCommand index
4455 name "Commands ! L ! \\textbackslash left"
4466 \begin_inset LatexCommand index
4467 name "Commands ! R ! \\textbackslash right"
4477 \begin_inset LatexCommand ref
4478 reference "sub:Automatic-Bracket-Size"
4482 , or by using the following commands:
4483 \begin_inset VSpace medskip
4489 \begin_layout Standard
4493 \begin_inset Tabular
4494 <lyxtabular version="3" rows="4" columns="2">
4496 <column alignment="center" valignment="top" leftline="true" width="0">
4497 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4498 <row topline="true" bottomline="true">
4499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4502 \begin_layout Standard
4508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4511 \begin_layout Standard
4513 \begin_inset Note Note
4516 \begin_layout Standard
4523 is only used as spacer.
4534 <row topline="true">
4535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4538 \begin_layout Standard
4545 \begin_layout Standard
4558 2\InsetSpace \thinspace{}
4564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4567 \begin_layout Standard
4568 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4569 0 & \textrm{-}\mathrm{i}\\
4570 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4579 <row topline="true">
4580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4583 \begin_layout Standard
4590 \begin_layout Standard
4603 2\InsetSpace \thinspace{}
4609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4612 \begin_layout Standard
4613 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4614 0 & \textrm{-}\mathrm{i}\\
4615 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4624 <row topline="true" bottomline="true">
4625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4628 \begin_layout Standard
4635 \begin_layout Standard
4648 2\InsetSpace \thinspace{}
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4657 \begin_layout Standard
4658 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4659 0 & \textrm{-}\mathrm{i}\\
4660 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4676 \begin_inset Tabular
4677 <lyxtabular version="3" rows="4" columns="2">
4679 <column alignment="center" valignment="top" leftline="true" width="0">
4680 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4681 <row topline="true" bottomline="true">
4682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4685 \begin_layout Standard
4691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4694 \begin_layout Standard
4701 <row topline="true">
4702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4705 \begin_layout Standard
4712 \begin_layout Standard
4725 2\InsetSpace \thinspace{}
4731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4734 \begin_layout Standard
4735 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4736 0 & \textrm{-}\mathrm{i}\\
4737 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4746 <row topline="true" bottomline="true">
4747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4750 \begin_layout Standard
4757 \begin_layout Standard
4770 2\InsetSpace \thinspace{}
4776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4779 \begin_layout Standard
4780 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4781 0 & \textrm{-}\mathrm{i}\\
4782 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4791 <row topline="true" bottomline="true">
4792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4795 \begin_layout Standard
4802 \begin_layout Standard
4815 2\InsetSpace \thinspace{}
4821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4824 \begin_layout Standard
4825 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4826 0 & \textrm{-}\mathrm{i}\\
4827 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4845 \begin_layout Standard
4846 \begin_inset VSpace medskip
4849 When e.\InsetSpace \thinspace{}
4857 is inserted, a blue box appears between two vertical lines where the matrix
4861 \begin_layout Standard
4862 \begin_inset VSpace bigskip
4865 As all multiline formulas are matrices, the length
4872 \begin_inset LatexCommand index
4873 name "Commands ! A ! \\textbackslash arraycolsep"
4877 that is described in
4878 \begin_inset LatexCommand ref
4879 reference "sub:Column-Separation"
4883 can also be used to change the column separation of matrices.
4886 \begin_layout Standard
4887 To change the row separation, the command
4894 \begin_inset LatexCommand index
4895 name "Commands ! A ! \\textbackslash arraystretch"
4900 It is used as follows:
4903 \begin_layout Standard
4910 arraystretch}{stretch factor}
4911 \begin_inset LatexCommand index
4912 name "Commands ! R ! \\textbackslash renewcommand"
4919 \begin_layout Standard
4926 assigns the stretch factor to the predefined command
4933 To double e.\InsetSpace \thinspace{}
4935 the row separation, use the factor 2.
4936 This is then used for all following matrices.
4937 To go back to the original separation, assign the factor 1 to
4946 \begin_layout Standard
4947 To set matrices into a text line, the command
4954 \begin_inset LatexCommand index
4955 name "Commands ! S ! \\textbackslash smallmatrix"
4960 When it is inserted a blue box with two dashed lines appears.
4961 In this box the matrix is inserted.
4964 \begin_layout Standard
4966 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
4967 C & D\end{smallmatrix}\right)$
4973 \begin_layout Section
4974 Brackets and Delimiters
4975 \begin_inset LatexCommand index
4981 \begin_inset LatexCommand index
4989 \begin_layout Subsection
4990 Vertical Brackets and Delimiters
4991 \begin_inset LatexCommand index
4992 name "Brackets ! vertical"
4999 \begin_layout Standard
5003 \begin_inset Tabular
5004 <lyxtabular version="3" rows="9" columns="2">
5006 <column alignment="center" valignment="top" leftline="true" width="0pt">
5007 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5008 <row topline="true" bottomline="true">
5009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5012 \begin_layout Standard
5018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5021 \begin_layout Standard
5028 <row topline="true">
5029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5032 \begin_layout Standard
5038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5041 \begin_layout Standard
5042 \begin_inset Formula $($
5051 <row topline="true">
5052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5055 \begin_layout Standard
5061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5064 \begin_layout Standard
5065 \begin_inset Formula $\{$
5074 <row topline="true">
5075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5078 \begin_layout Standard
5084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5087 \begin_layout Standard
5088 \begin_inset Formula $[$
5097 <row topline="true">
5098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5101 \begin_layout Standard
5109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5112 \begin_layout Standard
5113 \begin_inset Formula $\langle$
5122 <row topline="true">
5123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5126 \begin_layout Standard
5134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5137 \begin_layout Standard
5138 \begin_inset Formula $\lceil$
5147 <row topline="true">
5148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5151 \begin_layout Standard
5159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5162 \begin_layout Standard
5163 \begin_inset Formula $\lfloor$
5172 <row topline="true">
5173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5176 \begin_layout Standard
5182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5185 \begin_layout Standard
5186 \begin_inset Formula $/$
5195 <row topline="true" bottomline="true">
5196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5199 \begin_layout Standard
5205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5208 \begin_layout Standard
5209 \begin_inset Formula $|$
5225 \begin_inset Tabular
5226 <lyxtabular version="3" rows="9" columns="2">
5228 <column alignment="center" valignment="top" leftline="true" width="0pt">
5229 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5230 <row topline="true" bottomline="true">
5231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5234 \begin_layout Standard
5240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5243 \begin_layout Standard
5250 <row topline="true">
5251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5254 \begin_layout Standard
5260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5263 \begin_layout Standard
5264 \begin_inset Formula $)$
5273 <row topline="true">
5274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5277 \begin_layout Standard
5283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5286 \begin_layout Standard
5287 \begin_inset Formula $\}$
5296 <row topline="true">
5297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5300 \begin_layout Standard
5306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5309 \begin_layout Standard
5310 \begin_inset Formula $]$
5319 <row topline="true">
5320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5323 \begin_layout Standard
5331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5334 \begin_layout Standard
5335 \begin_inset Formula $\rangle$
5344 <row topline="true">
5345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5348 \begin_layout Standard
5356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5359 \begin_layout Standard
5360 \begin_inset Formula $\rceil$
5369 <row topline="true">
5370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5373 \begin_layout Standard
5381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5384 \begin_layout Standard
5385 \begin_inset Formula $\rfloor$
5394 <row topline="true">
5395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5398 \begin_layout Standard
5408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5411 \begin_layout Standard
5412 \begin_inset Formula $\backslash$
5421 <row topline="true" bottomline="true">
5422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5425 \begin_layout Standard
5433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5436 \begin_layout Standard
5437 \begin_inset Formula $\|$
5455 \begin_layout Standard
5458 \begin_inset Note Greyedout
5461 \begin_layout Standard
5466 In TeX-mode the command
5473 \begin_inset LatexCommand index
5474 name "Commands ! T ! \\textbackslash textbackslash"
5478 must be used for the backslash, because the command
5486 produces there a line break.
5494 \begin_layout Standard
5495 For all characters listed above the size can be adjusted with the commands
5496 described in the following two subsections.
5497 When using these commands, the characters < and > can directly be used
5498 instead of the commands
5513 \begin_layout Subsubsection
5515 \begin_inset LatexCommand label
5516 name "sub:Manual-Bracket-Size"
5521 \begin_inset LatexCommand index
5522 name "Bracket size ! manual"
5529 \begin_layout Standard
5530 The bracket size can be specified manually by the LaTeX-commands
5537 \begin_inset LatexCommand index
5538 name "Commands ! B ! \\textbackslash big"
5567 denotes the smallest and
5573 the largest bracket size.
5576 \begin_layout Standard
5577 These commands are used to emphasize levels of brackets:
5580 \begin_layout Standard
5582 \begin_inset Tabular
5583 <lyxtabular version="3" rows="2" columns="2">
5585 <column alignment="center" valignment="top" width="0pt">
5586 <column alignment="center" valignment="top" width="0pt">
5588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5591 \begin_layout Standard
5592 all brackets in the same size:
5597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5600 \begin_layout Standard
5601 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5614 \begin_layout Standard
5620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5623 \begin_layout Standard
5624 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5638 \begin_inset Note Note
5641 \begin_layout Standard
5648 is only used as spacer.
5656 \begin_layout Standard
5657 For the second formula the command
5667 \begin_layout Standard
5681 \begin_layout Standard
5682 Here is an overview about all bracket sizes:
5685 \begin_layout Standard
5705 \begin_layout Standard
5722 \begin_layout Standard
5735 \begin_layout Standard
5751 \begin_layout Standard
5753 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5759 \begin_layout Standard
5768 -commands there is the variant
5775 \begin_inset LatexCommand index
5776 name "Commands ! B ! \\textbackslash bigm"
5780 that adds a bit more space between the bracket and its content, and the
5794 \begin_inset LatexCommand index
5795 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5799 , that don't add additional space.
5804 at the end of the command
5810 is for a left bracket; for a right bracket this will be replaced by an
5816 A left or right bracket can each be an opening or closing bracket.
5819 \begin_layout Standard
5820 In the following table is a comparison of the variants:
5823 \begin_layout Standard
5825 \begin_inset Tabular
5826 <lyxtabular version="3" rows="5" columns="2">
5828 <column alignment="center" valignment="middle" leftline="true" width="0">
5829 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5830 <row topline="true" bottomline="true">
5831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5834 \begin_layout Standard
5840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5843 \begin_layout Standard
5845 \begin_inset Note Note
5848 \begin_layout Standard
5855 is only used as spacer.
5866 <row topline="true">
5867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5870 \begin_layout Standard
5885 \begin_layout Standard
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5906 \begin_layout Standard
5907 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5916 <row topline="true">
5917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5920 \begin_layout Standard
5935 \begin_layout Standard
5953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5956 \begin_layout Standard
5957 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
5966 <row topline="true" bottomline="true">
5967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5970 \begin_layout Standard
5985 \begin_layout Standard
6003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6006 \begin_layout Standard
6007 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6016 <row topline="true" bottomline="true">
6017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6020 \begin_layout Standard
6032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6035 \begin_layout Standard
6036 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6052 \begin_layout Subsubsection
6053 Automatic Bracket Size
6054 \begin_inset LatexCommand label
6055 name "sub:Automatic-Bracket-Size"
6060 \begin_inset LatexCommand index
6061 name "Bracket size ! automatic"
6068 \begin_layout Standard
6069 Brackets with variable size can be inserted with the commands
6076 \begin_inset LatexCommand index
6077 name "Commands ! L ! \\textbackslash left"
6088 \begin_inset LatexCommand index
6089 name "Commands ! R ! \\textbackslash right"
6093 or via the math toolbar button
6094 \begin_inset Graphics
6095 filename ../images/dialog-show_mathdelimiter.png
6113 the wanted bracket must be inserted.
6114 The bracket size will then automatically be calculated for the output.
6117 \begin_layout Standard
6119 normal bracket: The command
6129 \begin_layout Standard
6139 \begin_inset Formula $\downarrow$
6146 \begin_layout Standard
6158 \begin_inset Formula \[
6166 \begin_layout Standard
6168 multiline bracket: The command
6180 \begin_layout Standard
6190 \begin_inset Formula $\downarrow$
6197 \begin_layout Standard
6211 \begin_inset Formula \[
6212 \ln\left(\frac{A}{C}\right)\]
6219 \begin_layout Standard
6238 This has the advantage that you can see in LyX immediately the real bracket
6239 size and that the matching right bracket will be created too.
6242 for the last example would then be:
6256 \begin_layout Standard
6266 \begin_inset Formula $\downarrow$
6272 \begin_layout Standard
6273 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6274 For example the command
6284 \begin_layout Standard
6294 \begin_inset Formula $\downarrow$
6301 \begin_layout Standard
6317 \begin_inset Formula \[
6318 \left.\frac{A}{B}\right\} \]
6336 will be converted by LyX to brackets in the right size when the document
6337 is reloaded and an omitted bracket will appear as dashed line.
6340 \begin_layout Standard
6341 \begin_inset VSpace bigskip
6344 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6352 \begin_inset LatexCommand index
6353 name "Commands ! M ! \\textbackslash middle"
6357 is additionally available for all brackets and limits.
6358 With this command the height of the following character is adapted to the
6359 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6361 needed for physical vectors:
6362 \begin_inset Formula \[
6363 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6367 For physical vectors there is a special LaTeX-package, described in
6368 \begin_inset LatexCommand ref
6369 reference "sub:Physical-Vectors"
6376 \begin_layout Subsection
6378 \begin_inset LatexCommand index
6379 name "Brackets ! horizontal"
6386 \begin_layout Standard
6388 \begin_inset Tabular
6389 <lyxtabular version="3" rows="4" columns="2">
6391 <column alignment="center" valignment="top" leftline="true" width="0pt">
6392 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6393 <row topline="true" bottomline="true">
6394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6397 \begin_layout Standard
6399 \begin_inset Note Note
6402 \begin_layout Standard
6409 is only used as spacer.
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6422 \begin_layout Standard
6429 <row topline="true">
6430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6433 \begin_layout Standard
6437 \begin_layout Standard
6452 \begin_layout Standard
6465 \begin_layout Standard
6478 \begin_layout Standard
6491 \begin_layout Standard
6499 \begin_inset LatexCommand index
6500 name "Commands ! O ! \\textbackslash overbrace"
6509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6512 \begin_layout Standard
6513 \begin_inset Formula $\overbrace{A+B}^{3}$
6522 <row topline="true" bottomline="true">
6523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6526 \begin_layout Standard
6530 \begin_layout Standard
6545 \begin_layout Standard
6558 \begin_layout Standard
6571 \begin_layout Standard
6579 \begin_inset LatexCommand index
6580 name "Commands ! U ! \\textbackslash underbrace"
6589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6592 \begin_layout Standard
6593 \begin_inset Formula $\underbrace{A+B}_{5}$
6602 <row topline="true" bottomline="true">
6603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6606 \begin_layout Standard
6615 \begin_layout Standard
6628 \begin_layout Standard
6641 \begin_layout Standard
6654 \begin_layout Standard
6667 \begin_layout Standard
6680 \begin_layout Standard
6694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6697 \begin_layout Standard
6698 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6714 \begin_layout Standard
6715 In the last example it doesn't matter if
6727 is inserted at first.
6730 \begin_layout Standard
6731 \begin_inset VSpace bigskip
6734 When brackets are needed that overlap each other, multiline formulas, as
6736 \begin_inset LatexCommand ref
6737 reference "sec:Multiline-Formulas"
6742 \begin_inset Formula \begin{eqnarray*}
6743 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6744 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6748 In the first row the formula is inserted together with the first brace.
6749 It is hereby important that the space command
6753 \begin_layout Standard
6754 Space commands are explained in
6755 \begin_inset LatexCommand ref
6756 reference "sub:Predefined-Space"
6771 is inserted before the first
6772 \begin_inset Formula $d$
6775 , because the brace that ends behind the
6776 \begin_inset Formula $q$
6779 prevents that the following
6780 \begin_inset Quotes eld
6784 \begin_inset Quotes erd
6787 is surrounded by space.
6791 \begin_layout Standard
6792 because a bracket is not handled as character, see
6793 \begin_inset LatexCommand ref
6794 reference "sub:Binary-Operators"
6803 In the second row the second brace is inserted.
6804 As it should begin before the
6805 \begin_inset Formula $b$
6820 \begin_layout Standard
6828 \begin_inset LatexCommand ref
6829 reference "sub:Placeholders"
6838 This space is needed because the
6839 \begin_inset Quotes eld
6843 \begin_inset Quotes erd
6846 is also surrounded by space in the formula.
6847 The brace is placed under the command
6856 \begin_layout Standard
6857 It gets more complicated when brackets overlap each other, like in the following
6862 \begin_layout Standard
6874 \begin_inset Formula \begin{eqnarray*}
6875 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6876 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6884 \begin_layout Standard
6895 The first formula row is the same as the second row of the previous example,
6896 with the difference that the brace is above.
6897 The second row contains the formula together with the second brace.
6898 To avoid that there is space between the upper brace in the first row and
6899 the formula, the row spacing need to be reduced.
6900 This is not easily possible due to a bug in LyX
6904 \begin_layout Standard
6908 \begin_layout Standard
6912 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
6921 \begin_layout Standard
6934 As solution for the problem, the global formula row separation
6941 \begin_inset LatexCommand index
6942 name "Commands ! J ! \\textbackslash jot"
6946 must be changed to -6\InsetSpace \thinspace{}
6947 pt before the formula with the command
6962 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
6965 More about the row separation in formulas is explained in
6966 \begin_inset LatexCommand ref
6967 reference "sub:Line-Separation"
6974 \begin_layout Section
6976 \begin_inset LatexCommand index
6984 \begin_layout Standard
6985 Arrows can be inserted via the math toolbar button
6986 \begin_inset Graphics
6987 filename ../images/math/leftarrow.png
6992 or the commands listed in the following subsections.
6995 \begin_layout Subsection
6997 \begin_inset LatexCommand index
6998 name "Arrows ! horizontal"
7005 \begin_layout Standard
7009 \begin_inset Tabular
7010 <lyxtabular version="3" rows="8" columns="2">
7012 <column alignment="center" valignment="top" leftline="true" width="0pt">
7013 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7014 <row topline="true" bottomline="true">
7015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7018 \begin_layout Standard
7024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7027 \begin_layout Standard
7034 <row topline="true">
7035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7038 \begin_layout Standard
7046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7049 \begin_layout Standard
7050 \begin_inset Formula $\gets$
7059 <row topline="true">
7060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7063 \begin_layout Standard
7071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7074 \begin_layout Standard
7075 \begin_inset Formula $\Leftarrow$
7084 <row topline="true" bottomline="true">
7085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7088 \begin_layout Standard
7096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7099 \begin_layout Standard
7100 \begin_inset Formula $\longleftarrow$
7109 <row bottomline="true">
7110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7113 \begin_layout Standard
7121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7124 \begin_layout Standard
7125 \begin_inset Formula $\Longleftarrow$
7134 <row bottomline="true">
7135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7138 \begin_layout Standard
7146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7149 \begin_layout Standard
7150 \begin_inset Formula $\leftharpoonup$
7159 <row bottomline="true">
7160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7163 \begin_layout Standard
7171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7174 \begin_layout Standard
7175 \begin_inset Formula $\leftharpoondown$
7184 <row bottomline="true">
7185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7188 \begin_layout Standard
7196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7199 \begin_layout Standard
7200 \begin_inset Formula $\hookleftarrow$
7216 \begin_inset Tabular
7217 <lyxtabular version="3" rows="8" columns="2">
7219 <column alignment="center" valignment="top" leftline="true" width="0pt">
7220 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7221 <row topline="true" bottomline="true">
7222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7225 \begin_layout Standard
7231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7234 \begin_layout Standard
7241 <row topline="true">
7242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7245 \begin_layout Standard
7253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7256 \begin_layout Standard
7257 \begin_inset Formula $\to$
7266 <row topline="true">
7267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7270 \begin_layout Standard
7278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7281 \begin_layout Standard
7282 \begin_inset Formula $\Rightarrow$
7291 <row topline="true">
7292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7295 \begin_layout Standard
7303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7306 \begin_layout Standard
7307 \begin_inset Formula $\longrightarrow$
7316 <row topline="true">
7317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7320 \begin_layout Standard
7328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7331 \begin_layout Standard
7332 \begin_inset Formula $\Longrightarrow$
7341 <row topline="true">
7342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7345 \begin_layout Standard
7353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7356 \begin_layout Standard
7357 \begin_inset Formula $\rightharpoonup$
7366 <row topline="true" bottomline="true">
7367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7370 \begin_layout Standard
7378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7381 \begin_layout Standard
7382 \begin_inset Formula $\rightharpoondown$
7391 <row bottomline="true">
7392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7395 \begin_layout Standard
7403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7406 \begin_layout Standard
7407 \begin_inset Formula $\hookrightarrow$
7425 \begin_layout Standard
7429 \begin_inset Tabular
7430 <lyxtabular version="3" rows="6" columns="2">
7432 <column alignment="center" valignment="top" leftline="true" width="0pt">
7433 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7434 <row topline="true" bottomline="true">
7435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7438 \begin_layout Standard
7444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7447 \begin_layout Standard
7454 <row topline="true">
7455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7458 \begin_layout Standard
7466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7469 \begin_layout Standard
7470 \begin_inset Formula $\leftrightarrow$
7479 <row topline="true">
7480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7483 \begin_layout Standard
7491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7494 \begin_layout Standard
7495 \begin_inset Formula $\Leftrightarrow$
7504 <row topline="true">
7505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7508 \begin_layout Standard
7516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7519 \begin_layout Standard
7520 \begin_inset Formula $\longleftrightarrow$
7529 <row topline="true">
7530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7533 \begin_layout Standard
7541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7544 \begin_layout Standard
7545 \begin_inset Formula $\Longleftrightarrow$
7554 <row topline="true" bottomline="true">
7555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7558 \begin_layout Standard
7566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7569 \begin_layout Standard
7570 \begin_inset Formula $\rightleftharpoons$
7587 \begin_layout Standard
7599 \begin_inset Tabular
7600 <lyxtabular version="3" rows="5" columns="2">
7602 <column alignment="center" valignment="top" leftline="true" width="0pt">
7603 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7604 <row topline="true" bottomline="true">
7605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7608 \begin_layout Standard
7614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7617 \begin_layout Standard
7624 <row topline="true">
7625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7628 \begin_layout Standard
7636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7639 \begin_layout Standard
7640 \begin_inset Formula $\mapsto$
7649 <row topline="true">
7650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7653 \begin_layout Standard
7661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7664 \begin_layout Standard
7665 \begin_inset Formula $\longmapsto$
7674 <row topline="true">
7675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7678 \begin_layout Standard
7686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7689 \begin_layout Standard
7690 \begin_inset Formula $\leadsto$
7699 <row topline="true" bottomline="true">
7700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7703 \begin_layout Standard
7711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7714 \begin_layout Standard
7715 \begin_inset Formula $\dasharrow$
7733 \begin_layout Standard
7734 \begin_inset VSpace medskip
7737 Arrows used as accent like e.\InsetSpace \thinspace{}
7739 vector arrows are listed in
7740 \begin_inset LatexCommand ref
7741 reference "sec:Accents"
7748 \begin_layout Standard
7749 \begin_inset VSpace bigskip
7752 Furthermore there are the labeled arrows
7753 \begin_inset LatexCommand index
7754 name "Arrows ! labeled"
7765 \begin_inset LatexCommand index
7766 name "Commands ! X ! \\textbackslash xleftarrow"
7777 \begin_inset LatexCommand index
7778 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7783 When inserting one of these commands in a formula, an arrow with two blue
7784 boxes appear where the label can be inserted.
7785 The length of the arrow adapts to the label width.
7788 \begin_layout Standard
7790 \begin_inset Tabular
7791 <lyxtabular version="3" rows="3" columns="2">
7793 <column alignment="center" valignment="top" leftline="true" width="0pt">
7794 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7795 <row topline="true" bottomline="true">
7796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7799 \begin_layout Standard
7805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7808 \begin_layout Standard
7810 \begin_inset Note Note
7813 \begin_layout Standard
7820 is only used as spacer.
7831 <row topline="true">
7832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7835 \begin_layout Standard
7842 \begin_layout Standard
7852 \begin_inset Formula $\downarrow$
7856 \begin_inset Formula $\to$
7864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7867 \begin_layout Standard
7868 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7877 <row topline="true" bottomline="true">
7878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7881 \begin_layout Standard
7888 \begin_layout Standard
7898 \begin_inset Formula $\downarrow$
7902 \begin_inset Formula $\to$
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7913 \begin_layout Standard
7914 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
7930 \begin_layout Subsection
7931 Vertical and diagonal Arrows
7932 \begin_inset LatexCommand index
7933 name "Arrows ! diagonal"
7938 \begin_inset LatexCommand index
7939 name "Arrows ! vertical"
7946 \begin_layout Standard
7950 \begin_inset Tabular
7951 <lyxtabular version="3" rows="7" columns="2">
7953 <column alignment="center" valignment="top" leftline="true" width="0pt">
7954 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7955 <row topline="true" bottomline="true">
7956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7959 \begin_layout Standard
7965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7968 \begin_layout Standard
7975 <row topline="true">
7976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7979 \begin_layout Standard
7987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7990 \begin_layout Standard
7991 \begin_inset Formula $\uparrow$
8000 <row topline="true">
8001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8004 \begin_layout Standard
8012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8015 \begin_layout Standard
8016 \begin_inset Formula $\Uparrow$
8025 <row topline="true">
8026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8029 \begin_layout Standard
8037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8040 \begin_layout Standard
8041 \begin_inset Formula $\updownarrow$
8050 <row topline="true">
8051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8054 \begin_layout Standard
8062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8065 \begin_layout Standard
8066 \begin_inset Formula $\Updownarrow$
8075 <row topline="true" bottomline="true">
8076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8079 \begin_layout Standard
8087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8090 \begin_layout Standard
8091 \begin_inset Formula $\Downarrow$
8100 <row bottomline="true">
8101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8104 \begin_layout Standard
8112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8115 \begin_layout Standard
8116 \begin_inset Formula $\downarrow$
8132 \begin_inset Tabular
8133 <lyxtabular version="3" rows="5" columns="2">
8135 <column alignment="center" valignment="top" leftline="true" width="0pt">
8136 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8137 <row topline="true" bottomline="true">
8138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8141 \begin_layout Standard
8147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8150 \begin_layout Standard
8157 <row topline="true">
8158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8161 \begin_layout Standard
8169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8172 \begin_layout Standard
8173 \begin_inset Formula $\nearrow$
8182 <row topline="true">
8183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8186 \begin_layout Standard
8194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8197 \begin_layout Standard
8198 \begin_inset Formula $\searrow$
8207 <row topline="true" bottomline="true">
8208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8211 \begin_layout Standard
8219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8222 \begin_layout Standard
8223 \begin_inset Formula $\swarrow$
8232 <row bottomline="true">
8233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8236 \begin_layout Standard
8244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8247 \begin_layout Standard
8248 \begin_inset Formula $\nwarrow$
8266 \begin_layout Standard
8267 \begin_inset VSpace medskip
8270 Vertical arrows can be used also as delimiter together with the commands
8272 \begin_inset LatexCommand ref
8273 reference "sub:Manual-Bracket-Size"
8278 \begin_inset LatexCommand ref
8279 reference "sub:Automatic-Bracket-Size"
8286 \begin_layout Standard
8292 \begin_layout Section
8294 \begin_inset LatexCommand label
8300 \begin_inset LatexCommand index
8308 \begin_layout Standard
8309 Accents can be inserted via the math toolbar button
8310 \begin_inset Graphics
8311 filename ../images/math/hat.png
8316 or the commands listed in the following subsections.
8319 \begin_layout Subsection
8320 Accents for one Character
8324 \begin_layout Standard
8337 \begin_layout Standard
8339 \begin_inset LatexCommand ref
8340 reference "sub:Accents-in-Text"
8353 \begin_layout Standard
8361 \begin_inset Note Note
8364 \begin_layout Standard
8367 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8370 \begin_layout Standard
8373 texorpdfstring is in section
8374 \begin_inset LatexCommand ref
8375 reference "sub:Formulas-in-Section"
8385 \begin_inset LatexCommand label
8386 name "sub:Accents-for-one"
8391 \begin_inset LatexCommand index
8392 name "Accents ! for one character"
8399 \begin_layout Standard
8403 \begin_inset Tabular
8404 <lyxtabular version="3" rows="8" columns="2">
8406 <column alignment="center" valignment="top" leftline="true" width="0pt">
8407 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8408 <row topline="true" bottomline="true">
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8412 \begin_layout Standard
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8421 \begin_layout Standard
8423 \begin_inset Note Note
8426 \begin_layout Standard
8433 is only used as spacer.
8444 <row topline="true" bottomline="true">
8445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8448 \begin_layout Standard
8455 \begin_layout Standard
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8472 \begin_layout Standard
8473 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8482 <row bottomline="true">
8483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8486 \begin_layout Standard
8493 \begin_layout Standard
8507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8510 \begin_layout Standard
8511 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8520 <row bottomline="true">
8521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8524 \begin_layout Standard
8531 \begin_layout Standard
8545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Standard
8549 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8558 <row bottomline="true">
8559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8562 \begin_layout Standard
8570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8573 \begin_layout Standard
8574 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8583 <row bottomline="true">
8584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8587 \begin_layout Standard
8594 \begin_layout Standard
8604 \begin_inset LatexCommand index
8614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8617 \begin_layout Standard
8618 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8627 <row bottomline="true">
8628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8631 \begin_layout Standard
8638 \begin_layout Standard
8652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8655 \begin_layout Standard
8656 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8665 <row bottomline="true">
8666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8669 \begin_layout Standard
8676 \begin_layout Standard
8690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8693 \begin_layout Standard
8694 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8710 \begin_inset Tabular
8711 <lyxtabular version="3" rows="7" columns="2">
8713 <column alignment="center" valignment="top" leftline="true" width="0pt">
8714 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8715 <row topline="true" bottomline="true">
8716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8719 \begin_layout Standard
8725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8728 \begin_layout Standard
8735 <row topline="true" bottomline="true">
8736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8739 \begin_layout Standard
8746 \begin_layout Standard
8760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8763 \begin_layout Standard
8764 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8773 <row bottomline="true">
8774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8777 \begin_layout Standard
8784 \begin_layout Standard
8798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8801 \begin_layout Standard
8802 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8811 <row bottomline="true">
8812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8815 \begin_layout Standard
8822 \begin_layout Standard
8836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8839 \begin_layout Standard
8840 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8849 <row bottomline="true">
8850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8853 \begin_layout Standard
8860 \begin_layout Standard
8874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8877 \begin_layout Standard
8878 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8887 <row bottomline="true">
8888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8891 \begin_layout Standard
8898 \begin_layout Standard
8912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8915 \begin_layout Standard
8916 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
8925 <row bottomline="true">
8926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8929 \begin_layout Standard
8936 \begin_layout Standard
8950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8953 \begin_layout Standard
8954 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
8972 \begin_layout Standard
8973 \begin_inset VSpace bigskip
8977 \begin_inset LatexCommand index
8982 in formulas, a quotation mark is inserted before the vowel.
8983 These two characters are then treated by LaTeX as
8987 character when the formula part with the umlaut is marked as German.
8995 \begin_inset Quotes eld
8999 \begin_inset Quotes erd
9002 umlauts are created as demonstrated in the following example:
9005 \begin_layout Standard
9006 \begin_inset VSpace -2mm
9012 \begin_layout Standard
9014 \begin_inset Tabular
9015 <lyxtabular version="3" rows="3" columns="2">
9017 <column alignment="center" valignment="top" leftline="true" width="0">
9018 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9019 <row topline="true" bottomline="true">
9020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9023 \begin_layout Standard
9029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9032 \begin_layout Standard
9034 \begin_inset Note Note
9037 \begin_layout Standard
9044 is only used as spacer.
9055 <row topline="true">
9056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9059 \begin_layout Standard
9062 \begin_inset Quotes grd
9070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9073 \begin_layout Standard
9076 \begin_inset Formula $"i$
9085 <row topline="true" bottomline="true">
9086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9089 \begin_layout Standard
9096 \begin_layout Standard
9110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9113 \begin_layout Standard
9114 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9130 \begin_layout Standard
9131 Another advantage to
9137 is that umlauts can directly be converted to mathematical text because
9138 the accent commands above are
9144 in mathematical text
9147 To convert an accented character to mathematical text, only the character
9148 under the accent may be converted.
9149 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9154 \begin_layout Standard
9155 In mathematical text, umlauts and other accented characters can directly
9159 \begin_layout Subsection
9160 Accents for Operators
9161 \begin_inset LatexCommand index
9162 name "Accents ! for operators"
9169 \begin_layout Standard
9177 \begin_inset LatexCommand index
9178 name "Commands ! O ! \\textbackslash overset"
9189 \begin_inset LatexCommand index
9190 name "Commands ! U ! \\textbackslash underset"
9194 characters can be placed above or below an operator, respectively, to accent
9203 \begin_inset LatexCommand index
9204 name "Commands ! S ! \\textbackslash sideset"
9208 characters can be set before and behind an operator.
9209 The command scheme is:
9212 \begin_layout Standard
9228 \begin_layout Standard
9235 must always be before the operator that should be accented.
9236 You can accent with several characters and even with other operators and
9244 for example only characters behind an operator, write nothing between the
9245 first braces but don't omit the braces.
9248 \begin_layout Standard
9249 For example the command
9254 \begin_inset Formula $\to$
9264 \begin_inset Formula $\to$
9273 \begin_layout Standard
9289 \begin_inset Formula \[
9290 \sideset{}{'}\sum_{k=1}^{n}\]
9297 \begin_layout Standard
9306 \begin_layout Standard
9321 \begin_layout Standard
9333 \begin_inset Formula $\uparrow$
9341 \begin_inset Formula \[
9342 \overset{a}{\maltese}\]
9346 As seen in the last example, with
9358 also symbols and characters can be accented; with
9364 this is not possible.
9367 \begin_layout Subsection
9368 Accents for several Characters
9369 \begin_inset LatexCommand label
9370 name "sub:Accents-for-several"
9375 \begin_inset LatexCommand index
9376 name "Accents ! for several characters"
9383 \begin_layout Standard
9387 \begin_inset Tabular
9388 <lyxtabular version="3" rows="5" columns="2">
9390 <column alignment="center" valignment="top" leftline="true" width="0pt">
9391 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9392 <row topline="true" bottomline="true">
9393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9396 \begin_layout Standard
9402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9405 \begin_layout Standard
9407 \begin_inset Note Note
9410 \begin_layout Standard
9417 is only used as spacer.
9428 <row topline="true" bottomline="true">
9429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9432 \begin_layout Standard
9439 \begin_layout Standard
9453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9456 \begin_layout Standard
9457 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9466 <row bottomline="true">
9467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9470 \begin_layout Standard
9477 \begin_layout Standard
9491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9494 \begin_layout Standard
9495 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9504 <row bottomline="true">
9505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9508 \begin_layout Standard
9515 \begin_layout Standard
9529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9532 \begin_layout Standard
9533 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9542 <row bottomline="true">
9543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9546 \begin_layout Standard
9553 \begin_layout Standard
9567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9570 \begin_layout Standard
9571 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9587 \begin_inset Tabular
9588 <lyxtabular version="3" rows="5" columns="2">
9590 <column alignment="center" valignment="top" leftline="true" width="0pt">
9591 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9592 <row topline="true" bottomline="true">
9593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9596 \begin_layout Standard
9602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9605 \begin_layout Standard
9612 <row topline="true" bottomline="true">
9613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9616 \begin_layout Standard
9623 \begin_layout Standard
9637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9640 \begin_layout Standard
9641 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9650 <row bottomline="true">
9651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9654 \begin_layout Standard
9661 \begin_layout Standard
9675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9678 \begin_layout Standard
9679 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9688 <row bottomline="true">
9689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9692 \begin_layout Standard
9699 \begin_layout Standard
9713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9716 \begin_layout Standard
9717 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9726 <row bottomline="true">
9727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9730 \begin_layout Standard
9737 \begin_layout Standard
9751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9754 \begin_layout Standard
9755 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9773 \begin_layout Standard
9774 \begin_inset VSpace medskip
9777 With these commands as many characters as you like can be accented.
9790 will only be set in the output with a length of three characters, as shown
9791 in the following example:
9792 \begin_inset Formula \[
9793 \widetilde{A+B=C-D}\]
9800 \begin_layout Standard
9808 \begin_inset LatexCommand index
9809 name "Commands ! O ! \\textbackslash overset"
9820 \begin_inset LatexCommand index
9821 name "Commands ! U ! \\textbackslash underset"
9825 described in the previous subsection it is also possible to accent several
9835 \begin_layout Standard
9845 \begin_inset Formula $\downarrow$
9851 \begin_inset Formula \[
9852 \underset{***}{A=B}\]
9859 \begin_layout Section
9861 \begin_inset LatexCommand label
9867 \begin_inset LatexCommand index
9868 name "Space ! horizontal"
9875 \begin_layout Subsection
9877 \begin_inset LatexCommand label
9878 name "sub:Predefined-Space"
9883 \begin_inset LatexCommand index
9884 name "Space ! horizontal ! predefined"
9891 \begin_layout Standard
9892 Sometimes it is necessary to insert horizontal space to a formula.
9893 This is done by inserting a protected space (shortcut
9899 \begin_inset Quotes eld
9909 \begin_layout Standard
9922 \begin_inset Quotes erd
9925 appears and by pressing
9929 several times one can select one of eight different space sizes.
9930 The spaces can also be inserted using the math toolbar button
9931 \begin_inset Graphics
9932 filename ../images/math/space.png
9937 or special commands.
9938 Independent from the inserted command, one can select the size again by
9946 \begin_layout Standard
9949 \begin_inset VSpace -5mm
9953 \begin_inset Tabular
9954 <lyxtabular version="3" rows="3" columns="7">
9956 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
9957 <column alignment="center" valignment="top" leftline="true" width="0">
9958 <column alignment="center" valignment="top" leftline="true" width="0">
9959 <column alignment="center" valignment="top" leftline="true" width="0">
9960 <column alignment="center" valignment="top" leftline="true" width="0">
9961 <column alignment="center" valignment="top" leftline="true" width="0">
9962 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9963 <row topline="true">
9964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9967 \begin_layout Standard
9973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9976 \begin_layout Standard
9984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9987 \begin_layout Standard
9995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9998 \begin_layout Standard
10006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10009 \begin_layout Standard
10017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10020 \begin_layout Standard
10028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10031 \begin_layout Standard
10040 <row topline="true">
10041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10044 \begin_layout Standard
10049 keystrokes after inserting the protected space
10054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10057 \begin_layout Standard
10063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10066 \begin_layout Standard
10072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10075 \begin_layout Standard
10081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10084 \begin_layout Standard
10090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10093 \begin_layout Standard
10099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10102 \begin_layout Standard
10109 <row topline="true" bottomline="true">
10110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10113 \begin_layout Standard
10119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10122 \begin_layout Standard
10123 \begin_inset Formula $A\, B$
10131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10134 \begin_layout Standard
10135 \begin_inset Formula $A\: B$
10143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10146 \begin_layout Standard
10147 \begin_inset Formula $A\; B$
10155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10158 \begin_layout Standard
10159 \begin_inset Formula $A\quad B$
10167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10170 \begin_layout Standard
10171 \begin_inset Formula $A\qquad B$
10179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10182 \begin_layout Standard
10183 \begin_inset Formula $A\! B$
10199 \begin_layout Standard
10200 The last size seem to produce no space.
10201 It is displayed red in LyX contrary to the other sizes, because it is a
10203 There are two more negative spaces:
10206 \begin_layout Standard
10208 \begin_inset Tabular
10209 <lyxtabular version="3" rows="3" columns="3">
10211 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10212 <column alignment="center" valignment="top" leftline="true" width="0pt">
10213 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10214 <row topline="true" bottomline="true">
10215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10218 \begin_layout Standard
10224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10227 \begin_layout Standard
10235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10238 \begin_layout Standard
10247 <row bottomline="true">
10248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10251 \begin_layout Standard
10256 keystrokes after inserting the protected space
10261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10264 \begin_layout Standard
10270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10273 \begin_layout Standard
10280 <row bottomline="true">
10281 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10284 \begin_layout Standard
10290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10293 \begin_layout Standard
10294 \begin_inset Formula $A\negmedspace B$
10302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10305 \begin_layout Standard
10306 \begin_inset Formula $A\negthickspace B$
10322 \begin_layout Standard
10323 Negative spaces can lead to characters overlapping each other.
10324 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10326 useful for summation
10330 \begin_layout Standard
10332 \begin_inset Tabular
10333 <lyxtabular version="3" rows="3" columns="2">
10335 <column alignment="center" valignment="top" leftline="true" width="0">
10336 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10337 <row topline="true" bottomline="true">
10338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10341 \begin_layout Standard
10347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10350 \begin_layout Standard
10352 \begin_inset Note Note
10355 \begin_layout Standard
10362 is only used as spacer.
10373 <row topline="true">
10374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10377 \begin_layout Standard
10386 \begin_layout Standard
10400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10403 \begin_layout Standard
10404 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10413 <row topline="true" bottomline="true">
10414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10417 \begin_layout Standard
10428 \begin_layout Standard
10442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10445 \begin_layout Standard
10446 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10462 \begin_layout Standard
10463 Relations like for example equal signs, are always surrounded by space.
10464 To suppress this, the equal sign is placed into a TeX-brace.
10465 The following example demonstrates this:
10468 \begin_layout Standard
10470 \begin_inset Tabular
10471 <lyxtabular version="3" rows="2" columns="2">
10473 <column alignment="center" valignment="top" width="0pt">
10474 <column alignment="center" valignment="top" width="0pt">
10476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10479 \begin_layout Standard
10485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10488 \begin_layout Standard
10489 \begin_inset Formula $A=B$
10499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10502 \begin_layout Standard
10503 \begin_inset Note Note
10506 \begin_layout Standard
10513 is only used as spacer.
10519 \begin_inset Formula $\raisebox{5mm}{}$
10522 equation without space
10527 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10530 \begin_layout Standard
10531 \begin_inset Formula $A{=}B$
10547 \begin_layout Standard
10549 The command for the last formula is:
10554 \begin_inset Formula $\to$
10560 \begin_layout Standard
10561 \begin_inset VSpace bigskip
10564 Spaces are needed for physical units, because the space between the value
10565 and the unit is the smallest one and not a normal space.
10566 For units in text, the smallest space is inserted via the menu
10568 Insert\SpecialChar \menuseparator
10569 Formatting\SpecialChar \menuseparator
10580 \begin_layout Standard
10581 An example to visualize the difference:
10584 \begin_layout Standard
10585 \begin_inset Tabular
10586 <lyxtabular version="3" rows="2" columns="2">
10588 <column alignment="left" valignment="top" width="0">
10589 <column alignment="left" valignment="top" width="0">
10591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10594 \begin_layout Standard
10596 \begin_inset Formula $\cdot$
10604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Standard
10608 space between value and unit
10615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10618 \begin_layout Standard
10619 24\InsetSpace \thinspace{}
10621 \begin_inset Formula $\cdot$
10629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10632 \begin_layout Standard
10633 smallest space between value and unit
10646 \begin_layout Subsection
10651 \begin_layout Standard
10664 \begin_layout Standard
10665 for vertical space in formulas see
10666 \begin_inset LatexCommand ref
10667 reference "sub:Line-Separation"
10680 \begin_layout Standard
10688 \begin_inset Note Note
10691 \begin_layout Standard
10694 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10697 \begin_layout Standard
10700 texorpdfstring is in section
10701 \begin_inset LatexCommand ref
10702 reference "sub:Formulas-in-Section"
10712 \begin_inset LatexCommand label
10713 name "sub:Variable-Space"
10718 \begin_inset LatexCommand index
10719 name "Space ! horizontal ! variable"
10726 \begin_layout Standard
10727 Space with a defined length can be inserted in LyX with the command
10736 \begin_inset LatexCommand index
10737 name "Commands ! H ! \\textbackslash hspace"
10742 For the length all units listed in
10743 \begin_inset LatexCommand ref
10744 reference "tab:Used-units"
10748 are allowed, except of the unit
10749 \begin_inset Quotes eld
10753 \begin_inset Quotes erd
10757 The length may also be negative.
10758 To insert so many space that the formula uses all available space, the
10766 \begin_inset LatexCommand index
10767 name "Commands ! H ! \\textbackslash hfill"
10774 \begin_layout Standard
10775 \begin_inset VSpace -1mm
10781 \begin_layout Standard
10783 \begin_inset Tabular
10784 <lyxtabular version="3" rows="4" columns="2">
10786 <column alignment="center" valignment="top" leftline="true" width="0">
10787 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10788 <row topline="true" bottomline="true">
10789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10792 \begin_layout Standard
10798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10801 \begin_layout Standard
10808 <row topline="true">
10809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10812 \begin_layout Standard
10816 \begin_inset Formula $\to$
10826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10829 \begin_layout Standard
10830 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10839 <row topline="true" bottomline="true">
10840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10843 \begin_layout Standard
10847 \begin_inset Formula $\to$
10857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10860 \begin_layout Standard
10861 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10870 <row topline="true" bottomline="true">
10871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10874 \begin_layout Standard
10881 \begin_layout Standard
10895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10898 \begin_layout Standard
10899 \begin_inset Formula $A=A\hfill B=B$
10915 \begin_layout Standard
10916 In the last example the available space is given by the longest column entry
10918 In an inline formula the space depends on the length of the line in which
10926 Thus, when the line uses the full width, no space will be created.
10933 has only an effect on displayed formulas when the formula style
10938 (Formula styles are explained in
10939 \begin_inset LatexCommand ref
10940 reference "sec:Formula-Styles"
10947 \begin_layout Standard
10960 can also be inserted in TeX-mode to use them for text:
10963 \begin_layout Standard
10964 This is a line with
10968 \begin_layout Standard
10977 2\InsetSpace \thinspace{}
10981 \begin_layout Standard
10982 This is a line with
10987 \begin_layout Standard
10988 In the last example
10994 was inserted via the menu
10996 Insert\SpecialChar \menuseparator
10997 Formatting\SpecialChar \menuseparator
10998 Horizontal\InsetSpace ~
11001 , what is not possible in formulas.
11002 This has the advantage that one can directly see in LyX that this is a
11006 \begin_layout Standard
11007 When the commands are at the begin of a text line but not at the beginning
11008 of a paragraph, they will be ignored by LaTeX.
11009 To avoid that, the command
11022 To get the same with
11028 , a line break and an empty placeholder
11034 \begin_layout Standard
11035 for placeholders see
11036 \begin_inset LatexCommand ref
11037 reference "sub:Placeholders"
11048 is inserted in TeX-mode with the command
11064 \begin_layout Subsection
11065 Space besides inline Formulas
11066 \begin_inset LatexCommand index
11067 name "Space ! besides inline formulas"
11074 \begin_layout Standard
11075 The space that surrounds inline formulas can be adjusted with the length
11081 \begin_inset LatexCommand index
11082 name "Commands ! M ! \\textbackslash mathsurround"
11089 The value of a length is set with the command
11094 \begin_inset LatexCommand index
11095 name "Commands ! S ! \\textbackslash setlength"
11101 that has the following scheme:
11104 \begin_layout Standard
11109 setlength{length name}{value}
11112 \begin_layout Standard
11119 to the value 5\InsetSpace \thinspace{}
11123 \begin_layout Standard
11133 \begin_layout Standard
11134 is inserted in TeX-mode.
11135 5\InsetSpace \thinspace{}
11136 mm space will now be set around all inline formulas:
11140 \begin_layout Standard
11154 \begin_layout Standard
11155 This is a line with an inline formula
11156 \begin_inset Formula $A=B$
11159 with 5\InsetSpace \thinspace{}
11160 mm surrounding space.
11164 \begin_layout Standard
11178 \begin_layout Standard
11179 To return to the predefined value,
11185 is set to the value 0\InsetSpace \thinspace{}
11189 \begin_layout Section
11191 \begin_inset LatexCommand index
11197 \begin_inset LatexCommand index
11198 name "Frames | see {Boxes}"
11205 \begin_layout Standard
11206 Boxes for text are described in chapter
11212 Embedded\InsetSpace ~
11218 \begin_layout Subsection
11220 \begin_inset LatexCommand label
11221 name "sub:Boxes-with-Frame"
11226 \begin_inset LatexCommand index
11227 name "Boxes ! with frame"
11234 \begin_layout Standard
11235 It is possible to frame formulas or parts of it with the commands
11242 \begin_inset LatexCommand index
11243 name "Commands ! F ! \\textbackslash fbox"
11254 \begin_inset LatexCommand index
11255 name "Commands ! B ! \\textbackslash boxed"
11262 \begin_layout Standard
11263 When one of these commands is inserted to a formula, a blue box appears
11264 within a frame to enter formula parts.
11271 an additional formula has to be created by
11279 \begin_layout Standard
11280 Due to a bug in LyX it is not possible to create a new formula with
11288 \begin_layout Standard
11292 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11301 \begin_layout Standard
11313 , because the box content will otherwise be treated as mathematical text.
11320 is used, a new formula is automatically created inside the frame.
11323 \begin_layout Standard
11330 is not suitable to frame displayed formulas, because the formula will always
11331 be set in the size of the text.
11338 is in contrary not suitable to frame inline formulas, because the formula
11339 will always be set in the size of a displayed formula.
11342 \begin_layout Standard
11349 there is the command
11356 \begin_inset LatexCommand index
11357 name "Commands ! F ! \\textbackslash framebox"
11361 where additionally the frame width and the alignment can be specified.
11368 is used in the following scheme:
11371 \begin_layout Standard
11376 framebox[frame width][position]{box content}
11379 \begin_layout Standard
11380 The position can either be
11397 right aligns the formula in the box.
11398 When no position is given, the formula will be centered.
11401 also no position can be given.
11402 In this case the frame width is adjusted to the box content like for
11411 \begin_layout Standard
11418 is inserted, a box appears containing three blue boxes.
11422 \begin_layout Standard
11423 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11428 \begin_layout Standard
11432 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11441 \begin_layout Standard
11453 The first two boxes are surrounded by brackets and denote the two optional
11455 The third box is for formula parts like for
11464 \begin_layout Standard
11466 \begin_inset Note Note
11469 \begin_layout Standard
11470 The table has been set into a minipage to make the footnote appearing.
11471 Otherwise the footnote text would not be displayed.
11477 \begin_inset Box Frameless
11486 height_special "totalheight"
11489 \begin_layout Standard
11491 \begin_inset Tabular
11492 <lyxtabular version="3" rows="5" columns="2">
11494 <column alignment="center" valignment="top" leftline="true" width="0">
11495 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11496 <row topline="true" bottomline="true">
11497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11500 \begin_layout Standard
11505 \begin_layout Standard
11506 Due to a bug in LyX it is not possible to create a new formula with
11514 \begin_layout Standard
11518 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11527 \begin_layout Standard
11544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11547 \begin_layout Standard
11549 \begin_inset Note Note
11552 \begin_layout Standard
11559 is only used as spacer.
11570 <row topline="true">
11571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11574 \begin_layout Standard
11581 \begin_layout Standard
11600 \begin_layout Standard
11614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11617 \begin_layout Standard
11618 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11628 <row topline="true">
11629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11632 \begin_layout Standard
11639 \begin_layout Standard
11654 \begin_layout Standard
11668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11671 \begin_layout Standard
11672 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11681 <row topline="true">
11682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11685 \begin_layout Standard
11692 \begin_layout Standard
11706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11709 \begin_layout Standard
11710 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11719 <row topline="true" bottomline="true">
11720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11723 \begin_layout Standard
11730 \begin_layout Standard
11740 \begin_inset Formula $\to$
11744 \begin_inset Formula $\to$
11757 \begin_layout Standard
11767 \begin_inset Formula $\downarrow$
11775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11778 \begin_layout Standard
11779 \begin_inset Formula $\raisebox{6mm}{}$
11783 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11787 \begin_inset Formula $\raisebox{-4mm}{}$
11808 \begin_layout Standard
11809 The frame thickness can also be adjusted.
11810 To do this the following commands have to be inserted in TeX-mode before
11814 \begin_layout Standard
11824 \begin_inset Quotes eld
11828 \begin_inset Quotes erd
11842 \begin_inset Quotes eld
11846 \begin_inset Quotes erd
11852 \begin_layout Standard
11853 \begin_inset Quotes eld
11857 \begin_inset Quotes erd
11860 specifies the minimal distance between the frame and the first character
11862 An example for this is the following framed formula:
11866 \begin_layout Standard
11878 \begin_inset Formula \[
11883 Before this formula the commands
11886 \begin_layout Standard
11908 \begin_layout Standard
11909 were inserted in TeX-mode.
11910 The given values are used for all following boxes.
11913 \begin_layout Standard
11914 To return to the standard frame size, the command
11917 \begin_layout Standard
11942 \begin_layout Standard
11956 \begin_layout Standard
11957 is inserted in TeX-mode before the next formula.
11960 \begin_layout Subsection
11961 Boxes without Frame
11962 \begin_inset LatexCommand label
11963 name "sub:Boxes-without-Frame"
11968 \begin_inset LatexCommand index
11969 name "Boxes ! without frame"
11976 \begin_layout Standard
11977 For boxes without a frame there are the following box commands:
11984 \begin_inset LatexCommand index
11985 name "Commands ! M ! \\textbackslash mbox"
11996 \begin_inset LatexCommand index
11997 name "Commands ! M ! \\textbackslash makebox"
12008 \begin_inset LatexCommand index
12009 name "Commands ! R ! \\textbackslash raisebox"
12016 \begin_layout Standard
12023 a box can be super- or subscripted.
12024 But in contrary to normal super- and subscripting, the characters in the
12025 box keep their font size.
12032 is used in the following scheme:
12035 \begin_layout Standard
12040 raisebox{height}{box content}
12043 \begin_layout Standard
12044 When the box should contain a formula, an extra formula is needed like for
12054 \begin_layout Standard
12056 \begin_inset Tabular
12057 <lyxtabular version="3" rows="4" columns="2">
12059 <column alignment="center" valignment="top" leftline="true" width="0">
12060 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12061 <row topline="true" bottomline="true">
12062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12065 \begin_layout Standard
12071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12074 \begin_layout Standard
12081 <row topline="true">
12082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12085 \begin_layout Standard
12089 \begin_inset Formula $\to$
12095 \begin_inset Formula $\to$
12103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12106 \begin_layout Standard
12107 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12116 <row topline="true" bottomline="true">
12117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12120 \begin_layout Standard
12124 \begin_inset Formula $\to$
12130 \begin_inset Formula $\to$
12138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12141 \begin_layout Standard
12142 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12151 <row topline="true" bottomline="true">
12152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12155 \begin_layout Standard
12159 \begin_inset Formula $\to$
12174 \begin_layout Standard
12188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12191 \begin_layout Standard
12195 \begin_layout Standard
12219 \begin_layout Standard
12220 The last formula can currently only be created using TeX-mode because LyX
12221 inserts a box instead of the needed extra formula.
12225 \begin_layout Standard
12230 \begin_layout Standard
12234 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12243 \begin_layout Standard
12258 \begin_layout Standard
12283 , with the difference that there is no frame.
12286 \begin_layout Subsection
12288 \begin_inset LatexCommand label
12289 name "sub:Colored-Boxes"
12294 \begin_inset LatexCommand index
12295 name "Boxes ! colored"
12302 \begin_layout Standard
12303 To be able to use all commands explained in this section, the LaTeX-package
12312 \begin_layout Standard
12317 is part of every LaTeX standard installation.
12323 \begin_inset LatexCommand index
12324 name "Packages ! color"
12328 has to be loaded in the LaTeX-preamble with the line
12332 \begin_layout Standard
12333 When text is colored somewhere in the document with a predefined color,
12334 LyX loads the LaTeX-package
12339 Thus it is possible that the package is loaded twice, but this doesn't
12346 \begin_inset Note Note
12349 \begin_layout Standard
12350 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12359 \begin_layout Standard
12367 \begin_layout Standard
12368 \begin_inset VSpace medskip
12371 To color boxes, the command
12378 \begin_inset LatexCommand index
12379 name "Commands ! C ! \\textbackslash colorbox"
12383 is used in the following scheme:
12386 \begin_layout Standard
12391 colorbox{color}{box content}
12394 \begin_layout Standard
12395 The box content can also be a box and a
12401 can also be part of another box (see the 2nd and 3rd example).
12402 When the box should contain a formula, an extra formula has to be created,
12413 \begin_layout Standard
12414 This also applies for the command
12425 \begin_layout Standard
12429 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12438 \begin_layout Standard
12453 \begin_layout Standard
12454 One of the following predefined colors can be chosen:
12457 \begin_layout Standard
12491 \begin_layout Standard
12493 \begin_inset Tabular
12494 <lyxtabular version="3" rows="4" columns="2">
12496 <column alignment="center" valignment="top" leftline="true" width="0">
12497 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12498 <row topline="true" bottomline="true">
12499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12502 \begin_layout Standard
12508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12511 \begin_layout Standard
12513 \begin_inset Note Note
12516 \begin_layout Standard
12523 is only used as spacer.
12534 <row topline="true">
12535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12538 \begin_layout Standard
12542 \begin_inset Formula $\to$
12552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12555 \begin_layout Standard
12556 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12565 <row topline="true">
12566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12569 \begin_layout Standard
12573 \begin_inset Formula $\to$
12584 \begin_layout Standard
12598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12601 \begin_layout Standard
12602 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12611 <row topline="true" bottomline="true">
12612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12615 \begin_layout Standard
12622 \begin_layout Standard
12634 \begin_inset Formula $\to$
12644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12647 \begin_layout Standard
12648 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12664 \begin_layout Standard
12671 only colors the box but not the characters in the box.
12672 To color all characters, the whole formula is highlighted and the wanted
12673 color is chosen in the
12679 The dialog can be called with the toolbar button
12680 \begin_inset Graphics
12681 filename ../images/dialog-show_character.png
12688 Edit\SpecialChar \menuseparator
12690 Style\SpecialChar \menuseparator
12694 The formula number has then the same color as the formula.
12695 When the formula number should get another color than the formula characters,
12696 the color must be changed within the formula.
12699 \begin_layout Standard
12703 \begin_layout Standard
12706 \begin_inset Formula \begin{equation}
12707 \int A=B\label{eq:red}\end{equation}
12714 \begin_inset Formula \begin{equation}
12715 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12722 \begin_layout Standard
12724 \begin_inset LatexCommand eqref
12729 is completely colored red.
12732 \begin_inset LatexCommand eqref
12733 reference "eq:redgreen"
12737 was first completely colored green to set the color for the formula number.
12738 Subsequently the formula characters were colored red.
12741 \begin_layout Standard
12742 \begin_inset VSpace bigskip
12745 To color the frame different than the rest of the box, the command
12752 \begin_inset LatexCommand index
12753 name "Commands ! F ! \\textbackslash fcolorbox"
12757 is used in the following scheme:
12760 \begin_layout Standard
12765 fcolorbox{frame color}{color}{box content}
12768 \begin_layout Standard
12775 is an extension of the command
12782 The frame width is set, like for
12805 \begin_layout Standard
12817 \begin_inset Formula \[
12818 \fcolorbox{cyan}{magenta}{A=B}\]
12826 \begin_layout Standard
12840 \begin_layout Standard
12841 This formula was created with the command
12848 \begin_inset Formula $\to$
12854 \begin_inset Formula $\to$
12864 \begin_layout Standard
12865 \begin_inset VSpace bigskip
12868 To use other colors than the predefined ones, they have to be defined first.
12871 \begin_layout Standard
12872 One can for example define the color
12873 \begin_inset Quotes eld
12881 \begin_inset Quotes erd
12884 with the LaTeX-preamble line:
12887 \begin_layout Standard
12892 definecolor{darkgreen}{cmyk}{0.5,
12907 \begin_inset LatexCommand index
12908 name "Commands ! D ! \\textbackslash definecolor"
12915 \begin_layout Standard
12920 is the color space that denotes the colors
12937 The four comma separated numbers are the portion factor for the corresponding
12938 colors of the color space.
12939 The factors can be in the range of 0\InsetSpace \thinspace{}
12940 -\InsetSpace \thinspace{}
12946 also the color space
12950 can be used for definitions.
12967 , so that there are in this case three portion factors for the corresponding
12969 Furthermore there is the color space
12973 with one portion factor for the gray value.
12976 \begin_layout Standard
12977 As example a framed box with the new defined color
12981 where the characters have been colored
12986 \begin_inset Formula \begin{equation}
12987 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
12994 \begin_layout Standard
12995 Self-defined colors can also be be used for text with the help of the command
13003 \begin_inset LatexCommand index
13004 name "Text ! colored"
13011 \begin_layout Standard
13015 \begin_layout Standard
13019 textcolor{darkgreen}{
13025 \begin_inset Quotes eld
13029 \begin_inset Quotes erd
13036 \begin_layout Standard
13046 \begin_layout Standard
13054 \begin_inset LatexCommand index
13055 name "Commands ! T ! \\textbackslash textcolor"
13059 is used in the scheme
13063 textcolor{color}{characters to color}
13068 \begin_layout Subsection
13070 \begin_inset LatexCommand label
13071 name "sub:Paragraph-Boxes"
13076 \begin_inset LatexCommand index
13077 name "Boxes ! as paragraph"
13084 \begin_layout Standard
13085 A box that can contain several lines and paragraphs, a so called paragraph
13086 box (parbox), can be created with the menu
13088 Insert\SpecialChar \menuseparator
13091 or the toolbar button
13092 \begin_inset Graphics
13093 filename ../images/box-insert.png
13101 \begin_layout Standard
13102 The following example shows a framed parbox in a line:
13105 \begin_layout Standard
13106 \begin_inset VSpace medskip
13110 \begin_inset Box Boxed
13119 height_special "totalheight"
13122 \begin_layout Standard
13123 This is a paragraph box.
13124 It is exactly 5\InsetSpace \thinspace{}
13125 cm long and can also contain formulas:
13126 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13137 \begin_layout Standard
13138 \begin_inset VSpace medskip
13144 \begin_layout Standard
13145 Such a box is created by right-clicking on the gray box inset.
13146 A dialog pops up showing the box properties.
13159 : 5\InsetSpace \thinspace{}
13162 Vertical Box Alignment
13167 \begin_layout Standard
13168 \begin_inset VSpace medskip
13171 In LaTeX a parbox is created with the command
13178 \begin_inset LatexCommand index
13179 name "Commands ! P ! \\textbackslash parbox"
13183 that has the following scheme:
13186 \begin_layout Standard
13191 parbox[position]{width}{box content}
13194 \begin_layout Standard
13208 for bottom means that the box is aligned within the surrounding text with
13214 for top this is done with the first line.
13215 When no position is given, the box will be vertically centered, see section
13222 Embedded\InsetSpace ~
13225 manual for examples.
13228 \begin_layout Standard
13229 \begin_inset VSpace bigskip
13232 To frame formulas completely, including the formula number, the formula
13233 must be set into a parbox.
13234 To do this, the command
13248 is inserted in TeX-mode before the formula.
13254 \begin_inset LatexCommand index
13255 name "Commands ! L ! \\textbackslash linewidth"
13261 is hereby the line width set for the document.
13262 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13263 times the frame separation and
13264 the frame thickness must be subtracted from the line width.
13265 As this is not automatically done by LyX due to a bug
13269 \begin_layout Standard
13273 \begin_layout Standard
13277 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13286 \begin_layout Standard
13298 , TeX-mode has to be used.
13299 To be able to multiply and subtract in arguments, the LaTeX-package
13307 \begin_layout Standard
13312 is part of every LaTeX standard installation.
13318 \begin_inset LatexCommand index
13319 name "Packages ! calc"
13323 must be loaded in the LaTeX-preamble with the line
13326 \begin_layout Standard
13334 \begin_layout Standard
13335 Behind the formula both boxes are closed by entering
13340 Here is an example:
13344 \begin_layout Standard
13358 \begin_layout Standard
13362 \begin_layout Standard
13380 \begin_inset Formula \begin{equation}
13381 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13389 \begin_layout Standard
13400 \begin_layout Standard
13414 \begin_layout Standard
13415 \begin_inset VSpace medskip
13418 As a parbox is used as argument of
13424 , there is in this case no difference between
13439 \begin_layout Standard
13440 \begin_inset VSpace bigskip
13443 Paragraph boxes are very useful to comment formulas directly.
13450 is used in combination with the command
13464 \begin_inset LatexCommand ref
13465 reference "sub:User-defined-Numbering"
13472 \begin_layout Standard
13473 An example of a formula commented with
13482 \begin_layout Standard
13486 \begin_layout Standard
13499 This is a description.
13500 It is distinctly separated from the formula and multiline.
13504 \begin_layout Standard
13516 \begin_layout Standard
13517 Such a formula must be inserted completely in TeX-mode because LyX does
13518 not yet support the command
13525 The formula is created with the following command sequence:
13528 \begin_layout Standard
13541 is inserted in TeX-mode.
13545 \begin_layout Standard
13546 When the formula style
13558 can also be replaced by
13565 (formula styles see
13566 \begin_inset LatexCommand ref
13567 reference "sec:Formula-Styles"
13576 Then the description follows as normal text, and finally
13582 is inserted in TeX-mode.
13595 hereby create a displayed formula.
13598 \begin_layout Standard
13605 can be seen in this example that was
13606 \begin_inset Quotes eld
13610 \begin_inset Quotes erd
13613 using the mathematical textmode:
13614 \begin_inset Formula \[
13615 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13622 \begin_layout Section
13624 \begin_inset LatexCommand index
13632 \begin_layout Subsection
13634 \begin_inset LatexCommand label
13635 name "sub:Big-Operators"
13640 \begin_inset LatexCommand index
13641 name "Operators ! big"
13646 \begin_inset LatexCommand index
13652 \begin_inset LatexCommand index
13660 \begin_layout Standard
13661 To be able to use all integral operators listed here, the option
13663 Use esint package automatically
13665 must be set in the document settings under
13673 \begin_layout Standard
13677 \begin_inset Tabular
13678 <lyxtabular version="3" rows="11" columns="2">
13680 <column alignment="center" valignment="top" leftline="true" width="0pt">
13681 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13682 <row topline="true" bottomline="true">
13683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13686 \begin_layout Standard
13692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13695 \begin_layout Standard
13702 <row topline="true">
13703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13706 \begin_layout Standard
13710 \begin_inset LatexCommand index
13711 name "Commands ! S ! \\textbackslash sum"
13720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13723 \begin_layout Standard
13724 \begin_inset Formula $\sum$
13733 <row topline="true">
13734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13737 \begin_layout Standard
13741 \begin_inset LatexCommand index
13742 name "Commands ! I ! \\textbackslash int"
13751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13754 \begin_layout Standard
13755 \begin_inset Formula $\int$
13764 <row topline="true">
13765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13768 \begin_layout Standard
13776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13779 \begin_layout Standard
13780 \begin_inset Formula $\intop$
13789 <row topline="true">
13790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13793 \begin_layout Standard
13801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13804 \begin_layout Standard
13805 \begin_inset Formula $\oint$
13814 <row topline="true">
13815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13818 \begin_layout Standard
13826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13829 \begin_layout Standard
13830 \begin_inset Formula $\ointop$
13839 <row topline="true">
13840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13843 \begin_layout Standard
13851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13854 \begin_layout Standard
13855 \begin_inset Formula $\ointctrclockwise$
13864 <row topline="true">
13865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13868 \begin_layout Standard
13876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13879 \begin_layout Standard
13880 \begin_inset Formula $\ointclockwise$
13889 <row topline="true">
13890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13893 \begin_layout Standard
13901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13904 \begin_layout Standard
13905 \begin_inset Formula $\sqint$
13914 <row topline="true">
13915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13918 \begin_layout Standard
13926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13929 \begin_layout Standard
13930 \begin_inset Formula $\bigcap$
13939 <row topline="true" bottomline="true">
13940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13943 \begin_layout Standard
13951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13954 \begin_layout Standard
13955 \begin_inset Formula $\bigcup$
13971 \begin_inset Tabular
13972 <lyxtabular version="3" rows="10" columns="2">
13974 <column alignment="center" valignment="top" leftline="true" width="0pt">
13975 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13976 <row topline="true" bottomline="true">
13977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13980 \begin_layout Standard
13986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13989 \begin_layout Standard
13996 <row topline="true">
13997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14000 \begin_layout Standard
14004 \begin_inset LatexCommand index
14005 name "Commands ! P ! \\textbackslash prod"
14014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14017 \begin_layout Standard
14018 \begin_inset Formula $\prod$
14027 <row topline="true">
14028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14031 \begin_layout Standard
14039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14042 \begin_layout Standard
14043 \begin_inset Formula $\coprod$
14052 <row topline="true">
14053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14056 \begin_layout Standard
14064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14067 \begin_layout Standard
14068 \begin_inset Formula $\bigodot$
14077 <row topline="true">
14078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14081 \begin_layout Standard
14089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14092 \begin_layout Standard
14093 \begin_inset Formula $\bigotimes$
14102 <row topline="true">
14103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14106 \begin_layout Standard
14114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14117 \begin_layout Standard
14118 \begin_inset Formula $\bigoplus$
14127 <row topline="true">
14128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14131 \begin_layout Standard
14139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14142 \begin_layout Standard
14143 \begin_inset Formula $\bigwedge$
14152 <row topline="true">
14153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14156 \begin_layout Standard
14164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14167 \begin_layout Standard
14168 \begin_inset Formula $\bigvee$
14177 <row topline="true">
14178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14181 \begin_layout Standard
14189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14192 \begin_layout Standard
14193 \begin_inset Formula $\bigsqcup$
14202 <row topline="true" bottomline="true">
14203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14206 \begin_layout Standard
14214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14217 \begin_layout Standard
14218 \begin_inset Formula $\biguplus$
14236 \begin_layout Standard
14237 All big operators can also be inserted via the math toolbar button
14238 \begin_inset Graphics
14239 filename ../images/math/intop.png
14247 \begin_layout Standard
14248 The operators are called big because they are bigger than the sometimes
14249 equal looking binary operators.
14250 All big operators can have limits as described in the next subsection.
14253 \begin_layout Standard
14278 , resp.\InsetSpace ~
14279 in the style the operator limits are displayed, see
14280 \begin_inset LatexCommand ref
14281 reference "sub:Operator-Limits"
14289 \begin_layout Subsubsection*
14290 Advices for Integrals
14293 \begin_layout Standard
14298 in an integral is an operator, that therefore has to be set upright.
14299 This is done by highlighting the
14303 and using the keyboard shortcut
14312 \begin_layout Standard
14318 \begin_inset LatexCommand ref
14319 reference "sub:Font-Styles"
14329 Finally the smallest space is inserted before the
14333 , as this is usual for operators.
14337 \begin_layout Standard
14339 \begin_inset Formula $\int A(x)dx$
14348 \begin_layout Standard
14358 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14364 \begin_layout Standard
14365 For multiple integrals there are the following commands:
14366 \begin_inset VSpace medskip
14372 \begin_layout Standard
14376 \begin_inset Tabular
14377 <lyxtabular version="3" rows="4" columns="2">
14379 <column alignment="center" valignment="top" leftline="true" width="0">
14380 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14381 <row topline="true" bottomline="true">
14382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14385 \begin_layout Standard
14391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14394 \begin_layout Standard
14396 \begin_inset Note Note
14399 \begin_layout Standard
14406 is only used as spacer.
14417 <row topline="true">
14418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14421 \begin_layout Standard
14429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14432 \begin_layout Standard
14433 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14442 <row topline="true">
14443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14446 \begin_layout Standard
14454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14457 \begin_layout Standard
14458 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14467 <row topline="true" bottomline="true">
14468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14471 \begin_layout Standard
14479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14482 \begin_layout Standard
14483 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14499 \begin_inset Tabular
14500 <lyxtabular version="3" rows="4" columns="2">
14502 <column alignment="center" valignment="top" leftline="true" width="0">
14503 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14504 <row topline="true" bottomline="true">
14505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14508 \begin_layout Standard
14514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14517 \begin_layout Standard
14524 <row topline="true">
14525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14528 \begin_layout Standard
14536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14539 \begin_layout Standard
14540 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14549 <row topline="true">
14550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14553 \begin_layout Standard
14561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14564 \begin_layout Standard
14565 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14574 <row topline="true" bottomline="true">
14575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14578 \begin_layout Standard
14586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14589 \begin_layout Standard
14590 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14608 \begin_layout Subsection
14610 \begin_inset LatexCommand label
14611 name "sub:Operator-Limits"
14616 \begin_inset LatexCommand index
14617 name "Operators ! Limits"
14624 \begin_layout Standard
14625 Limits are created by super- and subscripts:
14628 \begin_layout Standard
14630 \begin_inset Tabular
14631 <lyxtabular version="3" rows="2" columns="2">
14633 <column alignment="center" valignment="top" leftline="true" width="0pt">
14634 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14635 <row topline="true" bottomline="true">
14636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14639 \begin_layout Standard
14645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14648 \begin_layout Standard
14650 \begin_inset Note Note
14653 \begin_layout Standard
14660 is only used as spacer.
14671 <row topline="true" bottomline="true">
14672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14675 \begin_layout Standard
14684 \begin_layout Standard
14694 \begin_inset Formula $\to$
14698 \begin_inset Formula $\to$
14706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14709 \begin_layout Standard
14710 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14726 \begin_layout Standard
14727 Limits of inline formulas are set right beside the operator.
14728 Limits in displayed formulas are set above or below the operator, except
14729 of integral limits.
14732 \begin_layout Standard
14733 To force that the limits are set beside the operator, the cursor is set
14734 directly behind the operator and the limits type is changed with the menu
14737 Edit\SpecialChar \menuseparator
14738 Math\SpecialChar \menuseparator
14756 \begin_layout Standard
14757 The default limits type is this:
14758 \begin_inset Formula \[
14759 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14763 This is how it looks when the limits type was changed to
14770 \begin_inset Formula \[
14771 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14775 For integrals, except of
14787 , the limits are by default set beside the operator.
14788 But for multiple integrals the limits are often set below the operator.
14789 In the following example the limits type was therefore set to
14793 and so set below the integrals:
14794 \begin_inset Formula \begin{equation}
14795 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14802 \begin_layout Standard
14803 \begin_inset VSpace medskip
14806 To specify conditions for limits, the commands
14813 \begin_inset LatexCommand index
14814 name "Commands ! S ! \\textbackslash subarray"
14825 \begin_inset LatexCommand index
14826 name "Commands ! S ! \\textbackslash substack"
14831 To create for example this expression
14832 \begin_inset Formula \begin{equation}
14833 \sum_{\begin{subarray}{c}
14835 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14842 \begin_layout Standard
14843 the following has to be done:
14857 \begin_layout Standard
14869 One is now in a blue box under the summation operator and insert there
14878 \begin_layout Standard
14890 The blue box is now within a purple box and now several lines can be written
14892 A new line is created by inserting a line break (
14901 0<k<1000 Ctrl-Return
14905 is typed in, a new box appears below for the new line.
14908 \begin_layout Standard
14909 The alignment of the lines can be changed to left aligned with the
14919 Edit\SpecialChar \menuseparator
14923 To get right alignment,
14931 \begin_layout Standard
14942 is inserted at the beginning of the line.
14945 \begin_layout Standard
14958 with the difference that the lines are always centered.
14961 \begin_layout Standard
14962 \begin_inset VSpace bigskip
14966 \begin_inset LatexCommand eqref
14967 reference "eq:substack"
14971 there can be too much space beside an operator, because the characters
14972 following the operator are set beside the limits.
14975 \begin_layout Standard
14976 To avoid this, the following macro can be used in the LaTeX-preamble:
14979 \begin_layout Standard
15008 mathclapinternal #1#2{
15012 mathsurround =0pt #1{#2}$}}
15015 \begin_layout Standard
15016 This defines the command
15023 \begin_inset LatexCommand index
15024 name "Commands ! M ! \\textbackslash mathclap"
15028 that sets the width of the limit to 0\InsetSpace \thinspace{}
15030 The command scheme is
15033 \begin_layout Standard
15041 \begin_layout Standard
15042 where the limit can consist of several conditions.
15045 \begin_layout Standard
15047 \begin_inset LatexCommand eqref
15048 reference "eq:substack"
15052 , one uses the command
15055 \begin_layout Standard
15068 \begin_layout Standard
15077 0<k<1000 Ctrl-Enter
15080 \begin_layout Standard
15081 to create the lower limit.
15082 The summand is now directly behind the summation operator:
15083 \begin_inset Formula \[
15084 \sum_{\mathclap{\substack{0<k<1000\\
15085 \\k\,\in\,\mathbb{N}}
15093 \begin_layout Standard
15094 \begin_inset VSpace bigskip
15097 How to use one limit for several operators is described in
15098 \begin_inset LatexCommand ref
15099 reference "sub:Self-defined-Operators"
15106 \begin_layout Subsection
15108 \begin_inset LatexCommand label
15109 name "sub:Binary-Operators"
15114 \begin_inset LatexCommand index
15115 name "Operators ! binary"
15122 \begin_layout Standard
15123 Binary operators are surrounded by space when there is a character before
15125 \begin_inset VSpace medskip
15131 \begin_layout Standard
15135 \begin_inset Tabular
15136 <lyxtabular version="3" rows="13" columns="2">
15138 <column alignment="center" valignment="top" leftline="true" width="0pt">
15139 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15140 <row topline="true" bottomline="true">
15141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15144 \begin_layout Standard
15146 \begin_inset Note Note
15149 \begin_layout Standard
15156 is only used as spacer.
15166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15169 \begin_layout Standard
15176 <row topline="true">
15177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15180 \begin_layout Standard
15186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Standard
15190 \begin_inset Formula $+$
15199 <row topline="true">
15200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15203 \begin_layout Standard
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15212 \begin_layout Standard
15213 \begin_inset Formula $-$
15222 <row topline="true">
15223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15226 \begin_layout Standard
15234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15237 \begin_layout Standard
15238 \begin_inset Formula $\pm$
15247 <row topline="true">
15248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15251 \begin_layout Standard
15259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15262 \begin_layout Standard
15263 \begin_inset Formula $\mp$
15272 <row topline="true">
15273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15276 \begin_layout Standard
15284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15287 \begin_layout Standard
15288 \begin_inset Formula $\cdot$
15297 <row topline="true">
15298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15301 \begin_layout Standard
15309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15312 \begin_layout Standard
15313 \begin_inset Formula $\times$
15322 <row topline="true">
15323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15326 \begin_layout Standard
15334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15337 \begin_layout Standard
15338 \begin_inset Formula $\div$
15347 <row topline="true">
15348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15351 \begin_layout Standard
15355 \begin_layout Standard
15368 \begin_layout Standard
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15383 \begin_layout Standard
15384 \begin_inset Formula $*$
15393 <row topline="true">
15394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15397 \begin_layout Standard
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15408 \begin_layout Standard
15409 \begin_inset Formula $\star$
15418 <row topline="true">
15419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15422 \begin_layout Standard
15430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Standard
15434 \begin_inset Formula $\circ$
15443 <row topline="true">
15444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15447 \begin_layout Standard
15455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15458 \begin_layout Standard
15459 \begin_inset Formula $\diamond$
15468 <row topline="true" bottomline="true">
15469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15472 \begin_layout Standard
15480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15483 \begin_layout Standard
15484 \begin_inset Formula $\bullet$
15500 \begin_inset Tabular
15501 <lyxtabular version="3" rows="13" columns="2">
15503 <column alignment="center" valignment="top" leftline="true" width="0pt">
15504 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15505 <row topline="true" bottomline="true">
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15509 \begin_layout Standard
15515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15518 \begin_layout Standard
15525 <row topline="true">
15526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15529 \begin_layout Standard
15537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15540 \begin_layout Standard
15541 \begin_inset Formula $\nabla$
15550 <row topline="true">
15551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15554 \begin_layout Standard
15562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15565 \begin_layout Standard
15566 \begin_inset Formula $\bigtriangledown$
15575 <row topline="true">
15576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15579 \begin_layout Standard
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15590 \begin_layout Standard
15591 \begin_inset Formula $\bigtriangleup$
15600 <row topline="true">
15601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15604 \begin_layout Standard
15612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15615 \begin_layout Standard
15616 \begin_inset Formula $\Box$
15625 <row topline="true">
15626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15629 \begin_layout Standard
15637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15640 \begin_layout Standard
15641 \begin_inset Formula $\cap$
15650 <row topline="true">
15651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15654 \begin_layout Standard
15662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15665 \begin_layout Standard
15666 \begin_inset Formula $\cup$
15675 <row topline="true">
15676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15679 \begin_layout Standard
15687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15690 \begin_layout Standard
15691 \begin_inset Formula $\dagger$
15700 <row topline="true">
15701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15704 \begin_layout Standard
15712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15715 \begin_layout Standard
15716 \begin_inset Formula $\ddagger$
15725 <row topline="true">
15726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15729 \begin_layout Standard
15737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15740 \begin_layout Standard
15741 \begin_inset Formula $\wr$
15750 <row topline="true">
15751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15754 \begin_layout Standard
15762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15765 \begin_layout Standard
15766 \begin_inset Formula $\bigcirc$
15775 <row topline="true">
15776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15779 \begin_layout Standard
15787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15790 \begin_layout Standard
15791 \begin_inset Formula $\wedge$
15800 <row topline="true" bottomline="true">
15801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15804 \begin_layout Standard
15812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15815 \begin_layout Standard
15816 \begin_inset Formula $\vee$
15832 \begin_inset Tabular
15833 <lyxtabular version="3" rows="13" columns="2">
15835 <column alignment="center" valignment="top" leftline="true" width="0pt">
15836 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15837 <row topline="true" bottomline="true">
15838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15841 \begin_layout Standard
15847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15850 \begin_layout Standard
15857 <row topline="true">
15858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15861 \begin_layout Standard
15869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15872 \begin_layout Standard
15873 \begin_inset Formula $\oplus$
15882 <row topline="true">
15883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15886 \begin_layout Standard
15894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15897 \begin_layout Standard
15898 \begin_inset Formula $\ominus$
15907 <row topline="true">
15908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15911 \begin_layout Standard
15919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15922 \begin_layout Standard
15923 \begin_inset Formula $\otimes$
15932 <row topline="true">
15933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15936 \begin_layout Standard
15944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15947 \begin_layout Standard
15948 \begin_inset Formula $\oslash$
15957 <row topline="true">
15958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15961 \begin_layout Standard
15969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15972 \begin_layout Standard
15973 \begin_inset Formula $\odot$
15982 <row topline="true">
15983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15986 \begin_layout Standard
15994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15997 \begin_layout Standard
15998 \begin_inset Formula $\amalg$
16007 <row topline="true">
16008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16011 \begin_layout Standard
16019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16022 \begin_layout Standard
16023 \begin_inset Formula $\uplus$
16032 <row topline="true">
16033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16036 \begin_layout Standard
16044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16047 \begin_layout Standard
16048 \begin_inset Formula $\setminus$
16057 <row topline="true">
16058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16061 \begin_layout Standard
16069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16072 \begin_layout Standard
16073 \begin_inset Formula $\sqcap$
16082 <row topline="true">
16083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16086 \begin_layout Standard
16094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16097 \begin_layout Standard
16098 \begin_inset Formula $\sqcup$
16107 <row topline="true">
16108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16111 \begin_layout Standard
16119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16122 \begin_layout Standard
16123 \begin_inset Formula $\triangleleft$
16132 <row topline="true" bottomline="true">
16133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16136 \begin_layout Standard
16144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16147 \begin_layout Standard
16148 \begin_inset Formula $\triangleright$
16166 \begin_layout Standard
16167 All binary operators can also be inserted via the math toolbar button
16168 \begin_inset Graphics
16169 filename ../images/math/pm.png
16177 \begin_layout Standard
16178 To typeset the Laplace operator also
16195 \begin_inset Formula $\nabla^{2}$
16198 ) can be used instead of
16207 \begin_layout Standard
16214 Insert\SpecialChar \menuseparator
16226 \begin_layout Subsection
16227 Self-defined Operators
16228 \begin_inset LatexCommand label
16229 name "sub:Self-defined-Operators"
16234 \begin_inset LatexCommand index
16235 name "Operators ! self-defined"
16242 \begin_layout Standard
16243 With the help of the command
16247 DeclareMathOperator
16250 \begin_inset LatexCommand index
16251 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16255 custom operators can be defined in the LaTeX-preamble.
16256 Its command scheme is:
16259 \begin_layout Standard
16264 DeclareMathOperator{new command}{display}
16267 \begin_layout Standard
16268 Display can be characters or symbols that define how the operator looks
16270 To define a big operator a * is set behind the command.
16271 All self-defined big operators can have limits as described in
16272 \begin_inset LatexCommand ref
16273 reference "sub:Operator-Limits"
16280 \begin_layout Standard
16281 For example the LaTeX-preamble line
16284 \begin_layout Standard
16289 DeclareMathOperator*{
16296 \begin_layout Standard
16297 defines the command
16303 , that inserts a big operator consisting of the lozenge symbol from
16304 \begin_inset LatexCommand ref
16305 reference "sub:Miscellaneous-Symbols"
16310 \begin_inset Formula \[
16311 \Lozenge_{n=1}^{\infty}\]
16315 The command for this formula is:
16326 \begin_inset Formula $\to$
16332 \begin_layout Standard
16333 \begin_inset VSpace bigskip
16336 When self-defined operators are not used several times in the document,
16337 they can also be defined with the commands
16344 \begin_inset LatexCommand index
16345 name "Commands ! M ! \\textbackslash mathop"
16356 \begin_inset LatexCommand index
16357 name "Commands ! M ! \\textbackslash mathbin"
16361 , which have the following scheme:
16364 \begin_layout Standard
16378 \begin_layout Standard
16385 defines big operators,
16394 \begin_layout Standard
16401 can e.\InsetSpace \thinspace{}
16403 be used to use one limit for several operators:
16406 \begin_layout Standard
16407 \begin_inset Formula \[
16408 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16415 \begin_layout Standard
16416 The command for the formula above is:
16434 \begin_layout Standard
16446 \begin_inset Formula $\to$
16455 \begin_layout Standard
16469 \begin_layout Section
16471 \begin_inset LatexCommand index
16479 \begin_layout Subsection
16481 \begin_inset LatexCommand label
16482 name "sub:Font-Styles"
16487 \begin_inset LatexCommand index
16488 name "Font ! style"
16495 \begin_layout Standard
16496 Latin letters in formulas can be set in one of the following font styles:
16497 \begin_inset VSpace -2mm
16503 \begin_layout Standard
16505 \begin_inset Tabular
16506 <lyxtabular version="3" rows="6" columns="3">
16508 <column alignment="center" valignment="top" leftline="true" width="0">
16509 <column alignment="center" valignment="top" leftline="true" width="0">
16510 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16511 <row topline="true" bottomline="true">
16512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16515 \begin_layout Standard
16521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16524 \begin_layout Standard
16530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16533 \begin_layout Standard
16540 <row topline="true">
16541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16544 \begin_layout Standard
16553 \begin_layout Standard
16569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16572 \begin_layout Standard
16573 \begin_inset Formula $\mathbb{ABC}$
16581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16584 \begin_layout Standard
16591 <row topline="true">
16592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16595 \begin_layout Standard
16604 \begin_layout Standard
16620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16623 \begin_layout Standard
16624 \begin_inset Formula $\mathbf{AbC}$
16632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16635 \begin_layout Standard
16642 <row topline="true">
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Standard
16655 \begin_layout Standard
16671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16674 \begin_layout Standard
16675 \begin_inset Formula $\boldsymbol{AbC}$
16683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16686 \begin_layout Standard
16693 <row topline="true">
16694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16697 \begin_layout Standard
16706 \begin_layout Standard
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16725 \begin_layout Standard
16726 \begin_inset Formula $\mathcal{ABC}$
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16737 \begin_layout Standard
16744 <row topline="true" bottomline="true">
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16748 \begin_layout Standard
16757 \begin_layout Standard
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16776 \begin_layout Standard
16777 \begin_inset Formula $\mathfrak{AbC}$
16785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16788 \begin_layout Standard
16802 \begin_layout Standard
16804 \begin_inset Tabular
16805 <lyxtabular version="3" rows="5" columns="3">
16807 <column alignment="center" valignment="top" leftline="true" width="0">
16808 <column alignment="center" valignment="top" leftline="true" width="0">
16809 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16810 <row topline="true" bottomline="true">
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16814 \begin_layout Standard
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16823 \begin_layout Standard
16829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16832 \begin_layout Standard
16839 <row topline="true">
16840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16843 \begin_layout Standard
16852 \begin_layout Standard
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Standard
16872 \begin_inset Formula $\mathit{AbC}$
16880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16883 \begin_layout Standard
16890 <row topline="true">
16891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16894 \begin_layout Standard
16903 \begin_layout Standard
16919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16922 \begin_layout Standard
16923 \begin_inset Formula $\mathrm{AbC}$
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Standard
16941 <row topline="true">
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16945 \begin_layout Standard
16954 \begin_layout Standard
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16973 \begin_layout Standard
16974 \begin_inset Formula $\mathsf{AbC}$
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Standard
16992 <row topline="true" bottomline="true">
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Standard
17005 \begin_layout Standard
17021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17024 \begin_layout Standard
17025 \begin_inset Formula $\mathtt{AbC}$
17033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17036 \begin_layout Standard
17050 \begin_layout Standard
17051 \begin_inset Note Greyedout
17054 \begin_layout Standard
17071 can only be used for big letters.
17079 \begin_layout Standard
17080 Predefined is the style
17089 \begin_layout Standard
17090 The style commands work also for letters in mathematical constructs:
17091 \begin_inset Formula \[
17092 \mathfrak{A=\frac{b}{C}}\]
17099 \begin_layout Standard
17100 Characters in mathematical text don't appear in a math font style but in
17101 the text font style
17108 That their style can't be set correctly via the text style dialog is a
17113 \begin_layout Standard
17118 \begin_layout Standard
17122 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17131 \begin_layout Standard
17146 \begin_layout Standard
17147 Instead of the style commands the dialog
17149 Edit\SpecialChar \menuseparator
17150 Math\SpecialChar \menuseparator
17153 or the toolbar button
17154 \begin_inset Graphics
17155 filename ../images/math/font.png
17163 \begin_layout Subsection
17165 \begin_inset LatexCommand label
17166 name "sub:Bold-Formulas"
17171 \begin_inset LatexCommand index
17172 name "Formula ! bold"
17179 \begin_layout Standard
17180 To make a complete formula bold, the command
17186 from the previous subsection cannot be used, because it doesn't work for
17187 small Greek letters.
17188 Furthermore it prints Latin letters always upright, like in the following
17192 \begin_layout Standard
17193 \begin_inset Formula \[
17194 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17201 \begin_layout Standard
17202 To display the formula correctly, the command
17209 \begin_inset Formula \[
17210 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17214 It is also possible to set the formula in a
17216 boldmath environment
17219 This environment is created by inserting the command
17224 \begin_inset LatexCommand index
17225 name "Commands ! B ! \\textbackslash boldmath"
17232 To end the environment, the command
17237 \begin_inset LatexCommand index
17238 name "Commands ! U ! \\textbackslash unboldmath"
17244 is inserted in TeX-mode.
17248 \begin_layout Standard
17258 \begin_inset Formula \[
17259 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17267 \begin_layout Standard
17279 \begin_layout Subsection
17281 \begin_inset LatexCommand label
17282 name "sub:Font-Sizes"
17287 \begin_inset LatexCommand index
17295 \begin_layout Standard
17296 For characters in formulas there are, analog to characters in text, the
17297 following size commands:
17300 \begin_layout Standard
17364 \begin_layout Standard
17365 The size produced by the commands depends on the document font size, that
17366 corresponds with the command
17373 The other commands produce smaller or larger sizes than
17380 The font size can however not exceed a certain value.
17381 Is for example the document font size 12\InsetSpace \thinspace{}
17388 switches to the same size as
17398 \begin_layout Standard
17399 A size command is inserted in TeX-mode before the formula and sets the size
17400 for all following formula and text characters.
17401 To switch back to the initial size, the command
17407 is inserted behind the formula in TeX-mode.
17410 \begin_layout Standard
17411 Within a formula the size can only be changed for symbols or letters in
17413 To do this, the size command is inserted in mathematical text.
17414 All following characters until the end of the mathematical text or until
17415 another size command will have the selected size.
17417 \begin_inset VSpace -2mm
17423 \begin_layout Standard
17427 \begin_layout Standard
17437 \begin_inset Formula \[
17438 A=\frac{B}{c}\cdot\maltese\]
17443 \begin_inset Formula \[
17444 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17452 \begin_layout Standard
17464 \begin_layout Standard
17465 \begin_inset VSpace medskip
17468 Before both formulas the command
17475 The command for the second formula is:
17485 \begin_layout Standard
17500 \begin_layout Standard
17515 \begin_layout Standard
17530 \begin_layout Standard
17540 \begin_inset Formula $\to$
17544 \begin_inset Formula $\to$
17553 \begin_layout Standard
17572 \begin_layout Standard
17587 \begin_layout Standard
17602 \begin_layout Standard
17614 \begin_layout Standard
17615 If a symbol cannot be displayed in different sizes, it will always be displayed
17616 in the default size.
17619 \begin_layout Section
17621 \begin_inset LatexCommand index
17622 name "Greek letters"
17629 \begin_layout Standard
17630 All Greek letters can also be inserted via the toolbar button
17631 \begin_inset Graphics
17632 filename ../images/math/alpha.png
17640 \begin_layout Subsection
17642 \begin_inset LatexCommand label
17643 name "sub:Small-Letters"
17648 \begin_inset LatexCommand index
17649 name "Greek letters ! small"
17656 \begin_layout Standard
17660 \begin_inset Tabular
17661 <lyxtabular version="3" rows="11" columns="2">
17663 <column alignment="center" valignment="top" leftline="true" width="0pt">
17664 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17665 <row topline="true" bottomline="true">
17666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17669 \begin_layout Standard
17675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17678 \begin_layout Standard
17685 <row topline="true">
17686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17689 \begin_layout Standard
17697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17700 \begin_layout Standard
17701 \begin_inset Formula $\alpha$
17710 <row topline="true">
17711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17714 \begin_layout Standard
17722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17725 \begin_layout Standard
17726 \begin_inset Formula $\beta$
17735 <row topline="true">
17736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17739 \begin_layout Standard
17747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Standard
17751 \begin_inset Formula $\gamma$
17760 <row topline="true">
17761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17764 \begin_layout Standard
17772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17775 \begin_layout Standard
17776 \begin_inset Formula $\delta$
17785 <row topline="true">
17786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17789 \begin_layout Standard
17797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Standard
17801 \begin_inset Formula $\epsilon$
17810 <row topline="true">
17811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17814 \begin_layout Standard
17822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17825 \begin_layout Standard
17826 \begin_inset Formula $\varepsilon$
17835 <row topline="true">
17836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17839 \begin_layout Standard
17847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17850 \begin_layout Standard
17851 \begin_inset Formula $\zeta$
17860 <row topline="true">
17861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17864 \begin_layout Standard
17872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17875 \begin_layout Standard
17876 \begin_inset Formula $\eta$
17885 <row topline="true">
17886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17889 \begin_layout Standard
17897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17900 \begin_layout Standard
17901 \begin_inset Formula $\theta$
17910 <row topline="true" bottomline="true">
17911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17914 \begin_layout Standard
17922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17925 \begin_layout Standard
17926 \begin_inset Formula $\vartheta$
17942 \begin_inset Tabular
17943 <lyxtabular version="3" rows="12" columns="2">
17945 <column alignment="center" valignment="top" leftline="true" width="0pt">
17946 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17947 <row topline="true" bottomline="true">
17948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17951 \begin_layout Standard
17957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17960 \begin_layout Standard
17967 <row topline="true">
17968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17971 \begin_layout Standard
17979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17982 \begin_layout Standard
17983 \begin_inset Formula $\iota$
17992 <row topline="true">
17993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17996 \begin_layout Standard
18004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18007 \begin_layout Standard
18008 \begin_inset Formula $\kappa$
18017 <row topline="true">
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18021 \begin_layout Standard
18029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18032 \begin_layout Standard
18033 \begin_inset Formula $\varkappa$
18042 <row topline="true">
18043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18046 \begin_layout Standard
18054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18057 \begin_layout Standard
18058 \begin_inset Formula $\lambda$
18067 <row topline="true">
18068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18071 \begin_layout Standard
18079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18082 \begin_layout Standard
18083 \begin_inset Formula $\mu$
18092 <row topline="true">
18093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18096 \begin_layout Standard
18104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18107 \begin_layout Standard
18108 \begin_inset Formula $\nu$
18117 <row topline="true">
18118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18121 \begin_layout Standard
18129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18132 \begin_layout Standard
18133 \begin_inset Formula $\xi$
18142 <row topline="true">
18143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18146 \begin_layout Standard
18152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18155 \begin_layout Standard
18156 \begin_inset Formula $o$
18165 <row topline="true">
18166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18169 \begin_layout Standard
18177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18180 \begin_layout Standard
18181 \begin_inset Formula $\pi$
18190 <row topline="true">
18191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18194 \begin_layout Standard
18202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18205 \begin_layout Standard
18206 \begin_inset Formula $\varpi$
18215 <row topline="true" bottomline="true">
18216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18219 \begin_layout Standard
18227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18230 \begin_layout Standard
18231 \begin_inset Formula $\rho$
18247 \begin_inset Tabular
18248 <lyxtabular version="3" rows="11" columns="2">
18250 <column alignment="center" valignment="top" leftline="true" width="0pt">
18251 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18252 <row topline="true" bottomline="true">
18253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18256 \begin_layout Standard
18262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18265 \begin_layout Standard
18272 <row topline="true">
18273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18276 \begin_layout Standard
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18287 \begin_layout Standard
18288 \begin_inset Formula $\varrho$
18297 <row topline="true">
18298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18301 \begin_layout Standard
18309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18312 \begin_layout Standard
18313 \begin_inset Formula $\sigma$
18322 <row topline="true">
18323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18326 \begin_layout Standard
18334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18337 \begin_layout Standard
18338 \begin_inset Formula $\varsigma$
18347 <row topline="true">
18348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18351 \begin_layout Standard
18359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18362 \begin_layout Standard
18363 \begin_inset Formula $\tau$
18372 <row topline="true">
18373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18376 \begin_layout Standard
18384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18387 \begin_layout Standard
18388 \begin_inset Formula $\upsilon$
18397 <row topline="true">
18398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18401 \begin_layout Standard
18409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18412 \begin_layout Standard
18413 \begin_inset Formula $\phi$
18422 <row topline="true">
18423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18426 \begin_layout Standard
18434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18437 \begin_layout Standard
18438 \begin_inset Formula $\varphi$
18447 <row topline="true">
18448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18451 \begin_layout Standard
18459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18462 \begin_layout Standard
18463 \begin_inset Formula $\chi$
18472 <row topline="true">
18473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18476 \begin_layout Standard
18484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18487 \begin_layout Standard
18488 \begin_inset Formula $\psi$
18497 <row topline="true" bottomline="true">
18498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18501 \begin_layout Standard
18509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18512 \begin_layout Standard
18513 \begin_inset Formula $\omega$
18531 \begin_layout Standard
18532 \begin_inset VSpace medskip
18538 \begin_layout Standard
18539 How to create upright Greek letters is explained in
18540 \begin_inset LatexCommand ref
18541 reference "sub:Upright-small-Greek"
18548 \begin_layout Subsection
18550 \begin_inset LatexCommand index
18551 name "Greek letters ! big"
18558 \begin_layout Standard
18562 \begin_inset Tabular
18563 <lyxtabular version="3" rows="7" columns="2">
18565 <column alignment="center" valignment="top" leftline="true" width="0pt">
18566 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18567 <row topline="true" bottomline="true">
18568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18571 \begin_layout Standard
18577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18580 \begin_layout Standard
18587 <row topline="true">
18588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18591 \begin_layout Standard
18599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18602 \begin_layout Standard
18603 \begin_inset Formula $\Gamma$
18612 <row topline="true">
18613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18616 \begin_layout Standard
18624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18627 \begin_layout Standard
18628 \begin_inset Formula $\Delta$
18637 <row topline="true">
18638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18641 \begin_layout Standard
18649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18652 \begin_layout Standard
18653 \begin_inset Formula $\Theta$
18662 <row topline="true">
18663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18666 \begin_layout Standard
18674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18677 \begin_layout Standard
18678 \begin_inset Formula $\Lambda$
18687 <row topline="true">
18688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18691 \begin_layout Standard
18699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18702 \begin_layout Standard
18703 \begin_inset Formula $\Xi$
18712 <row topline="true" bottomline="true">
18713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18716 \begin_layout Standard
18724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18727 \begin_layout Standard
18728 \begin_inset Formula $\Pi$
18744 \begin_inset Tabular
18745 <lyxtabular version="3" rows="6" columns="2">
18747 <column alignment="center" valignment="top" leftline="true" width="0pt">
18748 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18749 <row topline="true" bottomline="true">
18750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18753 \begin_layout Standard
18759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18762 \begin_layout Standard
18769 <row topline="true">
18770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18773 \begin_layout Standard
18781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18784 \begin_layout Standard
18785 \begin_inset Formula $\Sigma$
18794 <row topline="true">
18795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18798 \begin_layout Standard
18806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18809 \begin_layout Standard
18810 \begin_inset Formula $\Upsilon$
18819 <row topline="true">
18820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18823 \begin_layout Standard
18831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18834 \begin_layout Standard
18835 \begin_inset Formula $\Phi$
18844 <row topline="true">
18845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18848 \begin_layout Standard
18856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18859 \begin_layout Standard
18860 \begin_inset Formula $\Psi$
18869 <row topline="true" bottomline="true">
18870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18873 \begin_layout Standard
18881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18884 \begin_layout Standard
18885 \begin_inset Formula $\Omega$
18903 \begin_layout Standard
18904 \begin_inset VSpace medskip
18907 That the big Greek letters appear upright is caused by a design bug when
18909 To get correct italic big letters, begin every command with
18914 For example the command
18921 \begin_inset Formula $\varGamma$
18927 \begin_layout Subsection
18929 \begin_inset LatexCommand index
18930 name "Greek letters ! bold"
18937 \begin_layout Standard
18938 Greek letters cannot be set with different font styles like Latin letters.
18939 They can only be made bold with the command
18946 \begin_inset LatexCommand index
18947 name "Commands ! B ! \\textbackslash boldsymbol"
18954 \begin_layout Standard
18956 \begin_inset Tabular
18957 <lyxtabular version="3" rows="3" columns="2">
18959 <column alignment="center" valignment="top" leftline="true" width="0">
18960 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
18961 <row topline="true" bottomline="true">
18962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18965 \begin_layout Standard
18971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18974 \begin_layout Standard
18981 <row topline="true">
18982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18985 \begin_layout Standard
18997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19000 \begin_layout Standard
19001 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19010 <row topline="true" bottomline="true">
19011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19014 \begin_layout Standard
19026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19029 \begin_layout Standard
19030 \begin_inset Formula $\theta\boldsymbol{\theta}$
19046 \begin_layout Section
19051 \begin_layout Standard
19064 \begin_layout Standard
19065 A list with all symbols of most of the LaTeX-packages can be found in
19066 \begin_inset LatexCommand cite
19080 \begin_layout Standard
19088 \begin_inset Note Note
19091 \begin_layout Standard
19094 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19097 \begin_layout Standard
19100 texorpdfstring is in section
19101 \begin_inset LatexCommand ref
19102 reference "sub:Formulas-in-Section"
19112 \begin_inset LatexCommand index
19120 \begin_layout Standard
19121 Many of the symbols listed in this section can also be inserted via the
19123 \begin_inset Graphics
19124 filename ../images/math/nabla.png
19130 \begin_inset Graphics
19131 filename ../images/math/digamma.png
19139 \begin_layout Subsection
19140 Mathematical Symbols
19141 \begin_inset LatexCommand label
19142 name "sub:Mathematical-Symbols"
19147 \begin_inset LatexCommand index
19148 name "Symbols ! mathematical"
19155 \begin_layout Standard
19159 \begin_inset Tabular
19160 <lyxtabular version="3" rows="10" columns="2">
19162 <column alignment="center" valignment="top" leftline="true" width="0pt">
19163 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19164 <row topline="true" bottomline="true">
19165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19168 \begin_layout Standard
19174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19177 \begin_layout Standard
19184 <row topline="true">
19185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19188 \begin_layout Standard
19196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19199 \begin_layout Standard
19200 \begin_inset Formula $\neg$
19209 <row topline="true">
19210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19213 \begin_layout Standard
19221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Standard
19225 \begin_inset Formula $\Im$
19234 <row topline="true">
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19238 \begin_layout Standard
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Standard
19250 \begin_inset Formula $\Re$
19259 <row topline="true">
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19263 \begin_layout Standard
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Standard
19275 \begin_inset Formula $\aleph$
19284 <row topline="true">
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19288 \begin_layout Standard
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Standard
19300 \begin_inset Formula $\partial$
19309 <row topline="true">
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19313 \begin_layout Standard
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Standard
19325 \begin_inset Formula $\infty$
19334 <row topline="true" bottomline="true">
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19338 \begin_layout Standard
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19349 \begin_layout Standard
19350 \begin_inset Formula $\wp$
19359 <row bottomline="true">
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19363 \begin_layout Standard
19371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19374 \begin_layout Standard
19375 \begin_inset Formula $\imath$
19384 <row bottomline="true">
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19388 \begin_layout Standard
19396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19399 \begin_layout Standard
19400 \begin_inset Formula $\jmath$
19416 \begin_inset Tabular
19417 <lyxtabular version="3" rows="10" columns="2">
19419 <column alignment="center" valignment="top" leftline="true" width="0pt">
19420 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19421 <row topline="true" bottomline="true">
19422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19425 \begin_layout Standard
19431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19434 \begin_layout Standard
19436 \begin_inset Note Note
19439 \begin_layout Standard
19446 is only used as spacer.
19457 <row topline="true">
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Standard
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Standard
19473 \begin_inset Formula $\forall$
19482 <row topline="true">
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19486 \begin_layout Standard
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Standard
19498 \begin_inset Formula $\exists$
19507 <row topline="true">
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Standard
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Standard
19523 \begin_inset Formula $\nexists$
19532 <row topline="true">
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Standard
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Standard
19548 \begin_inset Formula $\emptyset$
19557 <row topline="true">
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Standard
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Standard
19573 \begin_inset Formula $\varnothing$
19582 <row topline="true">
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Standard
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Standard
19598 \begin_inset Formula $\dag$
19607 <row topline="true" bottomline="true">
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19611 \begin_layout Standard
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Standard
19623 \begin_inset Formula $\ddag$
19632 <row bottomline="true">
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19636 \begin_layout Standard
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19647 \begin_layout Standard
19651 \begin_layout Standard
19661 \begin_inset Formula $\complement$
19668 \begin_layout Standard
19681 <row bottomline="true">
19682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19685 \begin_layout Standard
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19696 \begin_layout Standard
19697 \begin_inset Formula $\Bbbk$
19713 \begin_inset Tabular
19714 <lyxtabular version="3" rows="10" columns="2">
19716 <column alignment="center" valignment="top" leftline="true" width="0pt">
19717 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19718 <row topline="true" bottomline="true">
19719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19722 \begin_layout Standard
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Standard
19738 <row topline="true">
19739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19742 \begin_layout Standard
19750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19753 \begin_layout Standard
19754 \begin_inset Formula $\prime$
19763 <row topline="true">
19764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19767 \begin_layout Standard
19775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19778 \begin_layout Standard
19779 \begin_inset Formula $\backprime$
19788 <row topline="true">
19789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19792 \begin_layout Standard
19800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19803 \begin_layout Standard
19804 \begin_inset Formula $\mho$
19813 <row topline="true">
19814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19817 \begin_layout Standard
19825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19828 \begin_layout Standard
19829 \begin_inset Formula $\triangle$
19838 <row topline="true">
19839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19842 \begin_layout Standard
19850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19853 \begin_layout Standard
19854 \begin_inset Formula $\angle$
19863 <row topline="true">
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19867 \begin_layout Standard
19875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19878 \begin_layout Standard
19879 \begin_inset Formula $\measuredangle$
19888 <row topline="true" bottomline="true">
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19892 \begin_layout Standard
19900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19903 \begin_layout Standard
19904 \begin_inset Formula $\sphericalangle$
19913 <row bottomline="true">
19914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19917 \begin_layout Standard
19925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19928 \begin_layout Standard
19929 \begin_inset Formula $\top$
19938 <row bottomline="true">
19939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19942 \begin_layout Standard
19950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19953 \begin_layout Standard
19954 \begin_inset Formula $\bot$
19972 \begin_layout Standard
19978 \begin_layout Subsection
19979 Miscellaneous Symbols
19980 \begin_inset LatexCommand label
19981 name "sub:Miscellaneous-Symbols"
19986 \begin_inset LatexCommand index
19987 name "Symbols ! miscellaneous"
19994 \begin_layout Standard
19995 \begin_inset Tabular
19996 <lyxtabular version="3" rows="10" columns="2">
19998 <column alignment="center" valignment="top" leftline="true" width="0pt">
19999 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20000 <row topline="true" bottomline="true">
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20004 \begin_layout Standard
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Standard
20020 <row topline="true">
20021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20024 \begin_layout Standard
20032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20035 \begin_layout Standard
20036 \begin_inset Formula $\flat$
20045 <row topline="true">
20046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20049 \begin_layout Standard
20057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20060 \begin_layout Standard
20061 \begin_inset Formula $\natural$
20070 <row topline="true">
20071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20074 \begin_layout Standard
20082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20085 \begin_layout Standard
20086 \begin_inset Formula $\sharp$
20095 <row topline="true" bottomline="true">
20096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20099 \begin_layout Standard
20107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20110 \begin_layout Standard
20111 \begin_inset Formula $\surd$
20120 <row bottomline="true">
20121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20124 \begin_layout Standard
20132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20135 \begin_layout Standard
20136 \begin_inset Formula $\checkmark$
20145 <row bottomline="true">
20146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20149 \begin_layout Standard
20157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20160 \begin_layout Standard
20161 \begin_inset Formula $\yen$
20170 <row bottomline="true">
20171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20174 \begin_layout Standard
20182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20185 \begin_layout Standard
20186 \begin_inset Formula $\pounds$
20195 <row bottomline="true">
20196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20199 \begin_layout Standard
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20208 \begin_layout Standard
20209 \begin_inset Formula $\$$
20218 <row bottomline="true">
20219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20222 \begin_layout Standard
20228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Standard
20232 \begin_inset Formula $§$
20246 \begin_inset Tabular
20247 <lyxtabular version="3" rows="10" columns="2">
20249 <column alignment="center" valignment="top" leftline="true" width="0">
20250 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20251 <row topline="true" bottomline="true">
20252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20255 \begin_layout Standard
20261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20264 \begin_layout Standard
20271 <row topline="true">
20272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20275 \begin_layout Standard
20283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20286 \begin_layout Standard
20287 \begin_inset Formula $\hbar$
20296 <row topline="true">
20297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20300 \begin_layout Standard
20308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20311 \begin_layout Standard
20312 \begin_inset Formula $\hslash$
20321 <row topline="true">
20322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20325 \begin_layout Standard
20333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Standard
20337 \begin_inset Formula $\clubsuit$
20346 <row topline="true">
20347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20350 \begin_layout Standard
20358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20361 \begin_layout Standard
20362 \begin_inset Formula $\spadesuit$
20371 <row topline="true">
20372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20375 \begin_layout Standard
20383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20386 \begin_layout Standard
20387 \begin_inset Formula $\bigstar$
20396 <row topline="true">
20397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20400 \begin_layout Standard
20408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20411 \begin_layout Standard
20412 \begin_inset Formula $\blacklozenge$
20421 <row topline="true">
20422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20425 \begin_layout Standard
20433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20436 \begin_layout Standard
20437 \begin_inset Formula $\blacktriangle$
20446 <row topline="true">
20447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20450 \begin_layout Standard
20458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20461 \begin_layout Standard
20462 \begin_inset Formula $\blacktriangledown$
20471 <row topline="true" bottomline="true">
20472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20475 \begin_layout Standard
20483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20486 \begin_layout Standard
20487 \begin_inset Formula $\bullet$
20501 \begin_inset Tabular
20502 <lyxtabular version="3" rows="10" columns="2">
20504 <column alignment="center" valignment="top" leftline="true" width="0pt">
20505 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20506 <row topline="true" bottomline="true">
20507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20510 \begin_layout Standard
20516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Standard
20526 <row topline="true">
20527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20530 \begin_layout Standard
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20541 \begin_layout Standard
20542 \begin_inset Formula $\diamondsuit$
20551 <row topline="true">
20552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20555 \begin_layout Standard
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20566 \begin_layout Standard
20567 \begin_inset Formula $\Diamond$
20576 <row topline="true">
20577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20580 \begin_layout Standard
20588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Standard
20592 \begin_inset Formula $\heartsuit$
20601 <row topline="true" bottomline="true">
20602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20605 \begin_layout Standard
20613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20616 \begin_layout Standard
20617 \begin_inset Formula $\P$
20626 <row bottomline="true">
20627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20630 \begin_layout Standard
20638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20641 \begin_layout Standard
20642 \begin_inset Formula $\copyright$
20651 <row bottomline="true">
20652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20655 \begin_layout Standard
20663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20666 \begin_layout Standard
20667 \begin_inset Formula $\circledR$
20676 <row bottomline="true">
20677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20680 \begin_layout Standard
20688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20691 \begin_layout Standard
20692 \begin_inset Formula $\maltese$
20701 <row bottomline="true">
20702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20705 \begin_layout Standard
20713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20716 \begin_layout Standard
20717 \begin_inset Formula $\diagup$
20726 <row bottomline="true">
20727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20730 \begin_layout Standard
20738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20741 \begin_layout Standard
20742 \begin_inset Formula $\diagdown$
20758 \begin_layout Standard
20759 \begin_inset VSpace medskip
20762 More symbols are listed in
20763 \begin_inset LatexCommand ref
20764 reference "sub:Miscellaneous-Special-Characters"
20771 \begin_layout Standard
20772 Some symbols can be displayed in different sizes, see
20773 \begin_inset LatexCommand ref
20774 reference "sub:Font-Sizes"
20781 \begin_layout Subsection
20783 \begin_inset LatexCommand index
20784 name "Symbols ! Euro-symbol"
20789 \begin_inset LatexCommand index
20790 name "\\textcent@\\officialeuro"
20797 \begin_layout Standard
20798 To use the Euro symbol in formulas, the LaTeX-package
20803 \begin_inset LatexCommand index
20804 name "Packages ! eurosym"
20808 must be installed and loaded with the LaTeX-preamble line
20811 \begin_layout Standard
20816 usepackage[gennarrow]{eurosym}
20819 \begin_layout Standard
20820 The Euro symbol can now be inserted with the command
20827 \begin_inset LatexCommand index
20828 name "Commands ! E ! \\textbackslash euro"
20835 \begin_layout Standard
20836 The Euro symbol can directly be inserted with the € key in mathematical
20837 text, without having
20852 can also be inserted in TeX-mode.
20853 The official currency symbol can then be inserted with the command
20860 \begin_inset LatexCommand index
20861 name "Commands ! O ! \\textbackslash officialeuro"
20865 , that is only available in TeX-mode.
20868 \begin_layout Standard
20872 \begin_layout Standard
20882 \begin_inset Note Note
20885 \begin_layout Standard
20886 The following table will only be displayed when the LaTeX-package
20898 \begin_layout Standard
20899 An overview about the different Euro symbols:
20902 \begin_layout Standard
20904 \begin_inset Tabular
20905 <lyxtabular version="3" rows="4" columns="3">
20907 <column alignment="center" valignment="top" leftline="true" width="0pt">
20908 <column alignment="center" valignment="top" leftline="true" width="0pt">
20909 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20910 <row topline="true" bottomline="true">
20911 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20914 \begin_layout Standard
20920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20923 \begin_layout Standard
20929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20932 \begin_layout Standard
20939 <row topline="true">
20940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20943 \begin_layout Standard
20949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20952 \begin_layout Standard
20960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20963 \begin_layout Standard
20964 \begin_inset Formula $\euro$
20973 <row topline="true">
20974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20977 \begin_layout Standard
20983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20986 \begin_layout Standard
20992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20995 \begin_layout Standard
20996 \begin_inset Formula $\mbox{€}$
21005 <row topline="true" bottomline="true">
21006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21009 \begin_layout Standard
21015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21018 \begin_layout Standard
21026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21029 \begin_layout Standard
21033 \begin_layout Standard
21055 \begin_layout Standard
21059 \begin_layout Standard
21069 \begin_inset Note Note
21072 \begin_layout Standard
21073 The following will be displayed when the LaTeX-package
21085 \begin_layout Standard
21086 You need to install the LaTeX-package
21090 to see the rest of this subsection in the output.
21093 \begin_layout Standard
21097 \begin_layout Standard
21109 \begin_layout Section
21111 \begin_inset LatexCommand label
21112 name "sec:Relations"
21117 \begin_inset LatexCommand index
21123 \begin_inset LatexCommand index
21124 name "Comparisons|see{Relations}"
21131 \begin_layout Standard
21132 All relations can also be inserted via the toolbar button
21133 \begin_inset Graphics
21134 filename ../images/math/leq.png
21142 \begin_layout Standard
21146 \begin_inset Tabular
21147 <lyxtabular version="3" rows="17" columns="2">
21149 <column alignment="center" valignment="top" leftline="true" width="0pt">
21150 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21151 <row topline="true" bottomline="true">
21152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21155 \begin_layout Standard
21161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21164 \begin_layout Standard
21171 <row topline="true">
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21175 \begin_layout Standard
21181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21184 \begin_layout Standard
21185 \begin_inset Formula $<$
21194 <row topline="true">
21195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21198 \begin_layout Standard
21206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21209 \begin_layout Standard
21210 \begin_inset Formula $\le$
21219 <row topline="true">
21220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21223 \begin_layout Standard
21231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21234 \begin_layout Standard
21235 \begin_inset Formula $\ll$
21244 <row topline="true">
21245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21248 \begin_layout Standard
21256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21259 \begin_layout Standard
21260 \begin_inset Formula $\prec$
21269 <row topline="true">
21270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21273 \begin_layout Standard
21281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21284 \begin_layout Standard
21285 \begin_inset Formula $\preceq$
21294 <row topline="true">
21295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21298 \begin_layout Standard
21306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Standard
21310 \begin_inset Formula $\subset$
21319 <row topline="true">
21320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21323 \begin_layout Standard
21331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Standard
21335 \begin_inset Formula $\subseteq$
21344 <row topline="true">
21345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21348 \begin_layout Standard
21356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21359 \begin_layout Standard
21360 \begin_inset Formula $\sqsubseteq$
21369 <row topline="true">
21370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21373 \begin_layout Standard
21381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21384 \begin_layout Standard
21385 \begin_inset Formula $\in$
21394 <row topline="true">
21395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21398 \begin_layout Standard
21406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Standard
21410 \begin_inset Formula $\vdash$
21419 <row topline="true">
21420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21423 \begin_layout Standard
21431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21434 \begin_layout Standard
21435 \begin_inset Formula $\smile$
21444 <row topline="true">
21445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21448 \begin_layout Standard
21456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21459 \begin_layout Standard
21460 \begin_inset Formula $\lhd$
21469 <row topline="true">
21470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21473 \begin_layout Standard
21481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21484 \begin_layout Standard
21485 \begin_inset Formula $\unlhd$
21494 <row topline="true">
21495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21498 \begin_layout Standard
21506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21509 \begin_layout Standard
21510 \begin_inset Formula $\gtrless$
21519 <row topline="true">
21520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21523 \begin_layout Standard
21531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21534 \begin_layout Standard
21535 \begin_inset Formula $\mid$
21544 <row topline="true" bottomline="true">
21545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21548 \begin_layout Standard
21556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21559 \begin_layout Standard
21560 \begin_inset Formula $\nmid$
21576 \begin_inset Tabular
21577 <lyxtabular version="3" rows="17" columns="2">
21579 <column alignment="center" valignment="top" leftline="true" width="0pt">
21580 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21581 <row topline="true" bottomline="true">
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21585 \begin_layout Standard
21591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Standard
21601 <row topline="true">
21602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21605 \begin_layout Standard
21611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Standard
21615 \begin_inset Formula $=$
21624 <row topline="true">
21625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21628 \begin_layout Standard
21636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21639 \begin_layout Standard
21640 \begin_inset Formula $\not=$
21649 <row topline="true">
21650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21653 \begin_layout Standard
21661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21664 \begin_layout Standard
21665 \begin_inset Formula $\equiv$
21674 <row topline="true">
21675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21678 \begin_layout Standard
21686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21689 \begin_layout Standard
21690 \begin_inset Formula $\sim$
21699 <row topline="true">
21700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21703 \begin_layout Standard
21711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21714 \begin_layout Standard
21715 \begin_inset Formula $\simeq$
21724 <row topline="true">
21725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21728 \begin_layout Standard
21736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21739 \begin_layout Standard
21740 \begin_inset Formula $\approx$
21749 <row topline="true">
21750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21753 \begin_layout Standard
21761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21764 \begin_layout Standard
21765 \begin_inset Formula $\cong$
21774 <row topline="true">
21775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21778 \begin_layout Standard
21786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21789 \begin_layout Standard
21790 \begin_inset Formula $\bowtie$
21799 <row topline="true">
21800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21803 \begin_layout Standard
21811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21814 \begin_layout Standard
21815 \begin_inset Formula $\notin$
21824 <row topline="true">
21825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21828 \begin_layout Standard
21836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21839 \begin_layout Standard
21840 \begin_inset Formula $\perp$
21849 <row topline="true">
21850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21853 \begin_layout Standard
21861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21864 \begin_layout Standard
21865 \begin_inset Formula $\propto$
21874 <row topline="true">
21875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21878 \begin_layout Standard
21886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21889 \begin_layout Standard
21890 \begin_inset Formula $\asymp$
21899 <row topline="true">
21900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21903 \begin_layout Standard
21911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21914 \begin_layout Standard
21915 \begin_inset Formula $\doteq$
21924 <row topline="true">
21925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21928 \begin_layout Standard
21936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21939 \begin_layout Standard
21940 \begin_inset Formula $\circeq$
21949 <row topline="true">
21950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21953 \begin_layout Standard
21961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21964 \begin_layout Standard
21965 \begin_inset Formula $\models$
21974 <row topline="true" bottomline="true">
21975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21978 \begin_layout Standard
21986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21989 \begin_layout Standard
21990 \begin_inset Formula $\widehat{=}$
22006 \begin_inset Tabular
22007 <lyxtabular version="3" rows="17" columns="2">
22009 <column alignment="center" valignment="top" leftline="true" width="0pt">
22010 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22011 <row topline="true" bottomline="true">
22012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22015 \begin_layout Standard
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22024 \begin_layout Standard
22031 <row topline="true">
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22035 \begin_layout Standard
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Standard
22045 \begin_inset Formula $>$
22054 <row topline="true">
22055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22058 \begin_layout Standard
22066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Standard
22070 \begin_inset Formula $\ge$
22079 <row topline="true">
22080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22083 \begin_layout Standard
22091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Standard
22095 \begin_inset Formula $\gg$
22104 <row topline="true">
22105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22108 \begin_layout Standard
22116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22119 \begin_layout Standard
22120 \begin_inset Formula $\succ$
22129 <row topline="true">
22130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22133 \begin_layout Standard
22141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22144 \begin_layout Standard
22145 \begin_inset Formula $\succeq$
22154 <row topline="true">
22155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22158 \begin_layout Standard
22166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22169 \begin_layout Standard
22170 \begin_inset Formula $\supset$
22179 <row topline="true">
22180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22183 \begin_layout Standard
22191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22194 \begin_layout Standard
22195 \begin_inset Formula $\supseteq$
22204 <row topline="true">
22205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22208 \begin_layout Standard
22216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22219 \begin_layout Standard
22220 \begin_inset Formula $\sqsupseteq$
22229 <row topline="true">
22230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22233 \begin_layout Standard
22241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22244 \begin_layout Standard
22245 \begin_inset Formula $\ni$
22254 <row topline="true">
22255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22258 \begin_layout Standard
22266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22269 \begin_layout Standard
22270 \begin_inset Formula $\dashv$
22279 <row topline="true">
22280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22283 \begin_layout Standard
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22294 \begin_layout Standard
22295 \begin_inset Formula $\frown$
22304 <row topline="true">
22305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22308 \begin_layout Standard
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22319 \begin_layout Standard
22320 \begin_inset Formula $\rhd$
22329 <row topline="true">
22330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22333 \begin_layout Standard
22341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22344 \begin_layout Standard
22345 \begin_inset Formula $\unrhd$
22354 <row topline="true">
22355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22358 \begin_layout Standard
22366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22369 \begin_layout Standard
22370 \begin_inset Formula $\lessgtr$
22379 <row topline="true">
22380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22383 \begin_layout Standard
22391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22394 \begin_layout Standard
22395 \begin_inset Formula $\parallel$
22404 <row topline="true" bottomline="true">
22405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22408 \begin_layout Standard
22416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22419 \begin_layout Standard
22420 \begin_inset Formula $\nparallel$
22438 \begin_layout Standard
22439 \begin_inset VSpace medskip
22454 are bigger than the equal looking operators
22469 \begin_layout Standard
22470 Relations are, in contrary to symbols, always surrounded by space.
22473 \begin_layout Standard
22474 Relations with labels can be created with the command
22481 \begin_inset LatexCommand index
22482 name "Commands ! S ! \\textbackslash stackrel"
22489 \begin_layout Standard
22491 \begin_inset Tabular
22492 <lyxtabular version="3" rows="2" columns="2">
22494 <column alignment="center" valignment="top" leftline="true" width="0">
22495 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22496 <row topline="true" bottomline="true">
22497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22500 \begin_layout Standard
22506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22509 \begin_layout Standard
22511 \begin_inset Note Note
22514 \begin_layout Standard
22521 is only used as spacer.
22532 <row topline="true" bottomline="true">
22533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22536 \begin_layout Standard
22543 \begin_layout Standard
22560 \begin_layout Standard
22570 \begin_inset Formula $\downarrow$
22579 \begin_layout Standard
22592 \begin_layout Standard
22606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22609 \begin_layout Standard
22610 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22626 \begin_layout Section
22630 \begin_layout Subsection
22631 Predefined Functions
22632 \begin_inset LatexCommand label
22633 name "sub:Predefined-Functions"
22638 \begin_inset LatexCommand index
22639 name "Functions ! predefined"
22646 \begin_layout Standard
22647 In general, variables are set
22651 in mathematical expressions, but not function names, because
22652 \begin_inset Formula $sin$
22655 could be misunderstood as
22656 \begin_inset Formula $s\cdot i\cdot n$
22660 Therefore there are predefined functions, that are additionally a bit separated
22662 They are inserted as commands starting with a backslash before their name.
22665 \begin_layout Standard
22667 \begin_inset Tabular
22668 <lyxtabular version="3" rows="2" columns="4">
22670 <column alignment="center" valignment="top" leftline="true" width="0pt">
22671 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22672 <column alignment="center" valignment="top" leftline="true" width="0pt">
22673 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22674 <row topline="true" bottomline="true">
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22678 \begin_layout Standard
22684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Standard
22693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22696 \begin_layout Standard
22702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22705 \begin_layout Standard
22712 <row topline="true" bottomline="true">
22713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22716 \begin_layout Standard
22722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22725 \begin_layout Standard
22726 \begin_inset Formula $Asin(x)+B$
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22737 \begin_layout Standard
22745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22748 \begin_layout Standard
22749 \begin_inset Formula $A\sin(x)+B$
22766 \begin_layout Standard
22778 \begin_layout Standard
22779 The following functions are predefined:
22782 \begin_layout Standard
22783 \begin_inset VSpace -2mm
22789 \begin_layout Standard
22791 \begin_inset Tabular
22792 <lyxtabular version="3" rows="9" columns="4">
22794 <column alignment="center" valignment="top" leftline="true" width="0pt">
22795 <column alignment="center" valignment="top" leftline="true" width="0pt">
22796 <column alignment="center" valignment="top" leftline="true" width="0pt">
22797 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22798 <row topline="true" bottomline="true">
22799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22802 \begin_layout Standard
22808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22811 \begin_layout Standard
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22820 \begin_layout Standard
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22829 \begin_layout Standard
22836 <row topline="true">
22837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22840 \begin_layout Standard
22848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22851 \begin_layout Standard
22859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22862 \begin_layout Standard
22870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22873 \begin_layout Standard
22882 <row topline="true">
22883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22886 \begin_layout Standard
22894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22897 \begin_layout Standard
22905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22908 \begin_layout Standard
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22919 \begin_layout Standard
22928 <row topline="true">
22929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22932 \begin_layout Standard
22940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22943 \begin_layout Standard
22951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22954 \begin_layout Standard
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22965 \begin_layout Standard
22974 <row topline="true">
22975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22978 \begin_layout Standard
22986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22989 \begin_layout Standard
22997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23000 \begin_layout Standard
23008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23011 \begin_layout Standard
23020 <row topline="true">
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23024 \begin_layout Standard
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23035 \begin_layout Standard
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23046 \begin_layout Standard
23054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23057 \begin_layout Standard
23066 <row topline="true">
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Standard
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23081 \begin_layout Standard
23089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23092 \begin_layout Standard
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23103 \begin_layout Standard
23112 <row topline="true">
23113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23116 \begin_layout Standard
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Standard
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23138 \begin_layout Standard
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Standard
23158 <row topline="true" bottomline="true">
23159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23162 \begin_layout Standard
23170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23173 \begin_layout Standard
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Standard
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23195 \begin_layout Standard
23211 \begin_layout Standard
23212 They can also be inserted with the math toolbar button
23213 \begin_inset Graphics
23214 filename ../images/math/functions.png
23222 \begin_layout Subsection
23223 Self-defined Functions
23224 \begin_inset LatexCommand index
23225 name "Functions ! self-defined"
23232 \begin_layout Standard
23233 To use a function that is not predefined, like for example the sign function
23234 sgn(x), there are two possibilities:
23237 \begin_layout Itemize
23238 Define the function by inserting the following line to the LaTeX-preamble
23242 \begin_layout Standard
23247 DeclareMathOperator
23250 \begin_inset LatexCommand ref
23251 reference "sub:Self-defined-Operators"
23263 \begin_inset VSpace -3mm
23272 DeclareMathOperator{
23277 \begin_inset LatexCommand index
23278 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23285 \begin_inset VSpace -2mm
23290 Now the new defined function can be called with the command
23299 \begin_layout Itemize
23300 Write the the formula as usual, mark the formula name, in our example the
23305 , and change it to mathematical text.
23306 At last a space is inserted between prefactor and function.
23309 \begin_layout Standard
23310 The result is the same with both methods as with a predefined function
23314 \begin_layout Standard
23315 In LyX self-defined functions are displayed red, predefined ones black.
23323 \begin_layout Standard
23325 \begin_inset Tabular
23326 <lyxtabular version="3" rows="3" columns="2">
23328 <column alignment="center" valignment="top" leftline="true" width="0pt">
23329 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23330 <row topline="true" bottomline="true">
23331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23334 \begin_layout Standard
23340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23343 \begin_layout Standard
23350 <row topline="true" bottomline="true">
23351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23354 \begin_layout Standard
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23365 \begin_layout Standard
23366 \begin_inset Formula $A\sgn(x)+B$
23375 <row topline="true" bottomline="true">
23376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23379 \begin_layout Standard
23383 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23394 \begin_layout Standard
23395 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23411 \begin_layout Standard
23412 The first method is more suitable when the self-defined function should
23413 be used several times.
23416 \begin_layout Subsection
23418 \begin_inset LatexCommand index
23426 \begin_layout Standard
23427 For limits there are defined besides
23434 \begin_inset LatexCommand index
23435 name "Commands ! L ! \\textbackslash lim"
23451 furthermore the following functions:
23454 \begin_layout Standard
23456 \begin_inset Tabular
23457 <lyxtabular version="3" rows="5" columns="2">
23459 <column alignment="center" valignment="top" leftline="true" width="0">
23460 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23461 <row topline="true" bottomline="true">
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Standard
23471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23474 \begin_layout Standard
23476 \begin_inset Note Note
23479 \begin_layout Standard
23486 is only used as spacer.
23497 <row topline="true">
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23501 \begin_layout Standard
23509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23512 \begin_layout Standard
23513 \begin_inset Formula $\varliminf$
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23526 \begin_layout Standard
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23537 \begin_layout Standard
23538 \begin_inset Formula $\varlimsup$
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23551 \begin_layout Standard
23559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23562 \begin_layout Standard
23563 \begin_inset Formula $\varprojlim$
23572 <row bottomline="true">
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23576 \begin_layout Standard
23584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23587 \begin_layout Standard
23588 \begin_inset Formula $\varinjlim$
23592 \begin_inset Formula $\raisebox{-2.5mm}{}$
23608 \begin_layout Standard
23609 \begin_inset VSpace medskip
23612 The limit is created by inserting a subscript.
23613 It is set right beside the function in an inline formula:
23616 \begin_layout Standard
23618 \begin_inset Tabular
23619 <lyxtabular version="3" rows="2" columns="2">
23621 <column alignment="center" valignment="top" width="0pt">
23622 <column alignment="center" valignment="top" width="0pt">
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23627 \begin_layout Standard
23633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23636 \begin_layout Standard
23640 \begin_layout Standard
23650 \begin_inset Note Note
23653 \begin_layout Standard
23666 are used here as spacer.
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Standard
23690 \begin_layout Standard
23703 \begin_layout Standard
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23720 \begin_layout Standard
23721 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23737 \begin_layout Standard
23738 In a displayed formula the limit is set below the formula, as usual:
23739 \begin_inset Formula \[
23747 \begin_layout Subsection
23749 \begin_inset LatexCommand index
23750 name "Functions ! modulo-"
23757 \begin_layout Standard
23758 The modulo-function is special, because it exists in four variants.
23761 \begin_layout Standard
23762 The variants in a displayed formula:
23763 \begin_inset Formula \begin{align*}
23764 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23765 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23766 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23767 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23768 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23775 \begin_layout Standard
23776 In an inline formula less space is set before the function names for all
23780 \begin_layout Section
23782 \begin_inset LatexCommand index
23783 name "Special characters"
23790 \begin_layout Subsection
23791 Special Characters in Mathematical Text
23794 \begin_layout Standard
23795 The following commands can only be used in mathematical text or in TeX-mode:
23798 \begin_layout Standard
23802 \begin_inset Tabular
23803 <lyxtabular version="3" rows="8" columns="2">
23805 <column alignment="block" valignment="top" leftline="true" width="0">
23806 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23807 <row topline="true" bottomline="true">
23808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23811 \begin_layout Standard
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Standard
23827 <row topline="true">
23828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23831 \begin_layout Standard
23839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23842 \begin_layout Standard
23843 \begin_inset Formula $\textrm{\oe}$
23852 <row topline="true">
23853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23856 \begin_layout Standard
23864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23867 \begin_layout Standard
23868 \begin_inset Formula $\textrm{\OE}$
23877 <row topline="true">
23878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23881 \begin_layout Standard
23889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23892 \begin_layout Standard
23893 \begin_inset Formula $\textrm{\ae}$
23902 <row topline="true">
23903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23906 \begin_layout Standard
23914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23917 \begin_layout Standard
23918 \begin_inset Formula $\textrm{\AE}$
23927 <row topline="true">
23928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23931 \begin_layout Standard
23939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23942 \begin_layout Standard
23943 \begin_inset Formula $\textrm{\aa}$
23952 <row topline="true" bottomline="true">
23953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23956 \begin_layout Standard
23960 \begin_inset LatexCommand index
23961 name "\\@\\textrm{\\AA}"
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Standard
23974 \begin_inset Formula $\textrm{\AA}$
23983 <row bottomline="true">
23984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23987 \begin_layout Standard
23995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Standard
23999 \begin_inset Formula $\textrm{\i}$
24015 \begin_inset Tabular
24016 <lyxtabular version="3" rows="8" columns="2">
24018 <column alignment="block" valignment="top" leftline="true" width="0">
24019 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24020 <row topline="true" bottomline="true">
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24024 \begin_layout Standard
24026 \begin_inset Note Note
24029 \begin_layout Standard
24036 is used for separation, because otherwise the output will be ¡ and ¿ respective
24047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24050 \begin_layout Standard
24057 <row topline="true">
24058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24061 \begin_layout Standard
24069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24072 \begin_layout Standard
24073 \begin_inset Formula $\textrm{\o}$
24082 <row topline="true">
24083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24086 \begin_layout Standard
24094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24097 \begin_layout Standard
24098 \begin_inset Formula $\textrm{\O}$
24107 <row topline="true">
24108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24111 \begin_layout Standard
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24122 \begin_layout Standard
24123 \begin_inset Formula $\textrm{\l}$
24132 <row topline="true">
24133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24136 \begin_layout Standard
24144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24147 \begin_layout Standard
24148 \begin_inset Formula $\textrm{\L}$
24157 <row topline="true" bottomline="true">
24158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24161 \begin_layout Standard
24166 \begin_layout Standard
24179 \begin_layout Standard
24193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24196 \begin_layout Standard
24197 \begin_inset Formula $\textrm{!`}$
24206 <row bottomline="true">
24207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24210 \begin_layout Standard
24215 \begin_layout Standard
24228 \begin_layout Standard
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24245 \begin_layout Standard
24246 \begin_inset Formula $\textrm{?`}$
24255 <row bottomline="true">
24256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24259 \begin_layout Standard
24267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Standard
24271 \begin_inset Formula $\textrm{\j}$
24289 \begin_layout Standard
24291 \begin_inset Formula $\textrm{\textrm{Å}}$
24295 \begin_inset Formula $\textrm{\textrm{Ø}}$
24298 can also be inserted via the math toolbar button
24299 \begin_inset Graphics
24300 filename ../images/math/digamma.png
24308 \begin_layout Standard
24309 An exception are the commands
24315 \begin_layout Standard
24332 \begin_layout Standard
24343 , because they can be inserted in LyX directly to text.
24346 \begin_layout Subsection
24348 \begin_inset LatexCommand label
24349 name "sub:Accents-in-Text"
24354 \begin_inset LatexCommand index
24355 name "Accents ! in text"
24362 \begin_layout Standard
24363 With the following commands all letters can be accented.
24364 The commands must be inserted in TeX-mode.
24367 \begin_layout Standard
24371 \begin_inset Tabular
24372 <lyxtabular version="3" rows="8" columns="2">
24374 <column alignment="block" valignment="top" leftline="true" width="0">
24375 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24376 <row topline="true" bottomline="true">
24377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24380 \begin_layout Standard
24386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24389 \begin_layout Standard
24396 <row topline="true">
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24400 \begin_layout Standard
24404 \begin_inset Quotes grd
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Standard
24419 \begin_layout Standard
24434 <row topline="true">
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24438 \begin_layout Standard
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24449 \begin_layout Standard
24453 \begin_layout Standard
24468 <row topline="true">
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Standard
24479 \begin_layout Standard
24493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24496 \begin_layout Standard
24500 \begin_layout Standard
24515 <row topline="true">
24516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24519 \begin_layout Standard
24527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24530 \begin_layout Standard
24534 \begin_layout Standard
24549 <row topline="true">
24550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24553 \begin_layout Standard
24560 \begin_layout Standard
24574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Standard
24581 \begin_layout Standard
24596 <row topline="true" bottomline="true">
24597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24600 \begin_layout Standard
24607 \begin_layout Standard
24621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24624 \begin_layout Standard
24628 \begin_layout Standard
24643 <row bottomline="true">
24644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24647 \begin_layout Standard
24654 \begin_layout Standard
24668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24671 \begin_layout Standard
24675 \begin_layout Standard
24697 \begin_inset Tabular
24698 <lyxtabular version="3" rows="8" columns="2">
24700 <column alignment="block" valignment="top" leftline="true" width="0">
24701 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24702 <row topline="true" bottomline="true">
24703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24706 \begin_layout Standard
24712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24715 \begin_layout Standard
24722 <row topline="true">
24723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24726 \begin_layout Standard
24733 \begin_layout Standard
24747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24750 \begin_layout Standard
24754 \begin_layout Standard
24769 <row topline="true">
24770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24773 \begin_layout Standard
24781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24784 \begin_layout Standard
24788 \begin_layout Standard
24803 <row topline="true">
24804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24807 \begin_layout Standard
24811 \begin_inset LatexCommand index
24821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24824 \begin_layout Standard
24828 \begin_layout Standard
24843 <row topline="true">
24844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24847 \begin_layout Standard
24855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24858 \begin_layout Standard
24862 \begin_layout Standard
24877 <row topline="true" bottomline="true">
24878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24881 \begin_layout Standard
24888 \begin_layout Standard
24902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24905 \begin_layout Standard
24909 \begin_layout Standard
24924 <row bottomline="true">
24925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24928 \begin_layout Standard
24935 \begin_layout Standard
24949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24952 \begin_layout Standard
24956 \begin_layout Standard
24971 <row bottomline="true">
24972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24975 \begin_layout Standard
24982 \begin_layout Standard
24996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24999 \begin_layout Standard
25003 \begin_layout Standard
25027 \begin_layout Standard
25028 \begin_inset VSpace medskip
25037 also two different characters can be accented.
25046 \begin_layout Standard
25061 \begin_layout Standard
25073 \begin_layout Standard
25086 can in combination with vowels directly be inserted with the keyboard without
25088 The same applies for the tilde
25092 \begin_layout Standard
25093 This only applies for keyboards where the tilde is defined as accent.
25102 in combination with
25117 \begin_layout Standard
25160 , and accents inserted directly with the keyboard are also available in
25162 For the other accents there are special math commands to be used in formulas,
25164 \begin_inset LatexCommand ref
25165 reference "sub:Accents-for-one"
25172 \begin_layout Standard
25173 \begin_inset VSpace bigskip
25176 Furthermore, with the command
25183 \begin_inset LatexCommand index
25184 name "Commands ! T ! \\textbackslash textcircled"
25188 all numbers and letters can be set into a circle, quasi accented with a
25189 circle, similar to the the copyright symbol.
25192 \begin_layout Standard
25194 \begin_inset Tabular
25195 <lyxtabular version="3" rows="3" columns="2">
25197 <column alignment="center" valignment="top" leftline="true" width="0">
25198 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25199 <row topline="true" bottomline="true">
25200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25203 \begin_layout Standard
25209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25212 \begin_layout Standard
25214 \begin_inset Note Note
25217 \begin_layout Standard
25224 is only used as spacer.
25235 <row topline="true">
25236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25239 \begin_layout Standard
25247 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25250 \begin_layout Standard
25254 \begin_layout Standard
25269 <row topline="true" bottomline="true">
25270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25273 \begin_layout Standard
25284 raisebox{-1.5pt}{W}}
25289 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25292 \begin_layout Standard
25293 \begin_inset Formula $\raisebox{4.5mm}{}$
25300 \begin_layout Standard
25318 \begin_inset Formula $\raisebox{-2mm}{}$
25334 \begin_layout Standard
25335 One has to take care that the character fits in the circle.
25346 \begin_layout Standard
25348 \begin_inset LatexCommand ref
25349 reference "sub:Font-Sizes"
25358 specifies thereby the size of the circle.
25369 \begin_layout Standard
25371 \begin_inset LatexCommand ref
25372 reference "sub:Boxes-without-Frame"
25381 the character can be centered.
25384 \begin_layout Subsection
25386 \begin_inset LatexCommand index
25387 name "Minuscule numbers"
25394 \begin_layout Standard
25395 Minuscule numbers are created with the command
25402 \begin_inset LatexCommand index
25403 name "Commands ! O ! \\textbackslash oldstylenums"
25408 The command can be used in formulas and in TeX-mode.
25409 The command scheme is:
25412 \begin_layout Standard
25417 oldstylenums{number}
25420 \begin_layout Standard
25425 oldstylenums{0123456789
25428 \begin_inset Formula $\oldstylenums{0123456789}$
25434 \begin_layout Subsection
25435 Miscellaneous Special Characters
25436 \begin_inset LatexCommand label
25437 name "sub:Miscellaneous-Special-Characters"
25442 \begin_inset LatexCommand index
25443 name "Special characters ! miscellaneous"
25450 \begin_layout Standard
25451 The following characters can only be inserted to formulas by using commands:
25454 \begin_layout Standard
25456 \begin_inset Tabular
25457 <lyxtabular version="3" rows="4" columns="2">
25459 <column alignment="center" valignment="top" leftline="true" width="0">
25460 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25461 <row topline="true" bottomline="true">
25462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25465 \begin_layout Standard
25471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25474 \begin_layout Standard
25481 <row topline="true">
25482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25485 \begin_layout Standard
25492 \begin_layout Standard
25506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25509 \begin_layout Standard
25510 \begin_inset Formula $\mathcircumflex$
25519 <row topline="true">
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25523 \begin_layout Standard
25531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25534 \begin_layout Standard
25535 \begin_inset Formula $\_$
25544 <row topline="true" bottomline="true">
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25548 \begin_layout Standard
25553 \begin_layout Standard
25565 \begin_inset LatexCommand index
25575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25578 \begin_layout Standard
25579 \begin_inset Formula $^{\circ}$
25595 \begin_layout Standard
25596 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25597 contains the following line
25601 \begin_layout Standard
25602 More about this is described in
25603 \begin_inset LatexCommand ref
25604 reference "sub:Text-Characters-in"
25616 \begin_layout Standard
25621 DeclareInputtext{176}{
25631 f\SpecialChar \textcompwordmark{}
25635 \begin_layout Standard
25636 \begin_inset VSpace bigskip
25640 \begin_inset LatexCommand index
25645 is designed as accent, thus is looks alone a bit misplaced: ~
25648 addresses (URLs) sometimes a single tilde is needed.
25649 In this case the relation sign
25657 \begin_layout Standard
25659 \begin_inset LatexCommand ref
25660 reference "sec:Relations"
25671 is used in a formula.
25672 As a formula cannot be created in an URL-box (menu
25674 Insert\SpecialChar \menuseparator
25677 ), the URL is inserted as normal text with the font style '
25682 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25692 \begin_layout Standard
25699 can only be used together with the LaTeX-package
25704 \begin_inset LatexCommand index
25705 name "Packages ! hyperref"
25716 is written in the section
25722 Embedded\InsetSpace ~
25731 \begin_inset LatexCommand index
25732 name "Commands ! H ! \\textbackslash href"
25739 \begin_layout Standard
25740 As example an URL with a tilde:
25743 \begin_layout Standard
25746 http://www.lyx.org/
25747 \begin_inset Formula $\sim$
25753 \begin_layout Standard
25764 \begin_layout Standard
25768 href{http://www.lyx.org/~mustermann}{
25773 http://www.lyx.org/
25774 \begin_inset Formula $\sim$
25781 \begin_layout Standard
25791 \begin_layout Section
25793 \begin_inset LatexCommand label
25794 name "sec:Formula-Styles"
25799 \begin_inset LatexCommand index
25800 name "Formula ! styles"
25807 \begin_layout Itemize
25808 There are two different alignment styles:
25812 \begin_layout Description
25813 Centered is the predefined standard
25816 \begin_layout Description
25817 Indented for this the option
25821 must be inserted in the menu
25823 Document\SpecialChar \menuseparator
25828 Document\InsetSpace ~
25832 \begin_layout Standard
25837 is used, the indentation can be adjusted with the length
25844 \begin_inset LatexCommand index
25845 name "Commands ! M ! \\textbackslash mathindent"
25850 Should the distance be 15\InsetSpace \thinspace{}
25851 mm, the following command line is inserted in
25855 \begin_layout Standard
25865 \begin_layout Standard
25866 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25871 \begin_layout Itemize
25872 And two different numbering styles:
25876 \begin_layout Description
25877 Right is the predefined standard
25880 \begin_layout Description
25881 Left for this the option
25885 must be inserted in the menu
25887 Document\SpecialChar \menuseparator
25892 Document\InsetSpace ~
25897 \begin_layout Standard
25906 can also be used together.
25907 In this case both options are inserted, separated by a comma.
25910 \begin_layout Standard
25911 The chosen styles are used for all displayed formulas of the document.
25912 When both, centered and indented formulas should be created in a document,
25918 The indented formulas are then set in a flalign environment, see
25919 \begin_inset LatexCommand ref
25920 reference "sub:Flalign-Environment"
25927 \begin_layout Section
25929 \begin_inset LatexCommand label
25930 name "sec:Multiline-Formulas"
25935 \begin_inset LatexCommand index
25936 name "Formula ! multiline"
25943 \begin_layout Subsection
25947 \begin_layout Standard
25948 In LyX multiline formulas are created by pressing
25959 that is described in
25960 \begin_inset LatexCommand ref
25961 reference "sub:Standard-align-Environment"
25968 \begin_layout Standard
25969 There are other multiline formula environments that can be created via the
25972 Insert\SpecialChar \menuseparator
25976 These environments are described in the following sections.
25979 \begin_layout Standard
25980 In all multiline formula environments a new line is created by pressing
25986 To add or delete lines, the math toolbar buttons
25987 \begin_inset Graphics
25988 filename ../images/tabular-feature_append-row.png
25994 \begin_inset Graphics
25995 filename ../images/tabular-feature_delete-row.png
26000 , respectively, or the menu
26002 Edit\SpecialChar \menuseparator
26008 \begin_layout Subsubsection
26010 \begin_inset LatexCommand label
26011 name "sub:Line-Separation"
26016 \begin_inset LatexCommand index
26017 name "Formula ! multiline ! Line separation"
26024 \begin_layout Standard
26025 There is sometimes not enough space in multiline formulas between the lines:
26026 \begin_inset Formula \begin{eqnarray*}
26027 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}\\
26028 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*}
26035 \begin_layout Standard
26036 In LaTeX additional line space is specified as optional argument of the
26038 This is not yet possible in LyX
26042 \begin_layout Standard
26047 \begin_layout Standard
26051 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26060 \begin_layout Standard
26072 , therefore the whole formula must be inserted in TeX-mode.
26073 To add in our example space, the command
26081 is inserted at the end of the first line.
26086 \begin_layout Standard
26093 \begin_layout Standard
26095 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26098 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26105 \begin_layout Standard
26109 left(B^{2}+x_{0}^{2}
26117 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26122 \begin_layout Standard
26134 \begin_layout Standard
26135 \begin_inset VSpace bigskip
26138 To set the the line separation for all lines in a formula, the length
26145 \begin_inset LatexCommand index
26146 name "Commands ! J ! \\textbackslash jot"
26152 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26162 is the value 3\InsetSpace \thinspace{}
26164 To create 3\InsetSpace \thinspace{}
26165 mm additional line separation as in the previous example, the
26169 \begin_layout Standard
26179 \begin_layout Standard
26180 is inserted in TeX-mode before the formula.
26181 This requires that the LaTeX-package
26189 \begin_layout Standard
26194 is part of every LaTeX standard installation.
26200 \begin_inset LatexCommand index
26201 name "Packages ! calc"
26205 was loaded in LaTeX-preamble with the line
26208 \begin_layout Standard
26216 \begin_layout Standard
26221 \begin_layout Standard
26233 \begin_inset Formula \begin{eqnarray*}
26234 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}\\
26235 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*}
26242 \begin_layout Standard
26246 \begin_layout Standard
26257 To get back to the predefined distance,
26263 is set to the value 3\InsetSpace \thinspace{}
26267 \begin_layout Subsubsection
26269 \begin_inset LatexCommand label
26270 name "sub:Column-Separation"
26275 \begin_inset LatexCommand index
26276 name "Formula ! multiline ! Column separation"
26283 \begin_layout Standard
26284 Multiline formulas form a matrix.
26285 A formula in the eqnarray environment is for example a matrix with three
26287 By changing the column separation in this environment, the space beside
26288 the relation sign can be changed.
26291 \begin_layout Standard
26292 The column separation is specified with the length
26299 \begin_inset LatexCommand index
26300 name "Commands ! A ! \\textbackslash arraycolsep"
26306 column separation = 2\InsetSpace \thinspace{}
26318 \begin_layout Standard
26328 \begin_layout Standard
26329 inserted in TeX-mode, sets for all following formulas a column separation
26330 of 2\InsetSpace \thinspace{}
26332 To get back to the predefined distance,
26338 is set to 5\InsetSpace \thinspace{}
26342 \begin_layout Standard
26343 A formula with 2\InsetSpace \thinspace{}
26344 cm column separation:
26348 \begin_layout Standard
26360 \begin_inset Formula \begin{eqnarray*}
26362 C & \ne & A\end{eqnarray*}
26366 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26371 \begin_layout Standard
26383 \begin_inset Formula \begin{eqnarray*}
26385 C & \ne & A\end{eqnarray*}
26392 \begin_layout Subsubsection
26394 \begin_inset LatexCommand index
26395 name "Formula ! long"
26402 \begin_layout Standard
26403 Long formulas can be typeset using these methods:
26406 \begin_layout Itemize
26407 When one side of the equation is much shorther than the line width, this
26408 one is chosen for the left side and the right side is typeset over two
26413 \begin_layout Standard
26423 \begin_inset Formula \begin{eqnarray}
26424 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 \\
26425 & & -\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}
26433 \begin_layout Standard
26444 The minus sign at the beginning of the second line does normally not appear
26445 as operator because it is the first character of the line.
26446 Thus it would not be surrounded by space and could not be distinguished
26447 from the fraction bar.
26448 To avoid this, space was inserted behind the minus sign with the command
26459 \begin_layout Standard
26467 \begin_inset LatexCommand ref
26468 reference "sub:Variable-Space"
26478 \begin_inset LatexCommand index
26479 name "Commands ! H ! \\textbackslash hspace"
26486 \begin_layout Itemize
26487 When both sides of the equation are too long, the command
26494 \begin_inset LatexCommand index
26495 name "Commands ! L ! \\textbackslash lefteqn"
26500 It is inserted to the first column of the first line and effects that all
26501 further insertions overwrite the following columns:
26505 \begin_layout Standard
26515 \begin_inset Formula \begin{eqnarray}
26516 \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 \\
26517 & & -\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 \\
26518 & & =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}
26526 \begin_layout Standard
26537 After the insertion of
26543 , the cursor is in a purple box that is a bit shifted to the left from the
26545 In this the formula is inserted.
26549 \begin_layout Standard
26560 The content of the further lines is inserted to the second or another formula
26562 The greater the column number where it was inserted, the larger the indentation.
26566 \begin_layout Standard
26578 \begin_inset Note Greyedout
26581 \begin_layout Standard
26582 Note the following when using
26591 \begin_layout Itemize
26592 The formula doesn't use the full page width.
26593 When e.\InsetSpace \thinspace{}
26596 \begin_inset Formula $-B^{2}$
26599 is added to the first line in the above example, it would have been outside
26601 To better use the width, negative space can be inserted at the beginning
26605 \begin_layout Itemize
26606 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26611 \begin_layout Standard
26615 \begin_layout Standard
26619 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26628 \begin_layout Standard
26640 One can only set the cursor at the beginning of the line and move it with
26649 \begin_layout Itemize
26650 Other methods to set long formulas are offered by the environments described
26652 \begin_inset LatexCommand ref
26653 reference "sub:Multline-Environment"
26658 \begin_inset LatexCommand ref
26659 reference "sub:Multiline-Formula-Parts"
26666 \begin_layout Subsubsection
26668 \begin_inset LatexCommand label
26669 name "sub:Multiline-Brackets"
26674 \begin_inset LatexCommand index
26675 name "Brackets ! for multiline expressions"
26682 \begin_layout Standard
26683 For brackets spanning multiple lines the following problem occurs:
26684 \begin_inset Formula \begin{eqnarray*}
26685 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26686 & & \left.\cdots+B-D\right]\end{eqnarray*}
26693 \begin_layout Standard
26694 The closing bracket is smaller than the opening bracket because brackets
26695 with variable size may not span multiple lines.
26698 \begin_layout Standard
26699 To set the bracket size for the second line correctly, the first line is
26707 \begin_inset LatexCommand index
26708 name "Commands ! R ! \\textbackslash right"
26712 and the second line with
26720 \begin_layout Standard
26734 \begin_inset LatexCommand ref
26735 reference "sub:Automatic-Bracket-Size"
26747 \begin_inset LatexCommand index
26748 name "Commands ! L ! \\textbackslash left"
26770 \begin_layout Standard
26789 \begin_layout Standard
26808 \begin_layout Standard
26820 \begin_inset Formula $\downarrow$
26826 \begin_inset LatexCommand index
26827 name "Commands ! V ! \\textbackslash vphantom"
26831 is inserted, because the multiplication operator with its limits is the
26832 largest symbol in the first line and this should be the size for the bracket
26833 in the second line.
26836 \begin_layout Standard
26837 The result is this:
26838 \begin_inset Formula \begin{eqnarray*}
26839 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26840 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26847 \begin_layout Subsection
26851 \begin_layout Standard
26852 Align environments can be used for every kind of multiline formulas.
26853 They are specially useful to set several formulas side by side.
26856 \begin_layout Standard
26857 Align environments consist of columns.
26858 The odd columns are right aligned, the even ones left aligned.
26859 Every line in an Align environment can be numbered.
26862 \begin_layout Standard
26863 Align environments are created via the menu
26865 Insert\SpecialChar \menuseparator
26871 Edit\SpecialChar \menuseparator
26872 Math\SpecialChar \menuseparator
26873 Change Formula Type
26875 already existing existing formulas can be converted to Align environments.
26878 \begin_layout Standard
26879 To add or delete columns, the math toolbar buttons
26880 \begin_inset Graphics
26881 filename ../images/tabular-feature_append-column.png
26887 \begin_inset Graphics
26888 filename ../images/tabular-feature_delete-column.png
26893 , respectively, or the menu
26895 Edit\SpecialChar \menuseparator
26901 \begin_layout Subsubsection
26902 Standard align Environment
26903 \begin_inset LatexCommand label
26904 name "sub:Standard-align-Environment"
26909 \begin_inset LatexCommand index
26910 name "Formula ! multiline ! align environment"
26917 \begin_layout Standard
26918 This Align environment is created by presssing
26922 in a formula or by the menu
26924 Insert\SpecialChar \menuseparator
26925 Math\SpecialChar \menuseparator
26926 AMS align Environment
26931 \begin_layout Standard
26932 An example for two formulas set side by side, that are created with a four
26933 column align environment:
26934 \begin_inset Formula \begin{align*}
26935 A & =\sin(B) & C & =D\\
26936 C & \ne A & B & \ne D\end{align*}
26940 As it can be seen, the formulas in this environment are placed so as if
26949 \begin_layout Standard
26957 \begin_inset LatexCommand ref
26958 reference "sub:Variable-Space"
26969 before the first and after every even column.
26970 When the formula style
26976 \begin_layout Standard
26978 \begin_inset LatexCommand ref
26979 reference "sec:Formula-Styles"
26990 is used, the formula is set without the
26996 before the first column.
26999 \begin_layout Subsubsection
27000 Alignat Environment
27001 \begin_inset LatexCommand index
27002 name "Formula ! multiline ! alignat environment"
27009 \begin_layout Standard
27010 The alignat environment has no predefined column separation.
27011 It can be inserted manually with the spaces that are described
27012 \begin_inset LatexCommand ref
27013 reference "sub:Space"
27020 \begin_layout Standard
27021 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27022 cm space was inserted
27023 at the beginning of the second formula:
27024 \begin_inset Formula \begin{alignat*}{2}
27025 A & =\sin(B) & \hspace{1cm}C & =D\\
27026 C & \ne A & B & \ne D\end{alignat*}
27030 Because the column separation can be set separately for every column, this
27031 environment is especially suitable to set three and more formulas side
27035 \begin_layout Subsubsection
27036 Flalign Environment
27037 \begin_inset LatexCommand label
27038 name "sub:Flalign-Environment"
27043 \begin_inset LatexCommand index
27044 name "Formula ! multiline ! flalign environment"
27051 \begin_layout Standard
27052 In this environment the first two columns are always set as much as possible
27053 to the left and the last two ones to the right.
27055 \begin_inset Formula \begin{flalign*}
27056 A & =1 & B & =2 & C & =3\\
27057 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27064 \begin_layout Standard
27065 By creating a flalign environment with an odd number of columns where an
27066 empty TeX-brace is inserted to the last column, several formulas in a document
27067 can be set to the left, although the formula style
27072 As example the indented formula
27073 \begin_inset LatexCommand eqref
27074 reference "eq:VolInt"
27079 \begin_inset Formula \begin{flalign}
27080 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27084 The first two columns contain the formula.
27085 To indent it as with the formula style
27089 , 30\InsetSpace \thinspace{}
27090 pt space was inserted at the beginning of the first column.
27093 \begin_layout Subsection
27094 Eqnarray Environment
27095 \begin_inset LatexCommand index
27096 name "Formula ! multiline ! eqnarray environment"
27103 \begin_layout Standard
27104 When this environment has been created, three blue boxes appear.
27105 The content of the first box is right aligned, the content of the last
27107 The content of the middle box appears centered and a bit smaller, because
27108 it is designed to insert there only relation characters.
27109 \begin_inset Formula \begin{eqnarray*}
27110 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27112 A & = & A\end{eqnarray*}
27119 \begin_layout Subsection
27121 \begin_inset LatexCommand index
27122 name "Formula ! multiline ! gather environment"
27129 \begin_layout Standard
27130 This environment consists of only one centered column.
27131 Every line can be numbered.
27132 \begin_inset Formula \begin{gather}
27134 X=\textrm{-}1\end{gather}
27141 \begin_layout Subsection
27142 Multline Environment
27143 \begin_inset LatexCommand label
27144 name "sub:Multline-Environment"
27149 \begin_inset LatexCommand index
27150 name "Formula ! multiline ! multline environment"
27157 \begin_layout Standard
27158 The multline environment consists, like the gather environment, of only
27160 But the first line is left aligned, the last one right aligned.
27161 All other lines are centered.
27162 Therefore this environment is suitable for long formulas.
27164 \begin_inset LatexCommand eqref
27165 reference "eq:lefteqn"
27169 in the multline environment:
27170 \begin_inset Formula \begin{multline}
27171 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}\\
27172 -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}\\
27173 =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}
27180 \begin_layout Standard
27181 In the output only the the last (first) line of a multline environment appears
27182 numbered when the document numbering is right (left).
27186 \begin_layout Standard
27187 numbering styles see
27188 \begin_inset LatexCommand ref
27189 reference "sec:Formula-Styles"
27198 This is also the case when there is a formula number displayed after every
27203 \begin_layout Standard
27208 \begin_layout Standard
27212 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27221 \begin_layout Standard
27236 \begin_layout Standard
27242 \begin_inset LatexCommand index
27243 name "Commands ! S ! \\textbackslash shoveright"
27254 \begin_inset LatexCommand index
27255 name "Commands ! S ! \\textbackslash shoveleft"
27261 a centered line can be right or left aligned, respectively.
27262 The commands are used as follows:
27265 \begin_layout Standard
27270 shoveright{line content}
27276 shoveleft{line content}
27279 \begin_layout Standard
27280 \begin_inset VSpace medskip
27288 \begin_inset LatexCommand index
27289 name "Commands ! M ! \\textbackslash multlinegap"
27295 specifies the distance of the first line from the left page margin.
27296 Predefined is the length 0\InsetSpace \thinspace{}
27300 \begin_layout Standard
27301 As example the above formula where the command
27304 \begin_layout Standard
27314 \begin_layout Standard
27315 was inserted in TeX-mode before:
27319 \begin_layout Standard
27331 \begin_inset Formula \begin{multline}
27332 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}\\
27333 \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}}\\
27334 =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}
27342 \begin_layout Standard
27353 The second line was left aligned using
27362 \begin_layout Subsection
27363 Multiline Formula Parts
27364 \begin_inset LatexCommand label
27365 name "sub:Multiline-Formula-Parts"
27370 \begin_inset LatexCommand index
27371 name "Formula ! multiline ! formula parts"
27378 \begin_layout Standard
27379 To display only parts of a formula with multiple lines, one of the following
27380 environments are used:
27397 They can be inserted via the menu
27399 Insert\SpecialChar \menuseparator
27402 or by using the commands described in this section.
27405 \begin_layout Standard
27406 The first three have the same properties as the corresponding multiline
27407 formula environments, but it is possible to set further formula parts beside
27410 \begin_inset Formula \[
27411 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27412 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27413 \right\} \textrm{Uncertainty relations}\]
27420 \begin_layout Standard
27421 To get this formula, a displayed formula is created where the command
27426 \begin_inset LatexCommand index
27427 name "Commands ! A ! \\textbackslash aligned"
27434 A purple box appears around the blue formula box where now columns and
27435 lines can be added.
27436 Outside the multiline environment other formula parts can be set, like
27440 \begin_layout Standard
27441 The aligned environment is also suitable for long formulas whose lines are
27442 horizontally aligned.
27443 Using aligned in a displayed formula has the advantage that the formula
27444 number is vertically centered behind the lines.
27446 \begin_inset LatexCommand eqref
27447 reference "eq:kurzlang"
27451 in the aligned environment:
27452 \begin_inset Formula \begin{equation}
27453 \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}|}\\
27454 & -\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}
27462 \begin_layout Standard
27463 To use the environments
27482 \begin_inset LatexCommand index
27483 name "Commands ! A ! \\textbackslash alignedat"
27494 \begin_inset LatexCommand index
27495 name "Commands ! G ! \\textbackslash gathered"
27506 \begin_inset LatexCommand index
27507 name "Commands ! S ! \\textbackslash split"
27511 are inserted, respectively.
27512 The split environment has the same properties as the aligned environment
27513 but it can only have two columns.
27516 \begin_layout Subsection
27517 Text in multiline Formulas
27518 \begin_inset LatexCommand label
27519 name "sub:Text-in-multiline"
27524 \begin_inset LatexCommand index
27525 name "Text ! in formulas"
27530 \begin_inset LatexCommand index
27531 name "Formula ! multiline ! text"
27538 \begin_layout Standard
27539 In the Align environments, and the multline and gather environment, text
27540 can be inserted that will appear in a separate line and doesn't affect
27541 the column alignment.
27542 To do this, the command
27547 \begin_inset LatexCommand index
27548 name "Commands ! I ! \\textbackslash intertext"
27554 is used in the following scheme:
27557 \begin_layout Standard
27565 \begin_layout Standard
27566 The text should not be longer than a line because it cannot be hyphenated.
27567 As LyX doesn't yet support
27573 directly, the text is written as mathematical text.
27580 must hereby be at the beginning of a line and appears in the output above
27582 An example where the text was inserted at the beginning of the second line:
27583 \begin_inset Formula \begin{align}
27584 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27585 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27592 \begin_layout Section
27594 \begin_inset LatexCommand index
27595 name "Formula numbering"
27600 \begin_inset LatexCommand index
27601 name "Formula ! numbering|see{Formula numbering}"
27608 \begin_layout Subsection
27612 \begin_layout Standard
27613 Numbered formulas can be created with the menu
27615 Insert\SpecialChar \menuseparator
27616 Math\SpecialChar \menuseparator
27617 Numbered\InsetSpace ~
27622 Ctrl-Alt\InsetSpace ~
27626 Existing formulas can be numbered with the menu
27628 Edit\SpecialChar \menuseparator
27629 Math\SpecialChar \menuseparator
27630 Toggle\InsetSpace ~
27639 The formula number is displayed in LyX behind the formula as number sign
27641 The number sign is replaced in the output by the formula number.
27644 \begin_layout Standard
27645 When numbering is turned on in multiline formulas, all lines will be numbered.
27646 But the numbering can be controlled with the menu
27648 Edit\SpecialChar \menuseparator
27649 Math\SpecialChar \menuseparator
27650 Toggle\InsetSpace ~
27651 Numbering\InsetSpace ~
27663 \begin_layout Standard
27664 Except of inline formulas, all formulas can be numbered with two different
27666 \begin_inset LatexCommand ref
27667 reference "sec:Formula-Styles"
27674 \begin_layout Subsection
27676 \begin_inset LatexCommand label
27677 name "sub:Cross-References"
27682 \begin_inset LatexCommand index
27683 name "Cross-references ! to formulas"
27690 \begin_layout Standard
27691 All labeled formulas can be cross-referenced.
27692 A label is added by the menu
27694 Insert\SpecialChar \menuseparator
27697 or the toolbar button
27698 \begin_inset Graphics
27699 filename ../images/label-insert.png
27705 The cursor must hereby be inside a displayed formula.
27706 A dialog pops up displaying the prefix
27711 The label is inserted there behind the prefix.
27712 The predefined prefix means
27713 \begin_inset Quotes eld
27717 \begin_inset Quotes erd
27720 and makes it easier to find labels in large documents because it marks
27721 it as formula label to divide it from e.\InsetSpace \thinspace{}
27724 To change a label, the menu
27726 Insert\SpecialChar \menuseparator
27732 \begin_layout Standard
27733 The name of the label is displayed in LyX within two parentheses behind
27735 A formula with a label is always numbered.
27736 The label is deleted when the numbering is turned off.
27737 This is at the moment the only way to delete a label, see
27741 \begin_layout Standard
27745 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27754 \begin_layout Standard
27764 \begin_layout Standard
27765 Cross-references are inserted via the menu
27767 Insert\SpecialChar \menuseparator
27770 or with the toolbar button
27771 \begin_inset Graphics
27772 filename ../images/dialog-show-new-inset_ref.png
27778 A formula cross-reference appears in the output as formula number.
27779 When in the cross-reference dialog window the format
27783 is chosen, the cross-reference appears in the output as formula number
27786 By right-clicking on a cross-reference in LyX, one jumps
27787 to the formula that is referenced.
27790 \begin_layout Standard
27791 Here are as examples cross-references to formulas of the following subsections:
27792 \begin_inset Note Note
27795 \begin_layout Standard
27796 Note the different cross-reference types.
27804 \begin_layout Standard
27806 \begin_inset LatexCommand eqref
27812 \begin_inset LatexCommand eqref
27819 \begin_inset LatexCommand ref
27824 ) big Latin letters are used for the numbering in contrary to (
27825 \begin_inset LatexCommand ref
27833 \begin_layout Standard
27834 \begin_inset VSpace medskip
27837 When the argument of
27845 \begin_layout Standard
27853 \begin_inset LatexCommand ref
27854 reference "sub:User-defined-Numbering"
27865 contains a box like in
27866 \begin_inset LatexCommand ref
27867 reference "sub:Paragraph-Boxes"
27871 , the formula cannot be referenced.
27874 \begin_layout Subsection
27876 \begin_inset LatexCommand index
27877 name "Formula numbering ! subnumbering"
27884 \begin_layout Standard
27885 With the help of the commands
27889 begin{subequations}
27897 formulas can be subnumbered.
27898 Both commands are inserted in TeX-mode.
27901 \begin_layout Standard
27903 \begin_inset Formula \begin{equation}
27904 A=C-B\label{eq:a}\end{equation}
27912 \begin_layout Standard
27916 addtocounter{equation}{-1}
27925 \begin_layout Standard
27929 begin{subequations}
27935 \begin_inset VSpace -5mm
27939 \begin_inset Formula \begin{equation}
27940 B=C-A\label{eq:b}\end{equation}
27945 \begin_inset Formula \begin{equation}
27946 C=A+B\label{eq:c}\end{equation}
27953 \begin_layout Standard
27957 \begin_layout Standard
27969 \begin_layout Standard
27970 To create the example, the following is done:
27973 \begin_layout Enumerate
27974 first formula is inserted
27977 \begin_layout Enumerate
27982 addtocounter{equation}{-1}
27984 begin{subequations}
27985 \begin_inset LatexCommand index
27986 name "Commands ! A ! \\textbackslash addtocounter"
27994 is inserted after the first formula
27997 \begin_layout Enumerate
27998 second formula is inserted
28001 \begin_layout Enumerate
28002 third formula is inserted
28005 \begin_layout Enumerate
28012 is inserted after the third formula
28015 \begin_layout Standard
28016 Every formula between the commands
28028 is subnumbered as a, b,
28032 \begin_layout Standard
28041 c, \SpecialChar \ldots{}
28042 For multiline formulas every line will be subnumbered.
28043 All subnumbered formulas are treated as
28048 But as every numbered formula increases the counter
28052 by one, the command
28058 is needed to decrease it.
28059 Otherwise the formulas
28060 \begin_inset LatexCommand eqref
28066 \begin_inset LatexCommand eqref
28072 \begin_inset LatexCommand eqref
28077 would be numbered as
28078 \begin_inset LatexCommand eqref
28084 \begin_inset LatexCommand eqref
28090 \begin_inset LatexCommand eqref
28098 \begin_layout Standard
28099 By inserting the commands in TeX-mode, a space is created between the first
28101 To revert this -5\InsetSpace \thinspace{}
28102 mm vertical space is inserted after the command
28106 begin{subequations}
28109 When the formula style
28115 \begin_layout Standard
28117 \begin_inset LatexCommand ref
28118 reference "sec:Formula-Styles"
28129 is used, -7\InsetSpace \thinspace{}
28130 mm space is inserted instead.
28133 \begin_layout Standard
28134 Here is an example for a multiline formula where the numbering was turned
28135 off for the second line:
28139 \begin_layout Standard
28143 begin{subequations}
28149 \begin_inset Formula \begin{eqnarray}
28150 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28151 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28152 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28160 \begin_layout Standard
28172 \begin_layout Subsection
28173 User-defined Numbering
28174 \begin_inset LatexCommand label
28175 name "sub:User-defined-Numbering"
28180 \begin_inset LatexCommand index
28181 name "Formula numbering ! user-defined"
28188 \begin_layout Standard
28189 \begin_inset LatexCommand index
28190 name "Formula numbering ! self-defined delimiters"
28194 With the standard numbering parentheses are set around the formula number.
28195 To replace the parentheses for example by vertical bars, the following
28196 line is added to the LaTeX-preamble:
28199 \begin_layout Standard
28211 \begin_inset Note Note
28214 \begin_layout Standard
28215 This macro is already declared in the LaTeX-preamble for testing.
28216 To activate it, remove the percent sign at the beginning.
28224 \begin_layout Standard
28225 To use other characters, the vertical bars besides the
28229 are replaced by one ore more characters.
28230 To get only the formula number the vertical bars are omitted.
28233 \begin_layout Standard
28234 \begin_inset VSpace bigskip
28237 When there should be an expression of your choice instead of the consecutive
28238 formula number in parentheses behind the formula, the command
28245 \begin_inset LatexCommand index
28246 name "Commands ! T ! \\textbackslash tag"
28251 \begin_inset Formula \begin{equation}
28252 A+B=C\tag{something}\label{eq:tag}\end{equation}
28256 In this example the command
28264 was inserted to the formula.
28267 \begin_layout Standard
28276 is inserted instead, the star prevents the parentheses around the expression:
28277 \begin_inset Formula \[
28278 A+B=C\tag*{something}\]
28285 \begin_layout Standard
28286 \begin_inset VSpace bigskip
28289 To restart the formula numbering with new document parts or sections, the
28290 following command is used:
28293 \begin_layout Standard
28298 @addtoreset{equation}{part}
28301 \begin_inset LatexCommand index
28302 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28314 @addtoreset{equation}{section}
28317 \begin_layout Standard
28318 To be able to use these commands in TeX-mode, the
28319 \begin_inset Quotes eld
28323 \begin_inset Quotes erd
28326 character has to be made
28327 \begin_inset Quotes eld
28331 \begin_inset Quotes erd
28334 for LaTeX using the command
28348 So the command sequence in TeX-mode is:
28351 \begin_layout Standard
28360 @addtoreset{equation}{section}
28367 \begin_layout Standard
28368 In the LaTeX-preamble
28380 can be omitted as they are automatically internally inserted by LyX.
28383 \begin_layout Standard
28398 \begin_layout Standard
28403 is part of the LaTeX-package
28408 \begin_inset LatexCommand index
28409 name "Packages ! carlisle"
28413 that is part of every LaTeX standard installation.
28419 \begin_inset LatexCommand index
28420 name "Packages ! remreset"
28424 has to be loaded in the LaTeX-preamble with the line
28427 \begin_layout Standard
28432 usepackage{remreset}
28435 \begin_layout Standard
28443 \begin_inset LatexCommand index
28444 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28448 can be used with the same scheme as
28457 \begin_layout Standard
28458 \begin_inset VSpace bigskip
28461 Sometimes formulas should be numbered in the following form:
28464 \begin_layout Standard
28467 (section number.formula number)
28470 \begin_layout Standard
28471 The formula number should start with every section with
28472 \begin_inset Quotes eld
28476 \begin_inset Quotes erd
28482 \begin_layout Standard
28483 For this case there is the command
28490 \begin_inset LatexCommand index
28491 name "Commands ! N ! \\textbackslash numberwithin"
28495 , which is used with the following scheme:
28498 \begin_layout Standard
28503 numberwithin{counter}{sectioning}
28506 \begin_layout Standard
28507 Counter denotes what kind of numbering is affected, sectioning denotes what
28508 number is before the dot.
28511 \begin_layout Standard
28512 Thus in our case the following LaTeX-preamble or ERT line is used:
28515 \begin_layout Standard
28520 numberwithin{equation}{section}
28523 \begin_layout Standard
28524 This is the result:
28528 \begin_layout Standard
28532 numberwithin{equation}{section}
28538 \begin_inset Formula \begin{equation}
28539 A+B=C\end{equation}
28546 \begin_layout Standard
28547 To number e.\InsetSpace \thinspace{}
28549 tables so that the number of the part is the sectioning,
28555 numberwithin{table}{part}
28560 \begin_layout Standard
28561 To go back to the standard numbering or to prevent this kind of numbering
28562 when it is defined by the document class, the following command is inserted
28563 as ERT or to the LaTeX-preamble:
28566 \begin_layout Standard
28576 \begin_inset LatexCommand index
28577 name "Commands ! A ! \\textbackslash arabic"
28587 \begin_layout Standard
28619 \begin_layout Standard
28626 uses internally the command
28632 , described above, that also needs to be reverted.
28636 \begin_layout Standard
28643 \begin_layout Standard
28647 @removefromreset{equation}{section}
28650 \begin_layout Standard
28662 \begin_layout Subsection
28663 Numbering with Roman Numbers and Letters
28664 \begin_inset LatexCommand label
28665 name "sub:Numbering-with-Roman"
28670 \begin_inset LatexCommand index
28671 name "Formula numbering ! with letters"
28676 \begin_inset LatexCommand index
28677 name "Formula numbering ! with Roman numbers"
28684 \begin_layout Standard
28685 Formulas can also be numbered with Roman numbers and Latin letters.
28686 To number for example with small Roman numbers, the command
28689 \begin_layout Standard
28701 \begin_layout Standard
28702 is inserted before the formula in TeX-mode.
28710 \begin_inset LatexCommand index
28711 name "Commands ! R ! \\textbackslash renewcommand"
28715 redefines the predefined command
28731 \begin_layout Standard
28738 has the same scheme like the command
28744 that is described in
28745 \begin_inset LatexCommand ref
28746 reference "sec:User-defined-commands"
28760 is the formula counter.
28767 is used as prefix for a counter, the value of the counter is output as
28769 When a formula is numbered, LaTeX sets internally the command
28775 behind the formula.
28781 \begin_inset LatexCommand index
28782 name "Commands ! R ! \\textbackslash roman"
28788 outputs the counter as small Roman number.
28791 \begin_layout Standard
28792 All formulas behind the command
28802 are now numbered Roman.
28803 To switch to numbering with big Roman numbers, the command is inserted
28817 \begin_inset LatexCommand index
28818 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28824 \begin_inset Quotes eld
28828 \begin_inset Quotes erd
28831 with small Latin letters there is the command
28838 \begin_inset LatexCommand index
28839 name "Commands ! A ! \\textbackslash alph"
28843 , for big ones there is the command
28850 \begin_inset LatexCommand index
28851 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28858 \begin_layout Standard
28859 \begin_inset Note Greyedout
28862 \begin_layout Standard
28867 Only maximal 26 formulas can be numbered with Latin letters in one document.
28875 \begin_layout Standard
28879 \begin_layout Standard
28895 \begin_layout Standard
28896 \begin_inset Formula \begin{equation}
28897 A=\textrm{small roman}\label{eq:rom}\end{equation}
28905 \begin_layout Standard
28919 \begin_inset Formula \begin{equation}
28920 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
28928 \begin_layout Standard
28942 \begin_inset Formula \begin{equation}
28943 C=\textrm{small Latin}\label{eq:lat}\end{equation}
28951 \begin_layout Standard
28965 \begin_inset Formula \begin{equation}
28966 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
28973 \begin_layout Standard
28974 To switch back to the default numbering, insert the command:
28977 \begin_layout Standard
28987 \begin_inset LatexCommand index
28988 name "Commands ! A ! \\textbackslash arabic"
28995 \begin_layout Standard
28999 \begin_layout Standard
29013 \begin_inset Formula \begin{equation}
29014 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29021 \begin_layout Standard
29022 \begin_inset VSpace medskip
29025 As you see, formulas are numbered serially independent from the numbering
29027 When then numbering should start with
29028 \begin_inset Quotes eld
29032 \begin_inset Quotes erd
29035 when the style is changed, new equation counters have to be defined.
29036 A description about this can be found in the file
29040 \begin_layout Standard
29044 href{Formula-numbering.pdf}{
29049 Formula-numbering.pdf
29053 \begin_layout Standard
29061 \begin_inset Note Note
29064 \begin_layout Standard
29065 More about the command
29072 \begin_inset LatexCommand ref
29073 reference "sub:Links-in-DVI-"
29085 \begin_layout Section
29086 User-defined commands
29087 \begin_inset LatexCommand label
29088 name "sec:User-defined-commands"
29093 \begin_inset LatexCommand index
29094 name "User-defined commands"
29101 \begin_layout Standard
29102 Many LaTeX-commands are too long to be used frequently.
29103 But it is possible to define with the command
29110 \begin_inset LatexCommand index
29111 name "Commands ! N ! \\textbackslash newcommand"
29115 new shorter commands.
29118 \begin_layout Standard
29119 The command scheme of
29128 \begin_layout Standard
29133 newcommand{new command name}[number of arguments][optional
29143 \begin_layout Standard
29158 \begin_layout Standard
29165 {command definition}
29168 \begin_layout Standard
29169 \begin_inset Note Greyedout
29172 \begin_layout Standard
29177 Assure that the name of the new command is not already used in your document
29178 or by LaTeX-packages that you use.
29179 When you for example define the command
29191 , you get an error message because
29197 is already defined as command for
29198 \begin_inset Quotes eld
29202 \begin_inset Formula $\le$
29206 \begin_inset Quotes erd
29217 \begin_layout Standard
29218 \begin_inset Note Greyedout
29221 \begin_layout Standard
29226 The names of user-defined commands may only consist of Latin letters.
29234 \begin_layout Standard
29235 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29236 -\InsetSpace \thinspace{}
29237 9 and specifies how
29238 many arguments the new command should have.
29239 With the optional value a value for an optional argument can be predefined.
29240 When this is done, the
29248 rgument of the new command is automatically an optional one.
29251 \begin_layout Standard
29252 Here are some examples:
29255 \begin_layout Itemize
29256 To define the command
29268 , the LaTeX-preamble line is:
29272 \begin_layout Standard
29294 \begin_layout Itemize
29295 To define the command
29307 , the argument (that should be underlined) must be taken into account.
29308 For this the preamble line is:
29312 \begin_layout Standard
29337 \begin_layout Standard
29356 acts as argument placeholder, the
29360 behind it denotes that it is the placeholder for the first argument.
29363 \begin_layout Itemize
29370 one can e.\InsetSpace \thinspace{}
29382 \begin_layout Standard
29401 framebox#1#2{$#3$}}
29407 \begin_layout Standard
29422 The two Dollar signs creates the extra formula needed for
29429 \begin_inset LatexCommand ref
29430 reference "sub:Boxes-with-Frame"
29437 \begin_layout Itemize
29438 To create a new command for
29444 where the color for the box needn't to be specified, the argument for the
29445 color is defined optional:
29449 \begin_layout Standard
29468 fcolorbox{#2}{#1}{$#3$}}
29474 \begin_layout Standard
29485 When the color is not specified when using
29491 , the predefined color
29498 \begin_layout Standard
29499 A test of the new defined commands:
29502 \begin_layout Standard
29504 \begin_inset Tabular
29505 <lyxtabular version="3" rows="6" columns="2">
29507 <column alignment="center" valignment="top" leftline="true" width="0">
29508 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29509 <row topline="true" bottomline="true">
29510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29513 \begin_layout Standard
29519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29522 \begin_layout Standard
29524 \begin_inset Note Note
29527 \begin_layout Standard
29534 is only used as spacer.
29545 <row topline="true">
29546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29549 \begin_layout Standard
29556 \begin_layout Standard
29570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29573 \begin_layout Standard
29574 \begin_inset Formula $A\gr B$
29583 <row topline="true">
29584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29587 \begin_layout Standard
29595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29598 \begin_layout Standard
29599 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29608 <row topline="true">
29609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29612 \begin_layout Standard
29616 \begin_inset Formula $\to$
29622 \begin_inset Formula $\to$
29633 \begin_layout Standard
29647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29650 \begin_layout Standard
29651 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29660 <row topline="true">
29661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29664 \begin_layout Standard
29668 \begin_inset Formula $\to$
29679 \begin_layout Standard
29693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29696 \begin_layout Standard
29697 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29706 <row topline="true" bottomline="true">
29707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29710 \begin_layout Standard
29716 \begin_inset Formula $\to$
29727 \begin_layout Standard
29741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29744 \begin_layout Standard
29745 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29761 \begin_layout Section
29763 \begin_inset LatexCommand index
29771 \begin_layout Standard
29772 To create diagrams, the LaTeX-package
29778 \begin_layout Standard
29783 is part of every LaTeX standard installation.
29791 \begin_inset LatexCommand index
29792 name "Packages ! amscd"
29797 It is loaded in the LaTeX-preamble with the line
29800 \begin_layout Standard
29808 \begin_layout Standard
29809 Diagrams visualize relations and look like this:
29810 \begin_inset Formula \[
29811 \begin{CD}A@>>>B@>>>C\\
29813 F@<<<E@<<<D\end{CD}\]
29820 \begin_layout Standard
29821 To get them, the command
29826 \begin_inset LatexCommand index
29827 name "Commands ! C ! \\textbackslash CD"
29833 is inserted to a formula.
29834 A blue box appears with two dashed lines where further commands can be
29840 a new line is created.
29841 Horizontal relations are inserted in odd, vertical in even formula lines.
29844 \begin_layout Standard
29845 To create the relations there are the following commands:
29848 \begin_layout Itemize
29853 creates a left arrow,
29864 \begin_layout Itemize
29869 creates an up arrow,
29877 a vertical equal sign
29880 \begin_layout Itemize
29886 is a placeholder for non-existent relations
29889 \begin_layout Standard
29890 All arrows can be labeled as follows:
29893 \begin_layout Itemize
29894 Is text inserted between the first and second < or >, resp., it is placed
29896 When it is inserted between the second and third one, it appears under
29900 \begin_layout Itemize
29901 When text for vertical arrows is inserted between the first and second A
29902 or V, resp., it is placed left beside the arrow.
29903 When it is inserted between the second and third one, it appears right
29905 If the text contains an A or V, these letters must be set into a TeX-brace.
29908 \begin_layout Standard
29909 As example a diagram with all possible relations:
29912 \begin_layout Standard
29913 \begin_inset Formula \[
29914 \begin{CD}A@>j>>B@>>k>C@=F\\
29916 D@<<j<E@>k>>F@=C\end{CD}\]
29923 \begin_layout Standard
29924 The command for this is:
29934 \begin_layout Standard
29943 A@>j>>B@>>k>C@=F Ctrl-Enter
29949 \begin_layout Standard
29964 \begin_layout Standard
29977 \begin_layout Standard
29989 \begin_inset Formula $\to$
30000 \begin_layout Standard
30015 \begin_layout Standard
30028 \begin_layout Standard
30038 \begin_layout Standard
30044 \begin_layout Section
30049 \begin_layout Standard
30062 \begin_layout Standard
30063 Other useful math tips can be found in
30064 \begin_inset LatexCommand cite
30078 \begin_layout Standard
30086 \begin_inset Note Note
30089 \begin_layout Standard
30092 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30095 \begin_layout Standard
30098 texorpdfstring is in section
30099 \begin_inset LatexCommand ref
30100 reference "sub:Formulas-in-Section"
30110 \begin_inset LatexCommand index
30116 \begin_inset LatexCommand index
30117 name "Ions|see{Chemical characters}"
30124 \begin_layout Subsection
30125 Chemical Symbols and Equations
30126 \begin_inset LatexCommand label
30127 name "sub:Chemical-Symbols-and"
30132 \begin_inset LatexCommand index
30133 name "Chemical characters ! Symbols"
30138 \begin_inset LatexCommand index
30139 name "Chemical equations"
30144 \begin_inset LatexCommand index
30145 name "Symbols ! chemical"
30152 \begin_layout Standard
30153 An example text from chemistry:
30156 \begin_layout Quote
30158 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30161 -ion reacts with two
30162 \begin_inset Formula $\mathrm{Na^{+}}$
30165 -ions to sodium sulfate
30166 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30170 The chemical equation for this is:
30171 \begin_inset Formula \[
30172 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30179 \begin_layout Standard
30180 This chemical equation can directly be created as formula.
30181 To avoid that the symbols appear italic, everything is highlighted and
30182 changed by the shortcut
30187 to the upright font style.
30191 \begin_layout Standard
30197 \begin_inset LatexCommand ref
30198 reference "sub:Font-Styles"
30210 \begin_layout Subsection
30212 \begin_inset LatexCommand index
30213 name "Numbers ! negative"
30220 \begin_layout Standard
30221 Negative numbers often look ugly in formulas because the minus sign before
30222 the number is set with the same length as the minus operator sign.
30223 When writing the negative number in normal text, the minus sign appears
30227 \begin_layout Standard
30228 Thus, the problem disappears when converting the minus sign to mathematical
30232 \begin_layout Standard
30233 An example to visualize the problem:
30236 \begin_layout Standard
30238 \begin_inset Tabular
30239 <lyxtabular version="3" rows="3" columns="2">
30241 <column alignment="right" valignment="top" leftline="true" width="0">
30242 <column alignment="left" valignment="top" rightline="true" width="0">
30243 <row topline="true">
30244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30247 \begin_layout Standard
30253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30256 \begin_layout Standard
30263 <row topline="true" bottomline="true">
30264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30267 \begin_layout Standard
30273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30276 \begin_layout Standard
30277 \begin_inset Formula $x=-2$
30286 <row topline="true" bottomline="true">
30287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30290 \begin_layout Standard
30296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30299 \begin_layout Standard
30300 \begin_inset Formula $x=\textrm{-}2$
30316 \begin_layout Subsection
30317 Comma as Decimal Separator
30318 \begin_inset LatexCommand index
30326 \begin_layout Standard
30327 In LaTeX a comma inside a formula is used, according to the English convention,
30328 as number group separator.
30329 So there will be space added behind all commas in formulas.
30332 \begin_layout Standard
30333 To avoid this, the comma is highlighted and changed to mathematical text
30342 \begin_layout Standard
30343 To use all formula commas in the document as decimal separator, the file
30352 \begin_layout Standard
30357 is part of the LaTeX-package
30362 \begin_inset LatexCommand index
30363 name "Packages ! was\\vspace{4mm}"
30373 \begin_inset LatexCommand index
30374 name "Packages ! icomma"
30378 is loaded with the LaTeX-preamble line
30381 \begin_layout Standard
30389 \begin_layout Subsection
30391 \begin_inset LatexCommand label
30392 name "sub:Physical-Vectors"
30397 \begin_inset LatexCommand index
30398 name "Vectors ! physical"
30405 \begin_layout Standard
30406 Predefined vectors are offered by the LaTeX-package
30414 \begin_layout Standard
30419 should be part of every LaTeX standard installation.
30425 \begin_inset LatexCommand index
30426 name "Packages ! braket"
30430 that is loaded with the LaTeX-preamble line
30433 \begin_layout Standard
30441 \begin_layout Standard
30445 \begin_layout Standard
30455 \begin_inset Note Note
30458 \begin_layout Standard
30459 The following table will only be displayed when the LaTeX-package
30468 The following commands are defined:
30471 \begin_layout Standard
30473 \begin_inset Tabular
30474 <lyxtabular version="3" rows="4" columns="2">
30476 <column alignment="center" valignment="top" leftline="true" width="0">
30477 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30478 <row topline="true" bottomline="true">
30479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30482 \begin_layout Standard
30488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30491 \begin_layout Standard
30498 <row topline="true">
30499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30502 \begin_layout Standard
30512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30515 \begin_layout Standard
30516 \begin_inset Formula $\Bra{\psi}$
30525 <row topline="true">
30526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30529 \begin_layout Standard
30539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30542 \begin_layout Standard
30543 \begin_inset Formula $\Ket{\psi}$
30552 <row topline="true" bottomline="true">
30553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30556 \begin_layout Standard
30568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30571 \begin_layout Standard
30572 \begin_inset Formula $\Braket{\psi|\phi}$
30588 \begin_layout Standard
30595 assures that all vertical bars are set in the size of the surrounding brackets:
30596 \begin_inset Formula \[
30597 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30605 \begin_layout Standard
30615 \begin_inset Note Note
30618 \begin_layout Standard
30619 The following will be displayed when the LaTeX-package
30631 \begin_layout Standard
30632 You need to install the LaTeX-package
30636 to see the rest of this subsection in the output.
30639 \begin_layout Standard
30643 \begin_layout Standard
30655 \begin_layout Standard
30662 can also be achieved using the command
30668 , that is described in
30669 \begin_inset LatexCommand ref
30670 reference "sub:Automatic-Bracket-Size"
30677 \begin_layout Subsection
30678 Self-defined Fractions
30679 \begin_inset LatexCommand label
30680 name "sub:Self-defined-Fractions"
30685 \begin_inset LatexCommand index
30686 name "Fractions ! self-defined"
30693 \begin_layout Standard
30694 To define custom commands for fractions, the command
30701 \begin_inset LatexCommand index
30702 name "Commands ! G ! \\textbackslash genfrac"
30706 is used in the following scheme:
30709 \begin_layout Standard
30722 bracket}{fraction bar thickness}{style}
30728 \begin_layout Standard
30743 \begin_layout Standard
30750 {numerator}{denominator}
30753 \begin_layout Standard
30754 The style is a number in the range of 0\InsetSpace \thinspace{}
30755 -\InsetSpace \thinspace{}
30759 \begin_layout Standard
30761 \begin_inset Tabular
30762 <lyxtabular version="3" rows="5" columns="2">
30764 <column alignment="center" valignment="top" leftline="true" width="0">
30765 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30766 <row topline="true" bottomline="true">
30767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30770 \begin_layout Standard
30776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30779 \begin_layout Standard
30786 <row topline="true">
30787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30790 \begin_layout Standard
30796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30799 \begin_layout Standard
30800 display style formula
30806 <row topline="true">
30807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30810 \begin_layout Standard
30816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30819 \begin_layout Standard
30826 <row topline="true">
30827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30830 \begin_layout Standard
30836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30839 \begin_layout Standard
30846 <row topline="true" bottomline="true">
30847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30850 \begin_layout Standard
30856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30859 \begin_layout Standard
30873 \begin_layout Standard
30874 When no style is given, the size is adjusted to the surrounding environment
30875 like for the command
30884 \begin_layout Standard
30885 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30890 \begin_layout Standard
30891 \begin_inset VSpace medskip
30894 For example, the commands
30907 \begin_inset LatexCommand ref
30908 reference "sub:Fractions"
30912 are defined with the commands
30915 \begin_layout Standard
30924 genfrac{}{}{}{0}{#1}{#2}}
30927 \begin_layout Standard
30931 \begin_layout Standard
30940 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30943 \begin_layout Standard
30944 \begin_inset VSpace medskip
30947 To define a fraction where the fraction bar thickness can be given as optional
30948 argument, the following line is inserted to the LaTeX-preamble:
30951 \begin_layout Standard
30960 genfrac{}{}{#1}{}{#2}{#3}}
30963 \begin_layout Standard
30965 \begin_inset Formula \begin{align*}
30966 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30967 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30971 As one can see, the distance of the numerator and the denominator to the
30972 fraction bar is round about three times the bar thickness.
30975 \begin_layout Subsection
30977 \begin_inset LatexCommand label
30978 name "sub:Canceled-Formulas"
30983 \begin_inset LatexCommand index
30984 name "Formula ! canceled"
30991 \begin_layout Standard
30992 To cancel formulas or formula parts, the LaTeX-package
31000 \begin_layout Standard
31005 is part of every LaTeX standard installation.
31011 \begin_inset LatexCommand index
31012 name "Packages ! cancel"
31016 has to be loaded with the LaTeX-preamble line
31019 \begin_layout Standard
31024 usepackage[samesize]{cancel}
31027 \begin_layout Standard
31028 There are four ways to cancel formulas:
31031 \begin_layout Standard
31033 \begin_inset Tabular
31034 <lyxtabular version="3" rows="5" columns="2">
31036 <column alignment="center" valignment="top" leftline="true" width="0">
31037 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31038 <row topline="true" bottomline="true">
31039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31042 \begin_layout Standard
31048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31051 \begin_layout Standard
31053 \begin_inset Note Note
31056 \begin_layout Standard
31069 are used here as spacer.
31080 <row topline="true">
31081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31084 \begin_layout Standard
31093 \begin_layout Standard
31107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31110 \begin_layout Standard
31111 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31120 <row topline="true">
31121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31124 \begin_layout Standard
31133 \begin_layout Standard
31147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31150 \begin_layout Standard
31151 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31160 <row topline="true" bottomline="true">
31161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31164 \begin_layout Standard
31173 \begin_layout Standard
31187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31190 \begin_layout Standard
31191 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31200 <row topline="true" bottomline="true">
31201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31204 \begin_layout Standard
31208 \begin_inset Formula $\to$
31219 \begin_layout Standard
31233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31236 \begin_layout Standard
31237 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31253 \begin_layout Standard
31260 is especially suitable to visualize the reduction of fractions within formulas:
31261 \begin_inset Formula \[
31262 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31269 \begin_layout Subsection
31270 Formulas in Section Headings
31271 \begin_inset LatexCommand label
31272 name "sub:Formulas-in-Section"
31277 \begin_inset LatexCommand index
31278 name "Formula ! in section headings"
31285 \begin_layout Standard
31286 When formulas are used in section headings, the following has to be taken
31290 \begin_layout Standard
31291 \begin_inset Note Greyedout
31294 \begin_layout Standard
31295 When the LaTeX-package
31300 \begin_inset LatexCommand index
31301 name "Packages ! hyperref"
31305 is used, PDF-bookmarks are automatically created for every section heading
31306 in the table of contents.
31307 If a section heading contains formulas, they are incorrectly displayed
31308 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31317 \begin_layout Standard
31318 Both problems can be solved by inserting at the end of the section heading
31319 a short title with the menu
31321 Insert\SpecialChar \menuseparator
31326 Short titles are used as alternative for multiline section headings to
31327 keep the table of contents clearly arranged.
31328 Only the short title appears in the table of contents and therefore also
31329 in the PDF-bookmark.
31332 \begin_layout Standard
31333 When formulas should be used in the table of contents but
31337 is used, one can use the following command in TeX-mode:
31340 \begin_layout Standard
31345 texorpdfstring{part}{alternative}
31346 \begin_inset LatexCommand index
31347 name "Commands ! T ! \\textbackslash texorpdfstring"
31354 \begin_layout Standard
31355 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31356 This can be characters, formulas, footnotes, but also cross-references.
31357 The alternative is used instead of the part for the bookmark.
31360 \begin_layout Standard
31361 Here are two example headings:
31362 \begin_inset VSpace -3mm
31369 \begin_layout Standard
31381 \begin_layout Subsubsection
31382 Heading without formula in table of contents
31383 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31387 \begin_inset OptArg
31390 \begin_layout Standard
31391 Heading without formula in table of contents
31399 \begin_layout Subsubsection
31400 Heading with formula in table of contents
31404 \begin_layout Standard
31414 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31421 \begin_layout Standard
31431 \begin_layout Standard
31435 \begin_layout Standard
31444 In the first heading a short title was used, in the second one
31453 \begin_layout Standard
31454 To get the same formatting as for the other headings, the complete heading
31457 boldmath environment
31463 \begin_layout Standard
31465 \begin_inset LatexCommand ref
31466 reference "sub:Bold-Formulas"
31478 \begin_layout Subsection
31479 Formulas in multi-column Text
31480 \begin_inset LatexCommand index
31481 name "Formula ! in multi-column text"
31488 \begin_layout Standard
31489 Formulas in multi-column text are often too wide to fit into a column and
31490 thus need to be set over the whole page width.
31491 This is done by using the LaTeX-package
31499 \begin_layout Standard
31504 is part of every LaTeX standard installation.
31510 \begin_inset LatexCommand index
31511 name "Packages ! multicol"
31515 , that is loaded with the LaTeX-preamble line
31518 \begin_layout Standard
31523 usepackage{multicol}
31526 \begin_layout Standard
31527 \begin_inset Note Greyedout
31530 \begin_layout Standard
31531 Note herby that the setting
31533 Two-column\InsetSpace ~
31538 Document\SpecialChar \menuseparator
31561 \begin_layout Standard
31562 Before the multi-column text the command
31565 \begin_layout Standard
31570 begin{multicols}{column number}
31573 \begin_layout Standard
31574 is written in TeX-mode.
31575 The column number is a number in the range of 2\InsetSpace \thinspace{}
31576 -\InsetSpace \thinspace{}
31578 Before the formula the multi-column text is ended by inserting the command
31581 \begin_layout Standard
31589 \begin_layout Standard
31593 \begin_layout Standard
31594 Due to the command some space is automatically added before the formula.
31595 To revert this, -6\InsetSpace \thinspace{}
31596 mm vertical space is inserted before the formula.
31597 When the formula style
31603 \begin_layout Standard
31605 \begin_inset LatexCommand ref
31606 reference "sec:Formula-Styles"
31617 is used, -9\InsetSpace \thinspace{}
31618 mm space is inserted instead.
31621 \begin_layout Standard
31622 As example a multi-column text with a displayed formula:
31625 \begin_layout Standard
31629 \begin_layout Standard
31633 begin{multicols}{2}
31638 Das Spektrum wird fouriertransformiert.
31639 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31640 , Lösungsmittel) zu trennen.
31641 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31642 nun das Aussehen des Ausgangssignals.
31643 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31644 über alle Phasen integrieren muss.
31646 \begin_inset Formula $S$
31649 unser normiertes Ausgangssignal and
31650 \begin_inset Formula $P$
31653 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31657 \begin_layout Standard
31667 \begin_inset VSpace -6mm
31671 \begin_inset Formula \begin{equation}
31672 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31680 \begin_layout Standard
31684 begin{multicols}{2}
31690 \begin_inset Formula $S_{0}$
31693 das Signal ohne Gradient ist and the Normierungsbedingung
31694 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31698 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31700 \begin_inset Formula $\nicefrac{\pi}{2}$
31703 \InsetSpace \thinspace{}
31704 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31705 das Signal zusätzlich abschwächt.
31706 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31708 \begin_inset Formula $T_{2}$
31714 \begin_layout Standard
31718 \begin_layout Standard
31730 \begin_layout Subsection
31731 Formulas with Description of Variables
31732 \begin_inset LatexCommand index
31733 name "Formula ! with description of variables"
31740 \begin_layout Standard
31741 To describe variables within a formula, like in formula
31742 \begin_inset LatexCommand eqref
31743 reference "eq:within"
31752 \begin_inset Formula $n$
31756 matrix is used with left aligned columns for the
31757 \begin_inset Formula $n$
31764 \begin_layout Standard
31766 \begin_inset LatexCommand ref
31767 reference "sec:Matrices"
31776 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31789 \begin_layout Standard
31791 \begin_inset LatexCommand ref
31792 reference "sub:Font-Sizes"
31804 \begin_layout Standard
31805 When the formula style
31811 \begin_layout Standard
31813 \begin_inset LatexCommand ref
31814 reference "sec:Formula-Styles"
31835 \begin_layout Standard
31842 only works in formulas with the style
31847 \begin_inset LatexCommand ref
31848 reference "sub:Variable-Space"
31857 is inserted before and after the matrix to have the same separation of
31858 the matrix from the equation and the side margin.
31861 \begin_layout Standard
31862 When the formula style
31866 is used, the method described in
31867 \begin_inset LatexCommand ref
31868 reference "sub:Flalign-Environment"
31872 is used to indent formulas.
31874 \begin_inset LatexCommand eqref
31875 reference "eq:within"
31879 consists of five columns whereas in the first two columns contain the equation,
31880 the third the matrix, and the last one an empty TeX-brace.
31881 \begin_inset Formula \begin{flalign}
31882 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31883 \rho & \textrm{density}\\
31884 V & \textrm{volume}\\
31885 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31892 \begin_layout Subsection
31893 Upright small Greek Letters
31894 \begin_inset LatexCommand label
31895 name "sub:Upright-small-Greek"
31900 \begin_inset LatexCommand index
31901 name "Greek letters ! upright"
31908 \begin_layout Standard
31909 Most of the math fonts only provide italic small Greek letters.
31910 But for symbols of elementary particles like pions and neutrinos, upright
31911 Greek letters are needed.
31920 \begin_layout Standard
31925 is part of the LaTeX-package
31930 \begin_inset LatexCommand index
31931 name "Packages ! was\\vspace{4mm}"
31941 \begin_inset LatexCommand index
31942 name "Packages ! upgreek"
31946 that is loaded with the LaTeX-preamble line
31949 \begin_layout Standard
31954 usepackage{upgreek}
31957 \begin_layout Standard
31963 \begin_layout Standard
31973 \begin_inset Note Note
31976 \begin_layout Standard
31977 The following table will only be displayed when the LaTeX-package
31986 They are created when the command for a small Greek letters is started
31992 For example the command
31999 \begin_inset Formula $\uptau$
32005 \begin_layout Standard
32006 With these commands reactions of elementary particles can be typeset:
32007 \begin_inset Formula \[
32008 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32015 \begin_layout Standard
32016 The upright letters are more bold and wider than the italic ones.
32017 They should therefore not be used for units like
32018 \begin_inset Quotes eld
32022 \begin_inset Quotes erd
32028 \begin_layout Standard
32032 \begin_layout Standard
32042 \begin_inset Note Note
32045 \begin_layout Standard
32046 The following will be displayed when the LaTeX-package
32058 \begin_layout Standard
32059 You need to install the LaTeX-package
32063 to see the rest of this subsection in the output.
32066 \begin_layout Standard
32070 \begin_layout Standard
32082 \begin_layout Subsection
32083 Text Characters in Formulas
32084 \begin_inset LatexCommand label
32085 name "sub:Text-Characters-in"
32090 \begin_inset LatexCommand index
32091 name "Text ! in formulas"
32098 \begin_layout Standard
32099 In some cases you might want to insert text characters directly into formulas.
32100 When for example the centered dot · is often used in formulas like
32101 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32104 , one would have to insert the command
32114 \begin_layout Standard
32116 \begin_inset LatexCommand ref
32117 reference "sub:Binary-Operators"
32126 all the time, because this character is defined in all encodings as text
32128 But the encoding can be changed by this LaTeX-preamble line:
32131 \begin_layout Standard
32136 Declare Inputtext{183}{
32146 f\SpecialChar \textcompwordmark{}
32150 \begin_layout Standard
32151 The character encoding (menu
32153 Document\SpecialChar \menuseparator
32154 Settings\SpecialChar \menuseparator
32157 ) specifies what character appears when a keyboard key is pressed.
32158 When the key for the character '·' is pressed, internally the command
32165 But this command is not available in a formula so that you would get LaTeX-erro
32167 With the changed encoding the right command is chosen automatically, depending
32168 on if the character was inserted into a formula or not.
32171 \begin_layout Standard
32172 The encoding of several characters is saved in definition files.
32173 Fore example the encoding
32177 is defined in the file
32181 that is in the installation folder of LaTeX.
32182 Encodings should only be changed via the LaTeX-preamble and not in the
32184 Otherwise own documents could not be edited by other LyX users working
32185 on other computers.
32188 \begin_layout Standard
32189 \begin_inset VSpace medskip
32192 Besides the centered dot, in this document the degree sign ° is defined
32193 with the following LaTeX-preamble line so that it can directly be inserted
32197 \begin_layout Standard
32202 DeclareInputtext{176}{
32212 f\SpecialChar \textcompwordmark{}
32216 \begin_layout Standard
32222 \begin_layout Section
32224 Typographic Advises
32225 \begin_inset LatexCommand index
32226 name "Typographic Advises"
32233 \begin_layout Standard
32234 This section is a summary of the most important typographic rules, listed
32239 \begin_layout Standard
32240 This collection was partly taken from the German semi-official dictionary
32242 \begin_inset Quotes eld
32246 \begin_inset Quotes erd
32250 \begin_inset LatexCommand cite
32255 that lists some of the ISO rules.
32263 \begin_layout Itemize
32272 \begin_layout Standard
32273 done with font styles, see
32274 \begin_inset LatexCommand ref
32275 reference "sub:Font-Styles"
32284 : 30\InsetSpace \thinspace{}
32287 Between the value and the unit is the smallest space, see
32288 \begin_inset LatexCommand ref
32289 reference "sub:Predefined-Space"
32296 \begin_layout Itemize
32297 Percent and perthousand signs are set like physical units:
32299 1,2\InsetSpace \thinspace{}
32304 \begin_layout Standard
32317 \begin_layout Itemize
32318 The degree sign follows directly on the value: 15°, but not when it is used
32319 in units: 15\InsetSpace \thinspace{}
32323 \begin_layout Itemize
32324 In numbers with more than four digits the smallest space is inserted before
32325 every third digit to group them:
32334 18\InsetSpace \thinspace{}
32335 473\InsetSpace \thinspace{}
32339 \begin_layout Itemize
32340 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32341 cm the multiplication sign
32342 \begin_inset Quotes eld
32346 \begin_inset Quotes erd
32350 It is available with the LaTeX-command
32356 , but can also directly be inserted with some keyboard definitions.
32359 \begin_layout Itemize
32360 Functions with names consisting of several letters are set upright to avoid
32362 \begin_inset LatexCommand ref
32363 reference "sub:Predefined-Functions"
32370 \begin_layout Itemize
32371 Indices consisting of several letters, are set upright:
32372 \begin_inset Formula $E_{\mathrm{kin}}$
32377 Components of matrices are set italic:
32378 \begin_inset Formula $\hat{H}_{kl}$
32384 \begin_layout Itemize
32385 The differentiation/integration operator 'd', the Euler's number 'e', and
32386 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32390 \begin_layout Standard
32396 \begin_layout Section
32398 \begin_inset LatexCommand index
32406 \begin_layout Standard
32407 Some characters and symbols can be created with several commands.
32408 Here is a list of the synonym commands:
32411 \begin_layout Standard
32412 \begin_inset VSpace bigskip
32418 \begin_inset Tabular
32419 <lyxtabular version="3" rows="12" columns="2">
32421 <column alignment="center" valignment="top" leftline="true" width="0pt">
32422 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32423 <row topline="true" bottomline="true">
32424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32427 \begin_layout Standard
32433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32436 \begin_layout Standard
32438 \begin_inset Note Note
32441 \begin_layout Standard
32448 is only used as spacer.
32459 <row topline="true">
32460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32463 \begin_layout Standard
32471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32474 \begin_layout Standard
32478 \begin_layout Standard
32491 \begin_layout Standard
32504 <row topline="true">
32505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32508 \begin_layout Standard
32516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32519 \begin_layout Standard
32528 <row topline="true">
32529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32532 \begin_layout Standard
32540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32543 \begin_layout Standard
32552 <row topline="true">
32553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32556 \begin_layout Standard
32564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32567 \begin_layout Standard
32574 <row topline="true">
32575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32578 \begin_layout Standard
32586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32589 \begin_layout Standard
32596 <row topline="true">
32597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32600 \begin_layout Standard
32608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32611 \begin_layout Standard
32620 <row topline="true">
32621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32624 \begin_layout Standard
32632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32635 \begin_layout Standard
32644 <row topline="true">
32645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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32659 \begin_layout Standard
32668 <row topline="true">
32669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32672 \begin_layout Standard
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32683 \begin_layout Standard
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32696 \begin_layout Standard
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32707 \begin_layout Standard
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32718 \begin_layout Standard
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32748 <row topline="true" bottomline="true">
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32752 \begin_layout Standard
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32761 \begin_layout Standard
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32783 \begin_layout Standard
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32798 \begin_layout Standard
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32809 \begin_layout Standard
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32833 \begin_layout Standard
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32857 \begin_layout Standard
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32868 \begin_layout Standard
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32901 \begin_layout Standard
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32914 \begin_layout Standard
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32925 \begin_layout Standard
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32938 \begin_layout Standard
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32949 \begin_layout Standard
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32962 \begin_layout Standard
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32973 \begin_layout Standard
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32986 \begin_layout Standard
32994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32997 \begin_layout Standard
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33010 \begin_layout Standard
33018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33021 \begin_layout Standard
33039 \begin_layout Standard
33045 \begin_layout Bibliography
33046 \begin_inset LatexCommand bibitem
33058 The LaTeX Companion
33061 Addison Wesley, 2004
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33074 \begin_layout Standard
33078 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
33087 \begin_layout Standard
33094 of LaTeX's math abilities
33097 \begin_layout Bibliography
33098 \begin_inset LatexCommand bibitem
33103 LaTeX tips and tricks-
33107 \begin_layout Standard
33111 href{http://tug.org/TeXnik/}{
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33130 \begin_layout Bibliography
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33140 \begin_layout Standard
33144 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
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33164 \begin_layout Standard
33176 \begin_layout Bibliography
33177 \begin_inset LatexCommand bibitem
33186 \begin_layout Standard
33190 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
33199 \begin_layout Standard
33206 of all symbols available with LaTeX-packages
33209 \begin_layout Bibliography
33210 \begin_inset LatexCommand bibitem
33219 \begin_layout Standard
33223 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
33232 \begin_layout Standard
33239 of the LaTeX-package
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33245 name "Packages ! hyperref"
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33262 \begin_layout Standard
33266 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
33275 \begin_layout Standard
33289 \begin_inset LatexCommand ref
33290 reference "sub:Operator-Limits"
33295 \begin_inset LatexCommand index
33296 name "Commands ! M ! \\textbackslash mathclap"
33303 \begin_layout Bibliography
33304 \begin_inset LatexCommand bibitem
33315 Auflage, Duden 2001
33318 \begin_layout Subsubsection*
33319 \begin_inset LatexCommand printindex