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
2755 \begin_layout Standard
2756 Umlauts and accents in formulas, like in the table above, are explained
2758 \begin_inset LatexCommand ref
2759 reference "sub:Accents-for-one"
2771 \begin_layout Standard
2778 is also available via the menu
2780 Insert\SpecialChar \menuseparator
2781 Math\SpecialChar \menuseparator
2787 \begin_layout Subsection
2789 \begin_inset LatexCommand index
2797 \begin_layout Standard
2805 \begin_inset LatexCommand index
2806 name "Commands ! N ! \\textbackslash not"
2810 every character can be displayed canceled.
2811 The characters are quasi accentuated by a slash.
2814 \begin_layout Standard
2816 \begin_inset Tabular
2817 <lyxtabular version="3" rows="4" columns="2">
2819 <column alignment="center" valignment="top" leftline="true" width="0pt">
2820 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2821 <row topline="true" bottomline="true">
2822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2825 \begin_layout Standard
2831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2834 \begin_layout Standard
2841 <row topline="true">
2842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2845 \begin_layout Standard
2853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2856 \begin_layout Standard
2857 \begin_inset Formula $\not=$
2866 <row topline="true" bottomline="true">
2867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2870 \begin_layout Standard
2880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2883 \begin_layout Standard
2884 \begin_inset Formula $\not\le$
2893 <row topline="true" bottomline="true">
2894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2897 \begin_layout Standard
2907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2910 \begin_layout Standard
2911 \begin_inset Formula $\not\parallel$
2927 \begin_layout Standard
2928 The last example shows, that not all negations look good.
2929 Therefore there are for some negations special commands (see
2930 \begin_inset LatexCommand ref
2931 reference "sub:Mathematical-Symbols"
2936 \begin_inset LatexCommand ref
2937 reference "sec:Relations"
2944 \begin_layout Subsection
2946 \begin_inset LatexCommand label
2947 name "sub:Placeholders"
2952 \begin_inset LatexCommand index
2958 \begin_inset LatexCommand index
2959 name "Chemical characters ! Isotopes"
2964 \begin_inset LatexCommand index
2965 name "Isotopes|see{Chemical characters}"
2972 \begin_layout Standard
2973 When displaying e.\InsetSpace \thinspace{}
2979 \begin_layout Standard
2980 More about chemical symbols is written in
2981 \begin_inset LatexCommand ref
2982 reference "sub:Chemical-Symbols-and"
2991 the following problem occurs:
2994 \begin_layout Standard
2996 \begin_inset Tabular
2997 <lyxtabular version="3" rows="2" columns="2">
2999 <column alignment="center" valignment="top" width="0pt">
3000 <column alignment="center" valignment="top" width="0pt">
3002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3005 \begin_layout Standard
3006 Indices created with sub- and superscripts:
3011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3014 \begin_layout Standard
3015 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3028 \begin_layout Standard
3034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3037 \begin_layout Standard
3038 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3052 \begin_inset Note Note
3055 \begin_layout Standard
3062 is only used as spacer.
3070 \begin_layout Standard
3071 The shorter index is by default placed below or above the first character
3072 of the longer index.
3073 To avoid this there is the command
3080 \begin_inset LatexCommand index
3081 name "Commands ! P ! \\textbackslash phantom"
3085 or the math toolbar button\InsetSpace \thinspace{}
3090 \begin_layout Standard
3091 can be found in the submenu of the toolbar button
3092 \begin_inset Graphics
3093 filename ../images/math/space.png
3104 \begin_inset Graphics
3105 filename ../images/math/phantom.png
3110 that creates one or more phantom characters.
3117 a small blue box appears that is superposed with two red arrows.
3118 The arrows indicate that the complete width and height of the box content
3119 will be created as placeholder.
3120 Phantom characters are accordingly placeholders with the size of the characters.
3123 \begin_layout Standard
3125 \begin_inset Tabular
3126 <lyxtabular version="3" rows="4" columns="2">
3128 <column alignment="center" valignment="top" leftline="true" width="0">
3129 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3130 <row topline="true" bottomline="true">
3131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3134 \begin_layout Standard
3140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3143 \begin_layout Standard
3145 \begin_inset Note Note
3148 \begin_layout Standard
3155 is only used as spacer.
3166 <row topline="true">
3167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3170 \begin_layout Standard
3175 \begin_layout Standard
3190 \begin_layout Standard
3200 \begin_inset Formula $\to$
3207 \begin_layout Standard
3221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3224 \begin_layout Standard
3225 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3234 <row topline="true" bottomline="true">
3235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3238 \begin_layout Standard
3243 \begin_layout Standard
3258 \begin_layout Standard
3268 \begin_inset Formula $\to$
3275 \begin_layout Standard
3289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3292 \begin_layout Standard
3293 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3302 <row topline="true" bottomline="true">
3303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3306 \begin_layout Standard
3313 \begin_layout Standard
3328 \begin_layout Standard
3338 \begin_inset Formula $\to$
3345 \begin_layout Standard
3359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3362 \begin_layout Standard
3363 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3379 \begin_layout Standard
3380 Furthermore there are the commands
3387 \begin_inset LatexCommand index
3388 name "Commands ! V ! \\textbackslash vphantom"
3392 (toolbar button \InsetSpace ~
3394 \begin_inset Graphics
3395 filename ../images/math/vphantom.png
3407 \begin_inset LatexCommand index
3408 name "Commands ! H ! \\textbackslash hphantom"
3412 (toolbar button \InsetSpace ~
3414 \begin_inset Graphics
3415 filename ../images/math/hphantom.png
3427 creates only space for the maximal height of the characters in the box
3428 but not for its width.
3435 creates only space for the width of the box content.
3436 Therefore the boxes of both commands have only one red arrow.
3439 \begin_layout Standard
3450 \begin_layout Standard
3465 space for the height of the integral sign,
3469 \begin_layout Standard
3476 creates an integral sign, see
3477 \begin_inset LatexCommand ref
3478 reference "sub:Big-Operators"
3487 because this is the larger character.
3488 An example application is in
3489 \begin_inset LatexCommand ref
3490 reference "sub:Multiline-Brackets"
3497 \begin_layout Subsection
3499 \begin_inset LatexCommand index
3505 \begin_inset LatexCommand index
3506 name "Formula ! underlined"
3513 \begin_layout Standard
3515 \begin_inset Tabular
3516 <lyxtabular version="3" rows="4" columns="2">
3518 <column alignment="center" valignment="top" leftline="true" width="0pt">
3519 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3520 <row topline="true" bottomline="true">
3521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3524 \begin_layout Standard
3530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3533 \begin_layout Standard
3535 \begin_inset Note Note
3538 \begin_layout Standard
3545 is only used as spacer.
3556 <row topline="true" bottomline="true">
3557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3560 \begin_layout Standard
3567 \begin_layout Standard
3577 \begin_inset LatexCommand index
3578 name "Commands ! O ! \\textbackslash overline"
3587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3590 \begin_layout Standard
3591 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3600 <row bottomline="true">
3601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3604 \begin_layout Standard
3611 \begin_layout Standard
3621 \begin_inset LatexCommand index
3622 name "Commands ! U ! \\textbackslash underline"
3631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3634 \begin_layout Standard
3635 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3644 <row topline="true" bottomline="true">
3645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3648 \begin_layout Standard
3655 \begin_layout Standard
3670 \begin_layout Standard
3684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3687 \begin_layout Standard
3688 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3704 \begin_layout Standard
3705 In the last example it doesn't matter if first
3720 \begin_layout Standard
3721 To double underline e.\InsetSpace \thinspace{}
3732 \begin_layout Standard
3733 It is possible to place up to 6 lines above or below characters.
3736 \begin_layout Subsection
3738 \begin_inset LatexCommand index
3746 \begin_layout Standard
3747 There are different types of ellipses available.
3751 \begin_layout Standard
3752 In the math toolbar in the submenu of the button
3753 \begin_inset Graphics
3754 filename ../images/math/ldots.png
3764 For listings dots at the baseline are used (
3771 \begin_inset LatexCommand index
3772 name "Commands ! L ! \\textbackslash ldots"
3776 ), while for operations dots are needed that are on the same height as the
3784 \begin_inset LatexCommand index
3785 name "Commands ! C ! \\textbackslash cdots"
3790 When using the command
3797 \begin_inset LatexCommand index
3798 name "Commands ! D ! \\textbackslash dots"
3802 , LaTeX decides on the basis of the next character what type is used.
3805 \begin_layout Standard
3807 \begin_inset Tabular
3808 <lyxtabular version="3" rows="8" columns="2">
3810 <column alignment="center" valignment="top" leftline="true" width="0pt">
3811 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3812 <row topline="true" bottomline="true">
3813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3816 \begin_layout Standard
3822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3825 \begin_layout Standard
3832 <row topline="true">
3833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3836 \begin_layout Standard
3841 \begin_layout Standard
3856 \begin_layout Standard
3870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3873 \begin_layout Standard
3874 \begin_inset Formula $A_{1},\dots,A_{n}$
3883 <row topline="true">
3884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3887 \begin_layout Standard
3892 \begin_layout Standard
3907 \begin_layout Standard
3921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3924 \begin_layout Standard
3925 \begin_inset Formula $A_{1}+\dots+A_{n}$
3934 <row topline="true">
3935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3938 \begin_layout Standard
3943 \begin_layout Standard
3958 \begin_layout Standard
3972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3975 \begin_layout Standard
3976 \begin_inset Formula $A_{1},\ldots,A_{n}$
3985 <row topline="true" bottomline="true">
3986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3989 \begin_layout Standard
3994 \begin_layout Standard
4009 \begin_layout Standard
4023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4026 \begin_layout Standard
4027 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4036 <row topline="true">
4037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4040 \begin_layout Standard
4048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4051 \begin_layout Standard
4052 \begin_inset Formula $\vdots$
4061 <row topline="true" bottomline="true">
4062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4065 \begin_layout Standard
4073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4076 \begin_layout Standard
4077 \begin_inset Formula $\ddots$
4086 <row topline="true" bottomline="true">
4087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4090 \begin_layout Standard
4091 3×3\InsetSpace \thinspace{}
4092 matrix with the different dots
4097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4100 \begin_layout Standard
4101 \begin_inset Formula $\begin{array}{ccc}
4102 A_{11} & \cdots & A_{1m}\\
4103 \vdots & \ddots & \vdots\\
4104 A_{n1} & \cdots & A_{nm}\end{array}$
4120 \begin_layout Standard
4121 The ellipses available in menu
4123 Insert\SpecialChar \menuseparator
4124 Special\InsetSpace ~
4136 \begin_layout Standard
4137 \begin_inset VSpace medskip
4140 Specially for matrices there are ellipses that span over several columns.
4141 They are created with the command
4148 \begin_inset LatexCommand index
4149 name "Commands ! H ! \\textbackslash hdotsfor"
4153 , that has the following scheme:
4156 \begin_layout Standard
4161 hdotsfor[distance]{number of columns}
4164 \begin_layout Standard
4165 The number of columns specifies how many columns should be spanned.
4166 Distance is a factor for the distance between the dots.
4169 \begin_layout Standard
4170 In the following matrix the command
4176 was inserted in the first box of the second line, to get an ellipsis with
4177 a dot distance twice as long as with the command
4184 \begin_inset Formula \[
4185 \left(\begin{array}{cccc}
4188 q & w & e & r\end{array}\right)\]
4192 Note that the matrix fields that should be spanned must be empty, otherwise
4193 you get LaTeX-errors.
4196 \begin_layout Standard
4197 \begin_inset VSpace bigskip
4200 Furthermore you can fill with the command
4207 \begin_inset LatexCommand index
4208 name "Commands ! D ! \\textbackslash dotfill"
4212 the rest of a line with dots.
4213 The effect of these commands is the same like with
4220 \begin_inset LatexCommand ref
4221 reference "sub:Variable-Space"
4228 \begin_layout Standard
4229 For example the command
4237 \begin_layout Standard
4251 \begin_layout Standard
4252 \begin_inset Formula $A\dotfill B$
4258 \begin_layout Standard
4265 there is for a line the command
4272 \begin_inset LatexCommand index
4273 name "Commands ! H ! \\textbackslash hrulefill"
4280 \begin_layout Standard
4281 \begin_inset Formula $A\hrulefill B$
4287 \begin_layout Standard
4288 To use the commands for text, they have to be inserted in TeX-mode.
4291 \begin_layout Section
4293 \begin_inset LatexCommand label
4299 \begin_inset LatexCommand index
4307 \begin_layout Standard
4308 Matrices can be inserted via the math toolbar button
4309 \begin_inset Graphics
4310 filename ../images/dialog-show_mathmatrix.png
4317 Insert\SpecialChar \menuseparator
4318 Math\SpecialChar \menuseparator
4322 You will be asked for the number of matrix columns and rows, and the alignment.
4323 The vertical alignment is hereby only of importance for matrices in inline
4327 \begin_layout Standard
4328 The first matrix is top
4329 \begin_inset Formula $\begin{array}[t]{cccc}
4332 C & F & I & L\end{array}$
4336 \begin_inset Formula $\begin{array}{cccc}
4339 C & F & I & L\end{array}$
4342 , and the third bottom
4343 \begin_inset Formula $\begin{array}[b]{cccc}
4346 C & F & I & L\end{array}$
4352 \begin_layout Standard
4353 The horizontal alignment specifies how the column entries should be aligned.
4354 It is set by entering a letter for every column.
4359 denotes left aligned,
4368 To create for example a 4
4373 matrix where the first column is left aligned, the second and third are
4374 centered, and the last one is right aligned, one enters for the horizontal
4380 Normally are in a matrix all columns centered, therefore the default is
4381 for every column is a
4388 \begin_layout Standard
4389 Horizontal alignment:
4392 \begin_layout Standard
4398 \begin_inset Formula $\begin{array}{lll}
4401 C & F & 10000\end{array}$
4409 \begin_inset Formula $\begin{array}{ccc}
4412 C & F & 10000\end{array}$
4420 \begin_inset Formula $\begin{array}{rrr}
4423 C & F & 10000\end{array}$
4429 \begin_layout Standard
4430 To add or delete rows and columns subsequently, the math toolbar buttons
4432 \begin_inset Graphics
4433 filename ../images/tabular-feature_append-row.png
4439 \begin_inset Graphics
4440 filename ../images/tabular-feature_delete-row.png
4445 , etc.\InsetSpace \thinspace{}
4448 Edit\SpecialChar \menuseparator
4452 New rows can also be created with
4459 \begin_layout Standard
4460 \begin_inset VSpace bigskip
4463 Parentheses around a matrix can can either be created with the commands
4471 \begin_inset LatexCommand index
4472 name "Commands ! L ! \\textbackslash left"
4483 \begin_inset LatexCommand index
4484 name "Commands ! R ! \\textbackslash right"
4494 \begin_inset LatexCommand ref
4495 reference "sub:Automatic-Bracket-Size"
4499 , or by using the following commands:
4500 \begin_inset VSpace medskip
4506 \begin_layout Standard
4510 \begin_inset Tabular
4511 <lyxtabular version="3" rows="4" columns="2">
4513 <column alignment="center" valignment="top" leftline="true" width="0">
4514 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4515 <row topline="true" bottomline="true">
4516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4519 \begin_layout Standard
4525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4528 \begin_layout Standard
4530 \begin_inset Note Note
4533 \begin_layout Standard
4540 is only used as spacer.
4551 <row topline="true">
4552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4555 \begin_layout Standard
4562 \begin_layout Standard
4575 2\InsetSpace \thinspace{}
4581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4584 \begin_layout Standard
4585 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4586 0 & \textrm{-}\mathrm{i}\\
4587 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4596 <row topline="true">
4597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4600 \begin_layout Standard
4607 \begin_layout Standard
4620 2\InsetSpace \thinspace{}
4626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4629 \begin_layout Standard
4630 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4631 0 & \textrm{-}\mathrm{i}\\
4632 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4641 <row topline="true" bottomline="true">
4642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4645 \begin_layout Standard
4652 \begin_layout Standard
4665 2\InsetSpace \thinspace{}
4671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4674 \begin_layout Standard
4675 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4676 0 & \textrm{-}\mathrm{i}\\
4677 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4693 \begin_inset Tabular
4694 <lyxtabular version="3" rows="4" columns="2">
4696 <column alignment="center" valignment="top" leftline="true" width="0">
4697 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4698 <row topline="true" bottomline="true">
4699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4702 \begin_layout Standard
4708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4711 \begin_layout Standard
4718 <row topline="true">
4719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4722 \begin_layout Standard
4729 \begin_layout Standard
4742 2\InsetSpace \thinspace{}
4748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4751 \begin_layout Standard
4752 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4753 0 & \textrm{-}\mathrm{i}\\
4754 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4763 <row topline="true" bottomline="true">
4764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4767 \begin_layout Standard
4774 \begin_layout Standard
4787 2\InsetSpace \thinspace{}
4793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4796 \begin_layout Standard
4797 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4798 0 & \textrm{-}\mathrm{i}\\
4799 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4808 <row topline="true" bottomline="true">
4809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4812 \begin_layout Standard
4819 \begin_layout Standard
4832 2\InsetSpace \thinspace{}
4838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4841 \begin_layout Standard
4842 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4843 0 & \textrm{-}\mathrm{i}\\
4844 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4862 \begin_layout Standard
4863 \begin_inset VSpace medskip
4866 When e.\InsetSpace \thinspace{}
4874 is inserted, a blue box appears between two vertical lines where the matrix
4878 \begin_layout Standard
4879 \begin_inset VSpace bigskip
4882 As all multiline formulas are matrices, the length
4889 \begin_inset LatexCommand index
4890 name "Commands ! A ! \\textbackslash arraycolsep"
4894 that is described in
4895 \begin_inset LatexCommand ref
4896 reference "sub:Column-Separation"
4900 can also be used to change the column separation of matrices.
4903 \begin_layout Standard
4904 To change the row separation, the command
4911 \begin_inset LatexCommand index
4912 name "Commands ! A ! \\textbackslash arraystretch"
4917 It is used as follows:
4920 \begin_layout Standard
4927 arraystretch}{stretch factor}
4928 \begin_inset LatexCommand index
4929 name "Commands ! R ! \\textbackslash renewcommand"
4936 \begin_layout Standard
4943 assigns the stretch factor to the predefined command
4950 To double e.\InsetSpace \thinspace{}
4952 the row separation, use the factor 2.
4953 This is then used for all following matrices.
4954 To go back to the original separation, assign the factor 1 to
4963 \begin_layout Standard
4964 To set matrices into a text line, the command
4971 \begin_inset LatexCommand index
4972 name "Commands ! S ! \\textbackslash smallmatrix"
4977 When it is inserted a blue box with two dashed lines appears.
4978 In this box the matrix is inserted.
4981 \begin_layout Standard
4983 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
4984 C & D\end{smallmatrix}\right)$
4990 \begin_layout Section
4991 Brackets and Delimiters
4992 \begin_inset LatexCommand index
4998 \begin_inset LatexCommand index
5006 \begin_layout Subsection
5007 Vertical Brackets and Delimiters
5008 \begin_inset LatexCommand index
5009 name "Brackets ! vertical"
5016 \begin_layout Standard
5020 \begin_inset Tabular
5021 <lyxtabular version="3" rows="9" columns="2">
5023 <column alignment="center" valignment="top" leftline="true" width="0pt">
5024 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5025 <row topline="true" bottomline="true">
5026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5029 \begin_layout Standard
5035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5038 \begin_layout Standard
5045 <row topline="true">
5046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5049 \begin_layout Standard
5055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5058 \begin_layout Standard
5059 \begin_inset Formula $($
5068 <row topline="true">
5069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5072 \begin_layout Standard
5078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5081 \begin_layout Standard
5082 \begin_inset Formula $\{$
5091 <row topline="true">
5092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5095 \begin_layout Standard
5101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5104 \begin_layout Standard
5105 \begin_inset Formula $[$
5114 <row topline="true">
5115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5118 \begin_layout Standard
5126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5129 \begin_layout Standard
5130 \begin_inset Formula $\langle$
5139 <row topline="true">
5140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5143 \begin_layout Standard
5151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5154 \begin_layout Standard
5155 \begin_inset Formula $\lceil$
5164 <row topline="true">
5165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5168 \begin_layout Standard
5176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5179 \begin_layout Standard
5180 \begin_inset Formula $\lfloor$
5189 <row topline="true">
5190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5193 \begin_layout Standard
5199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5202 \begin_layout Standard
5203 \begin_inset Formula $/$
5212 <row topline="true" bottomline="true">
5213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5216 \begin_layout Standard
5222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5225 \begin_layout Standard
5226 \begin_inset Formula $|$
5242 \begin_inset Tabular
5243 <lyxtabular version="3" rows="9" columns="2">
5245 <column alignment="center" valignment="top" leftline="true" width="0pt">
5246 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5247 <row topline="true" bottomline="true">
5248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5251 \begin_layout Standard
5257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5260 \begin_layout Standard
5267 <row topline="true">
5268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5271 \begin_layout Standard
5277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5280 \begin_layout Standard
5281 \begin_inset Formula $)$
5290 <row topline="true">
5291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5294 \begin_layout Standard
5300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5303 \begin_layout Standard
5304 \begin_inset Formula $\}$
5313 <row topline="true">
5314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5317 \begin_layout Standard
5323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5326 \begin_layout Standard
5327 \begin_inset Formula $]$
5336 <row topline="true">
5337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5340 \begin_layout Standard
5348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5351 \begin_layout Standard
5352 \begin_inset Formula $\rangle$
5361 <row topline="true">
5362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5365 \begin_layout Standard
5373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5376 \begin_layout Standard
5377 \begin_inset Formula $\rceil$
5386 <row topline="true">
5387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5390 \begin_layout Standard
5398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5401 \begin_layout Standard
5402 \begin_inset Formula $\rfloor$
5411 <row topline="true">
5412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5415 \begin_layout Standard
5425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5428 \begin_layout Standard
5429 \begin_inset Formula $\backslash$
5438 <row topline="true" bottomline="true">
5439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5442 \begin_layout Standard
5450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5453 \begin_layout Standard
5454 \begin_inset Formula $\|$
5472 \begin_layout Standard
5475 \begin_inset Note Greyedout
5478 \begin_layout Standard
5483 In TeX-mode the command
5490 \begin_inset LatexCommand index
5491 name "Commands ! T ! \\textbackslash textbackslash"
5495 must be used for the backslash, because the command
5503 produces there a line break.
5511 \begin_layout Standard
5512 For all characters listed above the size can be adjusted with the commands
5513 described in the following two subsections.
5514 When using these commands, the characters < and > can directly be used
5515 instead of the commands
5530 \begin_layout Subsubsection
5532 \begin_inset LatexCommand label
5533 name "sub:Manual-Bracket-Size"
5538 \begin_inset LatexCommand index
5539 name "Bracket size ! manual"
5546 \begin_layout Standard
5547 The bracket size can be specified manually by the LaTeX-commands
5554 \begin_inset LatexCommand index
5555 name "Commands ! B ! \\textbackslash big"
5584 denotes the smallest and
5590 the largest bracket size.
5593 \begin_layout Standard
5594 These commands are used to emphasize levels of brackets:
5597 \begin_layout Standard
5599 \begin_inset Tabular
5600 <lyxtabular version="3" rows="2" columns="2">
5602 <column alignment="center" valignment="top" width="0pt">
5603 <column alignment="center" valignment="top" width="0pt">
5605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5608 \begin_layout Standard
5609 all brackets in the same size:
5614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5617 \begin_layout Standard
5618 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5631 \begin_layout Standard
5637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5640 \begin_layout Standard
5641 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5655 \begin_inset Note Note
5658 \begin_layout Standard
5665 is only used as spacer.
5673 \begin_layout Standard
5674 For the second formula the command
5684 \begin_layout Standard
5698 \begin_layout Standard
5699 Here is an overview about all bracket sizes:
5702 \begin_layout Standard
5722 \begin_layout Standard
5739 \begin_layout Standard
5752 \begin_layout Standard
5768 \begin_layout Standard
5770 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5776 \begin_layout Standard
5785 -commands there is the variant
5792 \begin_inset LatexCommand index
5793 name "Commands ! B ! \\textbackslash bigm"
5797 that adds a bit more space between the bracket and its content, and the
5811 \begin_inset LatexCommand index
5812 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5816 , that don't add additional space.
5821 at the end of the command
5827 is for a left bracket; for a right bracket this will be replaced by an
5833 A left or right bracket can each be an opening or closing bracket.
5836 \begin_layout Standard
5837 In the following table is a comparison of the variants:
5840 \begin_layout Standard
5842 \begin_inset Tabular
5843 <lyxtabular version="3" rows="5" columns="2">
5845 <column alignment="center" valignment="middle" leftline="true" width="0">
5846 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5847 <row topline="true" bottomline="true">
5848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5851 \begin_layout Standard
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5860 \begin_layout Standard
5862 \begin_inset Note Note
5865 \begin_layout Standard
5872 is only used as spacer.
5883 <row topline="true">
5884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5887 \begin_layout Standard
5902 \begin_layout Standard
5920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5923 \begin_layout Standard
5924 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5933 <row topline="true">
5934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5937 \begin_layout Standard
5952 \begin_layout Standard
5970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Standard
5974 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
5983 <row topline="true" bottomline="true">
5984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5987 \begin_layout Standard
6002 \begin_layout Standard
6020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6023 \begin_layout Standard
6024 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6033 <row topline="true" bottomline="true">
6034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6037 \begin_layout Standard
6049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6052 \begin_layout Standard
6053 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6069 \begin_layout Subsubsection
6070 Automatic Bracket Size
6071 \begin_inset LatexCommand label
6072 name "sub:Automatic-Bracket-Size"
6077 \begin_inset LatexCommand index
6078 name "Bracket size ! automatic"
6085 \begin_layout Standard
6086 Brackets with variable size can be inserted with the commands
6093 \begin_inset LatexCommand index
6094 name "Commands ! L ! \\textbackslash left"
6105 \begin_inset LatexCommand index
6106 name "Commands ! R ! \\textbackslash right"
6110 or via the math toolbar button
6111 \begin_inset Graphics
6112 filename ../images/dialog-show_mathdelimiter.png
6130 the wanted bracket must be inserted.
6131 The bracket size will then automatically be calculated for the output.
6134 \begin_layout Standard
6136 normal bracket: The command
6146 \begin_layout Standard
6156 \begin_inset Formula $\downarrow$
6163 \begin_layout Standard
6175 \begin_inset Formula \[
6183 \begin_layout Standard
6185 multiline bracket: The command
6197 \begin_layout Standard
6207 \begin_inset Formula $\downarrow$
6214 \begin_layout Standard
6228 \begin_inset Formula \[
6229 \ln\left(\frac{A}{C}\right)\]
6236 \begin_layout Standard
6255 This has the advantage that you can see in LyX immediately the real bracket
6256 size and that the matching right bracket will be created too.
6259 for the last example would then be:
6273 \begin_layout Standard
6283 \begin_inset Formula $\downarrow$
6289 \begin_layout Standard
6290 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6291 For example the command
6301 \begin_layout Standard
6311 \begin_inset Formula $\downarrow$
6318 \begin_layout Standard
6334 \begin_inset Formula \[
6335 \left.\frac{A}{B}\right\} \]
6353 will be converted by LyX to brackets in the right size when the document
6354 is reloaded and an omitted bracket will appear as dashed line.
6357 \begin_layout Standard
6358 \begin_inset VSpace bigskip
6361 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6369 \begin_inset LatexCommand index
6370 name "Commands ! M ! \\textbackslash middle"
6374 is additionally available for all brackets and limits.
6375 With this command the height of the following character is adapted to the
6376 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6378 needed for physical vectors:
6379 \begin_inset Formula \[
6380 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6384 For physical vectors there is a special LaTeX-package, described in
6385 \begin_inset LatexCommand ref
6386 reference "sub:Physical-Vectors"
6393 \begin_layout Subsection
6395 \begin_inset LatexCommand index
6396 name "Brackets ! horizontal"
6403 \begin_layout Standard
6405 \begin_inset Tabular
6406 <lyxtabular version="3" rows="4" columns="2">
6408 <column alignment="center" valignment="top" leftline="true" width="0pt">
6409 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6410 <row topline="true" bottomline="true">
6411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6414 \begin_layout Standard
6416 \begin_inset Note Note
6419 \begin_layout Standard
6426 is only used as spacer.
6436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6439 \begin_layout Standard
6446 <row topline="true">
6447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6450 \begin_layout Standard
6454 \begin_layout Standard
6469 \begin_layout Standard
6482 \begin_layout Standard
6495 \begin_layout Standard
6508 \begin_layout Standard
6516 \begin_inset LatexCommand index
6517 name "Commands ! O ! \\textbackslash overbrace"
6526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6529 \begin_layout Standard
6530 \begin_inset Formula $\overbrace{A+B}^{3}$
6539 <row topline="true" bottomline="true">
6540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6543 \begin_layout Standard
6547 \begin_layout Standard
6562 \begin_layout Standard
6575 \begin_layout Standard
6588 \begin_layout Standard
6596 \begin_inset LatexCommand index
6597 name "Commands ! U ! \\textbackslash underbrace"
6606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6609 \begin_layout Standard
6610 \begin_inset Formula $\underbrace{A+B}_{5}$
6619 <row topline="true" bottomline="true">
6620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6623 \begin_layout Standard
6632 \begin_layout Standard
6645 \begin_layout Standard
6658 \begin_layout Standard
6671 \begin_layout Standard
6684 \begin_layout Standard
6697 \begin_layout Standard
6711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6714 \begin_layout Standard
6715 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6731 \begin_layout Standard
6732 In the last example it doesn't matter if
6744 is inserted at first.
6747 \begin_layout Standard
6748 \begin_inset VSpace bigskip
6751 When brackets are needed that overlap each other, multiline formulas, as
6753 \begin_inset LatexCommand ref
6754 reference "sec:Multiline-Formulas"
6759 \begin_inset Formula \begin{eqnarray*}
6760 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6761 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6765 In the first row the formula is inserted together with the first brace.
6766 It is hereby important that the space command
6770 \begin_layout Standard
6771 Space commands are explained in
6772 \begin_inset LatexCommand ref
6773 reference "sub:Predefined-Space"
6788 is inserted before the first
6789 \begin_inset Formula $d$
6792 , because the brace that ends behind the
6793 \begin_inset Formula $q$
6796 prevents that the following
6797 \begin_inset Quotes eld
6801 \begin_inset Quotes erd
6804 is surrounded by space.
6808 \begin_layout Standard
6809 because a bracket is not handled as character, see
6810 \begin_inset LatexCommand ref
6811 reference "sub:Binary-Operators"
6820 In the second row the second brace is inserted.
6821 As it should begin before the
6822 \begin_inset Formula $b$
6837 \begin_layout Standard
6845 \begin_inset LatexCommand ref
6846 reference "sub:Placeholders"
6855 This space is needed because the
6856 \begin_inset Quotes eld
6860 \begin_inset Quotes erd
6863 is also surrounded by space in the formula.
6864 The brace is placed under the command
6873 \begin_layout Standard
6874 It gets more complicated when brackets overlap each other, like in the following
6879 \begin_layout Standard
6891 \begin_inset Formula \begin{eqnarray*}
6892 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6893 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6901 \begin_layout Standard
6912 The first formula row is the same as the second row of the previous example,
6913 with the difference that the brace is above.
6914 The second row contains the formula together with the second brace.
6915 To avoid that there is space between the upper brace in the first row and
6916 the formula, the row spacing need to be reduced.
6917 This is not easily possible due to a bug in LyX
6921 \begin_layout Standard
6925 \begin_layout Standard
6929 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
6938 \begin_layout Standard
6951 As solution for the problem, the global formula row separation
6958 \begin_inset LatexCommand index
6959 name "Commands ! J ! \\textbackslash jot"
6963 must be changed to -6\InsetSpace \thinspace{}
6964 pt before the formula with the command
6979 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
6982 More about the row separation in formulas is explained in
6983 \begin_inset LatexCommand ref
6984 reference "sub:Line-Separation"
6991 \begin_layout Section
6993 \begin_inset LatexCommand index
7001 \begin_layout Standard
7002 Arrows can be inserted via the math toolbar button
7003 \begin_inset Graphics
7004 filename ../images/math/leftarrow.png
7009 or the commands listed in the following subsections.
7012 \begin_layout Subsection
7014 \begin_inset LatexCommand index
7015 name "Arrows ! horizontal"
7022 \begin_layout Standard
7026 \begin_inset Tabular
7027 <lyxtabular version="3" rows="8" columns="2">
7029 <column alignment="center" valignment="top" leftline="true" width="0pt">
7030 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7031 <row topline="true" bottomline="true">
7032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7035 \begin_layout Standard
7041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7044 \begin_layout Standard
7051 <row topline="true">
7052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7055 \begin_layout Standard
7063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7066 \begin_layout Standard
7067 \begin_inset Formula $\gets$
7076 <row topline="true">
7077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7080 \begin_layout Standard
7088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7091 \begin_layout Standard
7092 \begin_inset Formula $\Leftarrow$
7101 <row topline="true" bottomline="true">
7102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7105 \begin_layout Standard
7113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7116 \begin_layout Standard
7117 \begin_inset Formula $\longleftarrow$
7126 <row bottomline="true">
7127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7130 \begin_layout Standard
7138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7141 \begin_layout Standard
7142 \begin_inset Formula $\Longleftarrow$
7151 <row bottomline="true">
7152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7155 \begin_layout Standard
7163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7166 \begin_layout Standard
7167 \begin_inset Formula $\leftharpoonup$
7176 <row bottomline="true">
7177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7180 \begin_layout Standard
7188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7191 \begin_layout Standard
7192 \begin_inset Formula $\leftharpoondown$
7201 <row bottomline="true">
7202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7205 \begin_layout Standard
7213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7216 \begin_layout Standard
7217 \begin_inset Formula $\hookleftarrow$
7233 \begin_inset Tabular
7234 <lyxtabular version="3" rows="8" columns="2">
7236 <column alignment="center" valignment="top" leftline="true" width="0pt">
7237 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7238 <row topline="true" bottomline="true">
7239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7242 \begin_layout Standard
7248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7251 \begin_layout Standard
7258 <row topline="true">
7259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7262 \begin_layout Standard
7270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7273 \begin_layout Standard
7274 \begin_inset Formula $\to$
7283 <row topline="true">
7284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7287 \begin_layout Standard
7295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7298 \begin_layout Standard
7299 \begin_inset Formula $\Rightarrow$
7308 <row topline="true">
7309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7312 \begin_layout Standard
7320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7323 \begin_layout Standard
7324 \begin_inset Formula $\longrightarrow$
7333 <row topline="true">
7334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7337 \begin_layout Standard
7345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7348 \begin_layout Standard
7349 \begin_inset Formula $\Longrightarrow$
7358 <row topline="true">
7359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7362 \begin_layout Standard
7370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7373 \begin_layout Standard
7374 \begin_inset Formula $\rightharpoonup$
7383 <row topline="true" bottomline="true">
7384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7387 \begin_layout Standard
7395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7398 \begin_layout Standard
7399 \begin_inset Formula $\rightharpoondown$
7408 <row bottomline="true">
7409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7412 \begin_layout Standard
7420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7423 \begin_layout Standard
7424 \begin_inset Formula $\hookrightarrow$
7442 \begin_layout Standard
7446 \begin_inset Tabular
7447 <lyxtabular version="3" rows="6" columns="2">
7449 <column alignment="center" valignment="top" leftline="true" width="0pt">
7450 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7451 <row topline="true" bottomline="true">
7452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7455 \begin_layout Standard
7461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7464 \begin_layout Standard
7471 <row topline="true">
7472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7475 \begin_layout Standard
7483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7486 \begin_layout Standard
7487 \begin_inset Formula $\leftrightarrow$
7496 <row topline="true">
7497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7500 \begin_layout Standard
7508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7511 \begin_layout Standard
7512 \begin_inset Formula $\Leftrightarrow$
7521 <row topline="true">
7522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7525 \begin_layout Standard
7533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7536 \begin_layout Standard
7537 \begin_inset Formula $\longleftrightarrow$
7546 <row topline="true">
7547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7550 \begin_layout Standard
7558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7561 \begin_layout Standard
7562 \begin_inset Formula $\Longleftrightarrow$
7571 <row topline="true" bottomline="true">
7572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7575 \begin_layout Standard
7583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7586 \begin_layout Standard
7587 \begin_inset Formula $\rightleftharpoons$
7604 \begin_layout Standard
7616 \begin_inset Tabular
7617 <lyxtabular version="3" rows="5" columns="2">
7619 <column alignment="center" valignment="top" leftline="true" width="0pt">
7620 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7621 <row topline="true" bottomline="true">
7622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7625 \begin_layout Standard
7631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7634 \begin_layout Standard
7641 <row topline="true">
7642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7645 \begin_layout Standard
7653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7656 \begin_layout Standard
7657 \begin_inset Formula $\mapsto$
7666 <row topline="true">
7667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7670 \begin_layout Standard
7678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7681 \begin_layout Standard
7682 \begin_inset Formula $\longmapsto$
7691 <row topline="true">
7692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7695 \begin_layout Standard
7703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7706 \begin_layout Standard
7707 \begin_inset Formula $\leadsto$
7716 <row topline="true" bottomline="true">
7717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7720 \begin_layout Standard
7728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7731 \begin_layout Standard
7732 \begin_inset Formula $\dasharrow$
7750 \begin_layout Standard
7751 \begin_inset VSpace medskip
7754 Arrows used as accent like e.\InsetSpace \thinspace{}
7756 vector arrows are listed in
7757 \begin_inset LatexCommand ref
7758 reference "sec:Accents"
7765 \begin_layout Standard
7766 \begin_inset VSpace bigskip
7769 Furthermore there are the labeled arrows
7770 \begin_inset LatexCommand index
7771 name "Arrows ! labeled"
7782 \begin_inset LatexCommand index
7783 name "Commands ! X ! \\textbackslash xleftarrow"
7794 \begin_inset LatexCommand index
7795 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7800 When inserting one of these commands in a formula, an arrow with two blue
7801 boxes appear where the label can be inserted.
7802 The length of the arrow adapts to the label width.
7805 \begin_layout Standard
7807 \begin_inset Tabular
7808 <lyxtabular version="3" rows="3" columns="2">
7810 <column alignment="center" valignment="top" leftline="true" width="0pt">
7811 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7812 <row topline="true" bottomline="true">
7813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7816 \begin_layout Standard
7822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7825 \begin_layout Standard
7827 \begin_inset Note Note
7830 \begin_layout Standard
7837 is only used as spacer.
7848 <row topline="true">
7849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7852 \begin_layout Standard
7859 \begin_layout Standard
7869 \begin_inset Formula $\downarrow$
7873 \begin_inset Formula $\to$
7881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7884 \begin_layout Standard
7885 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7894 <row topline="true" bottomline="true">
7895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7898 \begin_layout Standard
7905 \begin_layout Standard
7915 \begin_inset Formula $\downarrow$
7919 \begin_inset Formula $\to$
7927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7930 \begin_layout Standard
7931 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
7947 \begin_layout Subsection
7948 Vertical and diagonal Arrows
7949 \begin_inset LatexCommand index
7950 name "Arrows ! diagonal"
7955 \begin_inset LatexCommand index
7956 name "Arrows ! vertical"
7963 \begin_layout Standard
7967 \begin_inset Tabular
7968 <lyxtabular version="3" rows="7" columns="2">
7970 <column alignment="center" valignment="top" leftline="true" width="0pt">
7971 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7972 <row topline="true" bottomline="true">
7973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7976 \begin_layout Standard
7982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7985 \begin_layout Standard
7992 <row topline="true">
7993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7996 \begin_layout Standard
8004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8007 \begin_layout Standard
8008 \begin_inset Formula $\uparrow$
8017 <row topline="true">
8018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8021 \begin_layout Standard
8029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8032 \begin_layout Standard
8033 \begin_inset Formula $\Uparrow$
8042 <row topline="true">
8043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8046 \begin_layout Standard
8054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8057 \begin_layout Standard
8058 \begin_inset Formula $\updownarrow$
8067 <row topline="true">
8068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8071 \begin_layout Standard
8079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8082 \begin_layout Standard
8083 \begin_inset Formula $\Updownarrow$
8092 <row topline="true" bottomline="true">
8093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8096 \begin_layout Standard
8104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8107 \begin_layout Standard
8108 \begin_inset Formula $\Downarrow$
8117 <row bottomline="true">
8118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8121 \begin_layout Standard
8129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8132 \begin_layout Standard
8133 \begin_inset Formula $\downarrow$
8149 \begin_inset Tabular
8150 <lyxtabular version="3" rows="5" columns="2">
8152 <column alignment="center" valignment="top" leftline="true" width="0pt">
8153 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8154 <row topline="true" bottomline="true">
8155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8158 \begin_layout Standard
8164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8167 \begin_layout Standard
8174 <row topline="true">
8175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8178 \begin_layout Standard
8186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8189 \begin_layout Standard
8190 \begin_inset Formula $\nearrow$
8199 <row topline="true">
8200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8203 \begin_layout Standard
8211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8214 \begin_layout Standard
8215 \begin_inset Formula $\searrow$
8224 <row topline="true" bottomline="true">
8225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8228 \begin_layout Standard
8236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8239 \begin_layout Standard
8240 \begin_inset Formula $\swarrow$
8249 <row bottomline="true">
8250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8253 \begin_layout Standard
8261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8264 \begin_layout Standard
8265 \begin_inset Formula $\nwarrow$
8283 \begin_layout Standard
8284 \begin_inset VSpace medskip
8287 Vertical arrows can be used also as delimiter together with the commands
8289 \begin_inset LatexCommand ref
8290 reference "sub:Manual-Bracket-Size"
8295 \begin_inset LatexCommand ref
8296 reference "sub:Automatic-Bracket-Size"
8303 \begin_layout Standard
8309 \begin_layout Section
8311 \begin_inset LatexCommand label
8317 \begin_inset LatexCommand index
8325 \begin_layout Standard
8326 Accents can be inserted via the math toolbar button
8327 \begin_inset Graphics
8328 filename ../images/math/hat.png
8333 or the commands listed in the following subsections.
8336 \begin_layout Subsection
8337 Accents for one Character
8341 \begin_layout Standard
8354 \begin_layout Standard
8356 \begin_inset LatexCommand ref
8357 reference "sub:Accents-in-Text"
8370 \begin_layout Standard
8378 \begin_inset Note Note
8381 \begin_layout Standard
8384 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8387 \begin_layout Standard
8390 texorpdfstring is in section
8391 \begin_inset LatexCommand ref
8392 reference "sub:Formulas-in-Section"
8402 \begin_inset LatexCommand label
8403 name "sub:Accents-for-one"
8408 \begin_inset LatexCommand index
8409 name "Accents ! for one character"
8416 \begin_layout Standard
8420 \begin_inset Tabular
8421 <lyxtabular version="3" rows="8" columns="2">
8423 <column alignment="center" valignment="top" leftline="true" width="0pt">
8424 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8425 <row topline="true" bottomline="true">
8426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8429 \begin_layout Standard
8435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8438 \begin_layout Standard
8440 \begin_inset Note Note
8443 \begin_layout Standard
8450 is only used as spacer.
8461 <row topline="true" bottomline="true">
8462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8465 \begin_layout Standard
8472 \begin_layout Standard
8486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8489 \begin_layout Standard
8490 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8499 <row bottomline="true">
8500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8503 \begin_layout Standard
8510 \begin_layout Standard
8524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8527 \begin_layout Standard
8528 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8537 <row bottomline="true">
8538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8541 \begin_layout Standard
8548 \begin_layout Standard
8562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8565 \begin_layout Standard
8566 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8575 <row bottomline="true">
8576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8579 \begin_layout Standard
8587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8590 \begin_layout Standard
8591 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8600 <row bottomline="true">
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8604 \begin_layout Standard
8611 \begin_layout Standard
8621 \begin_inset LatexCommand index
8631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8634 \begin_layout Standard
8635 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8644 <row bottomline="true">
8645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8648 \begin_layout Standard
8655 \begin_layout Standard
8669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8672 \begin_layout Standard
8673 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8682 <row bottomline="true">
8683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8686 \begin_layout Standard
8693 \begin_layout Standard
8707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8710 \begin_layout Standard
8711 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8727 \begin_inset Tabular
8728 <lyxtabular version="3" rows="7" columns="2">
8730 <column alignment="center" valignment="top" leftline="true" width="0pt">
8731 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8732 <row topline="true" bottomline="true">
8733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8736 \begin_layout Standard
8742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8745 \begin_layout Standard
8752 <row topline="true" bottomline="true">
8753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8756 \begin_layout Standard
8763 \begin_layout Standard
8777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8780 \begin_layout Standard
8781 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8790 <row bottomline="true">
8791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8794 \begin_layout Standard
8801 \begin_layout Standard
8815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8818 \begin_layout Standard
8819 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8828 <row bottomline="true">
8829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8832 \begin_layout Standard
8839 \begin_layout Standard
8853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8856 \begin_layout Standard
8857 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8866 <row bottomline="true">
8867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8870 \begin_layout Standard
8877 \begin_layout Standard
8891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8894 \begin_layout Standard
8895 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8904 <row bottomline="true">
8905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8908 \begin_layout Standard
8915 \begin_layout Standard
8929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8932 \begin_layout Standard
8933 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
8942 <row bottomline="true">
8943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8946 \begin_layout Standard
8953 \begin_layout Standard
8967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8970 \begin_layout Standard
8971 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
8989 \begin_layout Standard
8990 \begin_inset VSpace bigskip
8994 \begin_inset LatexCommand index
8999 in formulas, a quotation mark is inserted before the vowel.
9000 These two characters are then treated by LaTeX as
9004 character when the formula part with the umlaut is marked as German.
9012 \begin_inset Quotes eld
9016 \begin_inset Quotes erd
9019 umlauts are created as demonstrated in the following example:
9022 \begin_layout Standard
9023 \begin_inset VSpace -2mm
9029 \begin_layout Standard
9031 \begin_inset Tabular
9032 <lyxtabular version="3" rows="3" columns="2">
9034 <column alignment="center" valignment="top" leftline="true" width="0">
9035 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9036 <row topline="true" bottomline="true">
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9040 \begin_layout Standard
9046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9049 \begin_layout Standard
9051 \begin_inset Note Note
9054 \begin_layout Standard
9061 is only used as spacer.
9072 <row topline="true">
9073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9076 \begin_layout Standard
9079 \begin_inset Quotes grd
9087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9090 \begin_layout Standard
9093 \begin_inset Formula $"i$
9102 <row topline="true" bottomline="true">
9103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9106 \begin_layout Standard
9113 \begin_layout Standard
9127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9130 \begin_layout Standard
9131 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9147 \begin_layout Standard
9148 Another advantage to
9154 is that umlauts can directly be converted to mathematical text because
9155 the accent commands above are
9161 in mathematical text
9164 To convert an accented character to mathematical text, only the character
9165 under the accent may be converted.
9166 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9171 \begin_layout Standard
9172 In mathematical text, umlauts and other accented characters can directly
9176 \begin_layout Subsection
9177 Accents for Operators
9178 \begin_inset LatexCommand index
9179 name "Accents ! for operators"
9186 \begin_layout Standard
9194 \begin_inset LatexCommand index
9195 name "Commands ! O ! \\textbackslash overset"
9206 \begin_inset LatexCommand index
9207 name "Commands ! U ! \\textbackslash underset"
9211 characters can be placed above or below an operator, respectively, to accent
9220 \begin_inset LatexCommand index
9221 name "Commands ! S ! \\textbackslash sideset"
9225 characters can be set before and behind an operator.
9226 The command scheme is:
9229 \begin_layout Standard
9245 \begin_layout Standard
9252 must always be before the operator that should be accented.
9253 You can accent with several characters and even with other operators and
9261 for example only characters behind an operator, write nothing between the
9262 first braces but don't omit the braces.
9265 \begin_layout Standard
9266 For example the command
9271 \begin_inset Formula $\to$
9281 \begin_inset Formula $\to$
9290 \begin_layout Standard
9306 \begin_inset Formula \[
9307 \sideset{}{'}\sum_{k=1}^{n}\]
9314 \begin_layout Standard
9323 \begin_layout Standard
9338 \begin_layout Standard
9350 \begin_inset Formula $\uparrow$
9358 \begin_inset Formula \[
9359 \overset{a}{\maltese}\]
9363 As seen in the last example, with
9375 also symbols and characters can be accented; with
9381 this is not possible.
9384 \begin_layout Subsection
9385 Accents for several Characters
9386 \begin_inset LatexCommand label
9387 name "sub:Accents-for-several"
9392 \begin_inset LatexCommand index
9393 name "Accents ! for several characters"
9400 \begin_layout Standard
9404 \begin_inset Tabular
9405 <lyxtabular version="3" rows="5" columns="2">
9407 <column alignment="center" valignment="top" leftline="true" width="0pt">
9408 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9409 <row topline="true" bottomline="true">
9410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9413 \begin_layout Standard
9419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9422 \begin_layout Standard
9424 \begin_inset Note Note
9427 \begin_layout Standard
9434 is only used as spacer.
9445 <row topline="true" bottomline="true">
9446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9449 \begin_layout Standard
9456 \begin_layout Standard
9470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9473 \begin_layout Standard
9474 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9483 <row bottomline="true">
9484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9487 \begin_layout Standard
9494 \begin_layout Standard
9508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9511 \begin_layout Standard
9512 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9521 <row bottomline="true">
9522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9525 \begin_layout Standard
9532 \begin_layout Standard
9546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9549 \begin_layout Standard
9550 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9559 <row bottomline="true">
9560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9563 \begin_layout Standard
9570 \begin_layout Standard
9584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9587 \begin_layout Standard
9588 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9604 \begin_inset Tabular
9605 <lyxtabular version="3" rows="5" columns="2">
9607 <column alignment="center" valignment="top" leftline="true" width="0pt">
9608 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9609 <row topline="true" bottomline="true">
9610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9613 \begin_layout Standard
9619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9622 \begin_layout Standard
9629 <row topline="true" bottomline="true">
9630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9633 \begin_layout Standard
9640 \begin_layout Standard
9654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9657 \begin_layout Standard
9658 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9667 <row bottomline="true">
9668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9671 \begin_layout Standard
9678 \begin_layout Standard
9692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9695 \begin_layout Standard
9696 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9705 <row bottomline="true">
9706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9709 \begin_layout Standard
9716 \begin_layout Standard
9730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9733 \begin_layout Standard
9734 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9743 <row bottomline="true">
9744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9747 \begin_layout Standard
9754 \begin_layout Standard
9768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9771 \begin_layout Standard
9772 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9790 \begin_layout Standard
9791 \begin_inset VSpace medskip
9794 With these commands as many characters as you like can be accented.
9807 will only be set in the output with a length of three characters, as shown
9808 in the following example:
9809 \begin_inset Formula \[
9810 \widetilde{A+B=C-D}\]
9817 \begin_layout Standard
9825 \begin_inset LatexCommand index
9826 name "Commands ! O ! \\textbackslash overset"
9837 \begin_inset LatexCommand index
9838 name "Commands ! U ! \\textbackslash underset"
9842 described in the previous subsection it is also possible to accent several
9852 \begin_layout Standard
9862 \begin_inset Formula $\downarrow$
9868 \begin_inset Formula \[
9869 \underset{***}{A=B}\]
9876 \begin_layout Section
9878 \begin_inset LatexCommand label
9884 \begin_inset LatexCommand index
9885 name "Space ! horizontal"
9892 \begin_layout Subsection
9894 \begin_inset LatexCommand label
9895 name "sub:Predefined-Space"
9900 \begin_inset LatexCommand index
9901 name "Space ! horizontal ! predefined"
9908 \begin_layout Standard
9909 Sometimes it is necessary to insert horizontal space to a formula.
9910 This is done by inserting a protected space (shortcut
9916 \begin_inset Quotes eld
9926 \begin_layout Standard
9939 \begin_inset Quotes erd
9942 appears and by pressing
9946 several times one can select one of eight different space sizes.
9947 The spaces can also be inserted using the math toolbar button
9948 \begin_inset Graphics
9949 filename ../images/math/space.png
9954 or special commands.
9955 Independent from the inserted command, one can select the size again by
9963 \begin_layout Standard
9966 \begin_inset VSpace -5mm
9970 \begin_inset Tabular
9971 <lyxtabular version="3" rows="3" columns="7">
9973 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
9974 <column alignment="center" valignment="top" leftline="true" width="0">
9975 <column alignment="center" valignment="top" leftline="true" width="0">
9976 <column alignment="center" valignment="top" leftline="true" width="0">
9977 <column alignment="center" valignment="top" leftline="true" width="0">
9978 <column alignment="center" valignment="top" leftline="true" width="0">
9979 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9980 <row topline="true">
9981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9984 \begin_layout Standard
9990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9993 \begin_layout Standard
10001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10004 \begin_layout Standard
10012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10015 \begin_layout Standard
10023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10026 \begin_layout Standard
10034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10037 \begin_layout Standard
10045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10048 \begin_layout Standard
10057 <row topline="true">
10058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10061 \begin_layout Standard
10066 keystrokes after inserting the protected space
10071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10074 \begin_layout Standard
10080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10083 \begin_layout Standard
10089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10092 \begin_layout Standard
10098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10101 \begin_layout Standard
10107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10110 \begin_layout Standard
10116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10119 \begin_layout Standard
10126 <row topline="true" bottomline="true">
10127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10130 \begin_layout Standard
10136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10139 \begin_layout Standard
10140 \begin_inset Formula $A\, B$
10148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10151 \begin_layout Standard
10152 \begin_inset Formula $A\: B$
10160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10163 \begin_layout Standard
10164 \begin_inset Formula $A\; B$
10172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10175 \begin_layout Standard
10176 \begin_inset Formula $A\quad B$
10184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10187 \begin_layout Standard
10188 \begin_inset Formula $A\qquad B$
10196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10199 \begin_layout Standard
10200 \begin_inset Formula $A\! B$
10216 \begin_layout Standard
10217 The last size seem to produce no space.
10218 It is displayed red in LyX contrary to the other sizes, because it is a
10220 There are two more negative spaces:
10223 \begin_layout Standard
10225 \begin_inset Tabular
10226 <lyxtabular version="3" rows="3" columns="3">
10228 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10229 <column alignment="center" valignment="top" leftline="true" width="0pt">
10230 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10231 <row topline="true" bottomline="true">
10232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10235 \begin_layout Standard
10241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10244 \begin_layout Standard
10252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10255 \begin_layout Standard
10264 <row bottomline="true">
10265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10268 \begin_layout Standard
10273 keystrokes after inserting the protected space
10278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10281 \begin_layout Standard
10287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10290 \begin_layout Standard
10297 <row bottomline="true">
10298 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10301 \begin_layout Standard
10307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10310 \begin_layout Standard
10311 \begin_inset Formula $A\negmedspace B$
10319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10322 \begin_layout Standard
10323 \begin_inset Formula $A\negthickspace B$
10339 \begin_layout Standard
10340 Negative spaces can lead to characters overlapping each other.
10341 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10343 useful for summation
10347 \begin_layout Standard
10349 \begin_inset Tabular
10350 <lyxtabular version="3" rows="3" columns="2">
10352 <column alignment="center" valignment="top" leftline="true" width="0">
10353 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10354 <row topline="true" bottomline="true">
10355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10358 \begin_layout Standard
10364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10367 \begin_layout Standard
10369 \begin_inset Note Note
10372 \begin_layout Standard
10379 is only used as spacer.
10390 <row topline="true">
10391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10394 \begin_layout Standard
10403 \begin_layout Standard
10417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10420 \begin_layout Standard
10421 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10430 <row topline="true" bottomline="true">
10431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10434 \begin_layout Standard
10445 \begin_layout Standard
10459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10462 \begin_layout Standard
10463 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10479 \begin_layout Standard
10480 Relations like for example equal signs, are always surrounded by space.
10481 To suppress this, the equal sign is placed into a TeX-brace.
10482 The following example demonstrates this:
10485 \begin_layout Standard
10487 \begin_inset Tabular
10488 <lyxtabular version="3" rows="2" columns="2">
10490 <column alignment="center" valignment="top" width="0pt">
10491 <column alignment="center" valignment="top" width="0pt">
10493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10496 \begin_layout Standard
10502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10505 \begin_layout Standard
10506 \begin_inset Formula $A=B$
10516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10519 \begin_layout Standard
10520 \begin_inset Note Note
10523 \begin_layout Standard
10530 is only used as spacer.
10536 \begin_inset Formula $\raisebox{5mm}{}$
10539 equation without space
10544 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10547 \begin_layout Standard
10548 \begin_inset Formula $A{=}B$
10564 \begin_layout Standard
10566 The command for the last formula is:
10571 \begin_inset Formula $\to$
10577 \begin_layout Standard
10578 \begin_inset VSpace bigskip
10581 Spaces are needed for physical units, because the space between the value
10582 and the unit is the smallest one and not a normal space.
10583 For units in text, the smallest space is inserted via the menu
10585 Insert\SpecialChar \menuseparator
10586 Formatting\SpecialChar \menuseparator
10597 \begin_layout Standard
10598 An example to visualize the difference:
10601 \begin_layout Standard
10602 \begin_inset Tabular
10603 <lyxtabular version="3" rows="2" columns="2">
10605 <column alignment="left" valignment="top" width="0">
10606 <column alignment="left" valignment="top" width="0">
10608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10611 \begin_layout Standard
10613 \begin_inset Formula $\cdot$
10621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10624 \begin_layout Standard
10625 space between value and unit
10632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10635 \begin_layout Standard
10636 24\InsetSpace \thinspace{}
10638 \begin_inset Formula $\cdot$
10646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10649 \begin_layout Standard
10650 smallest space between value and unit
10663 \begin_layout Subsection
10668 \begin_layout Standard
10681 \begin_layout Standard
10682 for vertical space in formulas see
10683 \begin_inset LatexCommand ref
10684 reference "sub:Line-Separation"
10697 \begin_layout Standard
10705 \begin_inset Note Note
10708 \begin_layout Standard
10711 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10714 \begin_layout Standard
10717 texorpdfstring is in section
10718 \begin_inset LatexCommand ref
10719 reference "sub:Formulas-in-Section"
10729 \begin_inset LatexCommand label
10730 name "sub:Variable-Space"
10735 \begin_inset LatexCommand index
10736 name "Space ! horizontal ! variable"
10743 \begin_layout Standard
10744 Space with a defined length can be inserted in LyX with the command
10753 \begin_inset LatexCommand index
10754 name "Commands ! H ! \\textbackslash hspace"
10759 For the length all units listed in
10760 \begin_inset LatexCommand ref
10761 reference "tab:Used-units"
10765 are allowed, except of the unit
10766 \begin_inset Quotes eld
10770 \begin_inset Quotes erd
10774 The length may also be negative.
10775 To insert so many space that the formula uses all available space, the
10783 \begin_inset LatexCommand index
10784 name "Commands ! H ! \\textbackslash hfill"
10791 \begin_layout Standard
10792 \begin_inset VSpace -1mm
10798 \begin_layout Standard
10800 \begin_inset Tabular
10801 <lyxtabular version="3" rows="4" columns="2">
10803 <column alignment="center" valignment="top" leftline="true" width="0">
10804 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10805 <row topline="true" bottomline="true">
10806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10809 \begin_layout Standard
10815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10818 \begin_layout Standard
10825 <row topline="true">
10826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10829 \begin_layout Standard
10833 \begin_inset Formula $\to$
10843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10846 \begin_layout Standard
10847 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10856 <row topline="true" bottomline="true">
10857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10860 \begin_layout Standard
10864 \begin_inset Formula $\to$
10874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10877 \begin_layout Standard
10878 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10887 <row topline="true" bottomline="true">
10888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10891 \begin_layout Standard
10898 \begin_layout Standard
10912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10915 \begin_layout Standard
10916 \begin_inset Formula $A=A\hfill B=B$
10932 \begin_layout Standard
10933 In the last example the available space is given by the longest column entry
10935 In an inline formula the space depends on the length of the line in which
10943 Thus, when the line uses the full width, no space will be created.
10950 has only an effect on displayed formulas when the formula style
10955 (Formula styles are explained in
10956 \begin_inset LatexCommand ref
10957 reference "sec:Formula-Styles"
10964 \begin_layout Standard
10977 can also be inserted in TeX-mode to use them for text:
10980 \begin_layout Standard
10981 This is a line with
10985 \begin_layout Standard
10994 2\InsetSpace \thinspace{}
10998 \begin_layout Standard
10999 This is a line with
11004 \begin_layout Standard
11005 In the last example
11011 was inserted via the menu
11013 Insert\SpecialChar \menuseparator
11014 Formatting\SpecialChar \menuseparator
11015 Horizontal\InsetSpace ~
11018 , what is not possible in formulas.
11019 This has the advantage that one can directly see in LyX that this is a
11023 \begin_layout Standard
11024 When the commands are at the begin of a text line but not at the beginning
11025 of a paragraph, they will be ignored by LaTeX.
11026 To avoid that, the command
11039 To get the same with
11045 , a line break and an empty placeholder
11051 \begin_layout Standard
11052 for placeholders see
11053 \begin_inset LatexCommand ref
11054 reference "sub:Placeholders"
11065 is inserted in TeX-mode with the command
11081 \begin_layout Subsection
11082 Space besides inline Formulas
11083 \begin_inset LatexCommand index
11084 name "Space ! besides inline formulas"
11091 \begin_layout Standard
11092 The space that surrounds inline formulas can be adjusted with the length
11098 \begin_inset LatexCommand index
11099 name "Commands ! M ! \\textbackslash mathsurround"
11106 The value of a length is set with the command
11111 \begin_inset LatexCommand index
11112 name "Commands ! S ! \\textbackslash setlength"
11118 that has the following scheme:
11121 \begin_layout Standard
11126 setlength{length name}{value}
11129 \begin_layout Standard
11136 to the value 5\InsetSpace \thinspace{}
11140 \begin_layout Standard
11150 \begin_layout Standard
11151 is inserted in TeX-mode.
11152 5\InsetSpace \thinspace{}
11153 mm space will now be set around all inline formulas:
11157 \begin_layout Standard
11171 \begin_layout Standard
11172 This is a line with an inline formula
11173 \begin_inset Formula $A=B$
11176 with 5\InsetSpace \thinspace{}
11177 mm surrounding space.
11181 \begin_layout Standard
11195 \begin_layout Standard
11196 To return to the predefined value,
11202 is set to the value 0\InsetSpace \thinspace{}
11206 \begin_layout Section
11208 \begin_inset LatexCommand index
11214 \begin_inset LatexCommand index
11215 name "Frames | see {Boxes}"
11222 \begin_layout Standard
11223 Boxes for text are described in chapter
11229 Embedded\InsetSpace ~
11235 \begin_layout Subsection
11237 \begin_inset LatexCommand label
11238 name "sub:Boxes-with-Frame"
11243 \begin_inset LatexCommand index
11244 name "Boxes ! with frame"
11251 \begin_layout Standard
11252 It is possible to frame formulas or parts of it with the commands
11259 \begin_inset LatexCommand index
11260 name "Commands ! F ! \\textbackslash fbox"
11271 \begin_inset LatexCommand index
11272 name "Commands ! B ! \\textbackslash boxed"
11279 \begin_layout Standard
11280 When one of these commands is inserted to a formula, a blue box appears
11281 within a frame to enter formula parts.
11288 an additional formula has to be created by
11296 \begin_layout Standard
11297 Due to a bug in LyX it is not possible to create a new formula with
11305 \begin_layout Standard
11309 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11318 \begin_layout Standard
11330 , because the box content will otherwise be treated as mathematical text.
11337 is used, a new formula is automatically created inside the frame.
11340 \begin_layout Standard
11347 is not suitable to frame displayed formulas, because the formula will always
11348 be set in the size of the text.
11355 is in contrary not suitable to frame inline formulas, because the formula
11356 will always be set in the size of a displayed formula.
11359 \begin_layout Standard
11366 there is the command
11373 \begin_inset LatexCommand index
11374 name "Commands ! F ! \\textbackslash framebox"
11378 where additionally the frame width and the alignment can be specified.
11385 is used in the following scheme:
11388 \begin_layout Standard
11393 framebox[frame width][position]{box content}
11396 \begin_layout Standard
11397 The position can either be
11414 right aligns the formula in the box.
11415 When no position is given, the formula will be centered.
11418 also no position can be given.
11419 In this case the frame width is adjusted to the box content like for
11428 \begin_layout Standard
11435 is inserted, a box appears containing three blue boxes.
11439 \begin_layout Standard
11440 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11445 \begin_layout Standard
11449 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11458 \begin_layout Standard
11470 The first two boxes are surrounded by brackets and denote the two optional
11472 The third box is for formula parts like for
11481 \begin_layout Standard
11483 \begin_inset Note Note
11486 \begin_layout Standard
11487 The table has been set into a minipage to make the footnote appearing.
11488 Otherwise the footnote text would not be displayed.
11494 \begin_inset Box Frameless
11503 height_special "totalheight"
11506 \begin_layout Standard
11508 \begin_inset Tabular
11509 <lyxtabular version="3" rows="5" columns="2">
11511 <column alignment="center" valignment="top" leftline="true" width="0">
11512 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11513 <row topline="true" bottomline="true">
11514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11517 \begin_layout Standard
11522 \begin_layout Standard
11523 Due to a bug in LyX it is not possible to create a new formula with
11531 \begin_layout Standard
11535 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11544 \begin_layout Standard
11561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11564 \begin_layout Standard
11566 \begin_inset Note Note
11569 \begin_layout Standard
11576 is only used as spacer.
11587 <row topline="true">
11588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11591 \begin_layout Standard
11598 \begin_layout Standard
11617 \begin_layout Standard
11631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11634 \begin_layout Standard
11635 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11645 <row topline="true">
11646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11649 \begin_layout Standard
11656 \begin_layout Standard
11671 \begin_layout Standard
11685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11688 \begin_layout Standard
11689 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11698 <row topline="true">
11699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11702 \begin_layout Standard
11709 \begin_layout Standard
11723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11726 \begin_layout Standard
11727 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11736 <row topline="true" bottomline="true">
11737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11740 \begin_layout Standard
11747 \begin_layout Standard
11757 \begin_inset Formula $\to$
11761 \begin_inset Formula $\to$
11774 \begin_layout Standard
11784 \begin_inset Formula $\downarrow$
11792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11795 \begin_layout Standard
11796 \begin_inset Formula $\raisebox{6mm}{}$
11800 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11804 \begin_inset Formula $\raisebox{-4mm}{}$
11825 \begin_layout Standard
11826 The frame thickness can also be adjusted.
11827 To do this the following commands have to be inserted in TeX-mode before
11831 \begin_layout Standard
11841 \begin_inset Quotes eld
11845 \begin_inset Quotes erd
11859 \begin_inset Quotes eld
11863 \begin_inset Quotes erd
11869 \begin_layout Standard
11870 \begin_inset Quotes eld
11874 \begin_inset Quotes erd
11877 specifies the minimal distance between the frame and the first character
11879 An example for this is the following framed formula:
11883 \begin_layout Standard
11895 \begin_inset Formula \[
11900 Before this formula the commands
11903 \begin_layout Standard
11925 \begin_layout Standard
11926 were inserted in TeX-mode.
11927 The given values are used for all following boxes.
11930 \begin_layout Standard
11931 To return to the standard frame size, the command
11934 \begin_layout Standard
11959 \begin_layout Standard
11973 \begin_layout Standard
11974 is inserted in TeX-mode before the next formula.
11977 \begin_layout Subsection
11978 Boxes without Frame
11979 \begin_inset LatexCommand label
11980 name "sub:Boxes-without-Frame"
11985 \begin_inset LatexCommand index
11986 name "Boxes ! without frame"
11993 \begin_layout Standard
11994 For boxes without a frame there are the following box commands:
12001 \begin_inset LatexCommand index
12002 name "Commands ! M ! \\textbackslash mbox"
12013 \begin_inset LatexCommand index
12014 name "Commands ! M ! \\textbackslash makebox"
12025 \begin_inset LatexCommand index
12026 name "Commands ! R ! \\textbackslash raisebox"
12033 \begin_layout Standard
12040 a box can be super- or subscripted.
12041 But in contrary to normal super- and subscripting, the characters in the
12042 box keep their font size.
12049 is used in the following scheme:
12052 \begin_layout Standard
12057 raisebox{height}{box content}
12060 \begin_layout Standard
12061 When the box should contain a formula, an extra formula is needed like for
12071 \begin_layout Standard
12073 \begin_inset Tabular
12074 <lyxtabular version="3" rows="4" columns="2">
12076 <column alignment="center" valignment="top" leftline="true" width="0">
12077 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12078 <row topline="true" bottomline="true">
12079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12082 \begin_layout Standard
12088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12091 \begin_layout Standard
12098 <row topline="true">
12099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12102 \begin_layout Standard
12106 \begin_inset Formula $\to$
12112 \begin_inset Formula $\to$
12120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12123 \begin_layout Standard
12124 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12133 <row topline="true" bottomline="true">
12134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12137 \begin_layout Standard
12141 \begin_inset Formula $\to$
12147 \begin_inset Formula $\to$
12155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12158 \begin_layout Standard
12159 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12168 <row topline="true" bottomline="true">
12169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12172 \begin_layout Standard
12176 \begin_inset Formula $\to$
12191 \begin_layout Standard
12205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12208 \begin_layout Standard
12212 \begin_layout Standard
12236 \begin_layout Standard
12237 The last formula can currently only be created using TeX-mode because LyX
12238 inserts a box instead of the needed extra formula.
12242 \begin_layout Standard
12247 \begin_layout Standard
12251 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12260 \begin_layout Standard
12275 \begin_layout Standard
12300 , with the difference that there is no frame.
12303 \begin_layout Subsection
12305 \begin_inset LatexCommand label
12306 name "sub:Colored-Boxes"
12311 \begin_inset LatexCommand index
12312 name "Boxes ! colored"
12319 \begin_layout Standard
12320 To be able to use all commands explained in this section, the LaTeX-package
12329 \begin_layout Standard
12334 is part of every LaTeX standard installation.
12340 \begin_inset LatexCommand index
12341 name "Packages ! color"
12345 has to be loaded in the LaTeX-preamble with the line
12349 \begin_layout Standard
12350 When text is colored somewhere in the document with a predefined color,
12351 LyX loads the LaTeX-package
12356 Thus it is possible that the package is loaded twice, but this doesn't
12363 \begin_inset Note Note
12366 \begin_layout Standard
12367 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12376 \begin_layout Standard
12384 \begin_layout Standard
12385 \begin_inset VSpace medskip
12388 To color boxes, the command
12395 \begin_inset LatexCommand index
12396 name "Commands ! C ! \\textbackslash colorbox"
12400 is used in the following scheme:
12403 \begin_layout Standard
12408 colorbox{color}{box content}
12411 \begin_layout Standard
12412 The box content can also be a box and a
12418 can also be part of another box (see the 2nd and 3rd example).
12419 When the box should contain a formula, an extra formula has to be created,
12430 \begin_layout Standard
12431 This also applies for the command
12442 \begin_layout Standard
12446 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12455 \begin_layout Standard
12470 \begin_layout Standard
12471 One of the following predefined colors can be chosen:
12474 \begin_layout Standard
12508 \begin_layout Standard
12510 \begin_inset Tabular
12511 <lyxtabular version="3" rows="4" columns="2">
12513 <column alignment="center" valignment="top" leftline="true" width="0">
12514 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12515 <row topline="true" bottomline="true">
12516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12519 \begin_layout Standard
12525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12528 \begin_layout Standard
12530 \begin_inset Note Note
12533 \begin_layout Standard
12540 is only used as spacer.
12551 <row topline="true">
12552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12555 \begin_layout Standard
12559 \begin_inset Formula $\to$
12569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12572 \begin_layout Standard
12573 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12582 <row topline="true">
12583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12586 \begin_layout Standard
12590 \begin_inset Formula $\to$
12601 \begin_layout Standard
12615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12618 \begin_layout Standard
12619 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12628 <row topline="true" bottomline="true">
12629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12632 \begin_layout Standard
12639 \begin_layout Standard
12651 \begin_inset Formula $\to$
12661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12664 \begin_layout Standard
12665 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12681 \begin_layout Standard
12688 only colors the box but not the characters in the box.
12689 To color all characters, the whole formula is highlighted and the wanted
12690 color is chosen in the
12696 The dialog can be called with the toolbar button
12697 \begin_inset Graphics
12698 filename ../images/dialog-show_character.png
12705 Edit\SpecialChar \menuseparator
12707 Style\SpecialChar \menuseparator
12711 The formula number has then the same color as the formula.
12712 When the formula number should get another color than the formula characters,
12713 the color must be changed within the formula.
12716 \begin_layout Standard
12720 \begin_layout Standard
12723 \begin_inset Formula \begin{equation}
12724 \int A=B\label{eq:red}\end{equation}
12731 \begin_inset Formula \begin{equation}
12732 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12739 \begin_layout Standard
12741 \begin_inset LatexCommand eqref
12746 is completely colored red.
12749 \begin_inset LatexCommand eqref
12750 reference "eq:redgreen"
12754 was first completely colored green to set the color for the formula number.
12755 Subsequently the formula characters were colored red.
12758 \begin_layout Standard
12759 \begin_inset VSpace bigskip
12762 To color the frame different than the rest of the box, the command
12769 \begin_inset LatexCommand index
12770 name "Commands ! F ! \\textbackslash fcolorbox"
12774 is used in the following scheme:
12777 \begin_layout Standard
12782 fcolorbox{frame color}{color}{box content}
12785 \begin_layout Standard
12792 is an extension of the command
12799 The frame width is set, like for
12822 \begin_layout Standard
12834 \begin_inset Formula \[
12835 \fcolorbox{cyan}{magenta}{A=B}\]
12843 \begin_layout Standard
12857 \begin_layout Standard
12858 This formula was created with the command
12865 \begin_inset Formula $\to$
12871 \begin_inset Formula $\to$
12881 \begin_layout Standard
12882 \begin_inset VSpace bigskip
12885 To use other colors than the predefined ones, they have to be defined first.
12888 \begin_layout Standard
12889 One can for example define the color
12890 \begin_inset Quotes eld
12898 \begin_inset Quotes erd
12901 with the LaTeX-preamble line:
12904 \begin_layout Standard
12909 definecolor{darkgreen}{cmyk}{0.5,
12924 \begin_inset LatexCommand index
12925 name "Commands ! D ! \\textbackslash definecolor"
12932 \begin_layout Standard
12937 is the color space that denotes the colors
12954 The four comma separated numbers are the portion factor for the corresponding
12955 colors of the color space.
12956 The factors can be in the range of 0\InsetSpace \thinspace{}
12957 -\InsetSpace \thinspace{}
12963 also the color space
12967 can be used for definitions.
12984 , so that there are in this case three portion factors for the corresponding
12986 Furthermore there is the color space
12990 with one portion factor for the gray value.
12993 \begin_layout Standard
12994 As example a framed box with the new defined color
12998 where the characters have been colored
13003 \begin_inset Formula \begin{equation}
13004 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13011 \begin_layout Standard
13012 Self-defined colors can also be be used for text with the help of the command
13020 \begin_inset LatexCommand index
13021 name "Text ! colored"
13028 \begin_layout Standard
13032 \begin_layout Standard
13036 textcolor{darkgreen}{
13042 \begin_inset Quotes eld
13046 \begin_inset Quotes erd
13053 \begin_layout Standard
13063 \begin_layout Standard
13071 \begin_inset LatexCommand index
13072 name "Commands ! T ! \\textbackslash textcolor"
13076 is used in the scheme
13080 textcolor{color}{characters to color}
13085 \begin_layout Subsection
13087 \begin_inset LatexCommand label
13088 name "sub:Paragraph-Boxes"
13093 \begin_inset LatexCommand index
13094 name "Boxes ! as paragraph"
13101 \begin_layout Standard
13102 A box that can contain several lines and paragraphs, a so called paragraph
13103 box (parbox), can be created with the menu
13105 Insert\SpecialChar \menuseparator
13108 or the toolbar button
13109 \begin_inset Graphics
13110 filename ../images/box-insert.png
13118 \begin_layout Standard
13119 The following example shows a framed parbox in a line:
13122 \begin_layout Standard
13123 \begin_inset VSpace medskip
13127 \begin_inset Box Boxed
13136 height_special "totalheight"
13139 \begin_layout Standard
13140 This is a paragraph box.
13141 It is exactly 5\InsetSpace \thinspace{}
13142 cm long and can also contain formulas:
13143 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13154 \begin_layout Standard
13155 \begin_inset VSpace medskip
13161 \begin_layout Standard
13162 Such a box is created by right-clicking on the gray box inset.
13163 A dialog pops up showing the box properties.
13176 : 5\InsetSpace \thinspace{}
13179 Vertical Box Alignment
13184 \begin_layout Standard
13185 \begin_inset VSpace medskip
13188 In LaTeX a parbox is created with the command
13195 \begin_inset LatexCommand index
13196 name "Commands ! P ! \\textbackslash parbox"
13200 that has the following scheme:
13203 \begin_layout Standard
13208 parbox[position]{width}{box content}
13211 \begin_layout Standard
13225 for bottom means that the box is aligned within the surrounding text with
13231 for top this is done with the first line.
13232 When no position is given, the box will be vertically centered, see section
13239 Embedded\InsetSpace ~
13242 manual for examples.
13245 \begin_layout Standard
13246 \begin_inset VSpace bigskip
13249 To frame formulas completely, including the formula number, the formula
13250 must be set into a parbox.
13251 To do this, the command
13265 is inserted in TeX-mode before the formula.
13271 \begin_inset LatexCommand index
13272 name "Commands ! L ! \\textbackslash linewidth"
13278 is hereby the line width set for the document.
13279 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13280 times the frame separation and
13281 the frame thickness must be subtracted from the line width.
13282 As this is not automatically done by LyX due to a bug
13286 \begin_layout Standard
13290 \begin_layout Standard
13294 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13303 \begin_layout Standard
13315 , TeX-mode has to be used.
13316 To be able to multiply and subtract in arguments, the LaTeX-package
13324 \begin_layout Standard
13329 is part of every LaTeX standard installation.
13335 \begin_inset LatexCommand index
13336 name "Packages ! calc"
13340 must be loaded in the LaTeX-preamble with the line
13343 \begin_layout Standard
13351 \begin_layout Standard
13352 Behind the formula both boxes are closed by entering
13357 Here is an example:
13361 \begin_layout Standard
13375 \begin_layout Standard
13379 \begin_layout Standard
13397 \begin_inset Formula \begin{equation}
13398 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13406 \begin_layout Standard
13417 \begin_layout Standard
13431 \begin_layout Standard
13432 \begin_inset VSpace medskip
13435 As a parbox is used as argument of
13441 , there is in this case no difference between
13456 \begin_layout Standard
13457 \begin_inset VSpace bigskip
13460 Paragraph boxes are very useful to comment formulas directly.
13467 is used in combination with the command
13481 \begin_inset LatexCommand ref
13482 reference "sub:User-defined-Numbering"
13489 \begin_layout Standard
13490 An example of a formula commented with
13499 \begin_layout Standard
13503 \begin_layout Standard
13516 This is a description.
13517 It is distinctly separated from the formula and multiline.
13521 \begin_layout Standard
13533 \begin_layout Standard
13534 Such a formula must be inserted completely in TeX-mode because LyX does
13535 not yet support the command
13542 The formula is created with the following command sequence:
13545 \begin_layout Standard
13558 is inserted in TeX-mode.
13562 \begin_layout Standard
13563 When the formula style
13575 can also be replaced by
13582 (formula styles see
13583 \begin_inset LatexCommand ref
13584 reference "sec:Formula-Styles"
13593 Then the description follows as normal text, and finally
13599 is inserted in TeX-mode.
13612 hereby create a displayed formula.
13615 \begin_layout Standard
13622 can be seen in this example that was
13623 \begin_inset Quotes eld
13627 \begin_inset Quotes erd
13630 using the mathematical textmode:
13631 \begin_inset Formula \[
13632 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13639 \begin_layout Section
13641 \begin_inset LatexCommand index
13649 \begin_layout Subsection
13651 \begin_inset LatexCommand label
13652 name "sub:Big-Operators"
13657 \begin_inset LatexCommand index
13658 name "Operators ! big"
13663 \begin_inset LatexCommand index
13669 \begin_inset LatexCommand index
13677 \begin_layout Standard
13678 To be able to use all integral operators listed here, the option
13680 Use esint package automatically
13682 must be set in the document settings under
13690 \begin_layout Standard
13694 \begin_inset Tabular
13695 <lyxtabular version="3" rows="11" columns="2">
13697 <column alignment="center" valignment="top" leftline="true" width="0pt">
13698 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13699 <row topline="true" bottomline="true">
13700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13703 \begin_layout Standard
13709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13712 \begin_layout Standard
13719 <row topline="true">
13720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13723 \begin_layout Standard
13727 \begin_inset LatexCommand index
13728 name "Commands ! S ! \\textbackslash sum"
13737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13740 \begin_layout Standard
13741 \begin_inset Formula $\sum$
13750 <row topline="true">
13751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13754 \begin_layout Standard
13758 \begin_inset LatexCommand index
13759 name "Commands ! I ! \\textbackslash int"
13768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13771 \begin_layout Standard
13772 \begin_inset Formula $\int$
13781 <row topline="true">
13782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13785 \begin_layout Standard
13793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13796 \begin_layout Standard
13797 \begin_inset Formula $\intop$
13806 <row topline="true">
13807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13810 \begin_layout Standard
13818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13821 \begin_layout Standard
13822 \begin_inset Formula $\oint$
13831 <row topline="true">
13832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13835 \begin_layout Standard
13843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13846 \begin_layout Standard
13847 \begin_inset Formula $\ointop$
13856 <row topline="true">
13857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13860 \begin_layout Standard
13868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13871 \begin_layout Standard
13872 \begin_inset Formula $\ointctrclockwise$
13881 <row topline="true">
13882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13885 \begin_layout Standard
13893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13896 \begin_layout Standard
13897 \begin_inset Formula $\ointclockwise$
13906 <row topline="true">
13907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13910 \begin_layout Standard
13918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13921 \begin_layout Standard
13922 \begin_inset Formula $\sqint$
13931 <row topline="true">
13932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13935 \begin_layout Standard
13943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13946 \begin_layout Standard
13947 \begin_inset Formula $\bigcap$
13956 <row topline="true" bottomline="true">
13957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13960 \begin_layout Standard
13968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13971 \begin_layout Standard
13972 \begin_inset Formula $\bigcup$
13988 \begin_inset Tabular
13989 <lyxtabular version="3" rows="10" columns="2">
13991 <column alignment="center" valignment="top" leftline="true" width="0pt">
13992 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13993 <row topline="true" bottomline="true">
13994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13997 \begin_layout Standard
14003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14006 \begin_layout Standard
14013 <row topline="true">
14014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14017 \begin_layout Standard
14021 \begin_inset LatexCommand index
14022 name "Commands ! P ! \\textbackslash prod"
14031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14034 \begin_layout Standard
14035 \begin_inset Formula $\prod$
14044 <row topline="true">
14045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14048 \begin_layout Standard
14056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14059 \begin_layout Standard
14060 \begin_inset Formula $\coprod$
14069 <row topline="true">
14070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14073 \begin_layout Standard
14081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14084 \begin_layout Standard
14085 \begin_inset Formula $\bigodot$
14094 <row topline="true">
14095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14098 \begin_layout Standard
14106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14109 \begin_layout Standard
14110 \begin_inset Formula $\bigotimes$
14119 <row topline="true">
14120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14123 \begin_layout Standard
14131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14134 \begin_layout Standard
14135 \begin_inset Formula $\bigoplus$
14144 <row topline="true">
14145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14148 \begin_layout Standard
14156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14159 \begin_layout Standard
14160 \begin_inset Formula $\bigwedge$
14169 <row topline="true">
14170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14173 \begin_layout Standard
14181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14184 \begin_layout Standard
14185 \begin_inset Formula $\bigvee$
14194 <row topline="true">
14195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14198 \begin_layout Standard
14206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14209 \begin_layout Standard
14210 \begin_inset Formula $\bigsqcup$
14219 <row topline="true" bottomline="true">
14220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14223 \begin_layout Standard
14231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14234 \begin_layout Standard
14235 \begin_inset Formula $\biguplus$
14253 \begin_layout Standard
14254 All big operators can also be inserted via the math toolbar button
14255 \begin_inset Graphics
14256 filename ../images/math/intop.png
14264 \begin_layout Standard
14265 The operators are called big because they are bigger than the sometimes
14266 equal looking binary operators.
14267 All big operators can have limits as described in the next subsection.
14270 \begin_layout Standard
14295 , resp.\InsetSpace ~
14296 in the style the operator limits are displayed, see
14297 \begin_inset LatexCommand ref
14298 reference "sub:Operator-Limits"
14306 \begin_layout Subsubsection*
14307 Advices for Integrals
14310 \begin_layout Standard
14315 in an integral is an operator, that therefore has to be set upright.
14316 This is done by highlighting the
14320 and using the keyboard shortcut
14329 \begin_layout Standard
14335 \begin_inset LatexCommand ref
14336 reference "sub:Font-Styles"
14346 Finally the smallest space is inserted before the
14350 , as this is usual for operators.
14354 \begin_layout Standard
14356 \begin_inset Formula $\int A(x)dx$
14365 \begin_layout Standard
14375 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14381 \begin_layout Standard
14382 For multiple integrals there are the following commands:
14383 \begin_inset VSpace medskip
14389 \begin_layout Standard
14393 \begin_inset Tabular
14394 <lyxtabular version="3" rows="4" columns="2">
14396 <column alignment="center" valignment="top" leftline="true" width="0">
14397 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14398 <row topline="true" bottomline="true">
14399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14402 \begin_layout Standard
14408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14411 \begin_layout Standard
14413 \begin_inset Note Note
14416 \begin_layout Standard
14423 is only used as spacer.
14434 <row topline="true">
14435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14438 \begin_layout Standard
14446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14449 \begin_layout Standard
14450 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14459 <row topline="true">
14460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14463 \begin_layout Standard
14471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14474 \begin_layout Standard
14475 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14484 <row topline="true" bottomline="true">
14485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14488 \begin_layout Standard
14496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14499 \begin_layout Standard
14500 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14516 \begin_inset Tabular
14517 <lyxtabular version="3" rows="4" columns="2">
14519 <column alignment="center" valignment="top" leftline="true" width="0">
14520 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14521 <row topline="true" bottomline="true">
14522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14525 \begin_layout Standard
14531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14534 \begin_layout Standard
14541 <row topline="true">
14542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14545 \begin_layout Standard
14553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14556 \begin_layout Standard
14557 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14566 <row topline="true">
14567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14570 \begin_layout Standard
14578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14581 \begin_layout Standard
14582 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14591 <row topline="true" bottomline="true">
14592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14595 \begin_layout Standard
14603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14606 \begin_layout Standard
14607 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14625 \begin_layout Subsection
14627 \begin_inset LatexCommand label
14628 name "sub:Operator-Limits"
14633 \begin_inset LatexCommand index
14634 name "Operators ! Limits"
14641 \begin_layout Standard
14642 Limits are created by super- and subscripts:
14645 \begin_layout Standard
14647 \begin_inset Tabular
14648 <lyxtabular version="3" rows="2" columns="2">
14650 <column alignment="center" valignment="top" leftline="true" width="0pt">
14651 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14652 <row topline="true" bottomline="true">
14653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14656 \begin_layout Standard
14662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14665 \begin_layout Standard
14667 \begin_inset Note Note
14670 \begin_layout Standard
14677 is only used as spacer.
14688 <row topline="true" bottomline="true">
14689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14692 \begin_layout Standard
14701 \begin_layout Standard
14711 \begin_inset Formula $\to$
14715 \begin_inset Formula $\to$
14723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14726 \begin_layout Standard
14727 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14743 \begin_layout Standard
14744 Limits of inline formulas are set right beside the operator.
14745 Limits in displayed formulas are set above or below the operator, except
14746 of integral limits.
14749 \begin_layout Standard
14750 To force that the limits are set beside the operator, the cursor is set
14751 directly behind the operator and the limits type is changed with the menu
14754 Edit\SpecialChar \menuseparator
14755 Math\SpecialChar \menuseparator
14773 \begin_layout Standard
14774 The default limits type is this:
14775 \begin_inset Formula \[
14776 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14780 This is how it looks when the limits type was changed to
14787 \begin_inset Formula \[
14788 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14792 For integrals, except of
14804 , the limits are by default set beside the operator.
14805 But for multiple integrals the limits are often set below the operator.
14806 In the following example the limits type was therefore set to
14810 and so set below the integrals:
14811 \begin_inset Formula \begin{equation}
14812 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14819 \begin_layout Standard
14820 \begin_inset VSpace medskip
14823 To specify conditions for limits, the commands
14830 \begin_inset LatexCommand index
14831 name "Commands ! S ! \\textbackslash subarray"
14842 \begin_inset LatexCommand index
14843 name "Commands ! S ! \\textbackslash substack"
14848 To create for example this expression
14849 \begin_inset Formula \begin{equation}
14850 \sum_{\begin{subarray}{c}
14852 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14859 \begin_layout Standard
14860 the following has to be done:
14874 \begin_layout Standard
14886 One is now in a blue box under the summation operator and insert there
14895 \begin_layout Standard
14907 The blue box is now within a purple box and now several lines can be written
14909 A new line is created by inserting a line break (
14918 0<k<1000 Ctrl-Return
14922 is typed in, a new box appears below for the new line.
14925 \begin_layout Standard
14926 The alignment of the lines can be changed to left aligned with the
14936 Edit\SpecialChar \menuseparator
14940 To get right alignment,
14948 \begin_layout Standard
14959 is inserted at the beginning of the line.
14962 \begin_layout Standard
14975 with the difference that the lines are always centered.
14978 \begin_layout Standard
14979 \begin_inset VSpace bigskip
14983 \begin_inset LatexCommand eqref
14984 reference "eq:substack"
14988 there can be too much space beside an operator, because the characters
14989 following the operator are set beside the limits.
14992 \begin_layout Standard
14993 To avoid this, the following macro can be used in the LaTeX-preamble:
14996 \begin_layout Standard
15025 mathclapinternal #1#2{
15029 mathsurround =0pt #1{#2}$}}
15032 \begin_layout Standard
15033 This defines the command
15040 \begin_inset LatexCommand index
15041 name "Commands ! M ! \\textbackslash mathclap"
15045 that sets the width of the limit to 0\InsetSpace \thinspace{}
15047 The command scheme is
15050 \begin_layout Standard
15058 \begin_layout Standard
15059 where the limit can consist of several conditions.
15062 \begin_layout Standard
15064 \begin_inset LatexCommand eqref
15065 reference "eq:substack"
15069 , one uses the command
15072 \begin_layout Standard
15085 \begin_layout Standard
15094 0<k<1000 Ctrl-Enter
15097 \begin_layout Standard
15098 to create the lower limit.
15099 The summand is now directly behind the summation operator:
15100 \begin_inset Formula \[
15101 \sum_{\mathclap{\substack{0<k<1000\\
15102 \\k\,\in\,\mathbb{N}}
15110 \begin_layout Standard
15111 \begin_inset VSpace bigskip
15114 How to use one limit for several operators is described in
15115 \begin_inset LatexCommand ref
15116 reference "sub:Self-defined-Operators"
15123 \begin_layout Subsection
15125 \begin_inset LatexCommand label
15126 name "sub:Binary-Operators"
15131 \begin_inset LatexCommand index
15132 name "Operators ! binary"
15139 \begin_layout Standard
15140 Binary operators are surrounded by space when there is a character before
15142 \begin_inset VSpace medskip
15148 \begin_layout Standard
15152 \begin_inset Tabular
15153 <lyxtabular version="3" rows="13" columns="2">
15155 <column alignment="center" valignment="top" leftline="true" width="0pt">
15156 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15157 <row topline="true" bottomline="true">
15158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15161 \begin_layout Standard
15163 \begin_inset Note Note
15166 \begin_layout Standard
15173 is only used as spacer.
15183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15186 \begin_layout Standard
15193 <row topline="true">
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15197 \begin_layout Standard
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15206 \begin_layout Standard
15207 \begin_inset Formula $+$
15216 <row topline="true">
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15220 \begin_layout Standard
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15229 \begin_layout Standard
15230 \begin_inset Formula $-$
15239 <row topline="true">
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15243 \begin_layout Standard
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15254 \begin_layout Standard
15255 \begin_inset Formula $\pm$
15264 <row topline="true">
15265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15268 \begin_layout Standard
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Standard
15280 \begin_inset Formula $\mp$
15289 <row topline="true">
15290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15293 \begin_layout Standard
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15304 \begin_layout Standard
15305 \begin_inset Formula $\cdot$
15314 <row topline="true">
15315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15318 \begin_layout Standard
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15329 \begin_layout Standard
15330 \begin_inset Formula $\times$
15339 <row topline="true">
15340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15343 \begin_layout Standard
15351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15354 \begin_layout Standard
15355 \begin_inset Formula $\div$
15364 <row topline="true">
15365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15368 \begin_layout Standard
15372 \begin_layout Standard
15385 \begin_layout Standard
15397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15400 \begin_layout Standard
15401 \begin_inset Formula $*$
15410 <row topline="true">
15411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15414 \begin_layout Standard
15422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Standard
15426 \begin_inset Formula $\star$
15435 <row topline="true">
15436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15439 \begin_layout Standard
15447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15450 \begin_layout Standard
15451 \begin_inset Formula $\circ$
15460 <row topline="true">
15461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15464 \begin_layout Standard
15472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15475 \begin_layout Standard
15476 \begin_inset Formula $\diamond$
15485 <row topline="true" bottomline="true">
15486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15489 \begin_layout Standard
15497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15500 \begin_layout Standard
15501 \begin_inset Formula $\bullet$
15517 \begin_inset Tabular
15518 <lyxtabular version="3" rows="13" columns="2">
15520 <column alignment="center" valignment="top" leftline="true" width="0pt">
15521 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15522 <row topline="true" bottomline="true">
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15526 \begin_layout Standard
15532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15535 \begin_layout Standard
15542 <row topline="true">
15543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15546 \begin_layout Standard
15554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15557 \begin_layout Standard
15558 \begin_inset Formula $\nabla$
15567 <row topline="true">
15568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15571 \begin_layout Standard
15579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15582 \begin_layout Standard
15583 \begin_inset Formula $\bigtriangledown$
15592 <row topline="true">
15593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15596 \begin_layout Standard
15604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15607 \begin_layout Standard
15608 \begin_inset Formula $\bigtriangleup$
15617 <row topline="true">
15618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15621 \begin_layout Standard
15629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15632 \begin_layout Standard
15633 \begin_inset Formula $\Box$
15642 <row topline="true">
15643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15646 \begin_layout Standard
15654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15657 \begin_layout Standard
15658 \begin_inset Formula $\cap$
15667 <row topline="true">
15668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15671 \begin_layout Standard
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15682 \begin_layout Standard
15683 \begin_inset Formula $\cup$
15692 <row topline="true">
15693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15696 \begin_layout Standard
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15707 \begin_layout Standard
15708 \begin_inset Formula $\dagger$
15717 <row topline="true">
15718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15721 \begin_layout Standard
15729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15732 \begin_layout Standard
15733 \begin_inset Formula $\ddagger$
15742 <row topline="true">
15743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15746 \begin_layout Standard
15754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15757 \begin_layout Standard
15758 \begin_inset Formula $\wr$
15767 <row topline="true">
15768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15771 \begin_layout Standard
15779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15782 \begin_layout Standard
15783 \begin_inset Formula $\bigcirc$
15792 <row topline="true">
15793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15796 \begin_layout Standard
15804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15807 \begin_layout Standard
15808 \begin_inset Formula $\wedge$
15817 <row topline="true" bottomline="true">
15818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15821 \begin_layout Standard
15829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15832 \begin_layout Standard
15833 \begin_inset Formula $\vee$
15849 \begin_inset Tabular
15850 <lyxtabular version="3" rows="13" columns="2">
15852 <column alignment="center" valignment="top" leftline="true" width="0pt">
15853 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15854 <row topline="true" bottomline="true">
15855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15858 \begin_layout Standard
15864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15867 \begin_layout Standard
15874 <row topline="true">
15875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15878 \begin_layout Standard
15886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15889 \begin_layout Standard
15890 \begin_inset Formula $\oplus$
15899 <row topline="true">
15900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15903 \begin_layout Standard
15911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15914 \begin_layout Standard
15915 \begin_inset Formula $\ominus$
15924 <row topline="true">
15925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15928 \begin_layout Standard
15936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15939 \begin_layout Standard
15940 \begin_inset Formula $\otimes$
15949 <row topline="true">
15950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15953 \begin_layout Standard
15961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15964 \begin_layout Standard
15965 \begin_inset Formula $\oslash$
15974 <row topline="true">
15975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15978 \begin_layout Standard
15986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15989 \begin_layout Standard
15990 \begin_inset Formula $\odot$
15999 <row topline="true">
16000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16003 \begin_layout Standard
16011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16014 \begin_layout Standard
16015 \begin_inset Formula $\amalg$
16024 <row topline="true">
16025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16028 \begin_layout Standard
16036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16039 \begin_layout Standard
16040 \begin_inset Formula $\uplus$
16049 <row topline="true">
16050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16053 \begin_layout Standard
16061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16064 \begin_layout Standard
16065 \begin_inset Formula $\setminus$
16074 <row topline="true">
16075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16078 \begin_layout Standard
16086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16089 \begin_layout Standard
16090 \begin_inset Formula $\sqcap$
16099 <row topline="true">
16100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16103 \begin_layout Standard
16111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16114 \begin_layout Standard
16115 \begin_inset Formula $\sqcup$
16124 <row topline="true">
16125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16128 \begin_layout Standard
16136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16139 \begin_layout Standard
16140 \begin_inset Formula $\triangleleft$
16149 <row topline="true" bottomline="true">
16150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16153 \begin_layout Standard
16161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16164 \begin_layout Standard
16165 \begin_inset Formula $\triangleright$
16183 \begin_layout Standard
16184 All binary operators can also be inserted via the math toolbar button
16185 \begin_inset Graphics
16186 filename ../images/math/pm.png
16194 \begin_layout Standard
16195 To typeset the Laplace operator also
16212 \begin_inset Formula $\nabla^{2}$
16215 ) can be used instead of
16224 \begin_layout Standard
16231 Insert\SpecialChar \menuseparator
16243 \begin_layout Subsection
16244 Self-defined Operators
16245 \begin_inset LatexCommand label
16246 name "sub:Self-defined-Operators"
16251 \begin_inset LatexCommand index
16252 name "Operators ! self-defined"
16259 \begin_layout Standard
16260 With the help of the command
16264 DeclareMathOperator
16267 \begin_inset LatexCommand index
16268 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16272 custom operators can be defined in the LaTeX-preamble.
16273 Its command scheme is:
16276 \begin_layout Standard
16281 DeclareMathOperator{new command}{display}
16284 \begin_layout Standard
16285 Display can be characters or symbols that define how the operator looks
16287 To define a big operator a * is set behind the command.
16288 All self-defined big operators can have limits as described in
16289 \begin_inset LatexCommand ref
16290 reference "sub:Operator-Limits"
16297 \begin_layout Standard
16298 For example the LaTeX-preamble line
16301 \begin_layout Standard
16306 DeclareMathOperator*{
16313 \begin_layout Standard
16314 defines the command
16320 , that inserts a big operator consisting of the lozenge symbol from
16321 \begin_inset LatexCommand ref
16322 reference "sub:Miscellaneous-Symbols"
16327 \begin_inset Formula \[
16328 \Lozenge_{n=1}^{\infty}\]
16332 The command for this formula is:
16343 \begin_inset Formula $\to$
16349 \begin_layout Standard
16350 \begin_inset VSpace bigskip
16353 When self-defined operators are not used several times in the document,
16354 they can also be defined with the commands
16361 \begin_inset LatexCommand index
16362 name "Commands ! M ! \\textbackslash mathop"
16373 \begin_inset LatexCommand index
16374 name "Commands ! M ! \\textbackslash mathbin"
16378 , which have the following scheme:
16381 \begin_layout Standard
16395 \begin_layout Standard
16402 defines big operators,
16411 \begin_layout Standard
16418 can e.\InsetSpace \thinspace{}
16420 be used to use one limit for several operators:
16423 \begin_layout Standard
16424 \begin_inset Formula \[
16425 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16432 \begin_layout Standard
16433 The command for the formula above is:
16451 \begin_layout Standard
16463 \begin_inset Formula $\to$
16472 \begin_layout Standard
16486 \begin_layout Section
16488 \begin_inset LatexCommand index
16496 \begin_layout Subsection
16498 \begin_inset LatexCommand label
16499 name "sub:Font-Styles"
16504 \begin_inset LatexCommand index
16505 name "Font ! style"
16512 \begin_layout Standard
16513 Latin letters in formulas can be set in one of the following font styles:
16514 \begin_inset VSpace -2mm
16520 \begin_layout Standard
16522 \begin_inset Tabular
16523 <lyxtabular version="3" rows="6" columns="3">
16525 <column alignment="center" valignment="top" leftline="true" width="0">
16526 <column alignment="center" valignment="top" leftline="true" width="0">
16527 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16528 <row topline="true" bottomline="true">
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16532 \begin_layout Standard
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16541 \begin_layout Standard
16547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16550 \begin_layout Standard
16557 <row topline="true">
16558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16561 \begin_layout Standard
16570 \begin_layout Standard
16586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16589 \begin_layout Standard
16590 \begin_inset Formula $\mathbb{ABC}$
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16601 \begin_layout Standard
16608 <row topline="true">
16609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16612 \begin_layout Standard
16621 \begin_layout Standard
16637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16640 \begin_layout Standard
16641 \begin_inset Formula $\mathbf{AbC}$
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Standard
16659 <row topline="true">
16660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16663 \begin_layout Standard
16672 \begin_layout Standard
16688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16691 \begin_layout Standard
16692 \begin_inset Formula $\boldsymbol{AbC}$
16700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16703 \begin_layout Standard
16710 <row topline="true">
16711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16714 \begin_layout Standard
16723 \begin_layout Standard
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Standard
16743 \begin_inset Formula $\mathcal{ABC}$
16751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16754 \begin_layout Standard
16761 <row topline="true" bottomline="true">
16762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16765 \begin_layout Standard
16774 \begin_layout Standard
16790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16793 \begin_layout Standard
16794 \begin_inset Formula $\mathfrak{AbC}$
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16805 \begin_layout Standard
16819 \begin_layout Standard
16821 \begin_inset Tabular
16822 <lyxtabular version="3" rows="5" columns="3">
16824 <column alignment="center" valignment="top" leftline="true" width="0">
16825 <column alignment="center" valignment="top" leftline="true" width="0">
16826 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16827 <row topline="true" bottomline="true">
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16831 \begin_layout Standard
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16840 \begin_layout Standard
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16849 \begin_layout Standard
16856 <row topline="true">
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16860 \begin_layout Standard
16869 \begin_layout Standard
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16888 \begin_layout Standard
16889 \begin_inset Formula $\mathit{AbC}$
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16900 \begin_layout Standard
16907 <row topline="true">
16908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16911 \begin_layout Standard
16920 \begin_layout Standard
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16939 \begin_layout Standard
16940 \begin_inset Formula $\mathrm{AbC}$
16948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16951 \begin_layout Standard
16958 <row topline="true">
16959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16962 \begin_layout Standard
16971 \begin_layout Standard
16987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16990 \begin_layout Standard
16991 \begin_inset Formula $\mathsf{AbC}$
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17002 \begin_layout Standard
17009 <row topline="true" bottomline="true">
17010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17013 \begin_layout Standard
17022 \begin_layout Standard
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17041 \begin_layout Standard
17042 \begin_inset Formula $\mathtt{AbC}$
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Standard
17067 \begin_layout Standard
17068 \begin_inset Note Greyedout
17071 \begin_layout Standard
17088 can only be used for big letters.
17096 \begin_layout Standard
17097 Predefined is the style
17106 \begin_layout Standard
17107 The style commands work also for letters in mathematical constructs:
17108 \begin_inset Formula \[
17109 \mathfrak{A=\frac{b}{C}}\]
17116 \begin_layout Standard
17117 Characters in mathematical text don't appear in a math font style but in
17118 the text font style
17125 That their style can't be set correctly via the text style dialog is a
17130 \begin_layout Standard
17135 \begin_layout Standard
17139 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17148 \begin_layout Standard
17163 \begin_layout Standard
17164 Instead of the style commands the dialog
17166 Edit\SpecialChar \menuseparator
17167 Math\SpecialChar \menuseparator
17170 or the toolbar button
17171 \begin_inset Graphics
17172 filename ../images/math/font.png
17180 \begin_layout Subsection
17182 \begin_inset LatexCommand label
17183 name "sub:Bold-Formulas"
17188 \begin_inset LatexCommand index
17189 name "Formula ! bold"
17196 \begin_layout Standard
17197 To make a complete formula bold, the command
17203 from the previous subsection cannot be used, because it doesn't work for
17204 small Greek letters.
17205 Furthermore it prints Latin letters always upright, like in the following
17209 \begin_layout Standard
17210 \begin_inset Formula \[
17211 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17218 \begin_layout Standard
17219 To display the formula correctly, the command
17226 \begin_inset Formula \[
17227 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17231 It is also possible to set the formula in a
17233 boldmath environment
17236 This environment is created by inserting the command
17241 \begin_inset LatexCommand index
17242 name "Commands ! B ! \\textbackslash boldmath"
17249 To end the environment, the command
17254 \begin_inset LatexCommand index
17255 name "Commands ! U ! \\textbackslash unboldmath"
17261 is inserted in TeX-mode.
17265 \begin_layout Standard
17275 \begin_inset Formula \[
17276 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17284 \begin_layout Standard
17296 \begin_layout Subsection
17298 \begin_inset LatexCommand label
17299 name "sub:Font-Sizes"
17304 \begin_inset LatexCommand index
17312 \begin_layout Standard
17313 For characters in formulas there are, analog to characters in text, the
17314 following size commands:
17317 \begin_layout Standard
17381 \begin_layout Standard
17382 The size produced by the commands depends on the document font size, that
17383 corresponds with the command
17390 The other commands produce smaller or larger sizes than
17397 The font size can however not exceed a certain value.
17398 Is for example the document font size 12\InsetSpace \thinspace{}
17405 switches to the same size as
17415 \begin_layout Standard
17416 A size command is inserted in TeX-mode before the formula and sets the size
17417 for all following formula and text characters.
17418 To switch back to the initial size, the command
17424 is inserted behind the formula in TeX-mode.
17427 \begin_layout Standard
17428 Within a formula the size can only be changed for symbols or letters in
17430 To do this, the size command is inserted in mathematical text.
17431 All following characters until the end of the mathematical text or until
17432 another size command will have the selected size.
17434 \begin_inset VSpace -2mm
17440 \begin_layout Standard
17444 \begin_layout Standard
17454 \begin_inset Formula \[
17455 A=\frac{B}{c}\cdot\maltese\]
17460 \begin_inset Formula \[
17461 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17469 \begin_layout Standard
17481 \begin_layout Standard
17482 \begin_inset VSpace medskip
17485 Before both formulas the command
17492 The command for the second formula is:
17502 \begin_layout Standard
17517 \begin_layout Standard
17532 \begin_layout Standard
17547 \begin_layout Standard
17557 \begin_inset Formula $\to$
17561 \begin_inset Formula $\to$
17570 \begin_layout Standard
17589 \begin_layout Standard
17604 \begin_layout Standard
17619 \begin_layout Standard
17631 \begin_layout Standard
17632 If a symbol cannot be displayed in different sizes, it will always be displayed
17633 in the default size.
17636 \begin_layout Section
17638 \begin_inset LatexCommand index
17639 name "Greek letters"
17646 \begin_layout Standard
17647 All Greek letters can also be inserted via the toolbar button
17648 \begin_inset Graphics
17649 filename ../images/math/alpha.png
17657 \begin_layout Subsection
17659 \begin_inset LatexCommand label
17660 name "sub:Small-Letters"
17665 \begin_inset LatexCommand index
17666 name "Greek letters ! small"
17673 \begin_layout Standard
17677 \begin_inset Tabular
17678 <lyxtabular version="3" rows="11" columns="2">
17680 <column alignment="center" valignment="top" leftline="true" width="0pt">
17681 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17682 <row topline="true" bottomline="true">
17683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17686 \begin_layout Standard
17692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17695 \begin_layout Standard
17702 <row topline="true">
17703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17706 \begin_layout Standard
17714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17717 \begin_layout Standard
17718 \begin_inset Formula $\alpha$
17727 <row topline="true">
17728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17731 \begin_layout Standard
17739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17742 \begin_layout Standard
17743 \begin_inset Formula $\beta$
17752 <row topline="true">
17753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17756 \begin_layout Standard
17764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17767 \begin_layout Standard
17768 \begin_inset Formula $\gamma$
17777 <row topline="true">
17778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17781 \begin_layout Standard
17789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17792 \begin_layout Standard
17793 \begin_inset Formula $\delta$
17802 <row topline="true">
17803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17806 \begin_layout Standard
17814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17817 \begin_layout Standard
17818 \begin_inset Formula $\epsilon$
17827 <row topline="true">
17828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17831 \begin_layout Standard
17839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17842 \begin_layout Standard
17843 \begin_inset Formula $\varepsilon$
17852 <row topline="true">
17853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17856 \begin_layout Standard
17864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17867 \begin_layout Standard
17868 \begin_inset Formula $\zeta$
17877 <row topline="true">
17878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17881 \begin_layout Standard
17889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17892 \begin_layout Standard
17893 \begin_inset Formula $\eta$
17902 <row topline="true">
17903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17906 \begin_layout Standard
17914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17917 \begin_layout Standard
17918 \begin_inset Formula $\theta$
17927 <row topline="true" bottomline="true">
17928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17931 \begin_layout Standard
17939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17942 \begin_layout Standard
17943 \begin_inset Formula $\vartheta$
17959 \begin_inset Tabular
17960 <lyxtabular version="3" rows="12" columns="2">
17962 <column alignment="center" valignment="top" leftline="true" width="0pt">
17963 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17964 <row topline="true" bottomline="true">
17965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17968 \begin_layout Standard
17974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17977 \begin_layout Standard
17984 <row topline="true">
17985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17988 \begin_layout Standard
17996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17999 \begin_layout Standard
18000 \begin_inset Formula $\iota$
18009 <row topline="true">
18010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18013 \begin_layout Standard
18021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18024 \begin_layout Standard
18025 \begin_inset Formula $\kappa$
18034 <row topline="true">
18035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18038 \begin_layout Standard
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18049 \begin_layout Standard
18050 \begin_inset Formula $\varkappa$
18059 <row topline="true">
18060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18063 \begin_layout Standard
18071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18074 \begin_layout Standard
18075 \begin_inset Formula $\lambda$
18084 <row topline="true">
18085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18088 \begin_layout Standard
18096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18099 \begin_layout Standard
18100 \begin_inset Formula $\mu$
18109 <row topline="true">
18110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18113 \begin_layout Standard
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18124 \begin_layout Standard
18125 \begin_inset Formula $\nu$
18134 <row topline="true">
18135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18138 \begin_layout Standard
18146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18149 \begin_layout Standard
18150 \begin_inset Formula $\xi$
18159 <row topline="true">
18160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18163 \begin_layout Standard
18169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18172 \begin_layout Standard
18173 \begin_inset Formula $o$
18182 <row topline="true">
18183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18186 \begin_layout Standard
18194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18197 \begin_layout Standard
18198 \begin_inset Formula $\pi$
18207 <row topline="true">
18208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18211 \begin_layout Standard
18219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18222 \begin_layout Standard
18223 \begin_inset Formula $\varpi$
18232 <row topline="true" bottomline="true">
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18236 \begin_layout Standard
18244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18247 \begin_layout Standard
18248 \begin_inset Formula $\rho$
18264 \begin_inset Tabular
18265 <lyxtabular version="3" rows="11" columns="2">
18267 <column alignment="center" valignment="top" leftline="true" width="0pt">
18268 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18269 <row topline="true" bottomline="true">
18270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18273 \begin_layout Standard
18279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18282 \begin_layout Standard
18289 <row topline="true">
18290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18293 \begin_layout Standard
18301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18304 \begin_layout Standard
18305 \begin_inset Formula $\varrho$
18314 <row topline="true">
18315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18318 \begin_layout Standard
18326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18329 \begin_layout Standard
18330 \begin_inset Formula $\sigma$
18339 <row topline="true">
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18343 \begin_layout Standard
18351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18354 \begin_layout Standard
18355 \begin_inset Formula $\varsigma$
18364 <row topline="true">
18365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18368 \begin_layout Standard
18376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18379 \begin_layout Standard
18380 \begin_inset Formula $\tau$
18389 <row topline="true">
18390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18393 \begin_layout Standard
18401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18404 \begin_layout Standard
18405 \begin_inset Formula $\upsilon$
18414 <row topline="true">
18415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18418 \begin_layout Standard
18426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18429 \begin_layout Standard
18430 \begin_inset Formula $\phi$
18439 <row topline="true">
18440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18443 \begin_layout Standard
18451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18454 \begin_layout Standard
18455 \begin_inset Formula $\varphi$
18464 <row topline="true">
18465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18468 \begin_layout Standard
18476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Standard
18480 \begin_inset Formula $\chi$
18489 <row topline="true">
18490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18493 \begin_layout Standard
18501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18504 \begin_layout Standard
18505 \begin_inset Formula $\psi$
18514 <row topline="true" bottomline="true">
18515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18518 \begin_layout Standard
18526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18529 \begin_layout Standard
18530 \begin_inset Formula $\omega$
18548 \begin_layout Standard
18549 \begin_inset VSpace medskip
18555 \begin_layout Standard
18556 How to create upright Greek letters is explained in
18557 \begin_inset LatexCommand ref
18558 reference "sub:Upright-small-Greek"
18565 \begin_layout Subsection
18567 \begin_inset LatexCommand index
18568 name "Greek letters ! big"
18575 \begin_layout Standard
18579 \begin_inset Tabular
18580 <lyxtabular version="3" rows="7" columns="2">
18582 <column alignment="center" valignment="top" leftline="true" width="0pt">
18583 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18584 <row topline="true" bottomline="true">
18585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18588 \begin_layout Standard
18594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18597 \begin_layout Standard
18604 <row topline="true">
18605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18608 \begin_layout Standard
18616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18619 \begin_layout Standard
18620 \begin_inset Formula $\Gamma$
18629 <row topline="true">
18630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18633 \begin_layout Standard
18641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18644 \begin_layout Standard
18645 \begin_inset Formula $\Delta$
18654 <row topline="true">
18655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18658 \begin_layout Standard
18666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18669 \begin_layout Standard
18670 \begin_inset Formula $\Theta$
18679 <row topline="true">
18680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18683 \begin_layout Standard
18691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18694 \begin_layout Standard
18695 \begin_inset Formula $\Lambda$
18704 <row topline="true">
18705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18708 \begin_layout Standard
18716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18719 \begin_layout Standard
18720 \begin_inset Formula $\Xi$
18729 <row topline="true" bottomline="true">
18730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18733 \begin_layout Standard
18741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18744 \begin_layout Standard
18745 \begin_inset Formula $\Pi$
18761 \begin_inset Tabular
18762 <lyxtabular version="3" rows="6" columns="2">
18764 <column alignment="center" valignment="top" leftline="true" width="0pt">
18765 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18766 <row topline="true" bottomline="true">
18767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18770 \begin_layout Standard
18776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18779 \begin_layout Standard
18786 <row topline="true">
18787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18790 \begin_layout Standard
18798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18801 \begin_layout Standard
18802 \begin_inset Formula $\Sigma$
18811 <row topline="true">
18812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18815 \begin_layout Standard
18823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18826 \begin_layout Standard
18827 \begin_inset Formula $\Upsilon$
18836 <row topline="true">
18837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18840 \begin_layout Standard
18848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18851 \begin_layout Standard
18852 \begin_inset Formula $\Phi$
18861 <row topline="true">
18862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18865 \begin_layout Standard
18873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18876 \begin_layout Standard
18877 \begin_inset Formula $\Psi$
18886 <row topline="true" bottomline="true">
18887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18890 \begin_layout Standard
18898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18901 \begin_layout Standard
18902 \begin_inset Formula $\Omega$
18920 \begin_layout Standard
18921 \begin_inset VSpace medskip
18924 That the big Greek letters appear upright is caused by a design bug when
18926 To get correct italic big letters, begin every command with
18931 For example the command
18938 \begin_inset Formula $\varGamma$
18944 \begin_layout Subsection
18946 \begin_inset LatexCommand index
18947 name "Greek letters ! bold"
18954 \begin_layout Standard
18955 Greek letters cannot be set with different font styles like Latin letters.
18956 They can only be made bold with the command
18963 \begin_inset LatexCommand index
18964 name "Commands ! B ! \\textbackslash boldsymbol"
18971 \begin_layout Standard
18973 \begin_inset Tabular
18974 <lyxtabular version="3" rows="3" columns="2">
18976 <column alignment="center" valignment="top" leftline="true" width="0">
18977 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
18978 <row topline="true" bottomline="true">
18979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18982 \begin_layout Standard
18988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18991 \begin_layout Standard
18998 <row topline="true">
18999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19002 \begin_layout Standard
19014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19017 \begin_layout Standard
19018 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19027 <row topline="true" bottomline="true">
19028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19031 \begin_layout Standard
19043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19046 \begin_layout Standard
19047 \begin_inset Formula $\theta\boldsymbol{\theta}$
19063 \begin_layout Section
19068 \begin_layout Standard
19081 \begin_layout Standard
19082 A list with all symbols of most of the LaTeX-packages can be found in
19083 \begin_inset LatexCommand cite
19097 \begin_layout Standard
19105 \begin_inset Note Note
19108 \begin_layout Standard
19111 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19114 \begin_layout Standard
19117 texorpdfstring is in section
19118 \begin_inset LatexCommand ref
19119 reference "sub:Formulas-in-Section"
19129 \begin_inset LatexCommand index
19137 \begin_layout Standard
19138 Many of the symbols listed in this section can also be inserted via the
19140 \begin_inset Graphics
19141 filename ../images/math/nabla.png
19147 \begin_inset Graphics
19148 filename ../images/math/digamma.png
19156 \begin_layout Subsection
19157 Mathematical Symbols
19158 \begin_inset LatexCommand label
19159 name "sub:Mathematical-Symbols"
19164 \begin_inset LatexCommand index
19165 name "Symbols ! mathematical"
19172 \begin_layout Standard
19176 \begin_inset Tabular
19177 <lyxtabular version="3" rows="10" columns="2">
19179 <column alignment="center" valignment="top" leftline="true" width="0pt">
19180 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19181 <row topline="true" bottomline="true">
19182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19185 \begin_layout Standard
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19194 \begin_layout Standard
19201 <row topline="true">
19202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19205 \begin_layout Standard
19213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19216 \begin_layout Standard
19217 \begin_inset Formula $\neg$
19226 <row topline="true">
19227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19230 \begin_layout Standard
19238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19241 \begin_layout Standard
19242 \begin_inset Formula $\Im$
19251 <row topline="true">
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19255 \begin_layout Standard
19263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19266 \begin_layout Standard
19267 \begin_inset Formula $\Re$
19276 <row topline="true">
19277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19280 \begin_layout Standard
19288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19291 \begin_layout Standard
19292 \begin_inset Formula $\aleph$
19301 <row topline="true">
19302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19305 \begin_layout Standard
19313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19316 \begin_layout Standard
19317 \begin_inset Formula $\partial$
19326 <row topline="true">
19327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19330 \begin_layout Standard
19338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19341 \begin_layout Standard
19342 \begin_inset Formula $\infty$
19351 <row topline="true" bottomline="true">
19352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19355 \begin_layout Standard
19363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19366 \begin_layout Standard
19367 \begin_inset Formula $\wp$
19376 <row bottomline="true">
19377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19380 \begin_layout Standard
19388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19391 \begin_layout Standard
19392 \begin_inset Formula $\imath$
19401 <row bottomline="true">
19402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19405 \begin_layout Standard
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19416 \begin_layout Standard
19417 \begin_inset Formula $\jmath$
19433 \begin_inset Tabular
19434 <lyxtabular version="3" rows="10" columns="2">
19436 <column alignment="center" valignment="top" leftline="true" width="0pt">
19437 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19438 <row topline="true" bottomline="true">
19439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19442 \begin_layout Standard
19448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19451 \begin_layout Standard
19453 \begin_inset Note Note
19456 \begin_layout Standard
19463 is only used as spacer.
19474 <row topline="true">
19475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19478 \begin_layout Standard
19486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19489 \begin_layout Standard
19490 \begin_inset Formula $\forall$
19499 <row topline="true">
19500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19503 \begin_layout Standard
19511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19514 \begin_layout Standard
19515 \begin_inset Formula $\exists$
19524 <row topline="true">
19525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19528 \begin_layout Standard
19536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19539 \begin_layout Standard
19540 \begin_inset Formula $\nexists$
19549 <row topline="true">
19550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19553 \begin_layout Standard
19561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19564 \begin_layout Standard
19565 \begin_inset Formula $\emptyset$
19574 <row topline="true">
19575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19578 \begin_layout Standard
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19589 \begin_layout Standard
19590 \begin_inset Formula $\varnothing$
19599 <row topline="true">
19600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19603 \begin_layout Standard
19611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19614 \begin_layout Standard
19615 \begin_inset Formula $\dag$
19624 <row topline="true" bottomline="true">
19625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19628 \begin_layout Standard
19636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Standard
19640 \begin_inset Formula $\ddag$
19649 <row bottomline="true">
19650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19653 \begin_layout Standard
19661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19664 \begin_layout Standard
19668 \begin_layout Standard
19678 \begin_inset Formula $\complement$
19685 \begin_layout Standard
19698 <row bottomline="true">
19699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19702 \begin_layout Standard
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19713 \begin_layout Standard
19714 \begin_inset Formula $\Bbbk$
19730 \begin_inset Tabular
19731 <lyxtabular version="3" rows="10" columns="2">
19733 <column alignment="center" valignment="top" leftline="true" width="0pt">
19734 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19735 <row topline="true" bottomline="true">
19736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19739 \begin_layout Standard
19745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19748 \begin_layout Standard
19755 <row topline="true">
19756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19759 \begin_layout Standard
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19770 \begin_layout Standard
19771 \begin_inset Formula $\prime$
19780 <row topline="true">
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19784 \begin_layout Standard
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Standard
19796 \begin_inset Formula $\backprime$
19805 <row topline="true">
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19809 \begin_layout Standard
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Standard
19821 \begin_inset Formula $\mho$
19830 <row topline="true">
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19834 \begin_layout Standard
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19845 \begin_layout Standard
19846 \begin_inset Formula $\triangle$
19855 <row topline="true">
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19859 \begin_layout Standard
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19870 \begin_layout Standard
19871 \begin_inset Formula $\angle$
19880 <row topline="true">
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19884 \begin_layout Standard
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19895 \begin_layout Standard
19896 \begin_inset Formula $\measuredangle$
19905 <row topline="true" bottomline="true">
19906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19909 \begin_layout Standard
19917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19920 \begin_layout Standard
19921 \begin_inset Formula $\sphericalangle$
19930 <row bottomline="true">
19931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19934 \begin_layout Standard
19942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19945 \begin_layout Standard
19946 \begin_inset Formula $\top$
19955 <row bottomline="true">
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19959 \begin_layout Standard
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19970 \begin_layout Standard
19971 \begin_inset Formula $\bot$
19989 \begin_layout Standard
19995 \begin_layout Subsection
19996 Miscellaneous Symbols
19997 \begin_inset LatexCommand label
19998 name "sub:Miscellaneous-Symbols"
20003 \begin_inset LatexCommand index
20004 name "Symbols ! miscellaneous"
20011 \begin_layout Standard
20012 \begin_inset Tabular
20013 <lyxtabular version="3" rows="10" columns="2">
20015 <column alignment="center" valignment="top" leftline="true" width="0pt">
20016 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20017 <row topline="true" bottomline="true">
20018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20021 \begin_layout Standard
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Standard
20037 <row topline="true">
20038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20041 \begin_layout Standard
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Standard
20053 \begin_inset Formula $\flat$
20062 <row topline="true">
20063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20066 \begin_layout Standard
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20077 \begin_layout Standard
20078 \begin_inset Formula $\natural$
20087 <row topline="true">
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20091 \begin_layout Standard
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20102 \begin_layout Standard
20103 \begin_inset Formula $\sharp$
20112 <row topline="true" bottomline="true">
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20116 \begin_layout Standard
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20127 \begin_layout Standard
20128 \begin_inset Formula $\surd$
20137 <row bottomline="true">
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20141 \begin_layout Standard
20149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20152 \begin_layout Standard
20153 \begin_inset Formula $\checkmark$
20162 <row bottomline="true">
20163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20166 \begin_layout Standard
20174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20177 \begin_layout Standard
20178 \begin_inset Formula $\yen$
20187 <row bottomline="true">
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20191 \begin_layout Standard
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20202 \begin_layout Standard
20203 \begin_inset Formula $\pounds$
20212 <row bottomline="true">
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20216 \begin_layout Standard
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Standard
20226 \begin_inset Formula $\$$
20235 <row bottomline="true">
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Standard
20245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20248 \begin_layout Standard
20249 \begin_inset Formula $§$
20263 \begin_inset Tabular
20264 <lyxtabular version="3" rows="10" columns="2">
20266 <column alignment="center" valignment="top" leftline="true" width="0">
20267 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20268 <row topline="true" bottomline="true">
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20272 \begin_layout Standard
20278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20281 \begin_layout Standard
20288 <row topline="true">
20289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20292 \begin_layout Standard
20300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20303 \begin_layout Standard
20304 \begin_inset Formula $\hbar$
20313 <row topline="true">
20314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20317 \begin_layout Standard
20325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20328 \begin_layout Standard
20329 \begin_inset Formula $\hslash$
20338 <row topline="true">
20339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20342 \begin_layout Standard
20350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20353 \begin_layout Standard
20354 \begin_inset Formula $\clubsuit$
20363 <row topline="true">
20364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20367 \begin_layout Standard
20375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20378 \begin_layout Standard
20379 \begin_inset Formula $\spadesuit$
20388 <row topline="true">
20389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20392 \begin_layout Standard
20400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20403 \begin_layout Standard
20404 \begin_inset Formula $\bigstar$
20413 <row topline="true">
20414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20417 \begin_layout Standard
20425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20428 \begin_layout Standard
20429 \begin_inset Formula $\blacklozenge$
20438 <row topline="true">
20439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20442 \begin_layout Standard
20450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20453 \begin_layout Standard
20454 \begin_inset Formula $\blacktriangle$
20463 <row topline="true">
20464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20467 \begin_layout Standard
20475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20478 \begin_layout Standard
20479 \begin_inset Formula $\blacktriangledown$
20488 <row topline="true" bottomline="true">
20489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20492 \begin_layout Standard
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20503 \begin_layout Standard
20504 \begin_inset Formula $\bullet$
20518 \begin_inset Tabular
20519 <lyxtabular version="3" rows="10" columns="2">
20521 <column alignment="center" valignment="top" leftline="true" width="0pt">
20522 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20523 <row topline="true" bottomline="true">
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20527 \begin_layout Standard
20533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Standard
20543 <row topline="true">
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Standard
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Standard
20559 \begin_inset Formula $\diamondsuit$
20568 <row topline="true">
20569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20572 \begin_layout Standard
20580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20583 \begin_layout Standard
20584 \begin_inset Formula $\Diamond$
20593 <row topline="true">
20594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20597 \begin_layout Standard
20605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20608 \begin_layout Standard
20609 \begin_inset Formula $\heartsuit$
20618 <row topline="true" bottomline="true">
20619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20622 \begin_layout Standard
20630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20633 \begin_layout Standard
20634 \begin_inset Formula $\P$
20643 <row bottomline="true">
20644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20647 \begin_layout Standard
20655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20658 \begin_layout Standard
20659 \begin_inset Formula $\copyright$
20668 <row bottomline="true">
20669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20672 \begin_layout Standard
20680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Standard
20684 \begin_inset Formula $\circledR$
20693 <row bottomline="true">
20694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20697 \begin_layout Standard
20705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20708 \begin_layout Standard
20709 \begin_inset Formula $\maltese$
20718 <row bottomline="true">
20719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20722 \begin_layout Standard
20730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Standard
20734 \begin_inset Formula $\diagup$
20743 <row bottomline="true">
20744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20747 \begin_layout Standard
20755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Standard
20759 \begin_inset Formula $\diagdown$
20775 \begin_layout Standard
20776 \begin_inset VSpace medskip
20779 More symbols are listed in
20780 \begin_inset LatexCommand ref
20781 reference "sub:Miscellaneous-Special-Characters"
20788 \begin_layout Standard
20789 Some symbols can be displayed in different sizes, see
20790 \begin_inset LatexCommand ref
20791 reference "sub:Font-Sizes"
20798 \begin_layout Subsection
20800 \begin_inset LatexCommand index
20801 name "Symbols ! Euro-symbol"
20806 \begin_inset LatexCommand index
20807 name "\\textcent@\\officialeuro"
20814 \begin_layout Standard
20815 To use the Euro symbol in formulas, the LaTeX-package
20820 \begin_inset LatexCommand index
20821 name "Packages ! eurosym"
20825 must be installed and loaded with the LaTeX-preamble line
20828 \begin_layout Standard
20833 usepackage[gennarrow]{eurosym}
20836 \begin_layout Standard
20837 The Euro symbol can now be inserted with the command
20844 \begin_inset LatexCommand index
20845 name "Commands ! E ! \\textbackslash euro"
20852 \begin_layout Standard
20853 The Euro symbol can directly be inserted with the € key in mathematical
20854 text, without having
20869 can also be inserted in TeX-mode.
20870 The official currency symbol can then be inserted with the command
20877 \begin_inset LatexCommand index
20878 name "Commands ! O ! \\textbackslash officialeuro"
20882 , that is only available in TeX-mode.
20885 \begin_layout Standard
20889 \begin_layout Standard
20899 \begin_inset Note Note
20902 \begin_layout Standard
20903 The following table will only be displayed when the LaTeX-package
20915 \begin_layout Standard
20916 An overview about the different Euro symbols:
20919 \begin_layout Standard
20921 \begin_inset Tabular
20922 <lyxtabular version="3" rows="4" columns="3">
20924 <column alignment="center" valignment="top" leftline="true" width="0pt">
20925 <column alignment="center" valignment="top" leftline="true" width="0pt">
20926 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20927 <row topline="true" bottomline="true">
20928 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20931 \begin_layout Standard
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20940 \begin_layout Standard
20946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20949 \begin_layout Standard
20956 <row topline="true">
20957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20960 \begin_layout Standard
20966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20969 \begin_layout Standard
20977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20980 \begin_layout Standard
20981 \begin_inset Formula $\euro$
20990 <row topline="true">
20991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20994 \begin_layout Standard
21000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21003 \begin_layout Standard
21009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21012 \begin_layout Standard
21013 \begin_inset Formula $\mbox{€}$
21022 <row topline="true" bottomline="true">
21023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21026 \begin_layout Standard
21032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21035 \begin_layout Standard
21043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21046 \begin_layout Standard
21050 \begin_layout Standard
21072 \begin_layout Standard
21076 \begin_layout Standard
21086 \begin_inset Note Note
21089 \begin_layout Standard
21090 The following will be displayed when the LaTeX-package
21102 \begin_layout Standard
21103 You need to install the LaTeX-package
21107 to see the rest of this subsection in the output.
21110 \begin_layout Standard
21114 \begin_layout Standard
21126 \begin_layout Section
21128 \begin_inset LatexCommand label
21129 name "sec:Relations"
21134 \begin_inset LatexCommand index
21140 \begin_inset LatexCommand index
21141 name "Comparisons|see{Relations}"
21148 \begin_layout Standard
21149 All relations can also be inserted via the toolbar button
21150 \begin_inset Graphics
21151 filename ../images/math/leq.png
21159 \begin_layout Standard
21163 \begin_inset Tabular
21164 <lyxtabular version="3" rows="17" columns="2">
21166 <column alignment="center" valignment="top" leftline="true" width="0pt">
21167 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21168 <row topline="true" bottomline="true">
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21172 \begin_layout Standard
21178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21181 \begin_layout Standard
21188 <row topline="true">
21189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21192 \begin_layout Standard
21198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21201 \begin_layout Standard
21202 \begin_inset Formula $<$
21211 <row topline="true">
21212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21215 \begin_layout Standard
21223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21226 \begin_layout Standard
21227 \begin_inset Formula $\le$
21236 <row topline="true">
21237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21240 \begin_layout Standard
21248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21251 \begin_layout Standard
21252 \begin_inset Formula $\ll$
21261 <row topline="true">
21262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21265 \begin_layout Standard
21273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21276 \begin_layout Standard
21277 \begin_inset Formula $\prec$
21286 <row topline="true">
21287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21290 \begin_layout Standard
21298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21301 \begin_layout Standard
21302 \begin_inset Formula $\preceq$
21311 <row topline="true">
21312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21315 \begin_layout Standard
21323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21326 \begin_layout Standard
21327 \begin_inset Formula $\subset$
21336 <row topline="true">
21337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21340 \begin_layout Standard
21348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21351 \begin_layout Standard
21352 \begin_inset Formula $\subseteq$
21361 <row topline="true">
21362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21365 \begin_layout Standard
21373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21376 \begin_layout Standard
21377 \begin_inset Formula $\sqsubseteq$
21386 <row topline="true">
21387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21390 \begin_layout Standard
21398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21401 \begin_layout Standard
21402 \begin_inset Formula $\in$
21411 <row topline="true">
21412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21415 \begin_layout Standard
21423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21426 \begin_layout Standard
21427 \begin_inset Formula $\vdash$
21436 <row topline="true">
21437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21440 \begin_layout Standard
21448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21451 \begin_layout Standard
21452 \begin_inset Formula $\smile$
21461 <row topline="true">
21462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21465 \begin_layout Standard
21473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21476 \begin_layout Standard
21477 \begin_inset Formula $\lhd$
21486 <row topline="true">
21487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21490 \begin_layout Standard
21498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21501 \begin_layout Standard
21502 \begin_inset Formula $\unlhd$
21511 <row topline="true">
21512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21515 \begin_layout Standard
21523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21526 \begin_layout Standard
21527 \begin_inset Formula $\gtrless$
21536 <row topline="true">
21537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21540 \begin_layout Standard
21548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21551 \begin_layout Standard
21552 \begin_inset Formula $\mid$
21561 <row topline="true" bottomline="true">
21562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21565 \begin_layout Standard
21573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21576 \begin_layout Standard
21577 \begin_inset Formula $\nmid$
21593 \begin_inset Tabular
21594 <lyxtabular version="3" rows="17" columns="2">
21596 <column alignment="center" valignment="top" leftline="true" width="0pt">
21597 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21598 <row topline="true" bottomline="true">
21599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21602 \begin_layout Standard
21608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21611 \begin_layout Standard
21618 <row topline="true">
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21622 \begin_layout Standard
21628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21631 \begin_layout Standard
21632 \begin_inset Formula $=$
21641 <row topline="true">
21642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21645 \begin_layout Standard
21653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21656 \begin_layout Standard
21657 \begin_inset Formula $\not=$
21666 <row topline="true">
21667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21670 \begin_layout Standard
21678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21681 \begin_layout Standard
21682 \begin_inset Formula $\equiv$
21691 <row topline="true">
21692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21695 \begin_layout Standard
21703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21706 \begin_layout Standard
21707 \begin_inset Formula $\sim$
21716 <row topline="true">
21717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21720 \begin_layout Standard
21728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21731 \begin_layout Standard
21732 \begin_inset Formula $\simeq$
21741 <row topline="true">
21742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21745 \begin_layout Standard
21753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21756 \begin_layout Standard
21757 \begin_inset Formula $\approx$
21766 <row topline="true">
21767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21770 \begin_layout Standard
21778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21781 \begin_layout Standard
21782 \begin_inset Formula $\cong$
21791 <row topline="true">
21792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21795 \begin_layout Standard
21803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21806 \begin_layout Standard
21807 \begin_inset Formula $\bowtie$
21816 <row topline="true">
21817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21820 \begin_layout Standard
21828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21831 \begin_layout Standard
21832 \begin_inset Formula $\notin$
21841 <row topline="true">
21842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21845 \begin_layout Standard
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21856 \begin_layout Standard
21857 \begin_inset Formula $\perp$
21866 <row topline="true">
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21870 \begin_layout Standard
21878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21881 \begin_layout Standard
21882 \begin_inset Formula $\propto$
21891 <row topline="true">
21892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21895 \begin_layout Standard
21903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21906 \begin_layout Standard
21907 \begin_inset Formula $\asymp$
21916 <row topline="true">
21917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21920 \begin_layout Standard
21928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21931 \begin_layout Standard
21932 \begin_inset Formula $\doteq$
21941 <row topline="true">
21942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21945 \begin_layout Standard
21953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21956 \begin_layout Standard
21957 \begin_inset Formula $\circeq$
21966 <row topline="true">
21967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21970 \begin_layout Standard
21978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21981 \begin_layout Standard
21982 \begin_inset Formula $\models$
21991 <row topline="true" bottomline="true">
21992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21995 \begin_layout Standard
22003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Standard
22007 \begin_inset Formula $\widehat{=}$
22023 \begin_inset Tabular
22024 <lyxtabular version="3" rows="17" columns="2">
22026 <column alignment="center" valignment="top" leftline="true" width="0pt">
22027 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22028 <row topline="true" bottomline="true">
22029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22032 \begin_layout Standard
22038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Standard
22048 <row topline="true">
22049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22052 \begin_layout Standard
22058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22061 \begin_layout Standard
22062 \begin_inset Formula $>$
22071 <row topline="true">
22072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22075 \begin_layout Standard
22083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22086 \begin_layout Standard
22087 \begin_inset Formula $\ge$
22096 <row topline="true">
22097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22100 \begin_layout Standard
22108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22111 \begin_layout Standard
22112 \begin_inset Formula $\gg$
22121 <row topline="true">
22122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22125 \begin_layout Standard
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22136 \begin_layout Standard
22137 \begin_inset Formula $\succ$
22146 <row topline="true">
22147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22150 \begin_layout Standard
22158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22161 \begin_layout Standard
22162 \begin_inset Formula $\succeq$
22171 <row topline="true">
22172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22175 \begin_layout Standard
22183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22186 \begin_layout Standard
22187 \begin_inset Formula $\supset$
22196 <row topline="true">
22197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22200 \begin_layout Standard
22208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22211 \begin_layout Standard
22212 \begin_inset Formula $\supseteq$
22221 <row topline="true">
22222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22225 \begin_layout Standard
22233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22236 \begin_layout Standard
22237 \begin_inset Formula $\sqsupseteq$
22246 <row topline="true">
22247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22250 \begin_layout Standard
22258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Standard
22262 \begin_inset Formula $\ni$
22271 <row topline="true">
22272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22275 \begin_layout Standard
22283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22286 \begin_layout Standard
22287 \begin_inset Formula $\dashv$
22296 <row topline="true">
22297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22300 \begin_layout Standard
22308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22311 \begin_layout Standard
22312 \begin_inset Formula $\frown$
22321 <row topline="true">
22322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22325 \begin_layout Standard
22333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22336 \begin_layout Standard
22337 \begin_inset Formula $\rhd$
22346 <row topline="true">
22347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22350 \begin_layout Standard
22358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22361 \begin_layout Standard
22362 \begin_inset Formula $\unrhd$
22371 <row topline="true">
22372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22375 \begin_layout Standard
22383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22386 \begin_layout Standard
22387 \begin_inset Formula $\lessgtr$
22396 <row topline="true">
22397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22400 \begin_layout Standard
22408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22411 \begin_layout Standard
22412 \begin_inset Formula $\parallel$
22421 <row topline="true" bottomline="true">
22422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22425 \begin_layout Standard
22433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22436 \begin_layout Standard
22437 \begin_inset Formula $\nparallel$
22455 \begin_layout Standard
22456 \begin_inset VSpace medskip
22471 are bigger than the equal looking operators
22486 \begin_layout Standard
22487 Relations are, in contrary to symbols, always surrounded by space.
22490 \begin_layout Standard
22491 Relations with labels can be created with the command
22498 \begin_inset LatexCommand index
22499 name "Commands ! S ! \\textbackslash stackrel"
22506 \begin_layout Standard
22508 \begin_inset Tabular
22509 <lyxtabular version="3" rows="2" columns="2">
22511 <column alignment="center" valignment="top" leftline="true" width="0">
22512 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22513 <row topline="true" bottomline="true">
22514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22517 \begin_layout Standard
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22526 \begin_layout Standard
22528 \begin_inset Note Note
22531 \begin_layout Standard
22538 is only used as spacer.
22549 <row topline="true" bottomline="true">
22550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22553 \begin_layout Standard
22560 \begin_layout Standard
22577 \begin_layout Standard
22587 \begin_inset Formula $\downarrow$
22596 \begin_layout Standard
22609 \begin_layout Standard
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Standard
22627 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22643 \begin_layout Section
22647 \begin_layout Subsection
22648 Predefined Functions
22649 \begin_inset LatexCommand label
22650 name "sub:Predefined-Functions"
22655 \begin_inset LatexCommand index
22656 name "Functions ! predefined"
22663 \begin_layout Standard
22664 In general, variables are set
22668 in mathematical expressions, but not function names, because
22669 \begin_inset Formula $sin$
22672 could be misunderstood as
22673 \begin_inset Formula $s\cdot i\cdot n$
22677 Therefore there are predefined functions, that are additionally a bit separated
22679 They are inserted as commands starting with a backslash before their name.
22682 \begin_layout Standard
22684 \begin_inset Tabular
22685 <lyxtabular version="3" rows="2" columns="4">
22687 <column alignment="center" valignment="top" leftline="true" width="0pt">
22688 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22689 <column alignment="center" valignment="top" leftline="true" width="0pt">
22690 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22691 <row topline="true" bottomline="true">
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22695 \begin_layout Standard
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Standard
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22713 \begin_layout Standard
22719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Standard
22729 <row topline="true" bottomline="true">
22730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22733 \begin_layout Standard
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Standard
22743 \begin_inset Formula $Asin(x)+B$
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22754 \begin_layout Standard
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22765 \begin_layout Standard
22766 \begin_inset Formula $A\sin(x)+B$
22783 \begin_layout Standard
22795 \begin_layout Standard
22796 The following functions are predefined:
22799 \begin_layout Standard
22800 \begin_inset VSpace -2mm
22806 \begin_layout Standard
22808 \begin_inset Tabular
22809 <lyxtabular version="3" rows="9" columns="4">
22811 <column alignment="center" valignment="top" leftline="true" width="0pt">
22812 <column alignment="center" valignment="top" leftline="true" width="0pt">
22813 <column alignment="center" valignment="top" leftline="true" width="0pt">
22814 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22815 <row topline="true" bottomline="true">
22816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22819 \begin_layout Standard
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22828 \begin_layout Standard
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22837 \begin_layout Standard
22843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22846 \begin_layout Standard
22853 <row topline="true">
22854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22857 \begin_layout Standard
22865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22868 \begin_layout Standard
22876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22879 \begin_layout Standard
22887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22890 \begin_layout Standard
22899 <row topline="true">
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22903 \begin_layout Standard
22911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22914 \begin_layout Standard
22922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22925 \begin_layout Standard
22933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22936 \begin_layout Standard
22945 <row topline="true">
22946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22949 \begin_layout Standard
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22960 \begin_layout Standard
22968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22971 \begin_layout Standard
22979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22982 \begin_layout Standard
22991 <row topline="true">
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Standard
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23006 \begin_layout Standard
23014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23017 \begin_layout Standard
23025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23028 \begin_layout Standard
23037 <row topline="true">
23038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23041 \begin_layout Standard
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23052 \begin_layout Standard
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23063 \begin_layout Standard
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23074 \begin_layout Standard
23083 <row topline="true">
23084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23087 \begin_layout Standard
23095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23098 \begin_layout Standard
23106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23109 \begin_layout Standard
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Standard
23129 <row topline="true">
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Standard
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23144 \begin_layout Standard
23152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23155 \begin_layout Standard
23163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23166 \begin_layout Standard
23175 <row topline="true" bottomline="true">
23176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23179 \begin_layout Standard
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Standard
23198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23201 \begin_layout Standard
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23212 \begin_layout Standard
23228 \begin_layout Standard
23229 They can also be inserted with the math toolbar button
23230 \begin_inset Graphics
23231 filename ../images/math/functions.png
23239 \begin_layout Subsection
23240 Self-defined Functions
23241 \begin_inset LatexCommand index
23242 name "Functions ! self-defined"
23249 \begin_layout Standard
23250 To use a function that is not predefined, like for example the sign function
23251 sgn(x), there are two possibilities:
23254 \begin_layout Itemize
23255 Define the function by inserting the following line to the LaTeX-preamble
23259 \begin_layout Standard
23264 DeclareMathOperator
23267 \begin_inset LatexCommand ref
23268 reference "sub:Self-defined-Operators"
23280 \begin_inset VSpace -3mm
23289 DeclareMathOperator{
23294 \begin_inset LatexCommand index
23295 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23302 \begin_inset VSpace -2mm
23307 Now the new defined function can be called with the command
23316 \begin_layout Itemize
23317 Write the the formula as usual, mark the formula name, in our example the
23322 , and change it to mathematical text.
23323 At last a space is inserted between prefactor and function.
23326 \begin_layout Standard
23327 The result is the same with both methods as with a predefined function
23331 \begin_layout Standard
23332 In LyX self-defined functions are displayed red, predefined ones black.
23340 \begin_layout Standard
23342 \begin_inset Tabular
23343 <lyxtabular version="3" rows="3" columns="2">
23345 <column alignment="center" valignment="top" leftline="true" width="0pt">
23346 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23347 <row topline="true" bottomline="true">
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23351 \begin_layout Standard
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Standard
23367 <row topline="true" bottomline="true">
23368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23371 \begin_layout Standard
23379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23382 \begin_layout Standard
23383 \begin_inset Formula $A\sgn(x)+B$
23392 <row topline="true" bottomline="true">
23393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23396 \begin_layout Standard
23400 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23411 \begin_layout Standard
23412 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23428 \begin_layout Standard
23429 The first method is more suitable when the self-defined function should
23430 be used several times.
23433 \begin_layout Subsection
23435 \begin_inset LatexCommand index
23443 \begin_layout Standard
23444 For limits there are defined besides
23451 \begin_inset LatexCommand index
23452 name "Commands ! L ! \\textbackslash lim"
23468 furthermore the following functions:
23471 \begin_layout Standard
23473 \begin_inset Tabular
23474 <lyxtabular version="3" rows="5" columns="2">
23476 <column alignment="center" valignment="top" leftline="true" width="0">
23477 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23478 <row topline="true" bottomline="true">
23479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23482 \begin_layout Standard
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Standard
23493 \begin_inset Note Note
23496 \begin_layout Standard
23503 is only used as spacer.
23514 <row topline="true">
23515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23518 \begin_layout Standard
23526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23529 \begin_layout Standard
23530 \begin_inset Formula $\varliminf$
23540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23543 \begin_layout Standard
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23554 \begin_layout Standard
23555 \begin_inset Formula $\varlimsup$
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23568 \begin_layout Standard
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23579 \begin_layout Standard
23580 \begin_inset Formula $\varprojlim$
23589 <row bottomline="true">
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23593 \begin_layout Standard
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Standard
23605 \begin_inset Formula $\varinjlim$
23609 \begin_inset Formula $\raisebox{-2.5mm}{}$
23625 \begin_layout Standard
23626 \begin_inset VSpace medskip
23629 The limit is created by inserting a subscript.
23630 It is set right beside the function in an inline formula:
23633 \begin_layout Standard
23635 \begin_inset Tabular
23636 <lyxtabular version="3" rows="2" columns="2">
23638 <column alignment="center" valignment="top" width="0pt">
23639 <column alignment="center" valignment="top" width="0pt">
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23644 \begin_layout Standard
23650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23653 \begin_layout Standard
23657 \begin_layout Standard
23667 \begin_inset Note Note
23670 \begin_layout Standard
23683 are used here as spacer.
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23698 \begin_layout Standard
23707 \begin_layout Standard
23720 \begin_layout Standard
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23737 \begin_layout Standard
23738 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23754 \begin_layout Standard
23755 In a displayed formula the limit is set below the formula, as usual:
23756 \begin_inset Formula \[
23764 \begin_layout Subsection
23766 \begin_inset LatexCommand index
23767 name "Functions ! modulo-"
23774 \begin_layout Standard
23775 The modulo-function is special, because it exists in four variants.
23778 \begin_layout Standard
23779 The variants in a displayed formula:
23780 \begin_inset Formula \begin{align*}
23781 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23782 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23783 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23784 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23785 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23792 \begin_layout Standard
23793 In an inline formula less space is set before the function names for all
23797 \begin_layout Section
23799 \begin_inset LatexCommand index
23800 name "Special characters"
23807 \begin_layout Subsection
23808 Special Characters in Mathematical Text
23811 \begin_layout Standard
23812 The following commands can only be used in mathematical text or in TeX-mode:
23815 \begin_layout Standard
23819 \begin_inset Tabular
23820 <lyxtabular version="3" rows="8" columns="2">
23822 <column alignment="block" valignment="top" leftline="true" width="0">
23823 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23824 <row topline="true" bottomline="true">
23825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23828 \begin_layout Standard
23834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Standard
23844 <row topline="true">
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23848 \begin_layout Standard
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23859 \begin_layout Standard
23860 \begin_inset Formula $\textrm{\oe}$
23869 <row topline="true">
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23873 \begin_layout Standard
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23884 \begin_layout Standard
23885 \begin_inset Formula $\textrm{\OE}$
23894 <row topline="true">
23895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23898 \begin_layout Standard
23906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23909 \begin_layout Standard
23910 \begin_inset Formula $\textrm{\ae}$
23919 <row topline="true">
23920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23923 \begin_layout Standard
23931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23934 \begin_layout Standard
23935 \begin_inset Formula $\textrm{\AE}$
23944 <row topline="true">
23945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23948 \begin_layout Standard
23956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23959 \begin_layout Standard
23960 \begin_inset Formula $\textrm{\aa}$
23969 <row topline="true" bottomline="true">
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23973 \begin_layout Standard
23977 \begin_inset LatexCommand index
23978 name "\\@\\textrm{\\AA}"
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Standard
23991 \begin_inset Formula $\textrm{\AA}$
24000 <row bottomline="true">
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24004 \begin_layout Standard
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Standard
24016 \begin_inset Formula $\textrm{\i}$
24032 \begin_inset Tabular
24033 <lyxtabular version="3" rows="8" columns="2">
24035 <column alignment="block" valignment="top" leftline="true" width="0">
24036 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24037 <row topline="true" bottomline="true">
24038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24041 \begin_layout Standard
24043 \begin_inset Note Note
24046 \begin_layout Standard
24053 is used for separation, because otherwise the output will be ¡ and ¿ respective
24064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24067 \begin_layout Standard
24074 <row topline="true">
24075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24078 \begin_layout Standard
24086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24089 \begin_layout Standard
24090 \begin_inset Formula $\textrm{\o}$
24099 <row topline="true">
24100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24103 \begin_layout Standard
24111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24114 \begin_layout Standard
24115 \begin_inset Formula $\textrm{\O}$
24124 <row topline="true">
24125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24128 \begin_layout Standard
24136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24139 \begin_layout Standard
24140 \begin_inset Formula $\textrm{\l}$
24149 <row topline="true">
24150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24153 \begin_layout Standard
24161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24164 \begin_layout Standard
24165 \begin_inset Formula $\textrm{\L}$
24174 <row topline="true" bottomline="true">
24175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24178 \begin_layout Standard
24183 \begin_layout Standard
24196 \begin_layout Standard
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24213 \begin_layout Standard
24214 \begin_inset Formula $\textrm{!`}$
24223 <row bottomline="true">
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24227 \begin_layout Standard
24232 \begin_layout Standard
24245 \begin_layout Standard
24259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24262 \begin_layout Standard
24263 \begin_inset Formula $\textrm{?`}$
24272 <row bottomline="true">
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24276 \begin_layout Standard
24284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24287 \begin_layout Standard
24288 \begin_inset Formula $\textrm{\j}$
24306 \begin_layout Standard
24308 \begin_inset Formula $\textrm{\textrm{Å}}$
24312 \begin_inset Formula $\textrm{\textrm{Ø}}$
24315 can also be inserted via the math toolbar button
24316 \begin_inset Graphics
24317 filename ../images/math/digamma.png
24325 \begin_layout Standard
24326 An exception are the commands
24332 \begin_layout Standard
24349 \begin_layout Standard
24360 , because they can be inserted in LyX directly to text.
24363 \begin_layout Subsection
24365 \begin_inset LatexCommand label
24366 name "sub:Accents-in-Text"
24371 \begin_inset LatexCommand index
24372 name "Accents ! in text"
24379 \begin_layout Standard
24380 With the following commands all letters can be accented.
24381 The commands must be inserted in TeX-mode.
24384 \begin_layout Standard
24388 \begin_inset Tabular
24389 <lyxtabular version="3" rows="8" columns="2">
24391 <column alignment="block" valignment="top" leftline="true" width="0">
24392 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24393 <row topline="true" bottomline="true">
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24397 \begin_layout Standard
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Standard
24413 <row topline="true">
24414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24417 \begin_layout Standard
24421 \begin_inset Quotes grd
24429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24432 \begin_layout Standard
24436 \begin_layout Standard
24451 <row topline="true">
24452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24455 \begin_layout Standard
24463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24466 \begin_layout Standard
24470 \begin_layout Standard
24485 <row topline="true">
24486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24489 \begin_layout Standard
24496 \begin_layout Standard
24510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24513 \begin_layout Standard
24517 \begin_layout Standard
24532 <row topline="true">
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24536 \begin_layout Standard
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24547 \begin_layout Standard
24551 \begin_layout Standard
24566 <row topline="true">
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Standard
24577 \begin_layout Standard
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Standard
24598 \begin_layout Standard
24613 <row topline="true" bottomline="true">
24614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24617 \begin_layout Standard
24624 \begin_layout Standard
24638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24641 \begin_layout Standard
24645 \begin_layout Standard
24660 <row bottomline="true">
24661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24664 \begin_layout Standard
24671 \begin_layout Standard
24685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24688 \begin_layout Standard
24692 \begin_layout Standard
24714 \begin_inset Tabular
24715 <lyxtabular version="3" rows="8" columns="2">
24717 <column alignment="block" valignment="top" leftline="true" width="0">
24718 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24719 <row topline="true" bottomline="true">
24720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24723 \begin_layout Standard
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24732 \begin_layout Standard
24739 <row topline="true">
24740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24743 \begin_layout Standard
24750 \begin_layout Standard
24764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Standard
24771 \begin_layout Standard
24786 <row topline="true">
24787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24790 \begin_layout Standard
24798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24801 \begin_layout Standard
24805 \begin_layout Standard
24820 <row topline="true">
24821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24824 \begin_layout Standard
24828 \begin_inset LatexCommand index
24838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24841 \begin_layout Standard
24845 \begin_layout Standard
24860 <row topline="true">
24861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24864 \begin_layout Standard
24872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24875 \begin_layout Standard
24879 \begin_layout Standard
24894 <row topline="true" bottomline="true">
24895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24898 \begin_layout Standard
24905 \begin_layout Standard
24919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24922 \begin_layout Standard
24926 \begin_layout Standard
24941 <row bottomline="true">
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24945 \begin_layout Standard
24952 \begin_layout Standard
24966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24969 \begin_layout Standard
24973 \begin_layout Standard
24988 <row bottomline="true">
24989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24992 \begin_layout Standard
24999 \begin_layout Standard
25013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25016 \begin_layout Standard
25020 \begin_layout Standard
25044 \begin_layout Standard
25045 \begin_inset VSpace medskip
25054 also two different characters can be accented.
25063 \begin_layout Standard
25078 \begin_layout Standard
25090 \begin_layout Standard
25103 can in combination with vowels directly be inserted with the keyboard without
25105 The same applies for the tilde
25109 \begin_layout Standard
25110 This only applies for keyboards where the tilde is defined as accent.
25119 in combination with
25134 \begin_layout Standard
25177 , and accents inserted directly with the keyboard are also available in
25179 For the other accents there are special math commands to be used in formulas,
25181 \begin_inset LatexCommand ref
25182 reference "sub:Accents-for-one"
25189 \begin_layout Standard
25190 \begin_inset VSpace bigskip
25193 Furthermore, with the command
25200 \begin_inset LatexCommand index
25201 name "Commands ! T ! \\textbackslash textcircled"
25205 all numbers and letters can be set into a circle, quasi accented with a
25206 circle, similar to the the copyright symbol.
25209 \begin_layout Standard
25211 \begin_inset Tabular
25212 <lyxtabular version="3" rows="3" columns="2">
25214 <column alignment="center" valignment="top" leftline="true" width="0">
25215 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25216 <row topline="true" bottomline="true">
25217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25220 \begin_layout Standard
25226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25229 \begin_layout Standard
25231 \begin_inset Note Note
25234 \begin_layout Standard
25241 is only used as spacer.
25252 <row topline="true">
25253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25256 \begin_layout Standard
25264 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25267 \begin_layout Standard
25271 \begin_layout Standard
25286 <row topline="true" bottomline="true">
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25290 \begin_layout Standard
25301 raisebox{-1.5pt}{W}}
25306 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25309 \begin_layout Standard
25310 \begin_inset Formula $\raisebox{4.5mm}{}$
25317 \begin_layout Standard
25335 \begin_inset Formula $\raisebox{-2mm}{}$
25351 \begin_layout Standard
25352 One has to take care that the character fits in the circle.
25363 \begin_layout Standard
25365 \begin_inset LatexCommand ref
25366 reference "sub:Font-Sizes"
25375 specifies thereby the size of the circle.
25386 \begin_layout Standard
25388 \begin_inset LatexCommand ref
25389 reference "sub:Boxes-without-Frame"
25398 the character can be centered.
25401 \begin_layout Subsection
25403 \begin_inset LatexCommand index
25404 name "Minuscule numbers"
25411 \begin_layout Standard
25412 Minuscule numbers are created with the command
25419 \begin_inset LatexCommand index
25420 name "Commands ! O ! \\textbackslash oldstylenums"
25425 The command can be used in formulas and in TeX-mode.
25426 The command scheme is:
25429 \begin_layout Standard
25434 oldstylenums{number}
25437 \begin_layout Standard
25442 oldstylenums{0123456789
25445 \begin_inset Formula $\oldstylenums{0123456789}$
25451 \begin_layout Subsection
25452 Miscellaneous Special Characters
25453 \begin_inset LatexCommand label
25454 name "sub:Miscellaneous-Special-Characters"
25459 \begin_inset LatexCommand index
25460 name "Special characters ! miscellaneous"
25467 \begin_layout Standard
25468 The following characters can only be inserted to formulas by using commands:
25471 \begin_layout Standard
25473 \begin_inset Tabular
25474 <lyxtabular version="3" rows="4" columns="2">
25476 <column alignment="center" valignment="top" leftline="true" width="0">
25477 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25478 <row topline="true" bottomline="true">
25479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25482 \begin_layout Standard
25488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25491 \begin_layout Standard
25498 <row topline="true">
25499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25502 \begin_layout Standard
25509 \begin_layout Standard
25523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Standard
25527 \begin_inset Formula $\mathcircumflex$
25536 <row topline="true">
25537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25540 \begin_layout Standard
25548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25551 \begin_layout Standard
25552 \begin_inset Formula $\_$
25561 <row topline="true" bottomline="true">
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25565 \begin_layout Standard
25570 \begin_layout Standard
25582 \begin_inset LatexCommand index
25592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25595 \begin_layout Standard
25596 \begin_inset Formula $^{\circ}$
25612 \begin_layout Standard
25613 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25614 contains the following line
25618 \begin_layout Standard
25619 More about this is described in
25620 \begin_inset LatexCommand ref
25621 reference "sub:Text-Characters-in"
25633 \begin_layout Standard
25638 DeclareInputtext{176}{
25648 f\SpecialChar \textcompwordmark{}
25652 \begin_layout Standard
25653 \begin_inset VSpace bigskip
25657 \begin_inset LatexCommand index
25662 is designed as accent, thus is looks alone a bit misplaced: ~
25665 addresses (URLs) sometimes a single tilde is needed.
25666 In this case the relation sign
25674 \begin_layout Standard
25676 \begin_inset LatexCommand ref
25677 reference "sec:Relations"
25688 is used in a formula.
25689 As a formula cannot be created in an URL-box (menu
25691 Insert\SpecialChar \menuseparator
25694 ), the URL is inserted as normal text with the font style '
25699 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25709 \begin_layout Standard
25716 can only be used together with the LaTeX-package
25721 \begin_inset LatexCommand index
25722 name "Packages ! hyperref"
25733 is written in the section
25739 Embedded\InsetSpace ~
25748 \begin_inset LatexCommand index
25749 name "Commands ! H ! \\textbackslash href"
25756 \begin_layout Standard
25757 As example an URL with a tilde:
25760 \begin_layout Standard
25763 http://www.lyx.org/
25764 \begin_inset Formula $\sim$
25770 \begin_layout Standard
25781 \begin_layout Standard
25785 href{http://www.lyx.org/~mustermann}{
25790 http://www.lyx.org/
25791 \begin_inset Formula $\sim$
25798 \begin_layout Standard
25808 \begin_layout Section
25810 \begin_inset LatexCommand label
25811 name "sec:Formula-Styles"
25816 \begin_inset LatexCommand index
25817 name "Formula ! styles"
25824 \begin_layout Itemize
25825 There are two different alignment styles:
25829 \begin_layout Description
25830 Centered is the predefined standard
25833 \begin_layout Description
25834 Indented for this the option
25838 must be inserted in the menu
25840 Document\SpecialChar \menuseparator
25845 Document\InsetSpace ~
25849 \begin_layout Standard
25854 is used, the indentation can be adjusted with the length
25861 \begin_inset LatexCommand index
25862 name "Commands ! M ! \\textbackslash mathindent"
25867 Should the distance be 15\InsetSpace \thinspace{}
25868 mm, the following command line is inserted in
25872 \begin_layout Standard
25882 \begin_layout Standard
25883 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25888 \begin_layout Itemize
25889 And two different numbering styles:
25893 \begin_layout Description
25894 Right is the predefined standard
25897 \begin_layout Description
25898 Left for this the option
25902 must be inserted in the menu
25904 Document\SpecialChar \menuseparator
25909 Document\InsetSpace ~
25914 \begin_layout Standard
25923 can also be used together.
25924 In this case both options are inserted, separated by a comma.
25927 \begin_layout Standard
25928 The chosen styles are used for all displayed formulas of the document.
25929 When both, centered and indented formulas should be created in a document,
25935 The indented formulas are then set in a flalign environment, see
25936 \begin_inset LatexCommand ref
25937 reference "sub:Flalign-Environment"
25944 \begin_layout Section
25946 \begin_inset LatexCommand label
25947 name "sec:Multiline-Formulas"
25952 \begin_inset LatexCommand index
25953 name "Formula ! multiline"
25960 \begin_layout Subsection
25964 \begin_layout Standard
25965 In LyX multiline formulas are created by pressing
25976 that is described in
25977 \begin_inset LatexCommand ref
25978 reference "sub:Standard-align-Environment"
25985 \begin_layout Standard
25986 There are other multiline formula environments that can be created via the
25989 Insert\SpecialChar \menuseparator
25993 These environments are described in the following sections.
25996 \begin_layout Standard
25997 In all multiline formula environments a new line is created by pressing
26003 To add or delete lines, the math toolbar buttons
26004 \begin_inset Graphics
26005 filename ../images/tabular-feature_append-row.png
26011 \begin_inset Graphics
26012 filename ../images/tabular-feature_delete-row.png
26017 , respectively, or the menu
26019 Edit\SpecialChar \menuseparator
26025 \begin_layout Subsubsection
26027 \begin_inset LatexCommand label
26028 name "sub:Line-Separation"
26033 \begin_inset LatexCommand index
26034 name "Formula ! multiline ! Line separation"
26041 \begin_layout Standard
26042 There is sometimes not enough space in multiline formulas between the lines:
26043 \begin_inset Formula \begin{eqnarray*}
26044 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}\\
26045 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*}
26052 \begin_layout Standard
26053 In LaTeX additional line space is specified as optional argument of the
26055 This is not yet possible in LyX
26059 \begin_layout Standard
26064 \begin_layout Standard
26068 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26077 \begin_layout Standard
26089 , therefore the whole formula must be inserted in TeX-mode.
26090 To add in our example space, the command
26098 is inserted at the end of the first line.
26103 \begin_layout Standard
26110 \begin_layout Standard
26112 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26115 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26122 \begin_layout Standard
26126 left(B^{2}+x_{0}^{2}
26134 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26139 \begin_layout Standard
26151 \begin_layout Standard
26152 \begin_inset VSpace bigskip
26155 To set the the line separation for all lines in a formula, the length
26162 \begin_inset LatexCommand index
26163 name "Commands ! J ! \\textbackslash jot"
26169 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26179 is the value 3\InsetSpace \thinspace{}
26181 To create 3\InsetSpace \thinspace{}
26182 mm additional line separation as in the previous example, the
26186 \begin_layout Standard
26196 \begin_layout Standard
26197 is inserted in TeX-mode before the formula.
26198 This requires that the LaTeX-package
26206 \begin_layout Standard
26211 is part of every LaTeX standard installation.
26217 \begin_inset LatexCommand index
26218 name "Packages ! calc"
26222 was loaded in LaTeX-preamble with the line
26225 \begin_layout Standard
26233 \begin_layout Standard
26238 \begin_layout Standard
26250 \begin_inset Formula \begin{eqnarray*}
26251 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}\\
26252 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*}
26259 \begin_layout Standard
26263 \begin_layout Standard
26274 To get back to the predefined distance,
26280 is set to the value 3\InsetSpace \thinspace{}
26284 \begin_layout Subsubsection
26286 \begin_inset LatexCommand label
26287 name "sub:Column-Separation"
26292 \begin_inset LatexCommand index
26293 name "Formula ! multiline ! Column separation"
26300 \begin_layout Standard
26301 Multiline formulas form a matrix.
26302 A formula in the eqnarray environment is for example a matrix with three
26304 By changing the column separation in this environment, the space beside
26305 the relation sign can be changed.
26308 \begin_layout Standard
26309 The column separation is specified with the length
26316 \begin_inset LatexCommand index
26317 name "Commands ! A ! \\textbackslash arraycolsep"
26323 column separation = 2\InsetSpace \thinspace{}
26335 \begin_layout Standard
26345 \begin_layout Standard
26346 inserted in TeX-mode, sets for all following formulas a column separation
26347 of 2\InsetSpace \thinspace{}
26349 To get back to the predefined distance,
26355 is set to 5\InsetSpace \thinspace{}
26359 \begin_layout Standard
26360 A formula with 2\InsetSpace \thinspace{}
26361 cm column separation:
26365 \begin_layout Standard
26377 \begin_inset Formula \begin{eqnarray*}
26379 C & \ne & A\end{eqnarray*}
26383 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26388 \begin_layout Standard
26400 \begin_inset Formula \begin{eqnarray*}
26402 C & \ne & A\end{eqnarray*}
26409 \begin_layout Subsubsection
26411 \begin_inset LatexCommand index
26412 name "Formula ! long"
26419 \begin_layout Standard
26420 Long formulas can be typeset using these methods:
26423 \begin_layout Itemize
26424 When one side of the equation is much shorther than the line width, this
26425 one is chosen for the left side and the right side is typeset over two
26430 \begin_layout Standard
26440 \begin_inset Formula \begin{eqnarray}
26441 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 \\
26442 & & -\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}
26450 \begin_layout Standard
26461 The minus sign at the beginning of the second line does normally not appear
26462 as operator because it is the first character of the line.
26463 Thus it would not be surrounded by space and could not be distinguished
26464 from the fraction bar.
26465 To avoid this, space was inserted behind the minus sign with the command
26476 \begin_layout Standard
26484 \begin_inset LatexCommand ref
26485 reference "sub:Variable-Space"
26495 \begin_inset LatexCommand index
26496 name "Commands ! H ! \\textbackslash hspace"
26503 \begin_layout Itemize
26504 When both sides of the equation are too long, the command
26511 \begin_inset LatexCommand index
26512 name "Commands ! L ! \\textbackslash lefteqn"
26517 It is inserted to the first column of the first line and effects that all
26518 further insertions overwrite the following columns:
26522 \begin_layout Standard
26532 \begin_inset Formula \begin{eqnarray}
26533 \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 \\
26534 & & -\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 \\
26535 & & =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}
26543 \begin_layout Standard
26554 After the insertion of
26560 , the cursor is in a purple box that is a bit shifted to the left from the
26562 In this the formula is inserted.
26566 \begin_layout Standard
26577 The content of the further lines is inserted to the second or another formula
26579 The greater the column number where it was inserted, the larger the indentation.
26583 \begin_layout Standard
26595 \begin_inset Note Greyedout
26598 \begin_layout Standard
26599 Note the following when using
26608 \begin_layout Itemize
26609 The formula doesn't use the full page width.
26610 When e.\InsetSpace \thinspace{}
26613 \begin_inset Formula $-B^{2}$
26616 is added to the first line in the above example, it would have been outside
26618 To better use the width, negative space can be inserted at the beginning
26622 \begin_layout Itemize
26623 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26628 \begin_layout Standard
26632 \begin_layout Standard
26636 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26645 \begin_layout Standard
26657 One can only set the cursor at the beginning of the line and move it with
26666 \begin_layout Itemize
26667 Other methods to set long formulas are offered by the environments described
26669 \begin_inset LatexCommand ref
26670 reference "sub:Multline-Environment"
26675 \begin_inset LatexCommand ref
26676 reference "sub:Multiline-Formula-Parts"
26683 \begin_layout Subsubsection
26685 \begin_inset LatexCommand label
26686 name "sub:Multiline-Brackets"
26691 \begin_inset LatexCommand index
26692 name "Brackets ! for multiline expressions"
26699 \begin_layout Standard
26700 For brackets spanning multiple lines the following problem occurs:
26701 \begin_inset Formula \begin{eqnarray*}
26702 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26703 & & \left.\cdots+B-D\right]\end{eqnarray*}
26710 \begin_layout Standard
26711 The closing bracket is smaller than the opening bracket because brackets
26712 with variable size may not span multiple lines.
26715 \begin_layout Standard
26716 To set the bracket size for the second line correctly, the first line is
26724 \begin_inset LatexCommand index
26725 name "Commands ! R ! \\textbackslash right"
26729 and the second line with
26737 \begin_layout Standard
26751 \begin_inset LatexCommand ref
26752 reference "sub:Automatic-Bracket-Size"
26764 \begin_inset LatexCommand index
26765 name "Commands ! L ! \\textbackslash left"
26787 \begin_layout Standard
26806 \begin_layout Standard
26825 \begin_layout Standard
26837 \begin_inset Formula $\downarrow$
26843 \begin_inset LatexCommand index
26844 name "Commands ! V ! \\textbackslash vphantom"
26848 is inserted, because the multiplication operator with its limits is the
26849 largest symbol in the first line and this should be the size for the bracket
26850 in the second line.
26853 \begin_layout Standard
26854 The result is this:
26855 \begin_inset Formula \begin{eqnarray*}
26856 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26857 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26864 \begin_layout Subsection
26868 \begin_layout Standard
26869 Align environments can be used for every kind of multiline formulas.
26870 They are specially useful to set several formulas side by side.
26873 \begin_layout Standard
26874 Align environments consist of columns.
26875 The odd columns are right aligned, the even ones left aligned.
26876 Every line in an Align environment can be numbered.
26879 \begin_layout Standard
26880 Align environments are created via the menu
26882 Insert\SpecialChar \menuseparator
26888 Edit\SpecialChar \menuseparator
26889 Math\SpecialChar \menuseparator
26890 Change Formula Type
26892 already existing existing formulas can be converted to Align environments.
26895 \begin_layout Standard
26896 To add or delete columns, the math toolbar buttons
26897 \begin_inset Graphics
26898 filename ../images/tabular-feature_append-column.png
26904 \begin_inset Graphics
26905 filename ../images/tabular-feature_delete-column.png
26910 , respectively, or the menu
26912 Edit\SpecialChar \menuseparator
26918 \begin_layout Subsubsection
26919 Standard align Environment
26920 \begin_inset LatexCommand label
26921 name "sub:Standard-align-Environment"
26926 \begin_inset LatexCommand index
26927 name "Formula ! multiline ! align environment"
26934 \begin_layout Standard
26935 This Align environment is created by presssing
26939 in a formula or by the menu
26941 Insert\SpecialChar \menuseparator
26942 Math\SpecialChar \menuseparator
26943 AMS align Environment
26948 \begin_layout Standard
26949 An example for two formulas set side by side, that are created with a four
26950 column align environment:
26951 \begin_inset Formula \begin{align*}
26952 A & =\sin(B) & C & =D\\
26953 C & \ne A & B & \ne D\end{align*}
26957 As it can be seen, the formulas in this environment are placed so as if
26966 \begin_layout Standard
26974 \begin_inset LatexCommand ref
26975 reference "sub:Variable-Space"
26986 before the first and after every even column.
26987 When the formula style
26993 \begin_layout Standard
26995 \begin_inset LatexCommand ref
26996 reference "sec:Formula-Styles"
27007 is used, the formula is set without the
27013 before the first column.
27016 \begin_layout Subsubsection
27017 Alignat Environment
27018 \begin_inset LatexCommand index
27019 name "Formula ! multiline ! alignat environment"
27026 \begin_layout Standard
27027 The alignat environment has no predefined column separation.
27028 It can be inserted manually with the spaces that are described
27029 \begin_inset LatexCommand ref
27030 reference "sub:Space"
27037 \begin_layout Standard
27038 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27039 cm space was inserted
27040 at the beginning of the second formula:
27041 \begin_inset Formula \begin{alignat*}{2}
27042 A & =\sin(B) & \hspace{1cm}C & =D\\
27043 C & \ne A & B & \ne D\end{alignat*}
27047 Because the column separation can be set separately for every column, this
27048 environment is especially suitable to set three and more formulas side
27052 \begin_layout Subsubsection
27053 Flalign Environment
27054 \begin_inset LatexCommand label
27055 name "sub:Flalign-Environment"
27060 \begin_inset LatexCommand index
27061 name "Formula ! multiline ! flalign environment"
27068 \begin_layout Standard
27069 In this environment the first two columns are always set as much as possible
27070 to the left and the last two ones to the right.
27072 \begin_inset Formula \begin{flalign*}
27073 A & =1 & B & =2 & C & =3\\
27074 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27081 \begin_layout Standard
27082 By creating a flalign environment with an odd number of columns where an
27083 empty TeX-brace is inserted to the last column, several formulas in a document
27084 can be set to the left, although the formula style
27089 As example the indented formula
27090 \begin_inset LatexCommand eqref
27091 reference "eq:VolInt"
27096 \begin_inset Formula \begin{flalign}
27097 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27101 The first two columns contain the formula.
27102 To indent it as with the formula style
27106 , 30\InsetSpace \thinspace{}
27107 pt space was inserted at the beginning of the first column.
27110 \begin_layout Subsection
27111 Eqnarray Environment
27112 \begin_inset LatexCommand index
27113 name "Formula ! multiline ! eqnarray environment"
27120 \begin_layout Standard
27121 When this environment has been created, three blue boxes appear.
27122 The content of the first box is right aligned, the content of the last
27124 The content of the middle box appears centered and a bit smaller, because
27125 it is designed to insert there only relation characters.
27126 \begin_inset Formula \begin{eqnarray*}
27127 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27129 A & = & A\end{eqnarray*}
27136 \begin_layout Subsection
27138 \begin_inset LatexCommand index
27139 name "Formula ! multiline ! gather environment"
27146 \begin_layout Standard
27147 This environment consists of only one centered column.
27148 Every line can be numbered.
27149 \begin_inset Formula \begin{gather}
27151 X=\textrm{-}1\end{gather}
27158 \begin_layout Subsection
27159 Multline Environment
27160 \begin_inset LatexCommand label
27161 name "sub:Multline-Environment"
27166 \begin_inset LatexCommand index
27167 name "Formula ! multiline ! multline environment"
27174 \begin_layout Standard
27175 The multline environment consists, like the gather environment, of only
27177 But the first line is left aligned, the last one right aligned.
27178 All other lines are centered.
27179 Therefore this environment is suitable for long formulas.
27181 \begin_inset LatexCommand eqref
27182 reference "eq:lefteqn"
27186 in the multline environment:
27187 \begin_inset Formula \begin{multline}
27188 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}\\
27189 -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}\\
27190 =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}
27197 \begin_layout Standard
27198 In the output only the the last (first) line of a multline environment appears
27199 numbered when the document numbering is right (left).
27203 \begin_layout Standard
27204 numbering styles see
27205 \begin_inset LatexCommand ref
27206 reference "sec:Formula-Styles"
27215 This is also the case when there is a formula number displayed after every
27220 \begin_layout Standard
27225 \begin_layout Standard
27229 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27238 \begin_layout Standard
27253 \begin_layout Standard
27259 \begin_inset LatexCommand index
27260 name "Commands ! S ! \\textbackslash shoveright"
27271 \begin_inset LatexCommand index
27272 name "Commands ! S ! \\textbackslash shoveleft"
27278 a centered line can be right or left aligned, respectively.
27279 The commands are used as follows:
27282 \begin_layout Standard
27287 shoveright{line content}
27293 shoveleft{line content}
27296 \begin_layout Standard
27297 \begin_inset VSpace medskip
27305 \begin_inset LatexCommand index
27306 name "Commands ! M ! \\textbackslash multlinegap"
27312 specifies the distance of the first line from the left page margin.
27313 Predefined is the length 0\InsetSpace \thinspace{}
27317 \begin_layout Standard
27318 As example the above formula where the command
27321 \begin_layout Standard
27331 \begin_layout Standard
27332 was inserted in TeX-mode before:
27336 \begin_layout Standard
27348 \begin_inset Formula \begin{multline}
27349 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}\\
27350 \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}}\\
27351 =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}
27359 \begin_layout Standard
27370 The second line was left aligned using
27379 \begin_layout Subsection
27380 Multiline Formula Parts
27381 \begin_inset LatexCommand label
27382 name "sub:Multiline-Formula-Parts"
27387 \begin_inset LatexCommand index
27388 name "Formula ! multiline ! formula parts"
27395 \begin_layout Standard
27396 To display only parts of a formula with multiple lines, one of the following
27397 environments are used:
27414 They can be inserted via the menu
27416 Insert\SpecialChar \menuseparator
27419 or by using the commands described in this section.
27422 \begin_layout Standard
27423 The first three have the same properties as the corresponding multiline
27424 formula environments, but it is possible to set further formula parts beside
27427 \begin_inset Formula \[
27428 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27429 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27430 \right\} \textrm{Uncertainty relations}\]
27437 \begin_layout Standard
27438 To get this formula, a displayed formula is created where the command
27443 \begin_inset LatexCommand index
27444 name "Commands ! A ! \\textbackslash aligned"
27451 A purple box appears around the blue formula box where now columns and
27452 lines can be added.
27453 Outside the multiline environment other formula parts can be set, like
27457 \begin_layout Standard
27458 The aligned environment is also suitable for long formulas whose lines are
27459 horizontally aligned.
27460 Using aligned in a displayed formula has the advantage that the formula
27461 number is vertically centered behind the lines.
27463 \begin_inset LatexCommand eqref
27464 reference "eq:kurzlang"
27468 in the aligned environment:
27469 \begin_inset Formula \begin{equation}
27470 \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}|}\\
27471 & -\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}
27479 \begin_layout Standard
27480 To use the environments
27499 \begin_inset LatexCommand index
27500 name "Commands ! A ! \\textbackslash alignedat"
27511 \begin_inset LatexCommand index
27512 name "Commands ! G ! \\textbackslash gathered"
27523 \begin_inset LatexCommand index
27524 name "Commands ! S ! \\textbackslash split"
27528 are inserted, respectively.
27529 The split environment has the same properties as the aligned environment
27530 but it can only have two columns.
27533 \begin_layout Subsection
27534 Text in multiline Formulas
27535 \begin_inset LatexCommand label
27536 name "sub:Text-in-multiline"
27541 \begin_inset LatexCommand index
27542 name "Text ! in formulas"
27547 \begin_inset LatexCommand index
27548 name "Formula ! multiline ! text"
27555 \begin_layout Standard
27556 In the Align environments, and the multline and gather environment, text
27557 can be inserted that will appear in a separate line and doesn't affect
27558 the column alignment.
27559 To do this, the command
27564 \begin_inset LatexCommand index
27565 name "Commands ! I ! \\textbackslash intertext"
27571 is used in the following scheme:
27574 \begin_layout Standard
27582 \begin_layout Standard
27583 The text should not be longer than a line because it cannot be hyphenated.
27584 As LyX doesn't yet support
27590 directly, the text is written as mathematical text.
27597 must hereby be at the beginning of a line and appears in the output above
27599 An example where the text was inserted at the beginning of the second line:
27600 \begin_inset Formula \begin{align}
27601 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27602 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27609 \begin_layout Section
27611 \begin_inset LatexCommand index
27612 name "Formula numbering"
27617 \begin_inset LatexCommand index
27618 name "Formula ! numbering|see{Formula numbering}"
27625 \begin_layout Subsection
27629 \begin_layout Standard
27630 Numbered formulas can be created with the menu
27632 Insert\SpecialChar \menuseparator
27633 Math\SpecialChar \menuseparator
27634 Numbered\InsetSpace ~
27639 Ctrl-Alt\InsetSpace ~
27643 Existing formulas can be numbered with the menu
27645 Edit\SpecialChar \menuseparator
27646 Math\SpecialChar \menuseparator
27647 Toggle\InsetSpace ~
27656 The formula number is displayed in LyX behind the formula as number sign
27658 The number sign is replaced in the output by the formula number.
27661 \begin_layout Standard
27662 When numbering is turned on in multiline formulas, all lines will be numbered.
27663 But the numbering can be controlled with the menu
27665 Edit\SpecialChar \menuseparator
27666 Math\SpecialChar \menuseparator
27667 Toggle\InsetSpace ~
27668 Numbering\InsetSpace ~
27680 \begin_layout Standard
27681 Except of inline formulas, all formulas can be numbered with two different
27683 \begin_inset LatexCommand ref
27684 reference "sec:Formula-Styles"
27691 \begin_layout Subsection
27693 \begin_inset LatexCommand label
27694 name "sub:Cross-References"
27699 \begin_inset LatexCommand index
27700 name "Cross-references ! to formulas"
27707 \begin_layout Standard
27708 All labeled formulas can be cross-referenced.
27709 A label is added by the menu
27711 Insert\SpecialChar \menuseparator
27714 or the toolbar button
27715 \begin_inset Graphics
27716 filename ../images/label-insert.png
27722 The cursor must hereby be inside a displayed formula.
27723 A dialog pops up displaying the prefix
27728 The label is inserted there behind the prefix.
27729 The predefined prefix means
27730 \begin_inset Quotes eld
27734 \begin_inset Quotes erd
27737 and makes it easier to find labels in large documents because it marks
27738 it as formula label to divide it from e.\InsetSpace \thinspace{}
27741 To change a label, the menu
27743 Insert\SpecialChar \menuseparator
27749 \begin_layout Standard
27750 The name of the label is displayed in LyX within two parentheses behind
27752 A formula with a label is always numbered.
27753 The label is deleted when the numbering is turned off.
27754 This is at the moment the only way to delete a label, see
27758 \begin_layout Standard
27762 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27771 \begin_layout Standard
27781 \begin_layout Standard
27782 Cross-references are inserted via the menu
27784 Insert\SpecialChar \menuseparator
27787 or with the toolbar button
27788 \begin_inset Graphics
27789 filename ../images/dialog-show-new-inset_ref.png
27795 A formula cross-reference appears in the output as formula number.
27796 When in the cross-reference dialog window the format
27800 is chosen, the cross-reference appears in the output as formula number
27803 By right-clicking on a cross-reference in LyX, one jumps
27804 to the formula that is referenced.
27807 \begin_layout Standard
27808 Here are as examples cross-references to formulas of the following subsections:
27809 \begin_inset Note Note
27812 \begin_layout Standard
27813 Note the different cross-reference types.
27821 \begin_layout Standard
27823 \begin_inset LatexCommand eqref
27829 \begin_inset LatexCommand eqref
27836 \begin_inset LatexCommand ref
27841 ) big Latin letters are used for the numbering in contrary to (
27842 \begin_inset LatexCommand ref
27850 \begin_layout Standard
27851 \begin_inset VSpace medskip
27854 When the argument of
27862 \begin_layout Standard
27870 \begin_inset LatexCommand ref
27871 reference "sub:User-defined-Numbering"
27882 contains a box like in
27883 \begin_inset LatexCommand ref
27884 reference "sub:Paragraph-Boxes"
27888 , the formula cannot be referenced.
27891 \begin_layout Subsection
27893 \begin_inset LatexCommand index
27894 name "Formula numbering ! subnumbering"
27901 \begin_layout Standard
27902 With the help of the commands
27906 begin{subequations}
27914 formulas can be subnumbered.
27915 Both commands are inserted in TeX-mode.
27918 \begin_layout Standard
27920 \begin_inset Formula \begin{equation}
27921 A=C-B\label{eq:a}\end{equation}
27929 \begin_layout Standard
27933 addtocounter{equation}{-1}
27942 \begin_layout Standard
27946 begin{subequations}
27952 \begin_inset VSpace -5mm
27956 \begin_inset Formula \begin{equation}
27957 B=C-A\label{eq:b}\end{equation}
27962 \begin_inset Formula \begin{equation}
27963 C=A+B\label{eq:c}\end{equation}
27970 \begin_layout Standard
27974 \begin_layout Standard
27986 \begin_layout Standard
27987 To create the example, the following is done:
27990 \begin_layout Enumerate
27991 first formula is inserted
27994 \begin_layout Enumerate
27999 addtocounter{equation}{-1}
28001 begin{subequations}
28002 \begin_inset LatexCommand index
28003 name "Commands ! A ! \\textbackslash addtocounter"
28011 is inserted after the first formula
28014 \begin_layout Enumerate
28015 second formula is inserted
28018 \begin_layout Enumerate
28019 third formula is inserted
28022 \begin_layout Enumerate
28029 is inserted after the third formula
28032 \begin_layout Standard
28033 Every formula between the commands
28045 is subnumbered as a, b,
28049 \begin_layout Standard
28058 c, \SpecialChar \ldots{}
28059 For multiline formulas every line will be subnumbered.
28060 All subnumbered formulas are treated as
28065 But as every numbered formula increases the counter
28069 by one, the command
28075 is needed to decrease it.
28076 Otherwise the formulas
28077 \begin_inset LatexCommand eqref
28083 \begin_inset LatexCommand eqref
28089 \begin_inset LatexCommand eqref
28094 would be numbered as
28095 \begin_inset LatexCommand eqref
28101 \begin_inset LatexCommand eqref
28107 \begin_inset LatexCommand eqref
28115 \begin_layout Standard
28116 By inserting the commands in TeX-mode, a space is created between the first
28118 To revert this -5\InsetSpace \thinspace{}
28119 mm vertical space is inserted after the command
28123 begin{subequations}
28126 When the formula style
28132 \begin_layout Standard
28134 \begin_inset LatexCommand ref
28135 reference "sec:Formula-Styles"
28146 is used, -7\InsetSpace \thinspace{}
28147 mm space is inserted instead.
28150 \begin_layout Standard
28151 Here is an example for a multiline formula where the numbering was turned
28152 off for the second line:
28156 \begin_layout Standard
28160 begin{subequations}
28166 \begin_inset Formula \begin{eqnarray}
28167 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28168 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28169 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28177 \begin_layout Standard
28189 \begin_layout Subsection
28190 User-defined Numbering
28191 \begin_inset LatexCommand label
28192 name "sub:User-defined-Numbering"
28197 \begin_inset LatexCommand index
28198 name "Formula numbering ! user-defined"
28205 \begin_layout Standard
28206 \begin_inset LatexCommand index
28207 name "Formula numbering ! self-defined delimiters"
28211 With the standard numbering parentheses are set around the formula number.
28212 To replace the parentheses for example by vertical bars, the following
28213 line is added to the LaTeX-preamble:
28216 \begin_layout Standard
28228 \begin_inset Note Note
28231 \begin_layout Standard
28232 This macro is already declared in the LaTeX-preamble for testing.
28233 To activate it, remove the percent sign at the beginning.
28241 \begin_layout Standard
28242 To use other characters, the vertical bars besides the
28246 are replaced by one ore more characters.
28247 To get only the formula number the vertical bars are omitted.
28250 \begin_layout Standard
28251 \begin_inset VSpace bigskip
28254 When there should be an expression of your choice instead of the consecutive
28255 formula number in parentheses behind the formula, the command
28262 \begin_inset LatexCommand index
28263 name "Commands ! T ! \\textbackslash tag"
28268 \begin_inset Formula \begin{equation}
28269 A+B=C\tag{something}\label{eq:tag}\end{equation}
28273 In this example the command
28281 was inserted to the formula.
28284 \begin_layout Standard
28293 is inserted instead, the star prevents the parentheses around the expression:
28294 \begin_inset Formula \[
28295 A+B=C\tag*{something}\]
28302 \begin_layout Standard
28303 \begin_inset VSpace bigskip
28306 To restart the formula numbering with new document parts or sections, the
28307 following command is used:
28310 \begin_layout Standard
28315 @addtoreset{equation}{part}
28318 \begin_inset LatexCommand index
28319 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28331 @addtoreset{equation}{section}
28334 \begin_layout Standard
28335 To be able to use these commands in TeX-mode, the
28336 \begin_inset Quotes eld
28340 \begin_inset Quotes erd
28343 character has to be made
28344 \begin_inset Quotes eld
28348 \begin_inset Quotes erd
28351 for LaTeX using the command
28365 So the command sequence in TeX-mode is:
28368 \begin_layout Standard
28377 @addtoreset{equation}{section}
28384 \begin_layout Standard
28385 In the LaTeX-preamble
28397 can be omitted as they are automatically internally inserted by LyX.
28400 \begin_layout Standard
28415 \begin_layout Standard
28420 is part of the LaTeX-package
28425 \begin_inset LatexCommand index
28426 name "Packages ! carlisle"
28430 that is part of every LaTeX standard installation.
28436 \begin_inset LatexCommand index
28437 name "Packages ! remreset"
28441 has to be loaded in the LaTeX-preamble with the line
28444 \begin_layout Standard
28449 usepackage{remreset}
28452 \begin_layout Standard
28460 \begin_inset LatexCommand index
28461 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28465 can be used with the same scheme as
28474 \begin_layout Standard
28475 \begin_inset VSpace bigskip
28478 Sometimes formulas should be numbered in the following form:
28481 \begin_layout Standard
28484 (section number.formula number)
28487 \begin_layout Standard
28488 The formula number should start with every section with
28489 \begin_inset Quotes eld
28493 \begin_inset Quotes erd
28499 \begin_layout Standard
28500 For this case there is the command
28507 \begin_inset LatexCommand index
28508 name "Commands ! N ! \\textbackslash numberwithin"
28512 , which is used with the following scheme:
28515 \begin_layout Standard
28520 numberwithin{counter}{sectioning}
28523 \begin_layout Standard
28524 Counter denotes what kind of numbering is affected, sectioning denotes what
28525 number is before the dot.
28528 \begin_layout Standard
28529 Thus in our case the following LaTeX-preamble or ERT line is used:
28532 \begin_layout Standard
28537 numberwithin{equation}{section}
28540 \begin_layout Standard
28541 This is the result:
28545 \begin_layout Standard
28549 numberwithin{equation}{section}
28555 \begin_inset Formula \begin{equation}
28556 A+B=C\end{equation}
28563 \begin_layout Standard
28564 To number e.\InsetSpace \thinspace{}
28566 tables so that the number of the part is the sectioning,
28572 numberwithin{table}{part}
28577 \begin_layout Standard
28578 To go back to the standard numbering or to prevent this kind of numbering
28579 when it is defined by the document class, the following command is inserted
28580 as ERT or to the LaTeX-preamble:
28583 \begin_layout Standard
28593 \begin_inset LatexCommand index
28594 name "Commands ! A ! \\textbackslash arabic"
28604 \begin_layout Standard
28636 \begin_layout Standard
28643 uses internally the command
28649 , described above, that also needs to be reverted.
28653 \begin_layout Standard
28660 \begin_layout Standard
28664 @removefromreset{equation}{section}
28667 \begin_layout Standard
28679 \begin_layout Subsection
28680 Numbering with Roman Numbers and Letters
28681 \begin_inset LatexCommand label
28682 name "sub:Numbering-with-Roman"
28687 \begin_inset LatexCommand index
28688 name "Formula numbering ! with letters"
28693 \begin_inset LatexCommand index
28694 name "Formula numbering ! with Roman numbers"
28701 \begin_layout Standard
28702 Formulas can also be numbered with Roman numbers and Latin letters.
28703 To number for example with small Roman numbers, the command
28706 \begin_layout Standard
28718 \begin_layout Standard
28719 is inserted before the formula in TeX-mode.
28727 \begin_inset LatexCommand index
28728 name "Commands ! R ! \\textbackslash renewcommand"
28732 redefines the predefined command
28748 \begin_layout Standard
28755 has the same scheme like the command
28761 that is described in
28762 \begin_inset LatexCommand ref
28763 reference "sec:User-defined-commands"
28777 is the formula counter.
28784 is used as prefix for a counter, the value of the counter is output as
28786 When a formula is numbered, LaTeX sets internally the command
28792 behind the formula.
28798 \begin_inset LatexCommand index
28799 name "Commands ! R ! \\textbackslash roman"
28805 outputs the counter as small Roman number.
28808 \begin_layout Standard
28809 All formulas behind the command
28819 are now numbered Roman.
28820 To switch to numbering with big Roman numbers, the command is inserted
28834 \begin_inset LatexCommand index
28835 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28841 \begin_inset Quotes eld
28845 \begin_inset Quotes erd
28848 with small Latin letters there is the command
28855 \begin_inset LatexCommand index
28856 name "Commands ! A ! \\textbackslash alph"
28860 , for big ones there is the command
28867 \begin_inset LatexCommand index
28868 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28875 \begin_layout Standard
28876 \begin_inset Note Greyedout
28879 \begin_layout Standard
28884 Only maximal 26 formulas can be numbered with Latin letters in one document.
28892 \begin_layout Standard
28896 \begin_layout Standard
28912 \begin_layout Standard
28913 \begin_inset Formula \begin{equation}
28914 A=\textrm{small roman}\label{eq:rom}\end{equation}
28922 \begin_layout Standard
28936 \begin_inset Formula \begin{equation}
28937 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
28945 \begin_layout Standard
28959 \begin_inset Formula \begin{equation}
28960 C=\textrm{small Latin}\label{eq:lat}\end{equation}
28968 \begin_layout Standard
28982 \begin_inset Formula \begin{equation}
28983 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
28990 \begin_layout Standard
28991 To switch back to the default numbering, insert the command:
28994 \begin_layout Standard
29004 \begin_inset LatexCommand index
29005 name "Commands ! A ! \\textbackslash arabic"
29012 \begin_layout Standard
29016 \begin_layout Standard
29030 \begin_inset Formula \begin{equation}
29031 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29038 \begin_layout Standard
29039 \begin_inset VSpace medskip
29042 As you see, formulas are numbered serially independent from the numbering
29044 When then numbering should start with
29045 \begin_inset Quotes eld
29049 \begin_inset Quotes erd
29052 when the style is changed, new equation counters have to be defined.
29053 A description about this can be found in the file
29057 \begin_layout Standard
29061 href{Formula-numbering.pdf}{
29066 Formula-numbering.pdf
29070 \begin_layout Standard
29078 \begin_inset Note Note
29081 \begin_layout Standard
29082 More about the command
29089 \begin_inset LatexCommand ref
29090 reference "sub:Links-in-DVI-"
29102 \begin_layout Section
29103 User-defined commands
29104 \begin_inset LatexCommand label
29105 name "sec:User-defined-commands"
29110 \begin_inset LatexCommand index
29111 name "User-defined commands"
29118 \begin_layout Standard
29119 Many LaTeX-commands are too long to be used frequently.
29120 But it is possible to define with the command
29127 \begin_inset LatexCommand index
29128 name "Commands ! N ! \\textbackslash newcommand"
29132 new shorter commands.
29135 \begin_layout Standard
29136 The command scheme of
29145 \begin_layout Standard
29150 newcommand{new command name}[number of arguments][optional
29160 \begin_layout Standard
29175 \begin_layout Standard
29182 {command definition}
29185 \begin_layout Standard
29186 \begin_inset Note Greyedout
29189 \begin_layout Standard
29194 Assure that the name of the new command is not already used in your document
29195 or by LaTeX-packages that you use.
29196 When you for example define the command
29208 , you get an error message because
29214 is already defined as command for
29215 \begin_inset Quotes eld
29219 \begin_inset Formula $\le$
29223 \begin_inset Quotes erd
29234 \begin_layout Standard
29235 \begin_inset Note Greyedout
29238 \begin_layout Standard
29243 The names of user-defined commands may only consist of Latin letters.
29251 \begin_layout Standard
29252 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29253 -\InsetSpace \thinspace{}
29254 9 and specifies how
29255 many arguments the new command should have.
29256 With the optional value a value for an optional argument can be predefined.
29257 When this is done, the
29265 rgument of the new command is automatically an optional one.
29268 \begin_layout Standard
29269 Here are some examples:
29272 \begin_layout Itemize
29273 To define the command
29285 , the LaTeX-preamble line is:
29289 \begin_layout Standard
29311 \begin_layout Itemize
29312 To define the command
29324 , the argument (that should be underlined) must be taken into account.
29325 For this the preamble line is:
29329 \begin_layout Standard
29354 \begin_layout Standard
29373 acts as argument placeholder, the
29377 behind it denotes that it is the placeholder for the first argument.
29380 \begin_layout Itemize
29387 one can e.\InsetSpace \thinspace{}
29399 \begin_layout Standard
29418 framebox#1#2{$#3$}}
29424 \begin_layout Standard
29439 The two Dollar signs creates the extra formula needed for
29446 \begin_inset LatexCommand ref
29447 reference "sub:Boxes-with-Frame"
29454 \begin_layout Itemize
29455 To create a new command for
29461 where the color for the box needn't to be specified, the argument for the
29462 color is defined optional:
29466 \begin_layout Standard
29485 fcolorbox{#2}{#1}{$#3$}}
29491 \begin_layout Standard
29502 When the color is not specified when using
29508 , the predefined color
29515 \begin_layout Standard
29516 A test of the new defined commands:
29519 \begin_layout Standard
29521 \begin_inset Tabular
29522 <lyxtabular version="3" rows="6" columns="2">
29524 <column alignment="center" valignment="top" leftline="true" width="0">
29525 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29526 <row topline="true" bottomline="true">
29527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29530 \begin_layout Standard
29536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29539 \begin_layout Standard
29541 \begin_inset Note Note
29544 \begin_layout Standard
29551 is only used as spacer.
29562 <row topline="true">
29563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29566 \begin_layout Standard
29573 \begin_layout Standard
29587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29590 \begin_layout Standard
29591 \begin_inset Formula $A\gr B$
29600 <row topline="true">
29601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29604 \begin_layout Standard
29612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29615 \begin_layout Standard
29616 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29625 <row topline="true">
29626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29629 \begin_layout Standard
29633 \begin_inset Formula $\to$
29639 \begin_inset Formula $\to$
29650 \begin_layout Standard
29664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29667 \begin_layout Standard
29668 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29677 <row topline="true">
29678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29681 \begin_layout Standard
29685 \begin_inset Formula $\to$
29696 \begin_layout Standard
29710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29713 \begin_layout Standard
29714 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29723 <row topline="true" bottomline="true">
29724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29727 \begin_layout Standard
29733 \begin_inset Formula $\to$
29744 \begin_layout Standard
29758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29761 \begin_layout Standard
29762 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29778 \begin_layout Section
29780 \begin_inset LatexCommand index
29788 \begin_layout Standard
29789 To create diagrams, the LaTeX-package
29795 \begin_layout Standard
29800 is part of every LaTeX standard installation.
29808 \begin_inset LatexCommand index
29809 name "Packages ! amscd"
29814 It is loaded in the LaTeX-preamble with the line
29817 \begin_layout Standard
29825 \begin_layout Standard
29826 Diagrams visualize relations and look like this:
29827 \begin_inset Formula \[
29828 \begin{CD}A@>>>B@>>>C\\
29830 F@<<<E@<<<D\end{CD}\]
29837 \begin_layout Standard
29838 To get them, the command
29843 \begin_inset LatexCommand index
29844 name "Commands ! C ! \\textbackslash CD"
29850 is inserted to a formula.
29851 A blue box appears with two dashed lines where further commands can be
29857 a new line is created.
29858 Horizontal relations are inserted in odd, vertical in even formula lines.
29861 \begin_layout Standard
29862 To create the relations there are the following commands:
29865 \begin_layout Itemize
29870 creates a left arrow,
29881 \begin_layout Itemize
29886 creates an up arrow,
29894 a vertical equal sign
29897 \begin_layout Itemize
29903 is a placeholder for non-existent relations
29906 \begin_layout Standard
29907 All arrows can be labeled as follows:
29910 \begin_layout Itemize
29911 Is text inserted between the first and second < or >, resp., it is placed
29913 When it is inserted between the second and third one, it appears under
29917 \begin_layout Itemize
29918 When text for vertical arrows is inserted between the first and second A
29919 or V, resp., it is placed left beside the arrow.
29920 When it is inserted between the second and third one, it appears right
29922 If the text contains an A or V, these letters must be set into a TeX-brace.
29925 \begin_layout Standard
29926 As example a diagram with all possible relations:
29929 \begin_layout Standard
29930 \begin_inset Formula \[
29931 \begin{CD}A@>j>>B@>>k>C@=F\\
29933 D@<<j<E@>k>>F@=C\end{CD}\]
29940 \begin_layout Standard
29941 The command for this is:
29951 \begin_layout Standard
29960 A@>j>>B@>>k>C@=F Ctrl-Enter
29966 \begin_layout Standard
29981 \begin_layout Standard
29994 \begin_layout Standard
30006 \begin_inset Formula $\to$
30017 \begin_layout Standard
30032 \begin_layout Standard
30045 \begin_layout Standard
30055 \begin_layout Standard
30061 \begin_layout Section
30066 \begin_layout Standard
30079 \begin_layout Standard
30080 Other useful math tips can be found in
30081 \begin_inset LatexCommand cite
30095 \begin_layout Standard
30103 \begin_inset Note Note
30106 \begin_layout Standard
30109 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30112 \begin_layout Standard
30115 texorpdfstring is in section
30116 \begin_inset LatexCommand ref
30117 reference "sub:Formulas-in-Section"
30127 \begin_inset LatexCommand index
30133 \begin_inset LatexCommand index
30134 name "Ions|see{Chemical characters}"
30141 \begin_layout Subsection
30142 Chemical Symbols and Equations
30143 \begin_inset LatexCommand label
30144 name "sub:Chemical-Symbols-and"
30149 \begin_inset LatexCommand index
30150 name "Chemical characters ! Symbols"
30155 \begin_inset LatexCommand index
30156 name "Chemical equations"
30161 \begin_inset LatexCommand index
30162 name "Symbols ! chemical"
30169 \begin_layout Standard
30170 An example text from chemistry:
30173 \begin_layout Quote
30175 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30178 -ion reacts with two
30179 \begin_inset Formula $\mathrm{Na^{+}}$
30182 -ions to sodium sulfate
30183 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30187 The chemical equation for this is:
30188 \begin_inset Formula \[
30189 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30196 \begin_layout Standard
30197 This chemical equation can directly be created as formula.
30198 To avoid that the symbols appear italic, everything is highlighted and
30199 changed by the shortcut
30204 to the upright font style.
30208 \begin_layout Standard
30214 \begin_inset LatexCommand ref
30215 reference "sub:Font-Styles"
30227 \begin_layout Subsection
30229 \begin_inset LatexCommand index
30230 name "Numbers ! negative"
30237 \begin_layout Standard
30238 Negative numbers often look ugly in formulas because the minus sign before
30239 the number is set with the same length as the minus operator sign.
30240 When writing the negative number in normal text, the minus sign appears
30244 \begin_layout Standard
30245 Thus, the problem disappears when converting the minus sign to mathematical
30249 \begin_layout Standard
30250 An example to visualize the problem:
30253 \begin_layout Standard
30255 \begin_inset Tabular
30256 <lyxtabular version="3" rows="3" columns="2">
30258 <column alignment="right" valignment="top" leftline="true" width="0">
30259 <column alignment="left" valignment="top" rightline="true" width="0">
30260 <row topline="true">
30261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30264 \begin_layout Standard
30270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30273 \begin_layout Standard
30280 <row topline="true" bottomline="true">
30281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30284 \begin_layout Standard
30290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30293 \begin_layout Standard
30294 \begin_inset Formula $x=-2$
30303 <row topline="true" bottomline="true">
30304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30307 \begin_layout Standard
30313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30316 \begin_layout Standard
30317 \begin_inset Formula $x=\textrm{-}2$
30333 \begin_layout Subsection
30334 Comma as Decimal Separator
30335 \begin_inset LatexCommand index
30343 \begin_layout Standard
30344 In LaTeX a comma inside a formula is used, according to the English convention,
30345 as number group separator.
30346 So there will be space added behind all commas in formulas.
30349 \begin_layout Standard
30350 To avoid this, the comma is highlighted and changed to mathematical text
30359 \begin_layout Standard
30360 To use all formula commas in the document as decimal separator, the file
30369 \begin_layout Standard
30374 is part of the LaTeX-package
30379 \begin_inset LatexCommand index
30380 name "Packages ! was\\vspace{4mm}"
30390 \begin_inset LatexCommand index
30391 name "Packages ! icomma"
30395 is loaded with the LaTeX-preamble line
30398 \begin_layout Standard
30406 \begin_layout Subsection
30408 \begin_inset LatexCommand label
30409 name "sub:Physical-Vectors"
30414 \begin_inset LatexCommand index
30415 name "Vectors ! physical"
30422 \begin_layout Standard
30423 Predefined vectors are offered by the LaTeX-package
30431 \begin_layout Standard
30436 should be part of every LaTeX standard installation.
30442 \begin_inset LatexCommand index
30443 name "Packages ! braket"
30447 that is loaded with the LaTeX-preamble line
30450 \begin_layout Standard
30458 \begin_layout Standard
30462 \begin_layout Standard
30472 \begin_inset Note Note
30475 \begin_layout Standard
30476 The following table will only be displayed when the LaTeX-package
30485 The following commands are defined:
30488 \begin_layout Standard
30490 \begin_inset Tabular
30491 <lyxtabular version="3" rows="4" columns="2">
30493 <column alignment="center" valignment="top" leftline="true" width="0">
30494 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30495 <row topline="true" bottomline="true">
30496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30499 \begin_layout Standard
30505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30508 \begin_layout Standard
30515 <row topline="true">
30516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30519 \begin_layout Standard
30529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30532 \begin_layout Standard
30533 \begin_inset Formula $\Bra{\psi}$
30542 <row topline="true">
30543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30546 \begin_layout Standard
30556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30559 \begin_layout Standard
30560 \begin_inset Formula $\Ket{\psi}$
30569 <row topline="true" bottomline="true">
30570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30573 \begin_layout Standard
30585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30588 \begin_layout Standard
30589 \begin_inset Formula $\Braket{\psi|\phi}$
30605 \begin_layout Standard
30612 assures that all vertical bars are set in the size of the surrounding brackets:
30613 \begin_inset Formula \[
30614 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30622 \begin_layout Standard
30632 \begin_inset Note Note
30635 \begin_layout Standard
30636 The following will be displayed when the LaTeX-package
30648 \begin_layout Standard
30649 You need to install the LaTeX-package
30653 to see the rest of this subsection in the output.
30656 \begin_layout Standard
30660 \begin_layout Standard
30672 \begin_layout Standard
30679 can also be achieved using the command
30685 , that is described in
30686 \begin_inset LatexCommand ref
30687 reference "sub:Automatic-Bracket-Size"
30694 \begin_layout Subsection
30695 Self-defined Fractions
30696 \begin_inset LatexCommand label
30697 name "sub:Self-defined-Fractions"
30702 \begin_inset LatexCommand index
30703 name "Fractions ! self-defined"
30710 \begin_layout Standard
30711 To define custom commands for fractions, the command
30718 \begin_inset LatexCommand index
30719 name "Commands ! G ! \\textbackslash genfrac"
30723 is used in the following scheme:
30726 \begin_layout Standard
30739 bracket}{fraction bar thickness}{style}
30745 \begin_layout Standard
30760 \begin_layout Standard
30767 {numerator}{denominator}
30770 \begin_layout Standard
30771 The style is a number in the range of 0\InsetSpace \thinspace{}
30772 -\InsetSpace \thinspace{}
30776 \begin_layout Standard
30778 \begin_inset Tabular
30779 <lyxtabular version="3" rows="5" columns="2">
30781 <column alignment="center" valignment="top" leftline="true" width="0">
30782 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30783 <row topline="true" bottomline="true">
30784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30787 \begin_layout Standard
30793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30796 \begin_layout Standard
30803 <row topline="true">
30804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30807 \begin_layout Standard
30813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30816 \begin_layout Standard
30817 display style formula
30823 <row topline="true">
30824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30827 \begin_layout Standard
30833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30836 \begin_layout Standard
30843 <row topline="true">
30844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30847 \begin_layout Standard
30853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30856 \begin_layout Standard
30863 <row topline="true" bottomline="true">
30864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30867 \begin_layout Standard
30873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30876 \begin_layout Standard
30890 \begin_layout Standard
30891 When no style is given, the size is adjusted to the surrounding environment
30892 like for the command
30901 \begin_layout Standard
30902 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30907 \begin_layout Standard
30908 \begin_inset VSpace medskip
30911 For example, the commands
30924 \begin_inset LatexCommand ref
30925 reference "sub:Fractions"
30929 are defined with the commands
30932 \begin_layout Standard
30941 genfrac{}{}{}{0}{#1}{#2}}
30944 \begin_layout Standard
30948 \begin_layout Standard
30957 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30960 \begin_layout Standard
30961 \begin_inset VSpace medskip
30964 To define a fraction where the fraction bar thickness can be given as optional
30965 argument, the following line is inserted to the LaTeX-preamble:
30968 \begin_layout Standard
30977 genfrac{}{}{#1}{}{#2}{#3}}
30980 \begin_layout Standard
30982 \begin_inset Formula \begin{align*}
30983 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30984 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30988 As one can see, the distance of the numerator and the denominator to the
30989 fraction bar is round about three times the bar thickness.
30992 \begin_layout Subsection
30994 \begin_inset LatexCommand label
30995 name "sub:Canceled-Formulas"
31000 \begin_inset LatexCommand index
31001 name "Formula ! canceled"
31008 \begin_layout Standard
31009 To cancel formulas or formula parts, the LaTeX-package
31017 \begin_layout Standard
31022 is part of every LaTeX standard installation.
31028 \begin_inset LatexCommand index
31029 name "Packages ! cancel"
31033 has to be loaded with the LaTeX-preamble line
31036 \begin_layout Standard
31041 usepackage[samesize]{cancel}
31044 \begin_layout Standard
31045 There are four ways to cancel formulas:
31048 \begin_layout Standard
31050 \begin_inset Tabular
31051 <lyxtabular version="3" rows="5" columns="2">
31053 <column alignment="center" valignment="top" leftline="true" width="0">
31054 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31055 <row topline="true" bottomline="true">
31056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31059 \begin_layout Standard
31065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31068 \begin_layout Standard
31070 \begin_inset Note Note
31073 \begin_layout Standard
31086 are used here as spacer.
31097 <row topline="true">
31098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31101 \begin_layout Standard
31110 \begin_layout Standard
31124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31127 \begin_layout Standard
31128 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31137 <row topline="true">
31138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31141 \begin_layout Standard
31150 \begin_layout Standard
31164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31167 \begin_layout Standard
31168 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31177 <row topline="true" bottomline="true">
31178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31181 \begin_layout Standard
31190 \begin_layout Standard
31204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31207 \begin_layout Standard
31208 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31217 <row topline="true" bottomline="true">
31218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31221 \begin_layout Standard
31225 \begin_inset Formula $\to$
31236 \begin_layout Standard
31250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31253 \begin_layout Standard
31254 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31270 \begin_layout Standard
31277 is especially suitable to visualize the reduction of fractions within formulas:
31278 \begin_inset Formula \[
31279 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31286 \begin_layout Subsection
31287 Formulas in Section Headings
31288 \begin_inset LatexCommand label
31289 name "sub:Formulas-in-Section"
31294 \begin_inset LatexCommand index
31295 name "Formula ! in section headings"
31302 \begin_layout Standard
31303 When formulas are used in section headings, the following has to be taken
31307 \begin_layout Standard
31308 \begin_inset Note Greyedout
31311 \begin_layout Standard
31312 When the LaTeX-package
31317 \begin_inset LatexCommand index
31318 name "Packages ! hyperref"
31322 is used, PDF-bookmarks are automatically created for every section heading
31323 in the table of contents.
31324 If a section heading contains formulas, they are incorrectly displayed
31325 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31334 \begin_layout Standard
31335 Both problems can be solved by inserting at the end of the section heading
31336 a short title with the menu
31338 Insert\SpecialChar \menuseparator
31343 Short titles are used as alternative for multiline section headings to
31344 keep the table of contents clearly arranged.
31345 Only the short title appears in the table of contents and therefore also
31346 in the PDF-bookmark.
31349 \begin_layout Standard
31350 When formulas should be used in the table of contents but
31354 is used, one can use the following command in TeX-mode:
31357 \begin_layout Standard
31362 texorpdfstring{part}{alternative}
31363 \begin_inset LatexCommand index
31364 name "Commands ! T ! \\textbackslash texorpdfstring"
31371 \begin_layout Standard
31372 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31373 This can be characters, formulas, footnotes, but also cross-references.
31374 The alternative is used instead of the part for the bookmark.
31377 \begin_layout Standard
31378 Here are two example headings:
31379 \begin_inset VSpace -3mm
31386 \begin_layout Standard
31398 \begin_layout Subsubsection
31399 Heading without formula in table of contents
31400 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31404 \begin_inset OptArg
31407 \begin_layout Standard
31408 Heading without formula in table of contents
31416 \begin_layout Subsubsection
31417 Heading with formula in table of contents
31421 \begin_layout Standard
31431 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31438 \begin_layout Standard
31448 \begin_layout Standard
31452 \begin_layout Standard
31461 In the first heading a short title was used, in the second one
31470 \begin_layout Standard
31471 To get the same formatting as for the other headings, the complete heading
31474 boldmath environment
31480 \begin_layout Standard
31482 \begin_inset LatexCommand ref
31483 reference "sub:Bold-Formulas"
31495 \begin_layout Subsection
31496 Formulas in multi-column Text
31497 \begin_inset LatexCommand index
31498 name "Formula ! in multi-column text"
31505 \begin_layout Standard
31506 Formulas in multi-column text are often too wide to fit into a column and
31507 thus need to be set over the whole page width.
31508 This is done by using the LaTeX-package
31516 \begin_layout Standard
31521 is part of every LaTeX standard installation.
31527 \begin_inset LatexCommand index
31528 name "Packages ! multicol"
31532 , that is loaded with the LaTeX-preamble line
31535 \begin_layout Standard
31540 usepackage{multicol}
31543 \begin_layout Standard
31544 \begin_inset Note Greyedout
31547 \begin_layout Standard
31548 Note herby that the setting
31550 Two-column\InsetSpace ~
31555 Document\SpecialChar \menuseparator
31578 \begin_layout Standard
31579 Before the multi-column text the command
31582 \begin_layout Standard
31587 begin{multicols}{column number}
31590 \begin_layout Standard
31591 is written in TeX-mode.
31592 The column number is a number in the range of 2\InsetSpace \thinspace{}
31593 -\InsetSpace \thinspace{}
31595 Before the formula the multi-column text is ended by inserting the command
31598 \begin_layout Standard
31606 \begin_layout Standard
31610 \begin_layout Standard
31611 Due to the command some space is automatically added before the formula.
31612 To revert this, -6\InsetSpace \thinspace{}
31613 mm vertical space is inserted before the formula.
31614 When the formula style
31620 \begin_layout Standard
31622 \begin_inset LatexCommand ref
31623 reference "sec:Formula-Styles"
31634 is used, -9\InsetSpace \thinspace{}
31635 mm space is inserted instead.
31638 \begin_layout Standard
31639 As example a multi-column text with a displayed formula:
31642 \begin_layout Standard
31646 \begin_layout Standard
31650 begin{multicols}{2}
31655 Das Spektrum wird fouriertransformiert.
31656 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31657 , Lösungsmittel) zu trennen.
31658 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31659 nun das Aussehen des Ausgangssignals.
31660 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31661 über alle Phasen integrieren muss.
31663 \begin_inset Formula $S$
31666 unser normiertes Ausgangssignal and
31667 \begin_inset Formula $P$
31670 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31674 \begin_layout Standard
31684 \begin_inset VSpace -6mm
31688 \begin_inset Formula \begin{equation}
31689 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31697 \begin_layout Standard
31701 begin{multicols}{2}
31707 \begin_inset Formula $S_{0}$
31710 das Signal ohne Gradient ist and the Normierungsbedingung
31711 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31715 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31717 \begin_inset Formula $\nicefrac{\pi}{2}$
31720 \InsetSpace \thinspace{}
31721 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31722 das Signal zusätzlich abschwächt.
31723 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31725 \begin_inset Formula $T_{2}$
31731 \begin_layout Standard
31735 \begin_layout Standard
31747 \begin_layout Subsection
31748 Formulas with Description of Variables
31749 \begin_inset LatexCommand index
31750 name "Formula ! with description of variables"
31757 \begin_layout Standard
31758 To describe variables within a formula, like in formula
31759 \begin_inset LatexCommand eqref
31760 reference "eq:within"
31769 \begin_inset Formula $n$
31773 matrix is used with left aligned columns for the
31774 \begin_inset Formula $n$
31781 \begin_layout Standard
31783 \begin_inset LatexCommand ref
31784 reference "sec:Matrices"
31793 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31806 \begin_layout Standard
31808 \begin_inset LatexCommand ref
31809 reference "sub:Font-Sizes"
31821 \begin_layout Standard
31822 When the formula style
31828 \begin_layout Standard
31830 \begin_inset LatexCommand ref
31831 reference "sec:Formula-Styles"
31852 \begin_layout Standard
31859 only works in formulas with the style
31864 \begin_inset LatexCommand ref
31865 reference "sub:Variable-Space"
31874 is inserted before and after the matrix to have the same separation of
31875 the matrix from the equation and the side margin.
31878 \begin_layout Standard
31879 When the formula style
31883 is used, the method described in
31884 \begin_inset LatexCommand ref
31885 reference "sub:Flalign-Environment"
31889 is used to indent formulas.
31891 \begin_inset LatexCommand eqref
31892 reference "eq:within"
31896 consists of five columns whereas in the first two columns contain the equation,
31897 the third the matrix, and the last one an empty TeX-brace.
31898 \begin_inset Formula \begin{flalign}
31899 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31900 \rho & \textrm{density}\\
31901 V & \textrm{volume}\\
31902 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31909 \begin_layout Subsection
31910 Upright small Greek Letters
31911 \begin_inset LatexCommand label
31912 name "sub:Upright-small-Greek"
31917 \begin_inset LatexCommand index
31918 name "Greek letters ! upright"
31925 \begin_layout Standard
31926 Most of the math fonts only provide italic small Greek letters.
31927 But for symbols of elementary particles like pions and neutrinos, upright
31928 Greek letters are needed.
31937 \begin_layout Standard
31942 is part of the LaTeX-package
31947 \begin_inset LatexCommand index
31948 name "Packages ! was\\vspace{4mm}"
31958 \begin_inset LatexCommand index
31959 name "Packages ! upgreek"
31963 that is loaded with the LaTeX-preamble line
31966 \begin_layout Standard
31971 usepackage{upgreek}
31974 \begin_layout Standard
31980 \begin_layout Standard
31990 \begin_inset Note Note
31993 \begin_layout Standard
31994 The following table will only be displayed when the LaTeX-package
32003 They are created when the command for a small Greek letters is started
32009 For example the command
32016 \begin_inset Formula $\uptau$
32022 \begin_layout Standard
32023 With these commands reactions of elementary particles can be typeset:
32024 \begin_inset Formula \[
32025 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32032 \begin_layout Standard
32033 The upright letters are more bold and wider than the italic ones.
32034 They should therefore not be used for units like
32035 \begin_inset Quotes eld
32039 \begin_inset Quotes erd
32045 \begin_layout Standard
32049 \begin_layout Standard
32059 \begin_inset Note Note
32062 \begin_layout Standard
32063 The following will be displayed when the LaTeX-package
32075 \begin_layout Standard
32076 You need to install the LaTeX-package
32080 to see the rest of this subsection in the output.
32083 \begin_layout Standard
32087 \begin_layout Standard
32099 \begin_layout Subsection
32100 Text Characters in Formulas
32101 \begin_inset LatexCommand label
32102 name "sub:Text-Characters-in"
32107 \begin_inset LatexCommand index
32108 name "Text ! in formulas"
32115 \begin_layout Standard
32116 In some cases you might want to insert text characters directly into formulas.
32117 When for example the centered dot · is often used in formulas like
32118 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32121 , one would have to insert the command
32131 \begin_layout Standard
32133 \begin_inset LatexCommand ref
32134 reference "sub:Binary-Operators"
32143 all the time, because this character is defined in all encodings as text
32145 But the encoding can be changed by this LaTeX-preamble line:
32148 \begin_layout Standard
32153 Declare Inputtext{183}{
32163 f\SpecialChar \textcompwordmark{}
32167 \begin_layout Standard
32168 The character encoding (menu
32170 Document\SpecialChar \menuseparator
32171 Settings\SpecialChar \menuseparator
32174 ) specifies what character appears when a keyboard key is pressed.
32175 When the key for the character '·' is pressed, internally the command
32182 But this command is not available in a formula so that you would get LaTeX-erro
32184 With the changed encoding the right command is chosen automatically, depending
32185 on if the character was inserted into a formula or not.
32188 \begin_layout Standard
32189 The encoding of several characters is saved in definition files.
32190 Fore example the encoding
32194 is defined in the file
32198 that is in the installation folder of LaTeX.
32199 Encodings should only be changed via the LaTeX-preamble and not in the
32201 Otherwise own documents could not be edited by other LyX users working
32202 on other computers.
32205 \begin_layout Standard
32206 \begin_inset VSpace medskip
32209 Besides the centered dot, in this document the degree sign ° is defined
32210 with the following LaTeX-preamble line so that it can directly be inserted
32214 \begin_layout Standard
32219 DeclareInputtext{176}{
32229 f\SpecialChar \textcompwordmark{}
32233 \begin_layout Standard
32239 \begin_layout Section
32241 Typographic Advises
32242 \begin_inset LatexCommand index
32243 name "Typographic Advises"
32250 \begin_layout Standard
32251 This section is a summary of the most important typographic rules, listed
32256 \begin_layout Standard
32257 This collection was partly taken from the German semi-official dictionary
32259 \begin_inset Quotes eld
32263 \begin_inset Quotes erd
32267 \begin_inset LatexCommand cite
32272 that lists some of the ISO rules.
32280 \begin_layout Itemize
32289 \begin_layout Standard
32290 done with font styles, see
32291 \begin_inset LatexCommand ref
32292 reference "sub:Font-Styles"
32301 : 30\InsetSpace \thinspace{}
32304 Between the value and the unit is the smallest space, see
32305 \begin_inset LatexCommand ref
32306 reference "sub:Predefined-Space"
32313 \begin_layout Itemize
32314 Percent and perthousand signs are set like physical units:
32316 1,2\InsetSpace \thinspace{}
32321 \begin_layout Standard
32334 \begin_layout Itemize
32335 The degree sign follows directly on the value: 15°, but not when it is used
32336 in units: 15\InsetSpace \thinspace{}
32340 \begin_layout Itemize
32341 In numbers with more than four digits the smallest space is inserted before
32342 every third digit to group them:
32351 18\InsetSpace \thinspace{}
32352 473\InsetSpace \thinspace{}
32356 \begin_layout Itemize
32357 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32358 cm the multiplication sign
32359 \begin_inset Quotes eld
32363 \begin_inset Quotes erd
32367 It is available with the LaTeX-command
32373 , but can also directly be inserted with some keyboard definitions.
32376 \begin_layout Itemize
32377 Functions with names consisting of several letters are set upright to avoid
32379 \begin_inset LatexCommand ref
32380 reference "sub:Predefined-Functions"
32387 \begin_layout Itemize
32388 Indices consisting of several letters, are set upright:
32389 \begin_inset Formula $E_{\mathrm{kin}}$
32394 Components of matrices are set italic:
32395 \begin_inset Formula $\hat{H}_{kl}$
32401 \begin_layout Itemize
32402 The differentiation/integration operator 'd', the Euler's number 'e', and
32403 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32407 \begin_layout Standard
32413 \begin_layout Section
32415 \begin_inset LatexCommand index
32423 \begin_layout Standard
32424 Some characters and symbols can be created with several commands.
32425 Here is a list of the synonym commands:
32428 \begin_layout Standard
32429 \begin_inset VSpace bigskip
32435 \begin_inset Tabular
32436 <lyxtabular version="3" rows="12" columns="2">
32438 <column alignment="center" valignment="top" leftline="true" width="0pt">
32439 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32440 <row topline="true" bottomline="true">
32441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32444 \begin_layout Standard
32450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32453 \begin_layout Standard
32455 \begin_inset Note Note
32458 \begin_layout Standard
32465 is only used as spacer.
32476 <row topline="true">
32477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32480 \begin_layout Standard
32488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32491 \begin_layout Standard
32495 \begin_layout Standard
32508 \begin_layout Standard
32521 <row topline="true">
32522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32525 \begin_layout Standard
32533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32536 \begin_layout Standard
32545 <row topline="true">
32546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32549 \begin_layout Standard
32557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32560 \begin_layout Standard
32569 <row topline="true">
32570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32573 \begin_layout Standard
32581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32584 \begin_layout Standard
32591 <row topline="true">
32592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32595 \begin_layout Standard
32603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32606 \begin_layout Standard
32613 <row topline="true">
32614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32617 \begin_layout Standard
32625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32628 \begin_layout Standard
32637 <row topline="true">
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32641 \begin_layout Standard
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32652 \begin_layout Standard
32661 <row topline="true">
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32665 \begin_layout Standard
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32676 \begin_layout Standard
32685 <row topline="true">
32686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32689 \begin_layout Standard
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32700 \begin_layout Standard
32709 <row topline="true">
32710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32713 \begin_layout Standard
32721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32724 \begin_layout Standard
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32735 \begin_layout Standard
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32746 \begin_layout Standard
32760 \begin_inset Tabular
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32764 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32765 <row topline="true" bottomline="true">
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32778 \begin_layout Standard
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32800 \begin_layout Standard
32811 <row topline="true">
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32815 \begin_layout Standard
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32826 \begin_layout Standard
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32839 \begin_layout Standard
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32850 \begin_layout Standard
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32874 \begin_layout Standard
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32885 \begin_layout Standard
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32896 \begin_layout Standard
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32918 \begin_layout Standard
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32931 \begin_layout Standard
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32942 \begin_layout Standard
32951 <row topline="true">
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32955 \begin_layout Standard
32963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32966 \begin_layout Standard
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32976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32979 \begin_layout Standard
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32990 \begin_layout Standard
32999 <row topline="true">
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33003 \begin_layout Standard
33011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33014 \begin_layout Standard
33023 <row topline="true" bottomline="true">
33024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33027 \begin_layout Standard
33035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33038 \begin_layout Standard
33056 \begin_layout Standard
33062 \begin_layout Bibliography
33063 \begin_inset LatexCommand bibitem
33075 The LaTeX Companion
33078 Addison Wesley, 2004
33081 \begin_layout Bibliography
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33091 \begin_layout Standard
33095 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
33104 \begin_layout Standard
33111 of LaTeX's math abilities
33114 \begin_layout Bibliography
33115 \begin_inset LatexCommand bibitem
33120 LaTeX tips and tricks-
33124 \begin_layout Standard
33128 href{http://tug.org/TeXnik/}{
33137 \begin_layout Standard
33147 \begin_layout Bibliography
33148 \begin_inset LatexCommand bibitem
33157 \begin_layout Standard
33161 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
33170 \begin_layout Standard
33181 \begin_layout Standard
33193 \begin_layout Bibliography
33194 \begin_inset LatexCommand bibitem
33203 \begin_layout Standard
33207 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
33216 \begin_layout Standard
33223 of all symbols available with LaTeX-packages
33226 \begin_layout Bibliography
33227 \begin_inset LatexCommand bibitem
33236 \begin_layout Standard
33240 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
33249 \begin_layout Standard
33256 of the LaTeX-package
33261 \begin_inset LatexCommand index
33262 name "Packages ! hyperref"
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33270 \begin_inset LatexCommand bibitem
33279 \begin_layout Standard
33283 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
33292 \begin_layout Standard
33306 \begin_inset LatexCommand ref
33307 reference "sub:Operator-Limits"
33312 \begin_inset LatexCommand index
33313 name "Commands ! M ! \\textbackslash mathclap"
33320 \begin_layout Bibliography
33321 \begin_inset LatexCommand bibitem
33332 Auflage, Duden 2001
33335 \begin_layout Subsubsection*
33336 \begin_inset LatexCommand printindex