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 upgreek
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 $\begin{cases}
2709 A & \textrm{für }x>0\\
2710 B & \textrm{für }x=0\end{cases}$
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"
2939 \begin_layout Standard
2945 sectionautorefname}{
2955 \begin_inset LatexCommand ref
2956 reference "sec:Relations"
2964 \begin_layout Standard
2970 sectionautorefname}{sec.
2978 \begin_inset Note Note
2981 \begin_layout Standard
2988 -commands in TeX-mode are necessary that the cross-reference name
2989 \begin_inset Quotes eld
2993 \begin_inset Quotes erd
2996 don't appear twice, see sec.\InsetSpace \thinspace{}
2998 \begin_inset LatexCommand ref
2999 reference "sub:Verlinkte-Querverweise"
3011 \begin_layout Subsection
3013 \begin_inset LatexCommand label
3014 name "sub:Placeholders"
3019 \begin_inset LatexCommand index
3025 \begin_inset LatexCommand index
3026 name "Chemical characters ! Isotopes"
3031 \begin_inset LatexCommand index
3032 name "Isotopes|see{Chemical characters}"
3039 \begin_layout Standard
3040 When displaying e.\InsetSpace \thinspace{}
3046 \begin_layout Standard
3047 More about chemical symbols is written in
3048 \begin_inset LatexCommand ref
3049 reference "sub:Chemical-Symbols-and"
3058 the following problem occurs:
3061 \begin_layout Standard
3063 \begin_inset Tabular
3064 <lyxtabular version="3" rows="2" columns="2">
3066 <column alignment="center" valignment="top" width="0pt">
3067 <column alignment="center" valignment="top" width="0pt">
3069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3072 \begin_layout Standard
3073 Indices created with sub- and superscripts:
3078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3081 \begin_layout Standard
3082 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3095 \begin_layout Standard
3101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3104 \begin_layout Standard
3105 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3119 \begin_inset Note Note
3122 \begin_layout Standard
3129 is only used as spacer.
3137 \begin_layout Standard
3138 The shorter index is by default placed below or above the first character
3139 of the longer index.
3140 To avoid this there is the command
3147 \begin_inset LatexCommand index
3148 name "Commands ! P ! \\textbackslash phantom"
3152 or the math toolbar button \InsetSpace ~
3154 \begin_inset Graphics
3155 filename ../images/math/phantom.png
3160 that creates one or more phantom characters.
3167 a small blue box appears that is superposed with two red arrows.
3168 The arrows indicate that the complete width and height of the box content
3169 will be created as placeholder.
3170 Phantom characters are accordingly placeholders with the size of the characters.
3173 \begin_layout Standard
3175 \begin_inset Tabular
3176 <lyxtabular version="3" rows="4" columns="2">
3178 <column alignment="center" valignment="top" leftline="true" width="0">
3179 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3180 <row topline="true" bottomline="true">
3181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3184 \begin_layout Standard
3190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3193 \begin_layout Standard
3195 \begin_inset Note Note
3198 \begin_layout Standard
3205 is only used as spacer.
3216 <row topline="true">
3217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3220 \begin_layout Standard
3225 \begin_layout Standard
3240 \begin_layout Standard
3250 \begin_inset Formula $\to$
3257 \begin_layout Standard
3271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3274 \begin_layout Standard
3275 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3284 <row topline="true" bottomline="true">
3285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3288 \begin_layout Standard
3293 \begin_layout Standard
3308 \begin_layout Standard
3318 \begin_inset Formula $\to$
3325 \begin_layout Standard
3339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3342 \begin_layout Standard
3343 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3352 <row topline="true" bottomline="true">
3353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3356 \begin_layout Standard
3363 \begin_layout Standard
3378 \begin_layout Standard
3388 \begin_inset Formula $\to$
3395 \begin_layout Standard
3409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3412 \begin_layout Standard
3413 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3429 \begin_layout Standard
3430 Furthermore there are the commands
3437 \begin_inset LatexCommand index
3438 name "Commands ! V ! \\textbackslash vphantom"
3442 (toolbar button \InsetSpace ~
3444 \begin_inset Graphics
3445 filename ../images/math/vphantom.png
3457 \begin_inset LatexCommand index
3458 name "Commands ! H ! \\textbackslash hphantom"
3462 (toolbar button \InsetSpace ~
3464 \begin_inset Graphics
3465 filename ../images/math/hphantom.png
3477 creates only space for the maximal height of the characters in the box
3478 but not for its width.
3485 creates only space for the width of the box content.
3486 Therefore the boxes of both commands have only one red arrow.
3489 \begin_layout Standard
3500 \begin_layout Standard
3515 space for the height of the integral sign,
3519 \begin_layout Standard
3526 creates an integral sign, see
3527 \begin_inset LatexCommand ref
3528 reference "sub:Big-Operators"
3537 because this is the larger character.
3538 An example application is in
3539 \begin_inset LatexCommand ref
3540 reference "sub:Multiline-Brackets"
3547 \begin_layout Subsection
3549 \begin_inset LatexCommand index
3555 \begin_inset LatexCommand index
3556 name "Formula ! underlined"
3563 \begin_layout Standard
3565 \begin_inset Tabular
3566 <lyxtabular version="3" rows="4" columns="2">
3568 <column alignment="center" valignment="top" leftline="true" width="0pt">
3569 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3570 <row topline="true" bottomline="true">
3571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3574 \begin_layout Standard
3580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3583 \begin_layout Standard
3585 \begin_inset Note Note
3588 \begin_layout Standard
3595 is only used as spacer.
3606 <row topline="true" bottomline="true">
3607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3610 \begin_layout Standard
3617 \begin_layout Standard
3627 \begin_inset LatexCommand index
3628 name "Commands ! O ! \\textbackslash overline"
3637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3640 \begin_layout Standard
3641 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3650 <row bottomline="true">
3651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3654 \begin_layout Standard
3661 \begin_layout Standard
3671 \begin_inset LatexCommand index
3672 name "Commands ! U ! \\textbackslash underline"
3681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3684 \begin_layout Standard
3685 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3694 <row topline="true" bottomline="true">
3695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3698 \begin_layout Standard
3705 \begin_layout Standard
3720 \begin_layout Standard
3734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3737 \begin_layout Standard
3738 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3754 \begin_layout Standard
3755 In the last example it doesn't matter if first
3770 \begin_layout Standard
3771 To double underline e.\InsetSpace \thinspace{}
3782 \begin_layout Standard
3783 It is possible to place up to 6 lines above or below characters.
3786 \begin_layout Subsection
3788 \begin_inset LatexCommand index
3796 \begin_layout Standard
3797 There are different types of ellipses available.
3801 \begin_layout Standard
3802 In the math toolbar in the submenu of the button
3803 \begin_inset Graphics
3804 filename ../images/math/ldots.png
3814 For listings dots at the baseline are used (
3821 \begin_inset LatexCommand index
3822 name "Commands ! L ! \\textbackslash ldots"
3826 ), while for operations dots are needed that are on the same height as the
3834 \begin_inset LatexCommand index
3835 name "Commands ! C ! \\textbackslash cdots"
3840 When using the command
3847 \begin_inset LatexCommand index
3848 name "Commands ! D ! \\textbackslash dots"
3852 , LaTeX decides on the basis of the next character what type is used.
3855 \begin_layout Standard
3857 \begin_inset Tabular
3858 <lyxtabular version="3" rows="8" columns="2">
3860 <column alignment="center" valignment="top" leftline="true" width="0pt">
3861 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3862 <row topline="true" bottomline="true">
3863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3866 \begin_layout Standard
3872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3875 \begin_layout Standard
3882 <row topline="true">
3883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3886 \begin_layout Standard
3891 \begin_layout Standard
3906 \begin_layout Standard
3920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3923 \begin_layout Standard
3924 \begin_inset Formula $A_{1},\dots,A_{n}$
3933 <row topline="true">
3934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3937 \begin_layout Standard
3942 \begin_layout Standard
3957 \begin_layout Standard
3971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3974 \begin_layout Standard
3975 \begin_inset Formula $A_{1}+\dots+A_{n}$
3984 <row topline="true">
3985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3988 \begin_layout Standard
3993 \begin_layout Standard
4008 \begin_layout Standard
4022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4025 \begin_layout Standard
4026 \begin_inset Formula $A_{1},\ldots,A_{n}$
4035 <row topline="true" bottomline="true">
4036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4039 \begin_layout Standard
4044 \begin_layout Standard
4059 \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 $A_{1}+\cdots+A_{n}$
4086 <row topline="true">
4087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4090 \begin_layout Standard
4098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4101 \begin_layout Standard
4102 \begin_inset Formula $\vdots$
4111 <row topline="true" bottomline="true">
4112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4115 \begin_layout Standard
4123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4126 \begin_layout Standard
4127 \begin_inset Formula $\ddots$
4136 <row topline="true" bottomline="true">
4137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4140 \begin_layout Standard
4141 3×3\InsetSpace \thinspace{}
4142 matrix with the different dots
4147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4150 \begin_layout Standard
4151 \begin_inset Formula $\begin{array}{ccc}
4152 A_{11} & \cdots & A_{1m}\\
4153 \vdots & \ddots & \vdots\\
4154 A_{n1} & \cdots & A_{nm}\end{array}$
4170 \begin_layout Standard
4171 The ellipses available in menu
4173 Insert\SpecialChar \menuseparator
4174 Special\InsetSpace ~
4186 \begin_layout Standard
4187 \begin_inset VSpace medskip
4190 Specially for matrices there are ellipses that span over several columns.
4191 They are created with the command
4198 \begin_inset LatexCommand index
4199 name "Commands ! H ! \\textbackslash hdotsfor"
4203 , that has the following scheme:
4206 \begin_layout Standard
4211 hdotsfor[distance]{number of columns}
4214 \begin_layout Standard
4215 The number of columns specifies how many columns should be spanned.
4216 Distance is a factor for the distance between the dots.
4219 \begin_layout Standard
4220 In the following matrix the command
4226 was inserted in the first box of the second line, to get an ellipsis with
4227 a dot distance twice as long as with the command
4234 \begin_inset Formula \[
4235 \left(\begin{array}{cccc}
4238 q & w & e & r\end{array}\right)\]
4242 Note that the matrix fields that should be spanned must be empty, otherwise
4243 you get LaTeX-errors.
4246 \begin_layout Standard
4247 \begin_inset VSpace bigskip
4250 Furthermore you can fill with the command
4257 \begin_inset LatexCommand index
4258 name "Commands ! D ! \\textbackslash dotfill"
4262 the rest of a line with dots.
4263 The effect of these commands is the same like with
4270 \begin_inset LatexCommand ref
4271 reference "sub:Variable-Space"
4278 \begin_layout Standard
4279 For example the command
4287 \begin_layout Standard
4301 \begin_layout Standard
4302 \begin_inset Formula $A\dotfill B$
4308 \begin_layout Standard
4315 there is for a line the command
4322 \begin_inset LatexCommand index
4323 name "Commands ! H ! \\textbackslash hrulefill"
4330 \begin_layout Standard
4331 \begin_inset Formula $A\hrulefill B$
4337 \begin_layout Standard
4338 To use the commands for text, they have to be inserted in TeX-mode.
4341 \begin_layout Section
4343 \begin_inset LatexCommand label
4349 \begin_inset LatexCommand index
4357 \begin_layout Standard
4358 Matrices can be inserted via the math toolbar button
4359 \begin_inset Graphics
4360 filename ../images/dialog-show_mathmatrix.png
4367 Insert\SpecialChar \menuseparator
4368 Math\SpecialChar \menuseparator
4372 You will be asked for the number of matrix columns and rows, and the alignment.
4373 The vertical alignment is hereby only of importance for matrices in inline
4377 \begin_layout Standard
4378 The first matrix is top
4379 \begin_inset Formula $\begin{array}[t]{cccc}
4382 C & F & I & L\end{array}$
4386 \begin_inset Formula $\begin{array}{cccc}
4389 C & F & I & L\end{array}$
4392 , and the third bottom
4393 \begin_inset Formula $\begin{array}[b]{cccc}
4396 C & F & I & L\end{array}$
4402 \begin_layout Standard
4403 The horizontal alignment specifies how the column entries should be aligned.
4404 It is set by entering a letter for every column.
4409 denotes left aligned,
4418 To create for example a 4
4423 matrix where the first column is left aligned, the second and third are
4424 centered, and the last one is right aligned, one enters for the horizontal
4430 Normally are in a matrix all columns centered, therefore the default is
4431 for every column is a
4439 \begin_layout Standard
4451 \begin_layout Standard
4452 Horizontal alignment:
4455 \begin_layout Standard
4461 \begin_inset Formula $\begin{array}{lll}
4464 C & F & 10000\end{array}$
4472 \begin_inset Formula $\begin{array}{ccc}
4475 C & F & 10000\end{array}$
4483 \begin_inset Formula $\begin{array}{rrr}
4486 C & F & 10000\end{array}$
4492 \begin_layout Standard
4493 To add or delete rows and columns subsequently, the math toolbar buttons
4495 \begin_inset Graphics
4496 filename ../images/tabular-feature_append-row.png
4502 \begin_inset Graphics
4503 filename ../images/tabular-feature_delete-row.png
4508 , etc.\InsetSpace \thinspace{}
4511 Edit\SpecialChar \menuseparator
4515 New rows can also be created with
4522 \begin_layout Standard
4523 \begin_inset VSpace bigskip
4526 Parentheses around a matrix can can either be created with the commands
4534 \begin_inset LatexCommand index
4535 name "Commands ! L ! \\textbackslash left"
4546 \begin_inset LatexCommand index
4547 name "Commands ! R ! \\textbackslash right"
4557 \begin_inset LatexCommand ref
4558 reference "sub:Automatic-Bracket-Size"
4562 , or by using the following commands:
4563 \begin_inset VSpace medskip
4569 \begin_layout Standard
4573 \begin_inset Tabular
4574 <lyxtabular version="3" rows="4" columns="2">
4576 <column alignment="center" valignment="top" leftline="true" width="0">
4577 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4578 <row topline="true" bottomline="true">
4579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4582 \begin_layout Standard
4588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4591 \begin_layout Standard
4593 \begin_inset Note Note
4596 \begin_layout Standard
4603 is only used as spacer.
4614 <row topline="true">
4615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4618 \begin_layout Standard
4625 \begin_layout Standard
4638 2\InsetSpace \thinspace{}
4644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4647 \begin_layout Standard
4648 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4649 0 & \textrm{-}\mathrm{i}\\
4650 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4659 <row topline="true">
4660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4663 \begin_layout Standard
4670 \begin_layout Standard
4683 2\InsetSpace \thinspace{}
4689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4692 \begin_layout Standard
4693 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4694 0 & \textrm{-}\mathrm{i}\\
4695 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4704 <row topline="true" bottomline="true">
4705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4708 \begin_layout Standard
4715 \begin_layout Standard
4728 2\InsetSpace \thinspace{}
4734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4737 \begin_layout Standard
4738 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4739 0 & \textrm{-}\mathrm{i}\\
4740 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4756 \begin_inset Tabular
4757 <lyxtabular version="3" rows="4" columns="2">
4759 <column alignment="center" valignment="top" leftline="true" width="0">
4760 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4761 <row topline="true" bottomline="true">
4762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4765 \begin_layout Standard
4771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4774 \begin_layout Standard
4781 <row topline="true">
4782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4785 \begin_layout Standard
4792 \begin_layout Standard
4805 2\InsetSpace \thinspace{}
4811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4814 \begin_layout Standard
4815 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4816 0 & \textrm{-}\mathrm{i}\\
4817 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4826 <row topline="true" bottomline="true">
4827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4830 \begin_layout Standard
4837 \begin_layout Standard
4850 2\InsetSpace \thinspace{}
4856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4859 \begin_layout Standard
4860 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4861 0 & \textrm{-}\mathrm{i}\\
4862 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4871 <row topline="true" bottomline="true">
4872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4875 \begin_layout Standard
4882 \begin_layout Standard
4895 2\InsetSpace \thinspace{}
4901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4904 \begin_layout Standard
4905 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4906 0 & \textrm{-}\mathrm{i}\\
4907 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4925 \begin_layout Standard
4926 \begin_inset VSpace medskip
4929 When e.\InsetSpace \thinspace{}
4937 is inserted, a blue box appears between two vertical lines where the matrix
4941 \begin_layout Standard
4942 \begin_inset VSpace bigskip
4945 As all multiline formulas are matrices, the length
4952 \begin_inset LatexCommand index
4953 name "Commands ! A ! \\textbackslash arraycolsep"
4957 that is described in
4958 \begin_inset LatexCommand ref
4959 reference "sub:Column-Separation"
4963 can also be used to change the column separation of matrices.
4966 \begin_layout Standard
4967 To change the row separation, the command
4974 \begin_inset LatexCommand index
4975 name "Commands ! A ! \\textbackslash arraystretch"
4980 It is used as follows:
4983 \begin_layout Standard
4990 arraystretch}{stretch factor}
4991 \begin_inset LatexCommand index
4992 name "Commands ! R ! \\textbackslash renewcommand"
4999 \begin_layout Standard
5006 assigns the stretch factor to the predefined command
5013 To double e.\InsetSpace \thinspace{}
5015 the row separation, use the factor 2.
5016 This is then used for all following matrices.
5017 To go back to the original separation, assign the factor 1 to
5026 \begin_layout Standard
5027 To set matrices into a text line, the command
5034 \begin_inset LatexCommand index
5035 name "Commands ! S ! \\textbackslash smallmatrix"
5040 When it is inserted a blue box with two dashed lines appears.
5041 In this box the matrix is inserted.
5044 \begin_layout Standard
5046 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5047 C & D\end{smallmatrix}\right)$
5053 \begin_layout Section
5054 Brackets and Delimiters
5055 \begin_inset LatexCommand index
5061 \begin_inset LatexCommand index
5069 \begin_layout Subsection
5070 Vertical Brackets and Delimiters
5071 \begin_inset LatexCommand index
5072 name "Brackets ! vertical"
5079 \begin_layout Standard
5083 \begin_inset Tabular
5084 <lyxtabular version="3" rows="9" columns="2">
5086 <column alignment="center" valignment="top" leftline="true" width="0pt">
5087 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5088 <row topline="true" bottomline="true">
5089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5092 \begin_layout Standard
5098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5101 \begin_layout Standard
5108 <row topline="true">
5109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5112 \begin_layout Standard
5118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5121 \begin_layout Standard
5122 \begin_inset Formula $($
5131 <row topline="true">
5132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5135 \begin_layout Standard
5141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5144 \begin_layout Standard
5145 \begin_inset Formula $\{$
5154 <row topline="true">
5155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5158 \begin_layout Standard
5164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5167 \begin_layout Standard
5168 \begin_inset Formula $[$
5177 <row topline="true">
5178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5181 \begin_layout Standard
5189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5192 \begin_layout Standard
5193 \begin_inset Formula $\langle$
5202 <row topline="true">
5203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5206 \begin_layout Standard
5214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5217 \begin_layout Standard
5218 \begin_inset Formula $\lceil$
5227 <row topline="true">
5228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5231 \begin_layout Standard
5239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5242 \begin_layout Standard
5243 \begin_inset Formula $\lfloor$
5252 <row topline="true">
5253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5256 \begin_layout Standard
5262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5265 \begin_layout Standard
5266 \begin_inset Formula $/$
5275 <row topline="true" bottomline="true">
5276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5279 \begin_layout Standard
5285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5288 \begin_layout Standard
5289 \begin_inset Formula $|$
5305 \begin_inset Tabular
5306 <lyxtabular version="3" rows="9" columns="2">
5308 <column alignment="center" valignment="top" leftline="true" width="0pt">
5309 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5310 <row topline="true" bottomline="true">
5311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5314 \begin_layout Standard
5320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5323 \begin_layout Standard
5330 <row topline="true">
5331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5334 \begin_layout Standard
5340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5343 \begin_layout Standard
5344 \begin_inset Formula $)$
5353 <row topline="true">
5354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5357 \begin_layout Standard
5363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5366 \begin_layout Standard
5367 \begin_inset Formula $\}$
5376 <row topline="true">
5377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5380 \begin_layout Standard
5386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5389 \begin_layout Standard
5390 \begin_inset Formula $]$
5399 <row topline="true">
5400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5403 \begin_layout Standard
5411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5414 \begin_layout Standard
5415 \begin_inset Formula $\rangle$
5424 <row topline="true">
5425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5428 \begin_layout Standard
5436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5439 \begin_layout Standard
5440 \begin_inset Formula $\rceil$
5449 <row topline="true">
5450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5453 \begin_layout Standard
5461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5464 \begin_layout Standard
5465 \begin_inset Formula $\rfloor$
5474 <row topline="true">
5475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5478 \begin_layout Standard
5488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5491 \begin_layout Standard
5492 \begin_inset Formula $\backslash$
5501 <row topline="true" bottomline="true">
5502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5505 \begin_layout Standard
5513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5516 \begin_layout Standard
5517 \begin_inset Formula $\|$
5535 \begin_layout Standard
5538 \begin_inset Note Greyedout
5541 \begin_layout Standard
5546 In TeX-mode the command
5553 \begin_inset LatexCommand index
5554 name "Commands ! T ! \\textbackslash textbackslash"
5558 must be used for the backslash, because the command
5566 produces there a line break.
5574 \begin_layout Standard
5575 For all characters listed above the size can be adjusted with the commands
5576 described in the following two subsections.
5577 When using these commands, the characters < and > can directly be used
5578 instead of the commands
5593 \begin_layout Subsubsection
5595 \begin_inset LatexCommand label
5596 name "sub:Manual-Bracket-Size"
5601 \begin_inset LatexCommand index
5602 name "Bracket size ! manual"
5609 \begin_layout Standard
5610 The bracket size can be specified manually by the LaTeX-commands
5617 \begin_inset LatexCommand index
5618 name "Commands ! B ! \\textbackslash big"
5647 denotes the smallest and
5653 the largest bracket size.
5656 \begin_layout Standard
5657 These commands are used to emphasize levels of brackets:
5660 \begin_layout Standard
5662 \begin_inset Tabular
5663 <lyxtabular version="3" rows="2" columns="2">
5665 <column alignment="center" valignment="top" width="0pt">
5666 <column alignment="center" valignment="top" width="0pt">
5668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5671 \begin_layout Standard
5672 all brackets in the same size:
5677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5680 \begin_layout Standard
5681 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5694 \begin_layout Standard
5700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5703 \begin_layout Standard
5704 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5718 \begin_inset Note Note
5721 \begin_layout Standard
5728 is only used as spacer.
5736 \begin_layout Standard
5737 For the second formula the command
5747 \begin_layout Standard
5761 \begin_layout Standard
5762 Here is an overview about all bracket sizes:
5765 \begin_layout Standard
5785 \begin_layout Standard
5802 \begin_layout Standard
5815 \begin_layout Standard
5831 \begin_layout Standard
5833 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5839 \begin_layout Standard
5848 -commands there is the variant
5855 \begin_inset LatexCommand index
5856 name "Commands ! B ! \\textbackslash bigm"
5860 that adds a bit more space between the bracket and its content, and the
5874 \begin_inset LatexCommand index
5875 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5879 , that don't add additional space.
5884 at the end of the command
5890 is for a left bracket; for a right bracket this will be replaced by an
5896 A left or right bracket can each be an opening or closing bracket.
5899 \begin_layout Standard
5900 In the following table is a comparison of the variants:
5903 \begin_layout Standard
5905 \begin_inset Tabular
5906 <lyxtabular version="3" rows="5" columns="2">
5908 <column alignment="center" valignment="middle" leftline="true" width="0">
5909 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5910 <row topline="true" bottomline="true">
5911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5914 \begin_layout Standard
5920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5923 \begin_layout Standard
5925 \begin_inset Note Note
5928 \begin_layout Standard
5935 is only used as spacer.
5946 <row topline="true">
5947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5950 \begin_layout Standard
5965 \begin_layout Standard
5983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5986 \begin_layout Standard
5987 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5996 <row topline="true">
5997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6000 \begin_layout Standard
6015 \begin_layout Standard
6033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6036 \begin_layout Standard
6037 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6046 <row topline="true" bottomline="true">
6047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6050 \begin_layout Standard
6065 \begin_layout Standard
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6086 \begin_layout Standard
6087 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6096 <row topline="true" bottomline="true">
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6100 \begin_layout Standard
6112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6115 \begin_layout Standard
6116 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6132 \begin_layout Subsubsection
6133 Automatic Bracket Size
6134 \begin_inset LatexCommand label
6135 name "sub:Automatic-Bracket-Size"
6140 \begin_inset LatexCommand index
6141 name "Bracket size ! automatic"
6148 \begin_layout Standard
6149 Brackets with variable size can be inserted with the commands
6156 \begin_inset LatexCommand index
6157 name "Commands ! L ! \\textbackslash left"
6168 \begin_inset LatexCommand index
6169 name "Commands ! R ! \\textbackslash right"
6173 or via the math toolbar button
6174 \begin_inset Graphics
6175 filename ../images/dialog-show_mathdelimiter.png
6193 the wanted bracket must be inserted.
6194 The bracket size will then automatically be calculated for the output.
6197 \begin_layout Standard
6199 normal bracket: The command
6209 \begin_layout Standard
6219 \begin_inset Formula $\downarrow$
6226 \begin_layout Standard
6238 \begin_inset Formula \[
6246 \begin_layout Standard
6248 multiline bracket: The command
6260 \begin_layout Standard
6270 \begin_inset Formula $\downarrow$
6277 \begin_layout Standard
6291 \begin_inset Formula \[
6292 \ln\left(\frac{A}{C}\right)\]
6299 \begin_layout Standard
6318 This has the advantage that you can see in LyX immediately the real bracket
6319 size and that the matching right bracket will be created too.
6322 for the last example would then be:
6336 \begin_layout Standard
6346 \begin_inset Formula $\downarrow$
6352 \begin_layout Standard
6353 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6354 For example the command
6364 \begin_layout Standard
6374 \begin_inset Formula $\downarrow$
6381 \begin_layout Standard
6397 \begin_inset Formula \[
6398 \left.\frac{A}{B}\right\} \]
6416 will be converted by LyX to brackets in the right size when the document
6417 is reloaded and an omitted bracket will appear as dashed line.
6420 \begin_layout Standard
6421 \begin_inset VSpace bigskip
6424 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6432 \begin_inset LatexCommand index
6433 name "Commands ! M ! \\textbackslash middle"
6437 is additionally available for all brackets and limits.
6438 With this command the height of the following character is adapted to the
6439 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6441 needed for physical vectors:
6442 \begin_inset Formula \[
6443 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6447 For physical vectors there is a special LaTeX-package, described in
6448 \begin_inset LatexCommand ref
6449 reference "sub:Physical-Vectors"
6456 \begin_layout Subsection
6458 \begin_inset LatexCommand index
6459 name "Brackets ! horizontal"
6466 \begin_layout Standard
6468 \begin_inset Tabular
6469 <lyxtabular version="3" rows="4" columns="2">
6471 <column alignment="center" valignment="top" leftline="true" width="0pt">
6472 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6473 <row topline="true" bottomline="true">
6474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6477 \begin_layout Standard
6479 \begin_inset Note Note
6482 \begin_layout Standard
6489 is only used as spacer.
6499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6502 \begin_layout Standard
6509 <row topline="true">
6510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6513 \begin_layout Standard
6517 \begin_layout Standard
6532 \begin_layout Standard
6545 \begin_layout Standard
6558 \begin_layout Standard
6571 \begin_layout Standard
6579 \begin_inset LatexCommand index
6580 name "Commands ! O ! \\textbackslash overbrace"
6589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6592 \begin_layout Standard
6593 \begin_inset Formula $\overbrace{A+B}^{3}$
6602 <row topline="true" bottomline="true">
6603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6606 \begin_layout Standard
6610 \begin_layout Standard
6625 \begin_layout Standard
6638 \begin_layout Standard
6651 \begin_layout Standard
6659 \begin_inset LatexCommand index
6660 name "Commands ! U ! \\textbackslash underbrace"
6669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6672 \begin_layout Standard
6673 \begin_inset Formula $\underbrace{A+B}_{5}$
6682 <row topline="true" bottomline="true">
6683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6686 \begin_layout Standard
6695 \begin_layout Standard
6708 \begin_layout Standard
6721 \begin_layout Standard
6734 \begin_layout Standard
6747 \begin_layout Standard
6760 \begin_layout Standard
6774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6777 \begin_layout Standard
6778 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6794 \begin_layout Standard
6795 In the last example it doesn't matter if
6807 is inserted at first.
6810 \begin_layout Standard
6811 \begin_inset VSpace bigskip
6814 When brackets are needed that overlap each other, multiline formulas, as
6816 \begin_inset LatexCommand ref
6817 reference "sec:Multiline-Formulas"
6822 \begin_inset Formula \begin{eqnarray*}
6823 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6824 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6828 In the first row the formula is inserted together with the first brace.
6829 It is hereby important that the space command
6833 \begin_layout Standard
6834 Space commands are explained in
6835 \begin_inset LatexCommand ref
6836 reference "sub:Predefined-Space"
6851 is inserted before the first
6852 \begin_inset Formula $d$
6855 , because the brace that ends behind the
6856 \begin_inset Formula $q$
6859 prevents that the following
6860 \begin_inset Quotes eld
6864 \begin_inset Quotes erd
6867 is surrounded by space.
6871 \begin_layout Standard
6872 because a bracket is not handled as character, see
6873 \begin_inset LatexCommand ref
6874 reference "sub:Binary-Operators"
6883 In the second row the second brace is inserted.
6884 As it should begin before the
6885 \begin_inset Formula $b$
6900 \begin_layout Standard
6908 \begin_inset LatexCommand ref
6909 reference "sub:Placeholders"
6918 This space is needed because the
6919 \begin_inset Quotes eld
6923 \begin_inset Quotes erd
6926 is also surrounded by space in the formula.
6927 The brace is placed under the command
6936 \begin_layout Standard
6937 It gets more complicated when brackets overlap each other, like in the following
6942 \begin_layout Standard
6954 \begin_inset Formula \begin{eqnarray*}
6955 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6956 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6964 \begin_layout Standard
6975 The first formula row is the same as the second row of the previous example,
6976 with the difference that the brace is above.
6977 The second row contains the formula together with the second brace.
6978 To avoid that there is space between the upper brace in the first row and
6979 the formula, the row spacing need to be reduced.
6980 This is not easily possible due to a bug in LyX
6984 \begin_layout Standard
6988 \begin_layout Standard
6992 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
7001 \begin_layout Standard
7014 As solution for the problem, the global formula row separation
7021 \begin_inset LatexCommand index
7022 name "Commands ! J ! \\textbackslash jot"
7026 must be changed to -6\InsetSpace \thinspace{}
7027 pt before the formula with the command
7042 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
7045 More about the row separation in formulas is explained in
7046 \begin_inset LatexCommand ref
7047 reference "sub:Line-Separation"
7054 \begin_layout Section
7056 \begin_inset LatexCommand index
7064 \begin_layout Standard
7065 Arrows can be inserted via the math toolbar button
7066 \begin_inset Graphics
7067 filename ../images/math/leftarrow.png
7072 or the commands listed in the following subsections.
7075 \begin_layout Subsection
7077 \begin_inset LatexCommand index
7078 name "Arrows ! horizontal"
7085 \begin_layout Standard
7089 \begin_inset Tabular
7090 <lyxtabular version="3" rows="8" columns="2">
7092 <column alignment="center" valignment="top" leftline="true" width="0pt">
7093 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7094 <row topline="true" bottomline="true">
7095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7098 \begin_layout Standard
7104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7107 \begin_layout Standard
7114 <row topline="true">
7115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7118 \begin_layout Standard
7126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7129 \begin_layout Standard
7130 \begin_inset Formula $\gets$
7139 <row topline="true">
7140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7143 \begin_layout Standard
7151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7154 \begin_layout Standard
7155 \begin_inset Formula $\Leftarrow$
7164 <row topline="true" bottomline="true">
7165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7168 \begin_layout Standard
7176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7179 \begin_layout Standard
7180 \begin_inset Formula $\longleftarrow$
7189 <row bottomline="true">
7190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7193 \begin_layout Standard
7201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7204 \begin_layout Standard
7205 \begin_inset Formula $\Longleftarrow$
7214 <row bottomline="true">
7215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7218 \begin_layout Standard
7226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7229 \begin_layout Standard
7230 \begin_inset Formula $\leftharpoonup$
7239 <row bottomline="true">
7240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7243 \begin_layout Standard
7251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7254 \begin_layout Standard
7255 \begin_inset Formula $\leftharpoondown$
7264 <row bottomline="true">
7265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7268 \begin_layout Standard
7276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7279 \begin_layout Standard
7280 \begin_inset Formula $\hookleftarrow$
7296 \begin_inset Tabular
7297 <lyxtabular version="3" rows="8" columns="2">
7299 <column alignment="center" valignment="top" leftline="true" width="0pt">
7300 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7301 <row topline="true" bottomline="true">
7302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7305 \begin_layout Standard
7311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7314 \begin_layout Standard
7321 <row topline="true">
7322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7325 \begin_layout Standard
7333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7336 \begin_layout Standard
7337 \begin_inset Formula $\to$
7346 <row topline="true">
7347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7350 \begin_layout Standard
7358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7361 \begin_layout Standard
7362 \begin_inset Formula $\Rightarrow$
7371 <row topline="true">
7372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7375 \begin_layout Standard
7383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7386 \begin_layout Standard
7387 \begin_inset Formula $\longrightarrow$
7396 <row topline="true">
7397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7400 \begin_layout Standard
7408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7411 \begin_layout Standard
7412 \begin_inset Formula $\Longrightarrow$
7421 <row topline="true">
7422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7425 \begin_layout Standard
7433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7436 \begin_layout Standard
7437 \begin_inset Formula $\rightharpoonup$
7446 <row topline="true" bottomline="true">
7447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7450 \begin_layout Standard
7458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7461 \begin_layout Standard
7462 \begin_inset Formula $\rightharpoondown$
7471 <row bottomline="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 $\hookrightarrow$
7505 \begin_layout Standard
7509 \begin_inset Tabular
7510 <lyxtabular version="3" rows="6" columns="2">
7512 <column alignment="center" valignment="top" leftline="true" width="0pt">
7513 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7514 <row topline="true" bottomline="true">
7515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7518 \begin_layout Standard
7524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7527 \begin_layout Standard
7534 <row topline="true">
7535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7538 \begin_layout Standard
7546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7549 \begin_layout Standard
7550 \begin_inset Formula $\leftrightarrow$
7559 <row topline="true">
7560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7563 \begin_layout Standard
7571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7574 \begin_layout Standard
7575 \begin_inset Formula $\Leftrightarrow$
7584 <row topline="true">
7585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7588 \begin_layout Standard
7596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7599 \begin_layout Standard
7600 \begin_inset Formula $\longleftrightarrow$
7609 <row topline="true">
7610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7613 \begin_layout Standard
7621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7624 \begin_layout Standard
7625 \begin_inset Formula $\Longleftrightarrow$
7634 <row topline="true" bottomline="true">
7635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7638 \begin_layout Standard
7646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7649 \begin_layout Standard
7650 \begin_inset Formula $\rightleftharpoons$
7667 \begin_layout Standard
7679 \begin_inset Tabular
7680 <lyxtabular version="3" rows="5" columns="2">
7682 <column alignment="center" valignment="top" leftline="true" width="0pt">
7683 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7684 <row topline="true" bottomline="true">
7685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7688 \begin_layout Standard
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7697 \begin_layout Standard
7704 <row topline="true">
7705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7708 \begin_layout Standard
7716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7719 \begin_layout Standard
7720 \begin_inset Formula $\mapsto$
7729 <row topline="true">
7730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7733 \begin_layout Standard
7741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7744 \begin_layout Standard
7745 \begin_inset Formula $\longmapsto$
7754 <row topline="true">
7755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7758 \begin_layout Standard
7766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7769 \begin_layout Standard
7770 \begin_inset Formula $\leadsto$
7779 <row topline="true" bottomline="true">
7780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7783 \begin_layout Standard
7791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7794 \begin_layout Standard
7795 \begin_inset Formula $\dasharrow$
7813 \begin_layout Standard
7814 \begin_inset VSpace medskip
7817 Arrows used as accent like e.\InsetSpace \thinspace{}
7819 vector arrows are listed in
7820 \begin_inset LatexCommand ref
7821 reference "sec:Accents"
7828 \begin_layout Standard
7829 \begin_inset VSpace bigskip
7832 Furthermore there are the labeled arrows
7833 \begin_inset LatexCommand index
7834 name "Arrows ! labeled"
7845 \begin_inset LatexCommand index
7846 name "Commands ! X ! \\textbackslash xleftarrow"
7857 \begin_inset LatexCommand index
7858 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7863 When inserting one of these commands in a formula, an arrow with two blue
7864 boxes appear where the label can be inserted.
7865 The length of the arrow adapts to the label width.
7868 \begin_layout Standard
7870 \begin_inset Tabular
7871 <lyxtabular version="3" rows="3" columns="2">
7873 <column alignment="center" valignment="top" leftline="true" width="0pt">
7874 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7875 <row topline="true" bottomline="true">
7876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7879 \begin_layout Standard
7885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7888 \begin_layout Standard
7890 \begin_inset Note Note
7893 \begin_layout Standard
7900 is only used as spacer.
7911 <row topline="true">
7912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7915 \begin_layout Standard
7922 \begin_layout Standard
7932 \begin_inset Formula $\downarrow$
7936 \begin_inset Formula $\to$
7944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7947 \begin_layout Standard
7948 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7957 <row topline="true" bottomline="true">
7958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7961 \begin_layout Standard
7968 \begin_layout Standard
7978 \begin_inset Formula $\downarrow$
7982 \begin_inset Formula $\to$
7990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7993 \begin_layout Standard
7994 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8010 \begin_layout Subsection
8011 Vertical and diagonal Arrows
8012 \begin_inset LatexCommand index
8013 name "Arrows ! diagonal"
8018 \begin_inset LatexCommand index
8019 name "Arrows ! vertical"
8026 \begin_layout Standard
8030 \begin_inset Tabular
8031 <lyxtabular version="3" rows="7" columns="2">
8033 <column alignment="center" valignment="top" leftline="true" width="0pt">
8034 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8035 <row topline="true" bottomline="true">
8036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8039 \begin_layout Standard
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Standard
8055 <row topline="true">
8056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8059 \begin_layout Standard
8067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8070 \begin_layout Standard
8071 \begin_inset Formula $\uparrow$
8080 <row topline="true">
8081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8084 \begin_layout Standard
8092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8095 \begin_layout Standard
8096 \begin_inset Formula $\Uparrow$
8105 <row topline="true">
8106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8109 \begin_layout Standard
8117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8120 \begin_layout Standard
8121 \begin_inset Formula $\updownarrow$
8130 <row topline="true">
8131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8134 \begin_layout Standard
8142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8145 \begin_layout Standard
8146 \begin_inset Formula $\Updownarrow$
8155 <row topline="true" bottomline="true">
8156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8159 \begin_layout Standard
8167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8170 \begin_layout Standard
8171 \begin_inset Formula $\Downarrow$
8180 <row bottomline="true">
8181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8184 \begin_layout Standard
8192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8195 \begin_layout Standard
8196 \begin_inset Formula $\downarrow$
8212 \begin_inset Tabular
8213 <lyxtabular version="3" rows="5" columns="2">
8215 <column alignment="center" valignment="top" leftline="true" width="0pt">
8216 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8217 <row topline="true" bottomline="true">
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8221 \begin_layout Standard
8227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8230 \begin_layout Standard
8237 <row topline="true">
8238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8241 \begin_layout Standard
8249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8252 \begin_layout Standard
8253 \begin_inset Formula $\nearrow$
8262 <row topline="true">
8263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8266 \begin_layout Standard
8274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8277 \begin_layout Standard
8278 \begin_inset Formula $\searrow$
8287 <row topline="true" bottomline="true">
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8291 \begin_layout Standard
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8302 \begin_layout Standard
8303 \begin_inset Formula $\swarrow$
8312 <row bottomline="true">
8313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8316 \begin_layout Standard
8324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8327 \begin_layout Standard
8328 \begin_inset Formula $\nwarrow$
8346 \begin_layout Standard
8347 \begin_inset VSpace medskip
8350 Vertical arrows can be used also as delimiter together with the commands
8352 \begin_inset LatexCommand ref
8353 reference "sub:Manual-Bracket-Size"
8358 \begin_inset LatexCommand ref
8359 reference "sub:Automatic-Bracket-Size"
8366 \begin_layout Standard
8372 \begin_layout Section
8374 \begin_inset LatexCommand label
8380 \begin_inset LatexCommand index
8388 \begin_layout Standard
8389 Accents can be inserted via the math toolbar button
8390 \begin_inset Graphics
8391 filename ../images/math/hat.png
8396 or the commands listed in the following subsections.
8399 \begin_layout Subsection
8400 Accents for one Character
8404 \begin_layout Standard
8417 \begin_layout Standard
8419 \begin_inset LatexCommand ref
8420 reference "sub:Accents-in-Text"
8433 \begin_layout Standard
8441 \begin_inset Note Note
8444 \begin_layout Standard
8447 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8450 \begin_layout Standard
8453 texorpdfstring is in section
8454 \begin_inset LatexCommand ref
8455 reference "sub:Formulas-in-Section"
8465 \begin_inset LatexCommand label
8466 name "sub:Accents-for-one"
8471 \begin_inset LatexCommand index
8472 name "Accents ! for one character"
8479 \begin_layout Standard
8483 \begin_inset Tabular
8484 <lyxtabular version="3" rows="8" columns="2">
8486 <column alignment="center" valignment="top" leftline="true" width="0pt">
8487 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8488 <row topline="true" bottomline="true">
8489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8492 \begin_layout Standard
8498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8501 \begin_layout Standard
8503 \begin_inset Note Note
8506 \begin_layout Standard
8513 is only used as spacer.
8524 <row topline="true" bottomline="true">
8525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8528 \begin_layout Standard
8535 \begin_layout Standard
8549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8552 \begin_layout Standard
8553 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8562 <row bottomline="true">
8563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8566 \begin_layout Standard
8573 \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 $\raisebox{5mm}{}\ddot{A}$
8600 <row bottomline="true">
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8604 \begin_layout Standard
8611 \begin_layout Standard
8625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8628 \begin_layout Standard
8629 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8638 <row bottomline="true">
8639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8642 \begin_layout Standard
8650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8653 \begin_layout Standard
8654 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8663 <row bottomline="true">
8664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8667 \begin_layout Standard
8674 \begin_layout Standard
8684 \begin_inset LatexCommand index
8694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8697 \begin_layout Standard
8698 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8707 <row bottomline="true">
8708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8711 \begin_layout Standard
8718 \begin_layout Standard
8732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8735 \begin_layout Standard
8736 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8745 <row bottomline="true">
8746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8749 \begin_layout Standard
8756 \begin_layout Standard
8770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8773 \begin_layout Standard
8774 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8790 \begin_inset Tabular
8791 <lyxtabular version="3" rows="7" columns="2">
8793 <column alignment="center" valignment="top" leftline="true" width="0pt">
8794 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8795 <row topline="true" bottomline="true">
8796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8799 \begin_layout Standard
8805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8808 \begin_layout Standard
8815 <row topline="true" bottomline="true">
8816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8819 \begin_layout Standard
8826 \begin_layout Standard
8840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8843 \begin_layout Standard
8844 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8853 <row bottomline="true">
8854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8857 \begin_layout Standard
8864 \begin_layout Standard
8878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8881 \begin_layout Standard
8882 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8891 <row bottomline="true">
8892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8895 \begin_layout Standard
8902 \begin_layout Standard
8916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8919 \begin_layout Standard
8920 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8929 <row bottomline="true">
8930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8933 \begin_layout Standard
8940 \begin_layout Standard
8954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8957 \begin_layout Standard
8958 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8967 <row bottomline="true">
8968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8971 \begin_layout Standard
8978 \begin_layout Standard
8992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8995 \begin_layout Standard
8996 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9005 <row bottomline="true">
9006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9009 \begin_layout Standard
9016 \begin_layout Standard
9030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9033 \begin_layout Standard
9034 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9052 \begin_layout Standard
9053 \begin_inset VSpace bigskip
9057 \begin_inset LatexCommand index
9062 in formulas, a quotation mark is inserted before the vowel.
9063 These two characters are then treated by LaTeX as
9067 character when the formula part with the umlaut is marked as German.
9075 \begin_inset Quotes eld
9079 \begin_inset Quotes erd
9082 umlauts are created as demonstrated in the following example:
9085 \begin_layout Standard
9086 \begin_inset VSpace -2mm
9092 \begin_layout Standard
9094 \begin_inset Tabular
9095 <lyxtabular version="3" rows="3" columns="2">
9097 <column alignment="center" valignment="top" leftline="true" width="0">
9098 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9099 <row topline="true" bottomline="true">
9100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9103 \begin_layout Standard
9109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9112 \begin_layout Standard
9114 \begin_inset Note Note
9117 \begin_layout Standard
9124 is only used as spacer.
9135 <row topline="true">
9136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9139 \begin_layout Standard
9142 \begin_inset Quotes grd
9150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9153 \begin_layout Standard
9156 \begin_inset Formula $"i$
9165 <row topline="true" bottomline="true">
9166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9169 \begin_layout Standard
9176 \begin_layout Standard
9190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9193 \begin_layout Standard
9194 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9210 \begin_layout Standard
9211 Another advantage to
9217 is that umlauts can directly be converted to mathematical text because
9218 the accent commands above are
9224 in mathematical text
9227 To convert an accented character to mathematical text, only the character
9228 under the accent may be converted.
9229 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9234 \begin_layout Standard
9235 In mathematical text, umlauts and other accented characters can directly
9239 \begin_layout Subsection
9240 Accents for Operators
9241 \begin_inset LatexCommand index
9242 name "Accents ! for operators"
9249 \begin_layout Standard
9257 \begin_inset LatexCommand index
9258 name "Commands ! O ! \\textbackslash overset"
9269 \begin_inset LatexCommand index
9270 name "Commands ! U ! \\textbackslash underset"
9274 characters can be placed above or below an operator, respectively, to accent
9283 \begin_inset LatexCommand index
9284 name "Commands ! S ! \\textbackslash sideset"
9288 characters can be set before and behind an operator.
9289 The command scheme is:
9292 \begin_layout Standard
9308 \begin_layout Standard
9315 must always be before the operator that should be accented.
9316 You can accent with several characters and even with other operators and
9324 for example only characters behind an operator, write nothing between the
9325 first braces but don't omit the braces.
9328 \begin_layout Standard
9329 For example the command
9334 \begin_inset Formula $\to$
9344 \begin_inset Formula $\to$
9353 \begin_layout Standard
9369 \begin_inset Formula \[
9370 \sideset{}{'}\sum_{k=1}^{n}\]
9377 \begin_layout Standard
9386 \begin_layout Standard
9401 \begin_layout Standard
9413 \begin_inset Formula $\uparrow$
9421 \begin_inset Formula \[
9422 \overset{a}{\maltese}\]
9426 As seen in the last example, with
9438 also symbols and characters can be accented; with
9444 this is not possible.
9447 \begin_layout Subsection
9448 Accents for several Characters
9449 \begin_inset LatexCommand label
9450 name "sub:Accents-for-several"
9455 \begin_inset LatexCommand index
9456 name "Accents ! for several characters"
9463 \begin_layout Standard
9467 \begin_inset Tabular
9468 <lyxtabular version="3" rows="5" columns="2">
9470 <column alignment="center" valignment="top" leftline="true" width="0pt">
9471 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9472 <row topline="true" bottomline="true">
9473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9476 \begin_layout Standard
9482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9485 \begin_layout Standard
9487 \begin_inset Note Note
9490 \begin_layout Standard
9497 is only used as spacer.
9508 <row topline="true" bottomline="true">
9509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9512 \begin_layout Standard
9519 \begin_layout Standard
9533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9536 \begin_layout Standard
9537 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9546 <row bottomline="true">
9547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9550 \begin_layout Standard
9557 \begin_layout Standard
9571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9574 \begin_layout Standard
9575 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9584 <row bottomline="true">
9585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9588 \begin_layout Standard
9595 \begin_layout Standard
9609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9612 \begin_layout Standard
9613 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9622 <row bottomline="true">
9623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9626 \begin_layout Standard
9633 \begin_layout Standard
9647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9650 \begin_layout Standard
9651 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9667 \begin_inset Tabular
9668 <lyxtabular version="3" rows="5" columns="2">
9670 <column alignment="center" valignment="top" leftline="true" width="0pt">
9671 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9672 <row topline="true" bottomline="true">
9673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9676 \begin_layout Standard
9682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9685 \begin_layout Standard
9692 <row topline="true" bottomline="true">
9693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9696 \begin_layout Standard
9703 \begin_layout Standard
9717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9720 \begin_layout Standard
9721 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9730 <row bottomline="true">
9731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9734 \begin_layout Standard
9741 \begin_layout Standard
9755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9758 \begin_layout Standard
9759 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9768 <row bottomline="true">
9769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9772 \begin_layout Standard
9779 \begin_layout Standard
9793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9796 \begin_layout Standard
9797 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9806 <row bottomline="true">
9807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9810 \begin_layout Standard
9817 \begin_layout Standard
9831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9834 \begin_layout Standard
9835 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9853 \begin_layout Standard
9854 \begin_inset VSpace medskip
9857 With these commands as many characters as you like can be accented.
9870 will only be set in the output with a length of three characters, as shown
9871 in the following example:
9872 \begin_inset Formula \[
9873 \widetilde{A+B=C-D}\]
9880 \begin_layout Standard
9888 \begin_inset LatexCommand index
9889 name "Commands ! O ! \\textbackslash overset"
9900 \begin_inset LatexCommand index
9901 name "Commands ! U ! \\textbackslash underset"
9905 described in the previous subsection it is also possible to accent several
9915 \begin_layout Standard
9925 \begin_inset Formula $\downarrow$
9931 \begin_inset Formula \[
9932 \underset{***}{A=B}\]
9939 \begin_layout Section
9941 \begin_inset LatexCommand label
9947 \begin_inset LatexCommand index
9948 name "Space ! horizontal"
9955 \begin_layout Subsection
9957 \begin_inset LatexCommand label
9958 name "sub:Predefined-Space"
9963 \begin_inset LatexCommand index
9964 name "Space ! horizontal ! predefined"
9971 \begin_layout Standard
9972 Sometimes it is necessary to insert horizontal space to a formula.
9973 This is done by inserting a protected space (shortcut
9979 \begin_inset Quotes eld
9989 \begin_layout Standard
10002 \begin_inset Quotes erd
10005 appears and by pressing
10009 several times one can select one of eight different space sizes.
10010 The spaces can also be inserted using the math toolbar button
10011 \begin_inset Graphics
10012 filename ../images/math/space.png
10017 or special commands.
10018 Independent from the inserted command, one can select the size again by
10026 \begin_layout Standard
10029 \begin_inset VSpace -5mm
10033 \begin_inset Tabular
10034 <lyxtabular version="3" rows="3" columns="7">
10036 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10037 <column alignment="center" valignment="top" leftline="true" width="0">
10038 <column alignment="center" valignment="top" leftline="true" width="0">
10039 <column alignment="center" valignment="top" leftline="true" width="0">
10040 <column alignment="center" valignment="top" leftline="true" width="0">
10041 <column alignment="center" valignment="top" leftline="true" width="0">
10042 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10043 <row topline="true">
10044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10047 \begin_layout Standard
10053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10056 \begin_layout Standard
10064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10067 \begin_layout Standard
10075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10078 \begin_layout Standard
10086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10089 \begin_layout Standard
10097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10100 \begin_layout Standard
10108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10111 \begin_layout Standard
10120 <row topline="true">
10121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10124 \begin_layout Standard
10129 keystrokes after inserting the protected space
10134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10137 \begin_layout Standard
10143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10146 \begin_layout Standard
10152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10155 \begin_layout Standard
10161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10164 \begin_layout Standard
10170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10173 \begin_layout Standard
10179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10182 \begin_layout Standard
10189 <row topline="true" bottomline="true">
10190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10193 \begin_layout Standard
10199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10202 \begin_layout Standard
10203 \begin_inset Formula $A\, B$
10211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10214 \begin_layout Standard
10215 \begin_inset Formula $A\: B$
10223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10226 \begin_layout Standard
10227 \begin_inset Formula $A\; B$
10235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10238 \begin_layout Standard
10239 \begin_inset Formula $A\quad B$
10247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10250 \begin_layout Standard
10251 \begin_inset Formula $A\qquad B$
10259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10262 \begin_layout Standard
10263 \begin_inset Formula $A\! B$
10279 \begin_layout Standard
10280 The last size seem to produce no space.
10281 It is displayed red in LyX contrary to the other sizes, because it is a
10283 There are two more negative spaces:
10286 \begin_layout Standard
10288 \begin_inset Tabular
10289 <lyxtabular version="3" rows="3" columns="3">
10291 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10292 <column alignment="center" valignment="top" leftline="true" width="0pt">
10293 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10294 <row topline="true" bottomline="true">
10295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10298 \begin_layout Standard
10304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10307 \begin_layout Standard
10315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10318 \begin_layout Standard
10327 <row bottomline="true">
10328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10331 \begin_layout Standard
10336 keystrokes after inserting the protected space
10341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10344 \begin_layout Standard
10350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10353 \begin_layout Standard
10360 <row bottomline="true">
10361 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10364 \begin_layout Standard
10370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10373 \begin_layout Standard
10374 \begin_inset Formula $A\negmedspace B$
10382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10385 \begin_layout Standard
10386 \begin_inset Formula $A\negthickspace B$
10402 \begin_layout Standard
10403 Negative spaces can lead to characters overlapping each other.
10404 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10406 useful for summation
10410 \begin_layout Standard
10412 \begin_inset Tabular
10413 <lyxtabular version="3" rows="3" columns="2">
10415 <column alignment="center" valignment="top" leftline="true" width="0">
10416 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10417 <row topline="true" bottomline="true">
10418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10421 \begin_layout Standard
10427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10430 \begin_layout Standard
10432 \begin_inset Note Note
10435 \begin_layout Standard
10442 is only used as spacer.
10453 <row topline="true">
10454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10457 \begin_layout Standard
10466 \begin_layout Standard
10480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10483 \begin_layout Standard
10484 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10493 <row topline="true" bottomline="true">
10494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10497 \begin_layout Standard
10508 \begin_layout Standard
10522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10525 \begin_layout Standard
10526 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10542 \begin_layout Standard
10543 Relations like for example equal signs, are always surrounded by space.
10544 To suppress this, the equal sign is placed into a TeX-brace.
10545 The following example demonstrates this:
10548 \begin_layout Standard
10550 \begin_inset Tabular
10551 <lyxtabular version="3" rows="2" columns="2">
10553 <column alignment="center" valignment="top" width="0pt">
10554 <column alignment="center" valignment="top" width="0pt">
10556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10559 \begin_layout Standard
10565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10568 \begin_layout Standard
10569 \begin_inset Formula $A=B$
10579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10582 \begin_layout Standard
10583 \begin_inset Note Note
10586 \begin_layout Standard
10593 is only used as spacer.
10599 \begin_inset Formula $\raisebox{5mm}{}$
10602 equation without space
10607 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10610 \begin_layout Standard
10611 \begin_inset Formula $A{=}B$
10627 \begin_layout Standard
10629 The command for the last formula is:
10634 \begin_inset Formula $\to$
10640 \begin_layout Standard
10641 \begin_inset VSpace bigskip
10644 Spaces are needed for physical units, because the space between the value
10645 and the unit is the smallest one and not a normal space.
10646 For units in text, the smallest space is inserted via the menu
10648 Insert\SpecialChar \menuseparator
10649 Formatting\SpecialChar \menuseparator
10660 \begin_layout Standard
10661 An example to visualize the difference:
10664 \begin_layout Standard
10665 \begin_inset Tabular
10666 <lyxtabular version="3" rows="2" columns="2">
10668 <column alignment="left" valignment="top" width="0">
10669 <column alignment="left" valignment="top" width="0">
10671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10674 \begin_layout Standard
10676 \begin_inset Formula $\cdot$
10684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10687 \begin_layout Standard
10688 space between value and unit
10695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10698 \begin_layout Standard
10699 24\InsetSpace \thinspace{}
10701 \begin_inset Formula $\cdot$
10709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10712 \begin_layout Standard
10713 smallest space between value and unit
10726 \begin_layout Subsection
10731 \begin_layout Standard
10744 \begin_layout Standard
10745 for vertical space in formulas see
10746 \begin_inset LatexCommand ref
10747 reference "sub:Line-Separation"
10760 \begin_layout Standard
10768 \begin_inset Note Note
10771 \begin_layout Standard
10774 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10777 \begin_layout Standard
10780 texorpdfstring is in section
10781 \begin_inset LatexCommand ref
10782 reference "sub:Formulas-in-Section"
10792 \begin_inset LatexCommand label
10793 name "sub:Variable-Space"
10798 \begin_inset LatexCommand index
10799 name "Space ! horizontal ! variable"
10806 \begin_layout Standard
10807 Space with a defined length can be inserted in LyX with the command
10816 \begin_inset LatexCommand index
10817 name "Commands ! H ! \\textbackslash hspace"
10822 For the length all units listed in
10823 \begin_inset LatexCommand ref
10824 reference "tab:Used-units"
10828 are allowed, except of the unit
10829 \begin_inset Quotes eld
10833 \begin_inset Quotes erd
10837 The length may also be negative.
10838 To insert so many space that the formula uses all available space, the
10846 \begin_inset LatexCommand index
10847 name "Commands ! H ! \\textbackslash hfill"
10854 \begin_layout Standard
10855 \begin_inset VSpace -1mm
10861 \begin_layout Standard
10863 \begin_inset Tabular
10864 <lyxtabular version="3" rows="4" columns="2">
10866 <column alignment="center" valignment="top" leftline="true" width="0">
10867 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10868 <row topline="true" bottomline="true">
10869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10872 \begin_layout Standard
10878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10881 \begin_layout Standard
10888 <row topline="true">
10889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10892 \begin_layout Standard
10896 \begin_inset Formula $\to$
10906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10909 \begin_layout Standard
10910 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10919 <row topline="true" bottomline="true">
10920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10923 \begin_layout Standard
10927 \begin_inset Formula $\to$
10937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10940 \begin_layout Standard
10941 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10950 <row topline="true" bottomline="true">
10951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10954 \begin_layout Standard
10961 \begin_layout Standard
10975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10978 \begin_layout Standard
10979 \begin_inset Formula $A=A\hfill B=B$
10995 \begin_layout Standard
10996 In the last example the available space is given by the longest column entry
10998 In an inline formula the space depends on the length of the line in which
11006 Thus, when the line uses the full width, no space will be created.
11013 has only an effect on displayed formulas when the formula style
11018 (Formula styles are explained in
11019 \begin_inset LatexCommand ref
11020 reference "sec:Formula-Styles"
11027 \begin_layout Standard
11040 can also be inserted in TeX-mode to use them for text:
11043 \begin_layout Standard
11044 This is a line with
11048 \begin_layout Standard
11057 2\InsetSpace \thinspace{}
11061 \begin_layout Standard
11062 This is a line with
11067 \begin_layout Standard
11068 In the last example
11074 was inserted via the menu
11076 Insert\SpecialChar \menuseparator
11077 Formatting\SpecialChar \menuseparator
11078 Horizontal\InsetSpace ~
11081 , what is not possible in formulas.
11082 This has the advantage that one can directly see in LyX that this is a
11086 \begin_layout Standard
11087 When the commands are at the begin of a text line but not at the beginning
11088 of a paragraph, they will be ignored by LaTeX.
11089 To avoid that, the command
11102 To get the same with
11108 , a line break and an empty placeholder
11114 \begin_layout Standard
11115 for placeholders see
11116 \begin_inset LatexCommand ref
11117 reference "sub:Placeholders"
11128 is inserted in TeX-mode with the command
11144 \begin_layout Subsection
11145 Space besides inline Formulas
11146 \begin_inset LatexCommand index
11147 name "Space ! besides inline formulas"
11154 \begin_layout Standard
11155 The space that surrounds inline formulas can be adjusted with the length
11161 \begin_inset LatexCommand index
11162 name "Commands ! M ! \\textbackslash mathsurround"
11169 The value of a length is set with the command
11174 \begin_inset LatexCommand index
11175 name "Commands ! S ! \\textbackslash setlength"
11181 that has the following scheme:
11184 \begin_layout Standard
11189 setlength{length name}{value}
11192 \begin_layout Standard
11199 to the value 5\InsetSpace \thinspace{}
11203 \begin_layout Standard
11213 \begin_layout Standard
11214 is inserted in TeX-mode.
11215 5\InsetSpace \thinspace{}
11216 mm space will now be set around all inline formulas:
11220 \begin_layout Standard
11234 \begin_layout Standard
11235 This is a line with an inline formula
11236 \begin_inset Formula $A=B$
11239 with 5\InsetSpace \thinspace{}
11240 mm surrounding space.
11244 \begin_layout Standard
11258 \begin_layout Standard
11259 To return to the predefined value,
11265 is set to the value 0\InsetSpace \thinspace{}
11269 \begin_layout Section
11271 \begin_inset LatexCommand index
11277 \begin_inset LatexCommand index
11278 name "Frames | see {Boxes}"
11285 \begin_layout Standard
11286 Boxes for text are described in chapter
11292 Embedded\InsetSpace ~
11298 \begin_layout Subsection
11300 \begin_inset LatexCommand label
11301 name "sub:Boxes-with-Frame"
11306 \begin_inset LatexCommand index
11307 name "Boxes ! with frame"
11314 \begin_layout Standard
11315 It is possible to frame formulas or parts of it with the commands
11322 \begin_inset LatexCommand index
11323 name "Commands ! F ! \\textbackslash fbox"
11334 \begin_inset LatexCommand index
11335 name "Commands ! B ! \\textbackslash boxed"
11342 \begin_layout Standard
11343 When one of these commands is inserted to a formula, a blue box appears
11344 within a frame to enter formula parts.
11351 an additional formula has to be created by
11359 \begin_layout Standard
11360 Due to a bug in LyX it is not possible to create a new formula with
11368 \begin_layout Standard
11372 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11381 \begin_layout Standard
11393 , because the box content will otherwise be treated as mathematical text.
11400 is used, a new formula is automatically created inside the frame.
11403 \begin_layout Standard
11410 is not suitable to frame displayed formulas, because the formula will always
11411 be set in the size of the text.
11418 is in contrary not suitable to frame inline formulas, because the formula
11419 will always be set in the size of a displayed formula.
11422 \begin_layout Standard
11429 there is the command
11436 \begin_inset LatexCommand index
11437 name "Commands ! F ! \\textbackslash framebox"
11441 where additionally the frame width and the alignment can be specified.
11448 is used in the following scheme:
11451 \begin_layout Standard
11456 framebox[frame width][position]{box content}
11459 \begin_layout Standard
11460 The position can either be
11477 right aligns the formula in the box.
11478 When no position is given, the formula will be centered.
11481 also no position can be given.
11482 In this case the frame width is adjusted to the box content like for
11491 \begin_layout Standard
11498 is inserted, a box appears containing three blue boxes.
11502 \begin_layout Standard
11503 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11508 \begin_layout Standard
11512 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11521 \begin_layout Standard
11533 The first two boxes are surrounded by brackets and denote the two optional
11535 The third box is for formula parts like for
11544 \begin_layout Standard
11546 \begin_inset Note Note
11549 \begin_layout Standard
11550 The table has been set into a minipage to make the footnote appearing.
11551 Otherwise the footnote text would not be displayed.
11557 \begin_inset Box Frameless
11566 height_special "totalheight"
11569 \begin_layout Standard
11571 \begin_inset Tabular
11572 <lyxtabular version="3" rows="5" columns="2">
11574 <column alignment="center" valignment="top" leftline="true" width="0">
11575 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11576 <row topline="true" bottomline="true">
11577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11580 \begin_layout Standard
11585 \begin_layout Standard
11586 Due to a bug in LyX it is not possible to create a new formula with
11594 \begin_layout Standard
11598 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11607 \begin_layout Standard
11624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11627 \begin_layout Standard
11629 \begin_inset Note Note
11632 \begin_layout Standard
11639 is only used as spacer.
11650 <row topline="true">
11651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11654 \begin_layout Standard
11661 \begin_layout Standard
11680 \begin_layout Standard
11694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11697 \begin_layout Standard
11698 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11708 <row topline="true">
11709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11712 \begin_layout Standard
11719 \begin_layout Standard
11734 \begin_layout Standard
11748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11751 \begin_layout Standard
11752 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11761 <row topline="true">
11762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11765 \begin_layout Standard
11772 \begin_layout Standard
11786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11789 \begin_layout Standard
11790 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11799 <row topline="true" bottomline="true">
11800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11803 \begin_layout Standard
11810 \begin_layout Standard
11820 \begin_inset Formula $\to$
11824 \begin_inset Formula $\to$
11837 \begin_layout Standard
11847 \begin_inset Formula $\downarrow$
11855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11858 \begin_layout Standard
11859 \begin_inset Formula $\raisebox{6mm}{}$
11863 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11867 \begin_inset Formula $\raisebox{-4mm}{}$
11888 \begin_layout Standard
11889 The frame thickness can also be adjusted.
11890 To do this the following commands have to be inserted in TeX-mode before
11894 \begin_layout Standard
11904 \begin_inset Quotes eld
11908 \begin_inset Quotes erd
11922 \begin_inset Quotes eld
11926 \begin_inset Quotes erd
11932 \begin_layout Standard
11933 \begin_inset Quotes eld
11937 \begin_inset Quotes erd
11940 specifies the minimal distance between the frame and the first character
11942 An example for this is the following framed formula:
11946 \begin_layout Standard
11958 \begin_inset Formula \[
11963 Before this formula the commands
11966 \begin_layout Standard
11988 \begin_layout Standard
11989 were inserted in TeX-mode.
11990 The given values are used for all following boxes.
11993 \begin_layout Standard
11994 To return to the standard frame size, the command
11997 \begin_layout Standard
12022 \begin_layout Standard
12036 \begin_layout Standard
12037 is inserted in TeX-mode before the next formula.
12040 \begin_layout Subsection
12041 Boxes without Frame
12042 \begin_inset LatexCommand label
12043 name "sub:Boxes-without-Frame"
12048 \begin_inset LatexCommand index
12049 name "Boxes ! without frame"
12056 \begin_layout Standard
12057 For boxes without a frame there are the following box commands:
12064 \begin_inset LatexCommand index
12065 name "Commands ! M ! \\textbackslash mbox"
12076 \begin_inset LatexCommand index
12077 name "Commands ! M ! \\textbackslash makebox"
12088 \begin_inset LatexCommand index
12089 name "Commands ! R ! \\textbackslash raisebox"
12096 \begin_layout Standard
12103 a box can be super- or subscripted.
12104 But in contrary to normal super- and subscripting, the characters in the
12105 box keep their font size.
12112 is used in the following scheme:
12115 \begin_layout Standard
12120 raisebox{height}{box content}
12123 \begin_layout Standard
12124 When the box should contain a formula, an extra formula is needed like for
12134 \begin_layout Standard
12136 \begin_inset Tabular
12137 <lyxtabular version="3" rows="4" columns="2">
12139 <column alignment="center" valignment="top" leftline="true" width="0">
12140 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12141 <row topline="true" bottomline="true">
12142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12145 \begin_layout Standard
12151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12154 \begin_layout Standard
12161 <row topline="true">
12162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12165 \begin_layout Standard
12169 \begin_inset Formula $\to$
12175 \begin_inset Formula $\to$
12183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12186 \begin_layout Standard
12187 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12196 <row topline="true" bottomline="true">
12197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12200 \begin_layout Standard
12204 \begin_inset Formula $\to$
12210 \begin_inset Formula $\to$
12218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12221 \begin_layout Standard
12222 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12231 <row topline="true" bottomline="true">
12232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12235 \begin_layout Standard
12239 \begin_inset Formula $\to$
12254 \begin_layout Standard
12268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12271 \begin_layout Standard
12275 \begin_layout Standard
12299 \begin_layout Standard
12300 The last formula can currently only be created using TeX-mode because LyX
12301 inserts a box instead of the needed extra formula.
12305 \begin_layout Standard
12310 \begin_layout Standard
12314 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12323 \begin_layout Standard
12338 \begin_layout Standard
12363 , with the difference that there is no frame.
12366 \begin_layout Subsection
12368 \begin_inset LatexCommand label
12369 name "sub:Colored-Boxes"
12374 \begin_inset LatexCommand index
12375 name "Boxes ! colored"
12382 \begin_layout Standard
12383 To be able to use all commands explained in this section, the LaTeX-package
12392 \begin_layout Standard
12397 is part of every LaTeX standard installation.
12403 \begin_inset LatexCommand index
12404 name "Packages ! color"
12408 has to be loaded in the LaTeX-preamble with the line
12412 \begin_layout Standard
12413 When text is colored somewhere in the document with a predefined color,
12414 LyX loads the LaTeX-package
12419 Thus it is possible that the package is loaded twice, but this doesn't
12426 \begin_inset Note Note
12429 \begin_layout Standard
12430 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12439 \begin_layout Standard
12447 \begin_layout Standard
12448 \begin_inset VSpace medskip
12451 To color boxes, the command
12458 \begin_inset LatexCommand index
12459 name "Commands ! C ! \\textbackslash colorbox"
12463 is used in the following scheme:
12466 \begin_layout Standard
12471 colorbox{color}{box content}
12474 \begin_layout Standard
12475 The box content can also be a box and a
12481 can also be part of another box (see the 2nd and 3rd example).
12482 When the box should contain a formula, an extra formula has to be created,
12493 \begin_layout Standard
12494 This also applies for the command
12505 \begin_layout Standard
12509 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12518 \begin_layout Standard
12533 \begin_layout Standard
12534 One of the following predefined colors can be chosen:
12537 \begin_layout Standard
12571 \begin_layout Standard
12573 \begin_inset Tabular
12574 <lyxtabular version="3" rows="4" columns="2">
12576 <column alignment="center" valignment="top" leftline="true" width="0">
12577 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12578 <row topline="true" bottomline="true">
12579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12582 \begin_layout Standard
12588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12591 \begin_layout Standard
12593 \begin_inset Note Note
12596 \begin_layout Standard
12603 is only used as spacer.
12614 <row topline="true">
12615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12618 \begin_layout Standard
12622 \begin_inset Formula $\to$
12632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12635 \begin_layout Standard
12636 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12645 <row topline="true">
12646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12649 \begin_layout Standard
12653 \begin_inset Formula $\to$
12664 \begin_layout Standard
12678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12681 \begin_layout Standard
12682 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12691 <row topline="true" bottomline="true">
12692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12695 \begin_layout Standard
12702 \begin_layout Standard
12714 \begin_inset Formula $\to$
12724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12727 \begin_layout Standard
12728 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12744 \begin_layout Standard
12751 only colors the box but not the characters in the box.
12752 To color all characters, the whole formula is highlighted and the wanted
12753 color is chosen in the
12759 The dialog can be called with the toolbar button
12760 \begin_inset Graphics
12761 filename ../images/dialog-show_character.png
12768 Edit\SpecialChar \menuseparator
12770 Style\SpecialChar \menuseparator
12774 The formula number has then the same color as the formula.
12775 When the formula number should get another color than the formula characters,
12776 the color must be changed within the formula.
12779 \begin_layout Standard
12783 \begin_layout Standard
12786 \begin_inset Formula \begin{equation}
12787 \int A=B\label{eq:red}\end{equation}
12794 \begin_inset Formula \begin{equation}
12795 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12802 \begin_layout Standard
12804 \begin_inset LatexCommand eqref
12809 is completely colored red.
12812 \begin_inset LatexCommand eqref
12813 reference "eq:redgreen"
12817 was first completely colored green to set the color for the formula number.
12818 Subsequently the formula characters were colored red.
12821 \begin_layout Standard
12822 \begin_inset VSpace bigskip
12825 To color the frame different than the rest of the box, the command
12832 \begin_inset LatexCommand index
12833 name "Commands ! F ! \\textbackslash fcolorbox"
12837 is used in the following scheme:
12840 \begin_layout Standard
12845 fcolorbox{frame color}{color}{box content}
12848 \begin_layout Standard
12855 is an extension of the command
12862 The frame width is set, like for
12885 \begin_layout Standard
12897 \begin_inset Formula \[
12898 \fcolorbox{cyan}{magenta}{A=B}\]
12906 \begin_layout Standard
12920 \begin_layout Standard
12921 This formula was created with the command
12928 \begin_inset Formula $\to$
12934 \begin_inset Formula $\to$
12944 \begin_layout Standard
12945 \begin_inset VSpace bigskip
12948 To use other colors than the predefined ones, they have to be defined first.
12951 \begin_layout Standard
12952 One can for example define the color
12953 \begin_inset Quotes eld
12961 \begin_inset Quotes erd
12964 with the LaTeX-preamble line:
12967 \begin_layout Standard
12972 definecolor{darkgreen}{cmyk}{0.5,
12987 \begin_inset LatexCommand index
12988 name "Commands ! D ! \\textbackslash definecolor"
12995 \begin_layout Standard
13000 is the color space that denotes the colors
13017 The four comma separated numbers are the portion factor for the corresponding
13018 colors of the color space.
13019 The factors can be in the range of 0\InsetSpace \thinspace{}
13020 -\InsetSpace \thinspace{}
13026 also the color space
13030 can be used for definitions.
13047 , so that there are in this case three portion factors for the corresponding
13049 Furthermore there is the color space
13053 with one portion factor for the gray value.
13056 \begin_layout Standard
13057 As example a framed box with the new defined color
13061 where the characters have been colored
13066 \begin_inset Formula \begin{equation}
13067 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13074 \begin_layout Standard
13075 Self-defined colors can also be be used for text with the help of the command
13083 \begin_inset LatexCommand index
13084 name "Text ! colored"
13091 \begin_layout Standard
13095 \begin_layout Standard
13099 textcolor{darkgreen}{
13105 \begin_inset Quotes eld
13109 \begin_inset Quotes erd
13116 \begin_layout Standard
13126 \begin_layout Standard
13134 \begin_inset LatexCommand index
13135 name "Commands ! T ! \\textbackslash textcolor"
13139 is used in the scheme
13143 textcolor{color}{characters to color}
13148 \begin_layout Subsection
13150 \begin_inset LatexCommand label
13151 name "sub:Paragraph-Boxes"
13156 \begin_inset LatexCommand index
13157 name "Boxes ! as paragraph"
13164 \begin_layout Standard
13165 A box that can contain several lines and paragraphs, a so called paragraph
13166 box (parbox), can be created with the menu
13168 Insert\SpecialChar \menuseparator
13171 or the toolbar button
13172 \begin_inset Graphics
13173 filename ../images/box-insert.png
13181 \begin_layout Standard
13182 The following example shows a framed parbox in a line:
13185 \begin_layout Standard
13186 \begin_inset VSpace medskip
13190 \begin_inset Box Boxed
13199 height_special "totalheight"
13202 \begin_layout Standard
13203 This is a paragraph box.
13204 It is exactly 5\InsetSpace \thinspace{}
13205 cm long and can also contain formulas:
13206 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13217 \begin_layout Standard
13218 \begin_inset VSpace medskip
13224 \begin_layout Standard
13225 Such a box is created by right-clicking on the gray box inset.
13226 A dialog pops up showing the box properties.
13239 : 5\InsetSpace \thinspace{}
13242 Vertical Box Alignment
13247 \begin_layout Standard
13248 \begin_inset VSpace medskip
13251 In LaTeX a parbox is created with the command
13258 \begin_inset LatexCommand index
13259 name "Commands ! P ! \\textbackslash parbox"
13263 that has the following scheme:
13266 \begin_layout Standard
13271 parbox[position]{width}{box content}
13274 \begin_layout Standard
13288 for bottom means that the box is aligned within the surrounding text with
13294 for top this is done with the first line.
13295 When no position is given, the box will be vertically centered, see section
13302 Embedded\InsetSpace ~
13305 manual for examples.
13308 \begin_layout Standard
13309 \begin_inset VSpace bigskip
13312 To frame formulas completely, including the formula number, the formula
13313 must be set into a parbox.
13314 To do this, the command
13328 is inserted in TeX-mode before the formula.
13334 \begin_inset LatexCommand index
13335 name "Commands ! L ! \\textbackslash linewidth"
13341 is hereby the line width set for the document.
13342 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13343 times the frame separation and
13344 the frame thickness must be subtracted from the line width.
13345 As this is not automatically done by LyX due to a bug
13349 \begin_layout Standard
13353 \begin_layout Standard
13357 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13366 \begin_layout Standard
13378 , TeX-mode has to be used.
13379 To be able to multiply and subtract in arguments, the LaTeX-package
13387 \begin_layout Standard
13392 is part of every LaTeX standard installation.
13398 \begin_inset LatexCommand index
13399 name "Packages ! calc"
13403 must be loaded in the LaTeX-preamble with the line
13406 \begin_layout Standard
13414 \begin_layout Standard
13415 Behind the formula both boxes are closed by entering
13420 Here is an example:
13424 \begin_layout Standard
13438 \begin_layout Standard
13442 \begin_layout Standard
13460 \begin_inset Formula \begin{equation}
13461 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13469 \begin_layout Standard
13480 \begin_layout Standard
13494 \begin_layout Standard
13495 \begin_inset VSpace medskip
13498 As a parbox is used as argument of
13504 , there is in this case no difference between
13519 \begin_layout Standard
13520 \begin_inset VSpace bigskip
13523 Paragraph boxes are very useful to comment formulas directly.
13530 is used in combination with the command
13544 \begin_inset LatexCommand ref
13545 reference "sub:User-defined-Numbering"
13552 \begin_layout Standard
13553 An example of a formula commented with
13562 \begin_layout Standard
13566 \begin_layout Standard
13579 This is a description.
13580 It is distinctly separated from the formula and multiline.
13584 \begin_layout Standard
13596 \begin_layout Standard
13597 Such a formula must be inserted completely in TeX-mode because LyX does
13598 not yet support the command
13605 The formula is created with the following command sequence:
13608 \begin_layout Standard
13621 is inserted in TeX-mode.
13625 \begin_layout Standard
13626 When the formula style
13638 can also be replaced by
13645 (formula styles see
13646 \begin_inset LatexCommand ref
13647 reference "sec:Formula-Styles"
13656 Then the description follows as normal text, and finally
13662 is inserted in TeX-mode.
13675 hereby create a displayed formula.
13678 \begin_layout Standard
13685 can be seen in this example that was
13686 \begin_inset Quotes eld
13690 \begin_inset Quotes erd
13693 using the mathematical textmode:
13694 \begin_inset Formula \[
13695 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13702 \begin_layout Section
13704 \begin_inset LatexCommand index
13712 \begin_layout Subsection
13714 \begin_inset LatexCommand label
13715 name "sub:Big-Operators"
13720 \begin_inset LatexCommand index
13721 name "Operators ! big"
13726 \begin_inset LatexCommand index
13732 \begin_inset LatexCommand index
13740 \begin_layout Standard
13741 To be able to use all integral operators listed here, the option
13743 Use esint package automatically
13745 must be set in the document settings under
13753 \begin_layout Standard
13757 \begin_inset Tabular
13758 <lyxtabular version="3" rows="11" columns="2">
13760 <column alignment="center" valignment="top" leftline="true" width="0pt">
13761 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13762 <row topline="true" bottomline="true">
13763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13766 \begin_layout Standard
13772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13775 \begin_layout Standard
13782 <row topline="true">
13783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13786 \begin_layout Standard
13790 \begin_inset LatexCommand index
13791 name "Commands ! S ! \\textbackslash sum"
13800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13803 \begin_layout Standard
13804 \begin_inset Formula $\sum$
13813 <row topline="true">
13814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13817 \begin_layout Standard
13821 \begin_inset LatexCommand index
13822 name "Commands ! I ! \\textbackslash int"
13831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13834 \begin_layout Standard
13835 \begin_inset Formula $\int$
13844 <row topline="true">
13845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13848 \begin_layout Standard
13856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13859 \begin_layout Standard
13860 \begin_inset Formula $\intop$
13869 <row topline="true">
13870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13873 \begin_layout Standard
13881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13884 \begin_layout Standard
13885 \begin_inset Formula $\oint$
13894 <row topline="true">
13895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13898 \begin_layout Standard
13906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13909 \begin_layout Standard
13910 \begin_inset Formula $\ointop$
13919 <row topline="true">
13920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13923 \begin_layout Standard
13931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13934 \begin_layout Standard
13935 \begin_inset Formula $\ointctrclockwise$
13944 <row topline="true">
13945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13948 \begin_layout Standard
13956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13959 \begin_layout Standard
13960 \begin_inset Formula $\ointclockwise$
13969 <row topline="true">
13970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13973 \begin_layout Standard
13981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13984 \begin_layout Standard
13985 \begin_inset Formula $\sqint$
13994 <row topline="true">
13995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13998 \begin_layout Standard
14006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14009 \begin_layout Standard
14010 \begin_inset Formula $\bigcap$
14019 <row topline="true" bottomline="true">
14020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14023 \begin_layout Standard
14031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14034 \begin_layout Standard
14035 \begin_inset Formula $\bigcup$
14051 \begin_inset Tabular
14052 <lyxtabular version="3" rows="10" columns="2">
14054 <column alignment="center" valignment="top" leftline="true" width="0pt">
14055 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14056 <row topline="true" bottomline="true">
14057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14060 \begin_layout Standard
14066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14069 \begin_layout Standard
14076 <row topline="true">
14077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14080 \begin_layout Standard
14084 \begin_inset LatexCommand index
14085 name "Commands ! P ! \\textbackslash prod"
14094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14097 \begin_layout Standard
14098 \begin_inset Formula $\prod$
14107 <row topline="true">
14108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14111 \begin_layout Standard
14119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14122 \begin_layout Standard
14123 \begin_inset Formula $\coprod$
14132 <row topline="true">
14133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14136 \begin_layout Standard
14144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14147 \begin_layout Standard
14148 \begin_inset Formula $\bigodot$
14157 <row topline="true">
14158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14161 \begin_layout Standard
14169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14172 \begin_layout Standard
14173 \begin_inset Formula $\bigotimes$
14182 <row topline="true">
14183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14186 \begin_layout Standard
14194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14197 \begin_layout Standard
14198 \begin_inset Formula $\bigoplus$
14207 <row topline="true">
14208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14211 \begin_layout Standard
14219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14222 \begin_layout Standard
14223 \begin_inset Formula $\bigwedge$
14232 <row topline="true">
14233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14236 \begin_layout Standard
14244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14247 \begin_layout Standard
14248 \begin_inset Formula $\bigvee$
14257 <row topline="true">
14258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14261 \begin_layout Standard
14269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14272 \begin_layout Standard
14273 \begin_inset Formula $\bigsqcup$
14282 <row topline="true" bottomline="true">
14283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14286 \begin_layout Standard
14294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14297 \begin_layout Standard
14298 \begin_inset Formula $\biguplus$
14316 \begin_layout Standard
14317 All big operators can also be inserted via the math toolbar button
14318 \begin_inset Graphics
14319 filename ../images/math/intop.png
14327 \begin_layout Standard
14328 The operators are called big because they are bigger than the sometimes
14329 equal looking binary operators.
14330 All big operators can have limits as described in the next subsection.
14333 \begin_layout Standard
14358 , resp.\InsetSpace ~
14359 in the style the operator limits are displayed, see
14360 \begin_inset LatexCommand ref
14361 reference "sub:Operator-Limits"
14369 \begin_layout Subsubsection*
14370 Advices for Integrals
14373 \begin_layout Standard
14378 in an integral is an operator, that therefore has to be set upright.
14379 This is done by highlighting the
14383 and using the keyboard shortcut
14392 \begin_layout Standard
14398 \begin_inset LatexCommand ref
14399 reference "sub:Font-Styles"
14409 Finally the smallest space is inserted before the
14413 , as this is usual for operators.
14417 \begin_layout Standard
14419 \begin_inset Formula $\int A(x)dx$
14428 \begin_layout Standard
14438 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14444 \begin_layout Standard
14445 For multiple integrals there are the following commands:
14446 \begin_inset VSpace medskip
14452 \begin_layout Standard
14456 \begin_inset Tabular
14457 <lyxtabular version="3" rows="4" columns="2">
14459 <column alignment="center" valignment="top" leftline="true" width="0">
14460 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14461 <row topline="true" bottomline="true">
14462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14465 \begin_layout Standard
14471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14474 \begin_layout Standard
14476 \begin_inset Note Note
14479 \begin_layout Standard
14486 is only used as spacer.
14497 <row topline="true">
14498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14501 \begin_layout Standard
14509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14512 \begin_layout Standard
14513 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14522 <row topline="true">
14523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14526 \begin_layout Standard
14534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14537 \begin_layout Standard
14538 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14547 <row topline="true" bottomline="true">
14548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14551 \begin_layout Standard
14559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14562 \begin_layout Standard
14563 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14579 \begin_inset Tabular
14580 <lyxtabular version="3" rows="4" columns="2">
14582 <column alignment="center" valignment="top" leftline="true" width="0">
14583 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14584 <row topline="true" bottomline="true">
14585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14588 \begin_layout Standard
14594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14597 \begin_layout Standard
14604 <row topline="true">
14605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14608 \begin_layout Standard
14616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14619 \begin_layout Standard
14620 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14629 <row topline="true">
14630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14633 \begin_layout Standard
14641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14644 \begin_layout Standard
14645 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14654 <row topline="true" bottomline="true">
14655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14658 \begin_layout Standard
14666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14669 \begin_layout Standard
14670 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14688 \begin_layout Subsection
14690 \begin_inset LatexCommand label
14691 name "sub:Operator-Limits"
14696 \begin_inset LatexCommand index
14697 name "Operators ! Limits"
14704 \begin_layout Standard
14705 Limits are created by super- and subscripts:
14708 \begin_layout Standard
14710 \begin_inset Tabular
14711 <lyxtabular version="3" rows="2" columns="2">
14713 <column alignment="center" valignment="top" leftline="true" width="0pt">
14714 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14715 <row topline="true" bottomline="true">
14716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14719 \begin_layout Standard
14725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14728 \begin_layout Standard
14730 \begin_inset Note Note
14733 \begin_layout Standard
14740 is only used as spacer.
14751 <row topline="true" bottomline="true">
14752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14755 \begin_layout Standard
14764 \begin_layout Standard
14774 \begin_inset Formula $\to$
14778 \begin_inset Formula $\to$
14786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14789 \begin_layout Standard
14790 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14806 \begin_layout Standard
14807 Limits of inline formulas are set right beside the operator.
14808 Limits in displayed formulas are set above or below the operator, except
14809 of integral limits.
14812 \begin_layout Standard
14813 To force that the limits are set beside the operator, the cursor is set
14814 directly behind the operator and the limits type is changed with the menu
14817 Edit\SpecialChar \menuseparator
14818 Math\SpecialChar \menuseparator
14836 \begin_layout Standard
14837 The default limits type is this:
14838 \begin_inset Formula \[
14839 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14843 This is how it looks when the limits type was changed to
14850 \begin_inset Formula \[
14851 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14855 For integrals, except of
14867 , the limits are by default set beside the operator.
14868 But for multiple integrals the limits are often set below the operator.
14869 In the following example the limits type was therefore set to
14873 and so set below the integrals:
14874 \begin_inset Formula \begin{equation}
14875 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14882 \begin_layout Standard
14883 \begin_inset VSpace medskip
14886 To specify conditions for limits, the commands
14893 \begin_inset LatexCommand index
14894 name "Commands ! S ! \\textbackslash subarray"
14905 \begin_inset LatexCommand index
14906 name "Commands ! S ! \\textbackslash substack"
14911 To create for example this expression
14912 \begin_inset Formula \begin{equation}
14913 \sum_{\begin{subarray}{c}
14915 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14922 \begin_layout Standard
14923 the following has to be done:
14937 \begin_layout Standard
14949 One is now in a blue box under the summation operator and insert there
14958 \begin_layout Standard
14970 The blue box is now within a purple box and now several lines can be written
14972 A new line is created by inserting a line break (
14981 0<k<1000 Ctrl-Return
14985 is typed in, a new box appears below for the new line.
14988 \begin_layout Standard
14989 The alignment of the lines can be changed to left aligned with the
14999 Edit\SpecialChar \menuseparator
15003 To get right alignment,
15011 \begin_layout Standard
15022 is inserted at the beginning of the line.
15025 \begin_layout Standard
15038 with the difference that the lines are always centered.
15041 \begin_layout Standard
15042 \begin_inset VSpace bigskip
15046 \begin_inset LatexCommand eqref
15047 reference "eq:substack"
15051 there can be too much space beside an operator, because the characters
15052 following the operator are set beside the limits.
15055 \begin_layout Standard
15056 To avoid this, the following macro can be used in the LaTeX-preamble:
15059 \begin_layout Standard
15088 mathclapinternal #1#2{
15092 mathsurround =0pt #1{#2}$}}
15095 \begin_layout Standard
15096 This defines the command
15103 \begin_inset LatexCommand index
15104 name "Commands ! M ! \\textbackslash mathclap"
15108 that sets the width of the limit to 0\InsetSpace \thinspace{}
15110 The command scheme is
15113 \begin_layout Standard
15121 \begin_layout Standard
15122 where the limit can consist of several conditions.
15125 \begin_layout Standard
15127 \begin_inset LatexCommand eqref
15128 reference "eq:substack"
15132 , one uses the command
15135 \begin_layout Standard
15148 \begin_layout Standard
15157 0<k<1000 Ctrl-Enter
15160 \begin_layout Standard
15161 to create the lower limit.
15162 The summand is now directly behind the summation operator:
15163 \begin_inset Formula \[
15164 \sum_{\mathclap{\substack{0<k<1000\\
15165 \\k\,\in\,\mathbb{N}}
15173 \begin_layout Standard
15174 \begin_inset VSpace bigskip
15177 How to use one limit for several operators is described in
15178 \begin_inset LatexCommand ref
15179 reference "sub:Self-defined-Operators"
15186 \begin_layout Subsection
15188 \begin_inset LatexCommand label
15189 name "sub:Binary-Operators"
15194 \begin_inset LatexCommand index
15195 name "Operators ! binary"
15202 \begin_layout Standard
15203 Binary operators are surrounded by space when there is a character before
15205 \begin_inset VSpace medskip
15211 \begin_layout Standard
15215 \begin_inset Tabular
15216 <lyxtabular version="3" rows="13" columns="2">
15218 <column alignment="center" valignment="top" leftline="true" width="0pt">
15219 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15220 <row topline="true" bottomline="true">
15221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15224 \begin_layout Standard
15226 \begin_inset Note Note
15229 \begin_layout Standard
15236 is only used as spacer.
15246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15249 \begin_layout Standard
15256 <row topline="true">
15257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15260 \begin_layout Standard
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15269 \begin_layout Standard
15270 \begin_inset Formula $+$
15279 <row topline="true">
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15283 \begin_layout Standard
15289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Standard
15293 \begin_inset Formula $-$
15302 <row topline="true">
15303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15306 \begin_layout Standard
15314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15317 \begin_layout Standard
15318 \begin_inset Formula $\pm$
15327 <row topline="true">
15328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15331 \begin_layout Standard
15339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Standard
15343 \begin_inset Formula $\mp$
15352 <row topline="true">
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15356 \begin_layout Standard
15364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15367 \begin_layout Standard
15368 \begin_inset Formula $\cdot$
15377 <row topline="true">
15378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15381 \begin_layout Standard
15389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Standard
15393 \begin_inset Formula $\times$
15402 <row topline="true">
15403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15406 \begin_layout Standard
15414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Standard
15418 \begin_inset Formula $\div$
15427 <row topline="true">
15428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15431 \begin_layout Standard
15435 \begin_layout Standard
15448 \begin_layout Standard
15460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15463 \begin_layout Standard
15464 \begin_inset Formula $*$
15473 <row topline="true">
15474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15477 \begin_layout Standard
15485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15488 \begin_layout Standard
15489 \begin_inset Formula $\star$
15498 <row topline="true">
15499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15502 \begin_layout Standard
15510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15513 \begin_layout Standard
15514 \begin_inset Formula $\circ$
15523 <row topline="true">
15524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15527 \begin_layout Standard
15535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15538 \begin_layout Standard
15539 \begin_inset Formula $\diamond$
15548 <row topline="true" bottomline="true">
15549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15552 \begin_layout Standard
15560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15563 \begin_layout Standard
15564 \begin_inset Formula $\bullet$
15580 \begin_inset Tabular
15581 <lyxtabular version="3" rows="13" columns="2">
15583 <column alignment="center" valignment="top" leftline="true" width="0pt">
15584 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15585 <row topline="true" bottomline="true">
15586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15589 \begin_layout Standard
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15598 \begin_layout Standard
15605 <row topline="true">
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15609 \begin_layout Standard
15617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15620 \begin_layout Standard
15621 \begin_inset Formula $\nabla$
15630 <row topline="true">
15631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15634 \begin_layout Standard
15642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15645 \begin_layout Standard
15646 \begin_inset Formula $\bigtriangledown$
15655 <row topline="true">
15656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15659 \begin_layout Standard
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15670 \begin_layout Standard
15671 \begin_inset Formula $\bigtriangleup$
15680 <row topline="true">
15681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15684 \begin_layout Standard
15692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15695 \begin_layout Standard
15696 \begin_inset Formula $\Box$
15705 <row topline="true">
15706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15709 \begin_layout Standard
15717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15720 \begin_layout Standard
15721 \begin_inset Formula $\cap$
15730 <row topline="true">
15731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15734 \begin_layout Standard
15742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15745 \begin_layout Standard
15746 \begin_inset Formula $\cup$
15755 <row topline="true">
15756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15759 \begin_layout Standard
15767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15770 \begin_layout Standard
15771 \begin_inset Formula $\dagger$
15780 <row topline="true">
15781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15784 \begin_layout Standard
15792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15795 \begin_layout Standard
15796 \begin_inset Formula $\ddagger$
15805 <row topline="true">
15806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15809 \begin_layout Standard
15817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15820 \begin_layout Standard
15821 \begin_inset Formula $\wr$
15830 <row topline="true">
15831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15834 \begin_layout Standard
15842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15845 \begin_layout Standard
15846 \begin_inset Formula $\bigcirc$
15855 <row topline="true">
15856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15859 \begin_layout Standard
15867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15870 \begin_layout Standard
15871 \begin_inset Formula $\wedge$
15880 <row topline="true" bottomline="true">
15881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15884 \begin_layout Standard
15892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15895 \begin_layout Standard
15896 \begin_inset Formula $\vee$
15912 \begin_inset Tabular
15913 <lyxtabular version="3" rows="13" columns="2">
15915 <column alignment="center" valignment="top" leftline="true" width="0pt">
15916 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15917 <row topline="true" bottomline="true">
15918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15921 \begin_layout Standard
15927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15930 \begin_layout Standard
15937 <row topline="true">
15938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15941 \begin_layout Standard
15949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15952 \begin_layout Standard
15953 \begin_inset Formula $\oplus$
15962 <row topline="true">
15963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15966 \begin_layout Standard
15974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15977 \begin_layout Standard
15978 \begin_inset Formula $\ominus$
15987 <row topline="true">
15988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15991 \begin_layout Standard
15999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16002 \begin_layout Standard
16003 \begin_inset Formula $\otimes$
16012 <row topline="true">
16013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16016 \begin_layout Standard
16024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Standard
16028 \begin_inset Formula $\oslash$
16037 <row topline="true">
16038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16041 \begin_layout Standard
16049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16052 \begin_layout Standard
16053 \begin_inset Formula $\odot$
16062 <row topline="true">
16063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16066 \begin_layout Standard
16074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16077 \begin_layout Standard
16078 \begin_inset Formula $\amalg$
16087 <row topline="true">
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16091 \begin_layout Standard
16099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16102 \begin_layout Standard
16103 \begin_inset Formula $\uplus$
16112 <row topline="true">
16113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16116 \begin_layout Standard
16124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16127 \begin_layout Standard
16128 \begin_inset Formula $\setminus$
16137 <row topline="true">
16138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16141 \begin_layout Standard
16149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16152 \begin_layout Standard
16153 \begin_inset Formula $\sqcap$
16162 <row topline="true">
16163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16166 \begin_layout Standard
16174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16177 \begin_layout Standard
16178 \begin_inset Formula $\sqcup$
16187 <row topline="true">
16188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16191 \begin_layout Standard
16199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16202 \begin_layout Standard
16203 \begin_inset Formula $\triangleleft$
16212 <row topline="true" bottomline="true">
16213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16216 \begin_layout Standard
16224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16227 \begin_layout Standard
16228 \begin_inset Formula $\triangleright$
16246 \begin_layout Standard
16247 All binary operators can also be inserted via the math toolbar button
16248 \begin_inset Graphics
16249 filename ../images/math/pm.png
16257 \begin_layout Standard
16258 To typeset the Laplace operator also
16275 \begin_inset Formula $\nabla^{2}$
16278 ) can be used instead of
16287 \begin_layout Standard
16294 Insert\SpecialChar \menuseparator
16306 \begin_layout Subsection
16307 Self-defined Operators
16308 \begin_inset LatexCommand label
16309 name "sub:Self-defined-Operators"
16314 \begin_inset LatexCommand index
16315 name "Operators ! self-defined"
16322 \begin_layout Standard
16323 With the help of the command
16327 DeclareMathOperator
16330 \begin_inset LatexCommand index
16331 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16335 custom operators can be defined in the LaTeX-preamble.
16336 Its command scheme is:
16339 \begin_layout Standard
16344 DeclareMathOperator{new command}{display}
16347 \begin_layout Standard
16348 Display can be characters or symbols that define how the operator looks
16350 To define a big operator a * is set behind the command.
16351 All self-defined big operators can have limits as described in
16352 \begin_inset LatexCommand ref
16353 reference "sub:Operator-Limits"
16360 \begin_layout Standard
16361 For example the LaTeX-preamble line
16364 \begin_layout Standard
16369 DeclareMathOperator*{
16376 \begin_layout Standard
16377 defines the command
16383 , that inserts a big operator consisting of the lozenge symbol from
16384 \begin_inset LatexCommand ref
16385 reference "sub:Miscellaneous-Symbols"
16390 \begin_inset Formula \[
16391 \Lozenge_{n=1}^{\infty}\]
16395 The command for this formula is:
16406 \begin_inset Formula $\to$
16412 \begin_layout Standard
16413 \begin_inset VSpace bigskip
16416 When self-defined operators are not used several times in the document,
16417 they can also be defined with the commands
16424 \begin_inset LatexCommand index
16425 name "Commands ! M ! \\textbackslash mathop"
16436 \begin_inset LatexCommand index
16437 name "Commands ! M ! \\textbackslash mathbin"
16441 , which have the following scheme:
16444 \begin_layout Standard
16458 \begin_layout Standard
16465 defines big operators,
16474 \begin_layout Standard
16481 can e.\InsetSpace \thinspace{}
16483 be used to use one limit for several operators:
16486 \begin_layout Standard
16487 \begin_inset Formula \[
16488 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16495 \begin_layout Standard
16496 The command for the formula above is:
16514 \begin_layout Standard
16526 \begin_inset Formula $\to$
16535 \begin_layout Standard
16549 \begin_layout Section
16551 \begin_inset LatexCommand index
16559 \begin_layout Subsection
16561 \begin_inset LatexCommand label
16562 name "sub:Font-Styles"
16567 \begin_inset LatexCommand index
16568 name "Font ! style"
16575 \begin_layout Standard
16576 Latin letters in formulas can be set in one of the following font styles:
16577 \begin_inset VSpace -2mm
16583 \begin_layout Standard
16585 \begin_inset Tabular
16586 <lyxtabular version="3" rows="6" columns="3">
16588 <column alignment="center" valignment="top" leftline="true" width="0">
16589 <column alignment="center" valignment="top" leftline="true" width="0">
16590 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16591 <row topline="true" bottomline="true">
16592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16595 \begin_layout Standard
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16604 \begin_layout Standard
16610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16613 \begin_layout Standard
16620 <row topline="true">
16621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16624 \begin_layout Standard
16633 \begin_layout Standard
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Standard
16653 \begin_inset Formula $\mathbb{ABC}$
16661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16664 \begin_layout Standard
16671 <row topline="true">
16672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16675 \begin_layout Standard
16684 \begin_layout Standard
16700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16703 \begin_layout Standard
16704 \begin_inset Formula $\mathbf{AbC}$
16712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16715 \begin_layout Standard
16722 <row topline="true">
16723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16726 \begin_layout Standard
16735 \begin_layout Standard
16751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16754 \begin_layout Standard
16755 \begin_inset Formula $\boldsymbol{AbC}$
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16766 \begin_layout Standard
16773 <row topline="true">
16774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16777 \begin_layout Standard
16786 \begin_layout Standard
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16805 \begin_layout Standard
16806 \begin_inset Formula $\mathcal{ABC}$
16814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16817 \begin_layout Standard
16824 <row topline="true" bottomline="true">
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Standard
16837 \begin_layout Standard
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16856 \begin_layout Standard
16857 \begin_inset Formula $\mathfrak{AbC}$
16865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16868 \begin_layout Standard
16882 \begin_layout Standard
16884 \begin_inset Tabular
16885 <lyxtabular version="3" rows="5" columns="3">
16887 <column alignment="center" valignment="top" leftline="true" width="0">
16888 <column alignment="center" valignment="top" leftline="true" width="0">
16889 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16890 <row topline="true" bottomline="true">
16891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16894 \begin_layout Standard
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16903 \begin_layout Standard
16909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16912 \begin_layout Standard
16919 <row topline="true">
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Standard
16932 \begin_layout Standard
16948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16951 \begin_layout Standard
16952 \begin_inset Formula $\mathit{AbC}$
16960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16963 \begin_layout Standard
16970 <row topline="true">
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16974 \begin_layout Standard
16983 \begin_layout Standard
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17002 \begin_layout Standard
17003 \begin_inset Formula $\mathrm{AbC}$
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17014 \begin_layout Standard
17021 <row topline="true">
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17025 \begin_layout Standard
17034 \begin_layout Standard
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Standard
17054 \begin_inset Formula $\mathsf{AbC}$
17062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17065 \begin_layout Standard
17072 <row topline="true" bottomline="true">
17073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17076 \begin_layout Standard
17085 \begin_layout Standard
17101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17104 \begin_layout Standard
17105 \begin_inset Formula $\mathtt{AbC}$
17113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17116 \begin_layout Standard
17130 \begin_layout Standard
17131 \begin_inset Note Greyedout
17134 \begin_layout Standard
17151 can only be used for big letters.
17159 \begin_layout Standard
17160 Predefined is the style
17169 \begin_layout Standard
17170 The style commands work also for letters in mathematical constructs:
17171 \begin_inset Formula \[
17172 \mathfrak{A=\frac{b}{C}}\]
17179 \begin_layout Standard
17180 Characters in mathematical text don't appear in a math font style but in
17181 the text font style
17188 That their style can't be set correctly via the text style dialog is a
17193 \begin_layout Standard
17198 \begin_layout Standard
17202 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17211 \begin_layout Standard
17226 \begin_layout Standard
17227 Instead of the style commands the dialog
17229 Edit\SpecialChar \menuseparator
17230 Math\SpecialChar \menuseparator
17233 or the toolbar button
17234 \begin_inset Graphics
17235 filename ../images/math/font.png
17243 \begin_layout Subsection
17245 \begin_inset LatexCommand label
17246 name "sub:Bold-Formulas"
17251 \begin_inset LatexCommand index
17252 name "Formula ! bold"
17259 \begin_layout Standard
17260 To make a complete formula bold, the command
17266 from the previous subsection cannot be used, because it doesn't work for
17267 small Greek letters.
17268 Furthermore it prints Latin letters always upright, like in the following
17272 \begin_layout Standard
17273 \begin_inset Formula \[
17274 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17281 \begin_layout Standard
17282 To display the formula correctly, the command
17289 \begin_inset Formula \[
17290 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17294 It is also possible to set the formula in a
17296 boldmath environment
17299 This environment is created by inserting the command
17304 \begin_inset LatexCommand index
17305 name "Commands ! B ! \\textbackslash boldmath"
17312 To end the environment, the command
17317 \begin_inset LatexCommand index
17318 name "Commands ! U ! \\textbackslash unboldmath"
17324 is inserted in TeX-mode.
17328 \begin_layout Standard
17338 \begin_inset Formula \[
17339 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17347 \begin_layout Standard
17359 \begin_layout Subsection
17361 \begin_inset LatexCommand label
17362 name "sub:Font-Sizes"
17367 \begin_inset LatexCommand index
17375 \begin_layout Standard
17376 For characters in formulas there are, analog to characters in text, the
17377 following size commands:
17380 \begin_layout Standard
17444 \begin_layout Standard
17445 The size produced by the commands depends on the document font size, that
17446 corresponds with the command
17453 The other commands produce smaller or larger sizes than
17460 The font size can however not exceed a certain value.
17461 Is for example the document font size 12\InsetSpace \thinspace{}
17468 switches to the same size as
17478 \begin_layout Standard
17479 A size command is inserted in TeX-mode before the formula and sets the size
17480 for all following formula and text characters.
17481 To switch back to the initial size, the command
17487 is inserted behind the formula in TeX-mode.
17490 \begin_layout Standard
17491 Within a formula the size can only be changed for symbols or letters in
17493 To do this, the size command is inserted in mathematical text.
17494 All following characters until the end of the mathematical text or until
17495 another size command will have the selected size.
17497 \begin_inset VSpace -2mm
17503 \begin_layout Standard
17507 \begin_layout Standard
17517 \begin_inset Formula \[
17518 A=\frac{B}{c}\cdot\maltese\]
17523 \begin_inset Formula \[
17524 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17532 \begin_layout Standard
17544 \begin_layout Standard
17545 \begin_inset VSpace medskip
17548 Before both formulas the command
17555 The command for the second formula is:
17565 \begin_layout Standard
17580 \begin_layout Standard
17595 \begin_layout Standard
17610 \begin_layout Standard
17620 \begin_inset Formula $\to$
17624 \begin_inset Formula $\to$
17633 \begin_layout Standard
17652 \begin_layout Standard
17667 \begin_layout Standard
17682 \begin_layout Standard
17694 \begin_layout Standard
17695 If a symbol cannot be displayed in different sizes, it will always be displayed
17696 in the default size.
17699 \begin_layout Section
17701 \begin_inset LatexCommand index
17702 name "Greek letters"
17709 \begin_layout Standard
17710 All Greek letters can also be inserted via the toolbar button
17711 \begin_inset Graphics
17712 filename ../images/math/alpha.png
17720 \begin_layout Subsection
17722 \begin_inset LatexCommand label
17723 name "sub:Small-Letters"
17728 \begin_inset LatexCommand index
17729 name "Greek letters ! small"
17736 \begin_layout Standard
17740 \begin_inset Tabular
17741 <lyxtabular version="3" rows="11" columns="2">
17743 <column alignment="center" valignment="top" leftline="true" width="0pt">
17744 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17745 <row topline="true" bottomline="true">
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17749 \begin_layout Standard
17755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17758 \begin_layout Standard
17765 <row topline="true">
17766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17769 \begin_layout Standard
17777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17780 \begin_layout Standard
17781 \begin_inset Formula $\alpha$
17790 <row topline="true">
17791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17794 \begin_layout Standard
17802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17805 \begin_layout Standard
17806 \begin_inset Formula $\beta$
17815 <row topline="true">
17816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17819 \begin_layout Standard
17827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17830 \begin_layout Standard
17831 \begin_inset Formula $\gamma$
17840 <row topline="true">
17841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17844 \begin_layout Standard
17852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17855 \begin_layout Standard
17856 \begin_inset Formula $\delta$
17865 <row topline="true">
17866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17869 \begin_layout Standard
17877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17880 \begin_layout Standard
17881 \begin_inset Formula $\epsilon$
17890 <row topline="true">
17891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17894 \begin_layout Standard
17902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17905 \begin_layout Standard
17906 \begin_inset Formula $\varepsilon$
17915 <row topline="true">
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17919 \begin_layout Standard
17927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17930 \begin_layout Standard
17931 \begin_inset Formula $\zeta$
17940 <row topline="true">
17941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17944 \begin_layout Standard
17952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17955 \begin_layout Standard
17956 \begin_inset Formula $\eta$
17965 <row topline="true">
17966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17969 \begin_layout Standard
17977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17980 \begin_layout Standard
17981 \begin_inset Formula $\theta$
17990 <row topline="true" bottomline="true">
17991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17994 \begin_layout Standard
18002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18005 \begin_layout Standard
18006 \begin_inset Formula $\vartheta$
18022 \begin_inset Tabular
18023 <lyxtabular version="3" rows="12" columns="2">
18025 <column alignment="center" valignment="top" leftline="true" width="0pt">
18026 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18027 <row topline="true" bottomline="true">
18028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18031 \begin_layout Standard
18037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18040 \begin_layout Standard
18047 <row topline="true">
18048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18051 \begin_layout Standard
18059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18062 \begin_layout Standard
18063 \begin_inset Formula $\iota$
18072 <row topline="true">
18073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18076 \begin_layout Standard
18084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18087 \begin_layout Standard
18088 \begin_inset Formula $\kappa$
18097 <row topline="true">
18098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18101 \begin_layout Standard
18109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18112 \begin_layout Standard
18113 \begin_inset Formula $\varkappa$
18122 <row topline="true">
18123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18126 \begin_layout Standard
18134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18137 \begin_layout Standard
18138 \begin_inset Formula $\lambda$
18147 <row topline="true">
18148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18151 \begin_layout Standard
18159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18162 \begin_layout Standard
18163 \begin_inset Formula $\mu$
18172 <row topline="true">
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18176 \begin_layout Standard
18184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18187 \begin_layout Standard
18188 \begin_inset Formula $\nu$
18197 <row topline="true">
18198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18201 \begin_layout Standard
18209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18212 \begin_layout Standard
18213 \begin_inset Formula $\xi$
18222 <row topline="true">
18223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18226 \begin_layout Standard
18232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18235 \begin_layout Standard
18236 \begin_inset Formula $o$
18245 <row topline="true">
18246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18249 \begin_layout Standard
18257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18260 \begin_layout Standard
18261 \begin_inset Formula $\pi$
18270 <row topline="true">
18271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18274 \begin_layout Standard
18282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18285 \begin_layout Standard
18286 \begin_inset Formula $\varpi$
18295 <row topline="true" bottomline="true">
18296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18299 \begin_layout Standard
18307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18310 \begin_layout Standard
18311 \begin_inset Formula $\rho$
18327 \begin_inset Tabular
18328 <lyxtabular version="3" rows="11" columns="2">
18330 <column alignment="center" valignment="top" leftline="true" width="0pt">
18331 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18332 <row topline="true" bottomline="true">
18333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18336 \begin_layout Standard
18342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18345 \begin_layout Standard
18352 <row topline="true">
18353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18356 \begin_layout Standard
18364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18367 \begin_layout Standard
18368 \begin_inset Formula $\varrho$
18377 <row topline="true">
18378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18381 \begin_layout Standard
18389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18392 \begin_layout Standard
18393 \begin_inset Formula $\sigma$
18402 <row topline="true">
18403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18406 \begin_layout Standard
18414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18417 \begin_layout Standard
18418 \begin_inset Formula $\varsigma$
18427 <row topline="true">
18428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18431 \begin_layout Standard
18439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18442 \begin_layout Standard
18443 \begin_inset Formula $\tau$
18452 <row topline="true">
18453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18456 \begin_layout Standard
18464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18467 \begin_layout Standard
18468 \begin_inset Formula $\upsilon$
18477 <row topline="true">
18478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18481 \begin_layout Standard
18489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18492 \begin_layout Standard
18493 \begin_inset Formula $\phi$
18502 <row topline="true">
18503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18506 \begin_layout Standard
18514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18517 \begin_layout Standard
18518 \begin_inset Formula $\varphi$
18527 <row topline="true">
18528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18531 \begin_layout Standard
18539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18542 \begin_layout Standard
18543 \begin_inset Formula $\chi$
18552 <row topline="true">
18553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18556 \begin_layout Standard
18564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18567 \begin_layout Standard
18568 \begin_inset Formula $\psi$
18577 <row topline="true" bottomline="true">
18578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18581 \begin_layout Standard
18589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18592 \begin_layout Standard
18593 \begin_inset Formula $\omega$
18611 \begin_layout Standard
18612 \begin_inset VSpace medskip
18618 \begin_layout Standard
18619 How to create upright Greek letters is explained in
18620 \begin_inset LatexCommand ref
18621 reference "sub:Upright-small-Greek"
18628 \begin_layout Subsection
18630 \begin_inset LatexCommand index
18631 name "Greek letters ! big"
18638 \begin_layout Standard
18642 \begin_inset Tabular
18643 <lyxtabular version="3" rows="7" columns="2">
18645 <column alignment="center" valignment="top" leftline="true" width="0pt">
18646 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18647 <row topline="true" bottomline="true">
18648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18651 \begin_layout Standard
18657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18660 \begin_layout Standard
18667 <row topline="true">
18668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18671 \begin_layout Standard
18679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18682 \begin_layout Standard
18683 \begin_inset Formula $\Gamma$
18692 <row topline="true">
18693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18696 \begin_layout Standard
18704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18707 \begin_layout Standard
18708 \begin_inset Formula $\Delta$
18717 <row topline="true">
18718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18721 \begin_layout Standard
18729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18732 \begin_layout Standard
18733 \begin_inset Formula $\Theta$
18742 <row topline="true">
18743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18746 \begin_layout Standard
18754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18757 \begin_layout Standard
18758 \begin_inset Formula $\Lambda$
18767 <row topline="true">
18768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18771 \begin_layout Standard
18779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18782 \begin_layout Standard
18783 \begin_inset Formula $\Xi$
18792 <row topline="true" bottomline="true">
18793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18796 \begin_layout Standard
18804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18807 \begin_layout Standard
18808 \begin_inset Formula $\Pi$
18824 \begin_inset Tabular
18825 <lyxtabular version="3" rows="6" columns="2">
18827 <column alignment="center" valignment="top" leftline="true" width="0pt">
18828 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18829 <row topline="true" bottomline="true">
18830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18833 \begin_layout Standard
18839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18842 \begin_layout Standard
18849 <row topline="true">
18850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18853 \begin_layout Standard
18861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18864 \begin_layout Standard
18865 \begin_inset Formula $\Sigma$
18874 <row topline="true">
18875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18878 \begin_layout Standard
18886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18889 \begin_layout Standard
18890 \begin_inset Formula $\Upsilon$
18899 <row topline="true">
18900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18903 \begin_layout Standard
18911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18914 \begin_layout Standard
18915 \begin_inset Formula $\Phi$
18924 <row topline="true">
18925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18928 \begin_layout Standard
18936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18939 \begin_layout Standard
18940 \begin_inset Formula $\Psi$
18949 <row topline="true" bottomline="true">
18950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18953 \begin_layout Standard
18961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18964 \begin_layout Standard
18965 \begin_inset Formula $\Omega$
18983 \begin_layout Standard
18984 \begin_inset VSpace medskip
18987 That the big Greek letters appear upright is caused by a design bug when
18989 To get correct italic big letters, begin every command with
18994 For example the command
19001 \begin_inset Formula $\varGamma$
19007 \begin_layout Subsection
19009 \begin_inset LatexCommand index
19010 name "Greek letters ! bold"
19017 \begin_layout Standard
19018 Greek letters cannot be set with different font styles like Latin letters.
19019 They can only be made bold with the command
19026 \begin_inset LatexCommand index
19027 name "Commands ! B ! \\textbackslash boldsymbol"
19034 \begin_layout Standard
19036 \begin_inset Tabular
19037 <lyxtabular version="3" rows="3" columns="2">
19039 <column alignment="center" valignment="top" leftline="true" width="0">
19040 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
19041 <row topline="true" bottomline="true">
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19045 \begin_layout Standard
19051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19054 \begin_layout Standard
19061 <row topline="true">
19062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19065 \begin_layout Standard
19077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19080 \begin_layout Standard
19081 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19090 <row topline="true" bottomline="true">
19091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19094 \begin_layout Standard
19106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19109 \begin_layout Standard
19110 \begin_inset Formula $\theta\boldsymbol{\theta}$
19126 \begin_layout Section
19131 \begin_layout Standard
19144 \begin_layout Standard
19145 A list with all symbols of most of the LaTeX-packages can be found in
19146 \begin_inset LatexCommand cite
19160 \begin_layout Standard
19168 \begin_inset Note Note
19171 \begin_layout Standard
19174 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19177 \begin_layout Standard
19180 texorpdfstring is in section
19181 \begin_inset LatexCommand ref
19182 reference "sub:Formulas-in-Section"
19192 \begin_inset LatexCommand index
19200 \begin_layout Standard
19201 Many of the symbols listed in this section can also be inserted via the
19203 \begin_inset Graphics
19204 filename ../images/math/nabla.png
19210 \begin_inset Graphics
19211 filename ../images/math/digamma.png
19219 \begin_layout Subsection
19220 Mathematical Symbols
19221 \begin_inset LatexCommand label
19222 name "sub:Mathematical-Symbols"
19227 \begin_inset LatexCommand index
19228 name "Symbols ! mathematical"
19235 \begin_layout Standard
19239 \begin_inset Tabular
19240 <lyxtabular version="3" rows="10" columns="2">
19242 <column alignment="center" valignment="top" leftline="true" width="0pt">
19243 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19244 <row topline="true" bottomline="true">
19245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19248 \begin_layout Standard
19254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19257 \begin_layout Standard
19264 <row topline="true">
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19268 \begin_layout Standard
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Standard
19280 \begin_inset Formula $\neg$
19289 <row topline="true">
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19293 \begin_layout Standard
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Standard
19305 \begin_inset Formula $\Im$
19314 <row topline="true">
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19318 \begin_layout Standard
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Standard
19330 \begin_inset Formula $\Re$
19339 <row topline="true">
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19343 \begin_layout Standard
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Standard
19355 \begin_inset Formula $\aleph$
19364 <row topline="true">
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Standard
19376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Standard
19380 \begin_inset Formula $\partial$
19389 <row topline="true">
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19393 \begin_layout Standard
19401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Standard
19405 \begin_inset Formula $\infty$
19414 <row topline="true" bottomline="true">
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19418 \begin_layout Standard
19426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Standard
19430 \begin_inset Formula $\wp$
19439 <row bottomline="true">
19440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19443 \begin_layout Standard
19451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19454 \begin_layout Standard
19455 \begin_inset Formula $\imath$
19464 <row bottomline="true">
19465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19468 \begin_layout Standard
19476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19479 \begin_layout Standard
19480 \begin_inset Formula $\jmath$
19496 \begin_inset Tabular
19497 <lyxtabular version="3" rows="10" columns="2">
19499 <column alignment="center" valignment="top" leftline="true" width="0pt">
19500 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19501 <row topline="true" bottomline="true">
19502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19505 \begin_layout Standard
19511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19514 \begin_layout Standard
19516 \begin_inset Note Note
19519 \begin_layout Standard
19526 is only used as spacer.
19537 <row topline="true">
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19541 \begin_layout Standard
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Standard
19553 \begin_inset Formula $\forall$
19562 <row topline="true">
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19566 \begin_layout Standard
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Standard
19578 \begin_inset Formula $\exists$
19587 <row topline="true">
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19591 \begin_layout Standard
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19602 \begin_layout Standard
19603 \begin_inset Formula $\nexists$
19612 <row topline="true">
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19616 \begin_layout Standard
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19627 \begin_layout Standard
19628 \begin_inset Formula $\emptyset$
19637 <row topline="true">
19638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19641 \begin_layout Standard
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19652 \begin_layout Standard
19653 \begin_inset Formula $\varnothing$
19662 <row topline="true">
19663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19666 \begin_layout Standard
19674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19677 \begin_layout Standard
19678 \begin_inset Formula $\dag$
19687 <row topline="true" bottomline="true">
19688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19691 \begin_layout Standard
19699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19702 \begin_layout Standard
19703 \begin_inset Formula $\ddag$
19712 <row bottomline="true">
19713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19716 \begin_layout Standard
19724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19727 \begin_layout Standard
19731 \begin_layout Standard
19741 \begin_inset Formula $\complement$
19748 \begin_layout Standard
19761 <row bottomline="true">
19762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19765 \begin_layout Standard
19773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19776 \begin_layout Standard
19777 \begin_inset Formula $\Bbbk$
19793 \begin_inset Tabular
19794 <lyxtabular version="3" rows="10" columns="2">
19796 <column alignment="center" valignment="top" leftline="true" width="0pt">
19797 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19798 <row topline="true" bottomline="true">
19799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19802 \begin_layout Standard
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Standard
19818 <row topline="true">
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19822 \begin_layout Standard
19830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19833 \begin_layout Standard
19834 \begin_inset Formula $\prime$
19843 <row topline="true">
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19847 \begin_layout Standard
19855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19858 \begin_layout Standard
19859 \begin_inset Formula $\backprime$
19868 <row topline="true">
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19872 \begin_layout Standard
19880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Standard
19884 \begin_inset Formula $\mho$
19893 <row topline="true">
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19897 \begin_layout Standard
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Standard
19909 \begin_inset Formula $\triangle$
19918 <row topline="true">
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19922 \begin_layout Standard
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Standard
19934 \begin_inset Formula $\angle$
19943 <row topline="true">
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Standard
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Standard
19959 \begin_inset Formula $\measuredangle$
19968 <row topline="true" bottomline="true">
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Standard
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Standard
19984 \begin_inset Formula $\sphericalangle$
19993 <row bottomline="true">
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Standard
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Standard
20009 \begin_inset Formula $\top$
20018 <row bottomline="true">
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Standard
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Standard
20034 \begin_inset Formula $\bot$
20052 \begin_layout Standard
20058 \begin_layout Subsection
20059 Miscellaneous Symbols
20060 \begin_inset LatexCommand label
20061 name "sub:Miscellaneous-Symbols"
20066 \begin_inset LatexCommand index
20067 name "Symbols ! miscellaneous"
20074 \begin_layout Standard
20075 \begin_inset Tabular
20076 <lyxtabular version="3" rows="10" columns="2">
20078 <column alignment="center" valignment="top" leftline="true" width="0pt">
20079 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20080 <row topline="true" bottomline="true">
20081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20084 \begin_layout Standard
20090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20093 \begin_layout Standard
20100 <row topline="true">
20101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20104 \begin_layout Standard
20112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20115 \begin_layout Standard
20116 \begin_inset Formula $\flat$
20125 <row topline="true">
20126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20129 \begin_layout Standard
20137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20140 \begin_layout Standard
20141 \begin_inset Formula $\natural$
20150 <row topline="true">
20151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20154 \begin_layout Standard
20162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20165 \begin_layout Standard
20166 \begin_inset Formula $\sharp$
20175 <row topline="true" bottomline="true">
20176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20179 \begin_layout Standard
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20190 \begin_layout Standard
20191 \begin_inset Formula $\surd$
20200 <row bottomline="true">
20201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20204 \begin_layout Standard
20212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20215 \begin_layout Standard
20216 \begin_inset Formula $\checkmark$
20225 <row bottomline="true">
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20229 \begin_layout Standard
20237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20240 \begin_layout Standard
20241 \begin_inset Formula $\yen$
20250 <row bottomline="true">
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20254 \begin_layout Standard
20262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Standard
20266 \begin_inset Formula $\pounds$
20275 <row bottomline="true">
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20279 \begin_layout Standard
20285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Standard
20289 \begin_inset Formula $\$$
20298 <row bottomline="true">
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20302 \begin_layout Standard
20308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20311 \begin_layout Standard
20312 \begin_inset Formula $§$
20326 \begin_inset Tabular
20327 <lyxtabular version="3" rows="10" columns="2">
20329 <column alignment="center" valignment="top" leftline="true" width="0">
20330 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20331 <row topline="true" bottomline="true">
20332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20335 \begin_layout Standard
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Standard
20351 <row topline="true">
20352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20355 \begin_layout Standard
20363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20366 \begin_layout Standard
20367 \begin_inset Formula $\hbar$
20376 <row topline="true">
20377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20380 \begin_layout Standard
20388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20391 \begin_layout Standard
20392 \begin_inset Formula $\hslash$
20401 <row topline="true">
20402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20405 \begin_layout Standard
20413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20416 \begin_layout Standard
20417 \begin_inset Formula $\clubsuit$
20426 <row topline="true">
20427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20430 \begin_layout Standard
20438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20441 \begin_layout Standard
20442 \begin_inset Formula $\spadesuit$
20451 <row topline="true">
20452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20455 \begin_layout Standard
20463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20466 \begin_layout Standard
20467 \begin_inset Formula $\bigstar$
20476 <row topline="true">
20477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20480 \begin_layout Standard
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20491 \begin_layout Standard
20492 \begin_inset Formula $\blacklozenge$
20501 <row topline="true">
20502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20505 \begin_layout Standard
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20516 \begin_layout Standard
20517 \begin_inset Formula $\blacktriangle$
20526 <row topline="true">
20527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20530 \begin_layout Standard
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20541 \begin_layout Standard
20542 \begin_inset Formula $\blacktriangledown$
20551 <row topline="true" bottomline="true">
20552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20555 \begin_layout Standard
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20566 \begin_layout Standard
20567 \begin_inset Formula $\bullet$
20581 \begin_inset Tabular
20582 <lyxtabular version="3" rows="10" columns="2">
20584 <column alignment="center" valignment="top" leftline="true" width="0pt">
20585 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20586 <row topline="true" bottomline="true">
20587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20590 \begin_layout Standard
20596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Standard
20606 <row topline="true">
20607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20610 \begin_layout Standard
20618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20621 \begin_layout Standard
20622 \begin_inset Formula $\diamondsuit$
20631 <row topline="true">
20632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20635 \begin_layout Standard
20643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20646 \begin_layout Standard
20647 \begin_inset Formula $\Diamond$
20656 <row topline="true">
20657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20660 \begin_layout Standard
20668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20671 \begin_layout Standard
20672 \begin_inset Formula $\heartsuit$
20681 <row topline="true" bottomline="true">
20682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20685 \begin_layout Standard
20693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20696 \begin_layout Standard
20697 \begin_inset Formula $\P$
20706 <row bottomline="true">
20707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20710 \begin_layout Standard
20718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20721 \begin_layout Standard
20722 \begin_inset Formula $\copyright$
20731 <row bottomline="true">
20732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20735 \begin_layout Standard
20743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20746 \begin_layout Standard
20747 \begin_inset Formula $\circledR$
20756 <row bottomline="true">
20757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20760 \begin_layout Standard
20768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20771 \begin_layout Standard
20772 \begin_inset Formula $\maltese$
20781 <row bottomline="true">
20782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20785 \begin_layout Standard
20793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20796 \begin_layout Standard
20797 \begin_inset Formula $\diagup$
20806 <row bottomline="true">
20807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20810 \begin_layout Standard
20818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20821 \begin_layout Standard
20822 \begin_inset Formula $\diagdown$
20838 \begin_layout Standard
20839 \begin_inset VSpace medskip
20842 More symbols are listed in
20843 \begin_inset LatexCommand ref
20844 reference "sub:Miscellaneous-Special-Characters"
20851 \begin_layout Standard
20852 Some symbols can be displayed in different sizes, see
20853 \begin_inset LatexCommand ref
20854 reference "sub:Font-Sizes"
20861 \begin_layout Subsection
20863 \begin_inset LatexCommand index
20864 name "Symbols ! Euro-symbol"
20869 \begin_inset LatexCommand index
20870 name "\\textcent@\\officialeuro"
20877 \begin_layout Standard
20878 To use the Euro symbol in formulas, the LaTeX-package
20883 \begin_inset LatexCommand index
20884 name "Packages ! eurosym"
20888 must be installed and loaded with the LaTeX-preamble line
20891 \begin_layout Standard
20896 usepackage[gennarrow]{eurosym}
20899 \begin_layout Standard
20900 The Euro symbol can now be inserted with the command
20907 \begin_inset LatexCommand index
20908 name "Commands ! E ! \\textbackslash euro"
20915 \begin_layout Standard
20916 The Euro symbol can directly be inserted with the € key in mathematical
20917 text, without having
20932 can also be inserted in TeX-mode.
20933 The official currency symbol can then be inserted with the command
20940 \begin_inset LatexCommand index
20941 name "Commands ! O ! \\textbackslash officialeuro"
20945 , that is only available in TeX-mode.
20948 \begin_layout Standard
20952 \begin_layout Standard
20962 \begin_inset Note Note
20965 \begin_layout Standard
20966 The following table will only be displayed when the LaTeX-package
20978 \begin_layout Standard
20979 An overview about the different Euro symbols:
20982 \begin_layout Standard
20984 \begin_inset Tabular
20985 <lyxtabular version="3" rows="4" columns="3">
20987 <column alignment="center" valignment="top" leftline="true" width="0pt">
20988 <column alignment="center" valignment="top" leftline="true" width="0pt">
20989 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20990 <row topline="true" bottomline="true">
20991 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20994 \begin_layout Standard
21000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21003 \begin_layout Standard
21009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21012 \begin_layout Standard
21019 <row topline="true">
21020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21023 \begin_layout Standard
21029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21032 \begin_layout Standard
21040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21043 \begin_layout Standard
21044 \begin_inset Formula $\euro$
21053 <row topline="true">
21054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21057 \begin_layout Standard
21063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21066 \begin_layout Standard
21072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21075 \begin_layout Standard
21076 \begin_inset Formula $\mbox{€}$
21085 <row topline="true" bottomline="true">
21086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21089 \begin_layout Standard
21095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21098 \begin_layout Standard
21106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21109 \begin_layout Standard
21113 \begin_layout Standard
21135 \begin_layout Standard
21139 \begin_layout Standard
21149 \begin_inset Note Note
21152 \begin_layout Standard
21153 The following will be displayed when the LaTeX-package
21165 \begin_layout Standard
21166 You need to install the LaTeX-package
21170 to see the rest of this subsection in the output.
21173 \begin_layout Standard
21177 \begin_layout Standard
21189 \begin_layout Section
21191 \begin_inset LatexCommand label
21192 name "sec:Relations"
21197 \begin_inset LatexCommand index
21203 \begin_inset LatexCommand index
21204 name "Comparisons|see{Relations}"
21211 \begin_layout Standard
21212 All relations can also be inserted via the toolbar button
21213 \begin_inset Graphics
21214 filename ../images/math/leq.png
21222 \begin_layout Standard
21226 \begin_inset Tabular
21227 <lyxtabular version="3" rows="17" columns="2">
21229 <column alignment="center" valignment="top" leftline="true" width="0pt">
21230 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21231 <row topline="true" bottomline="true">
21232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21235 \begin_layout Standard
21241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21244 \begin_layout Standard
21251 <row topline="true">
21252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21255 \begin_layout Standard
21261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21264 \begin_layout Standard
21265 \begin_inset Formula $<$
21274 <row topline="true">
21275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21278 \begin_layout Standard
21286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21289 \begin_layout Standard
21290 \begin_inset Formula $\le$
21299 <row topline="true">
21300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21303 \begin_layout Standard
21311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21314 \begin_layout Standard
21315 \begin_inset Formula $\ll$
21324 <row topline="true">
21325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21328 \begin_layout Standard
21336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21339 \begin_layout Standard
21340 \begin_inset Formula $\prec$
21349 <row topline="true">
21350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21353 \begin_layout Standard
21361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21364 \begin_layout Standard
21365 \begin_inset Formula $\preceq$
21374 <row topline="true">
21375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21378 \begin_layout Standard
21386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21389 \begin_layout Standard
21390 \begin_inset Formula $\subset$
21399 <row topline="true">
21400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21403 \begin_layout Standard
21411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21414 \begin_layout Standard
21415 \begin_inset Formula $\subseteq$
21424 <row topline="true">
21425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21428 \begin_layout Standard
21436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21439 \begin_layout Standard
21440 \begin_inset Formula $\sqsubseteq$
21449 <row topline="true">
21450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21453 \begin_layout Standard
21461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21464 \begin_layout Standard
21465 \begin_inset Formula $\in$
21474 <row topline="true">
21475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21478 \begin_layout Standard
21486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21489 \begin_layout Standard
21490 \begin_inset Formula $\vdash$
21499 <row topline="true">
21500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21503 \begin_layout Standard
21511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Standard
21515 \begin_inset Formula $\smile$
21524 <row topline="true">
21525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21528 \begin_layout Standard
21536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21539 \begin_layout Standard
21540 \begin_inset Formula $\lhd$
21549 <row topline="true">
21550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21553 \begin_layout Standard
21561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21564 \begin_layout Standard
21565 \begin_inset Formula $\unlhd$
21574 <row topline="true">
21575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21578 \begin_layout Standard
21586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21589 \begin_layout Standard
21590 \begin_inset Formula $\gtrless$
21599 <row topline="true">
21600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21603 \begin_layout Standard
21611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Standard
21615 \begin_inset Formula $\mid$
21624 <row topline="true" bottomline="true">
21625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21628 \begin_layout Standard
21636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21639 \begin_layout Standard
21640 \begin_inset Formula $\nmid$
21656 \begin_inset Tabular
21657 <lyxtabular version="3" rows="17" columns="2">
21659 <column alignment="center" valignment="top" leftline="true" width="0pt">
21660 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21661 <row topline="true" bottomline="true">
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21665 \begin_layout Standard
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21674 \begin_layout Standard
21681 <row topline="true">
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21685 \begin_layout Standard
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Standard
21695 \begin_inset Formula $=$
21704 <row topline="true">
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21708 \begin_layout Standard
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Standard
21720 \begin_inset Formula $\not=$
21729 <row topline="true">
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21733 \begin_layout Standard
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Standard
21745 \begin_inset Formula $\equiv$
21754 <row topline="true">
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21758 \begin_layout Standard
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Standard
21770 \begin_inset Formula $\sim$
21779 <row topline="true">
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21783 \begin_layout Standard
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21794 \begin_layout Standard
21795 \begin_inset Formula $\simeq$
21804 <row topline="true">
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21808 \begin_layout Standard
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Standard
21820 \begin_inset Formula $\approx$
21829 <row topline="true">
21830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21833 \begin_layout Standard
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Standard
21845 \begin_inset Formula $\cong$
21854 <row topline="true">
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21858 \begin_layout Standard
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Standard
21870 \begin_inset Formula $\bowtie$
21879 <row topline="true">
21880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21883 \begin_layout Standard
21891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Standard
21895 \begin_inset Formula $\notin$
21904 <row topline="true">
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21908 \begin_layout Standard
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Standard
21920 \begin_inset Formula $\perp$
21929 <row topline="true">
21930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21933 \begin_layout Standard
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Standard
21945 \begin_inset Formula $\propto$
21954 <row topline="true">
21955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21958 \begin_layout Standard
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Standard
21970 \begin_inset Formula $\asymp$
21979 <row topline="true">
21980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21983 \begin_layout Standard
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Standard
21995 \begin_inset Formula $\doteq$
22004 <row topline="true">
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Standard
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Standard
22020 \begin_inset Formula $\circeq$
22029 <row topline="true">
22030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22033 \begin_layout Standard
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Standard
22045 \begin_inset Formula $\models$
22054 <row topline="true" bottomline="true">
22055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22058 \begin_layout Standard
22066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Standard
22070 \begin_inset Formula $\widehat{=}$
22086 \begin_inset Tabular
22087 <lyxtabular version="3" rows="17" columns="2">
22089 <column alignment="center" valignment="top" leftline="true" width="0pt">
22090 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22091 <row topline="true" bottomline="true">
22092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22095 \begin_layout Standard
22101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22104 \begin_layout Standard
22111 <row topline="true">
22112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22115 \begin_layout Standard
22121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22124 \begin_layout Standard
22125 \begin_inset Formula $>$
22134 <row topline="true">
22135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22138 \begin_layout Standard
22146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22149 \begin_layout Standard
22150 \begin_inset Formula $\ge$
22159 <row topline="true">
22160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22163 \begin_layout Standard
22171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22174 \begin_layout Standard
22175 \begin_inset Formula $\gg$
22184 <row topline="true">
22185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22188 \begin_layout Standard
22196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22199 \begin_layout Standard
22200 \begin_inset Formula $\succ$
22209 <row topline="true">
22210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22213 \begin_layout Standard
22221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Standard
22225 \begin_inset Formula $\succeq$
22234 <row topline="true">
22235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22238 \begin_layout Standard
22246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Standard
22250 \begin_inset Formula $\supset$
22259 <row topline="true">
22260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22263 \begin_layout Standard
22271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Standard
22275 \begin_inset Formula $\supseteq$
22284 <row topline="true">
22285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22288 \begin_layout Standard
22296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22299 \begin_layout Standard
22300 \begin_inset Formula $\sqsupseteq$
22309 <row topline="true">
22310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22313 \begin_layout Standard
22321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22324 \begin_layout Standard
22325 \begin_inset Formula $\ni$
22334 <row topline="true">
22335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22338 \begin_layout Standard
22346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22349 \begin_layout Standard
22350 \begin_inset Formula $\dashv$
22359 <row topline="true">
22360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22363 \begin_layout Standard
22371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22374 \begin_layout Standard
22375 \begin_inset Formula $\frown$
22384 <row topline="true">
22385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22388 \begin_layout Standard
22396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22399 \begin_layout Standard
22400 \begin_inset Formula $\rhd$
22409 <row topline="true">
22410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22413 \begin_layout Standard
22421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22424 \begin_layout Standard
22425 \begin_inset Formula $\unrhd$
22434 <row topline="true">
22435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22438 \begin_layout Standard
22446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22449 \begin_layout Standard
22450 \begin_inset Formula $\lessgtr$
22459 <row topline="true">
22460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22463 \begin_layout Standard
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22474 \begin_layout Standard
22475 \begin_inset Formula $\parallel$
22484 <row topline="true" bottomline="true">
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22488 \begin_layout Standard
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Standard
22500 \begin_inset Formula $\nparallel$
22518 \begin_layout Standard
22519 \begin_inset VSpace medskip
22534 are bigger than the equal looking operators
22549 \begin_layout Standard
22550 Relations are, in contrary to symbols, always surrounded by space.
22553 \begin_layout Standard
22554 Relations with labels can be created with the command
22561 \begin_inset LatexCommand index
22562 name "Commands ! S ! \\textbackslash stackrel"
22569 \begin_layout Standard
22571 \begin_inset Tabular
22572 <lyxtabular version="3" rows="2" columns="2">
22574 <column alignment="center" valignment="top" leftline="true" width="0">
22575 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22576 <row topline="true" bottomline="true">
22577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22580 \begin_layout Standard
22586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22589 \begin_layout Standard
22591 \begin_inset Note Note
22594 \begin_layout Standard
22601 is only used as spacer.
22612 <row topline="true" bottomline="true">
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22616 \begin_layout Standard
22623 \begin_layout Standard
22640 \begin_layout Standard
22650 \begin_inset Formula $\downarrow$
22659 \begin_layout Standard
22672 \begin_layout Standard
22686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22689 \begin_layout Standard
22690 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22706 \begin_layout Section
22710 \begin_layout Subsection
22711 Predefined Functions
22712 \begin_inset LatexCommand label
22713 name "sub:Predefined-Functions"
22718 \begin_inset LatexCommand index
22719 name "Functions ! predefined"
22726 \begin_layout Standard
22727 In general, variables are set
22731 in mathematical expressions, but not function names, because
22732 \begin_inset Formula $sin$
22735 could be misunderstood as
22736 \begin_inset Formula $s\cdot i\cdot n$
22740 Therefore there are predefined functions, that are additionally a bit separated
22742 They are inserted as commands starting with a backslash before their name.
22745 \begin_layout Standard
22747 \begin_inset Tabular
22748 <lyxtabular version="3" rows="2" columns="4">
22750 <column alignment="center" valignment="top" leftline="true" width="0pt">
22751 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22752 <column alignment="center" valignment="top" leftline="true" width="0pt">
22753 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22754 <row topline="true" bottomline="true">
22755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22758 \begin_layout Standard
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22767 \begin_layout Standard
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Standard
22782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22785 \begin_layout Standard
22792 <row topline="true" bottomline="true">
22793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22796 \begin_layout Standard
22802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22805 \begin_layout Standard
22806 \begin_inset Formula $Asin(x)+B$
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22817 \begin_layout Standard
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Standard
22829 \begin_inset Formula $A\sin(x)+B$
22846 \begin_layout Standard
22858 \begin_layout Standard
22859 The following functions are predefined:
22862 \begin_layout Standard
22863 \begin_inset VSpace -2mm
22869 \begin_layout Standard
22871 \begin_inset Tabular
22872 <lyxtabular version="3" rows="9" columns="4">
22874 <column alignment="center" valignment="top" leftline="true" width="0pt">
22875 <column alignment="center" valignment="top" leftline="true" width="0pt">
22876 <column alignment="center" valignment="top" leftline="true" width="0pt">
22877 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22878 <row topline="true" bottomline="true">
22879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22882 \begin_layout Standard
22888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22891 \begin_layout Standard
22897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22900 \begin_layout Standard
22906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22909 \begin_layout Standard
22916 <row topline="true">
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22920 \begin_layout Standard
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22931 \begin_layout Standard
22939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22942 \begin_layout Standard
22950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22953 \begin_layout Standard
22962 <row topline="true">
22963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22966 \begin_layout Standard
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22977 \begin_layout Standard
22985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22988 \begin_layout Standard
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Standard
23008 <row topline="true">
23009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23012 \begin_layout Standard
23020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23023 \begin_layout Standard
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23034 \begin_layout Standard
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Standard
23054 <row topline="true">
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23058 \begin_layout Standard
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23069 \begin_layout Standard
23077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23080 \begin_layout Standard
23088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23091 \begin_layout Standard
23100 <row topline="true">
23101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23104 \begin_layout Standard
23112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23115 \begin_layout Standard
23123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23126 \begin_layout Standard
23134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23137 \begin_layout Standard
23146 <row topline="true">
23147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23150 \begin_layout Standard
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23161 \begin_layout Standard
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23172 \begin_layout Standard
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Standard
23192 <row topline="true">
23193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23196 \begin_layout Standard
23204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23207 \begin_layout Standard
23215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23218 \begin_layout Standard
23226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23229 \begin_layout Standard
23238 <row topline="true" bottomline="true">
23239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23242 \begin_layout Standard
23250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23253 \begin_layout Standard
23261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23264 \begin_layout Standard
23272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23275 \begin_layout Standard
23291 \begin_layout Standard
23292 They can also be inserted with the math toolbar button
23293 \begin_inset Graphics
23294 filename ../images/math/functions.png
23302 \begin_layout Subsection
23303 Self-defined Functions
23304 \begin_inset LatexCommand index
23305 name "Functions ! self-defined"
23312 \begin_layout Standard
23313 To use a function that is not predefined, like for example the sign function
23314 sgn(x), there are two possibilities:
23317 \begin_layout Itemize
23318 Define the function by inserting the following line to the LaTeX-preamble
23322 \begin_layout Standard
23327 DeclareMathOperator
23330 \begin_inset LatexCommand ref
23331 reference "sub:Self-defined-Operators"
23343 \begin_inset VSpace -3mm
23352 DeclareMathOperator{
23357 \begin_inset LatexCommand index
23358 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23365 \begin_inset VSpace -2mm
23370 Now the new defined function can be called with the command
23379 \begin_layout Itemize
23380 Write the the formula as usual, mark the formula name, in our example the
23385 , and change it to mathematical text.
23386 At last a space is inserted between prefactor and function.
23389 \begin_layout Standard
23390 The result is the same with both methods as with a predefined function
23394 \begin_layout Standard
23395 In LyX self-defined functions are displayed red, predefined ones black.
23403 \begin_layout Standard
23405 \begin_inset Tabular
23406 <lyxtabular version="3" rows="3" columns="2">
23408 <column alignment="center" valignment="top" leftline="true" width="0pt">
23409 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23410 <row topline="true" bottomline="true">
23411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23414 \begin_layout Standard
23420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23423 \begin_layout Standard
23430 <row topline="true" bottomline="true">
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Standard
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Standard
23446 \begin_inset Formula $A\sgn(x)+B$
23455 <row topline="true" bottomline="true">
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Standard
23463 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23474 \begin_layout Standard
23475 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23491 \begin_layout Standard
23492 The first method is more suitable when the self-defined function should
23493 be used several times.
23496 \begin_layout Subsection
23498 \begin_inset LatexCommand index
23506 \begin_layout Standard
23507 For limits there are defined besides
23514 \begin_inset LatexCommand index
23515 name "Commands ! L ! \\textbackslash lim"
23531 furthermore the following functions:
23534 \begin_layout Standard
23536 \begin_inset Tabular
23537 <lyxtabular version="3" rows="5" columns="2">
23539 <column alignment="center" valignment="top" leftline="true" width="0">
23540 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23541 <row topline="true" bottomline="true">
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23545 \begin_layout Standard
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23554 \begin_layout Standard
23556 \begin_inset Note Note
23559 \begin_layout Standard
23566 is only used as spacer.
23577 <row topline="true">
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Standard
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Standard
23593 \begin_inset Formula $\varliminf$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Standard
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Standard
23618 \begin_inset Formula $\varlimsup$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Standard
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Standard
23643 \begin_inset Formula $\varprojlim$
23652 <row bottomline="true">
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Standard
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Standard
23668 \begin_inset Formula $\varinjlim$
23672 \begin_inset Formula $\raisebox{-2.5mm}{}$
23688 \begin_layout Standard
23689 \begin_inset VSpace medskip
23692 The limit is created by inserting a subscript.
23693 It is set right beside the function in an inline formula:
23696 \begin_layout Standard
23698 \begin_inset Tabular
23699 <lyxtabular version="3" rows="2" columns="2">
23701 <column alignment="center" valignment="top" width="0pt">
23702 <column alignment="center" valignment="top" width="0pt">
23704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23707 \begin_layout Standard
23713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23716 \begin_layout Standard
23720 \begin_layout Standard
23730 \begin_inset Note Note
23733 \begin_layout Standard
23746 are used here as spacer.
23758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23761 \begin_layout Standard
23770 \begin_layout Standard
23783 \begin_layout Standard
23797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23800 \begin_layout Standard
23801 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23817 \begin_layout Standard
23818 In a displayed formula the limit is set below the formula, as usual:
23819 \begin_inset Formula \[
23827 \begin_layout Subsection
23829 \begin_inset LatexCommand index
23830 name "Functions ! modulo-"
23837 \begin_layout Standard
23838 The modulo-function is special, because it exists in four variants.
23841 \begin_layout Standard
23842 The variants in a displayed formula:
23843 \begin_inset Formula \begin{align*}
23844 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23845 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23846 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23847 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23848 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23855 \begin_layout Standard
23856 In an inline formula less space is set before the function names for all
23860 \begin_layout Section
23862 \begin_inset LatexCommand index
23863 name "Special characters"
23870 \begin_layout Subsection
23871 Special Characters in Mathematical Text
23874 \begin_layout Standard
23875 The following commands can only be used in mathematical text or in TeX-mode:
23878 \begin_layout Standard
23882 \begin_inset Tabular
23883 <lyxtabular version="3" rows="8" columns="2">
23885 <column alignment="block" valignment="top" leftline="true" width="0">
23886 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23887 <row topline="true" bottomline="true">
23888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23891 \begin_layout Standard
23897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23900 \begin_layout Standard
23907 <row topline="true">
23908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23911 \begin_layout Standard
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23922 \begin_layout Standard
23923 \begin_inset Formula $\textrm{\oe}$
23932 <row topline="true">
23933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23936 \begin_layout Standard
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23947 \begin_layout Standard
23948 \begin_inset Formula $\textrm{\OE}$
23957 <row topline="true">
23958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23961 \begin_layout Standard
23969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23972 \begin_layout Standard
23973 \begin_inset Formula $\textrm{\ae}$
23982 <row topline="true">
23983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23986 \begin_layout Standard
23994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23997 \begin_layout Standard
23998 \begin_inset Formula $\textrm{\AE}$
24007 <row topline="true">
24008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24011 \begin_layout Standard
24019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24022 \begin_layout Standard
24023 \begin_inset Formula $\textrm{\aa}$
24032 <row topline="true" bottomline="true">
24033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24036 \begin_layout Standard
24040 \begin_inset LatexCommand index
24041 name "\\@\\textrm{\\AA}"
24050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Standard
24054 \begin_inset Formula $\textrm{\AA}$
24063 <row bottomline="true">
24064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24067 \begin_layout Standard
24075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Standard
24079 \begin_inset Formula $\textrm{\i}$
24095 \begin_inset Tabular
24096 <lyxtabular version="3" rows="8" columns="2">
24098 <column alignment="block" valignment="top" leftline="true" width="0">
24099 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24100 <row topline="true" bottomline="true">
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24104 \begin_layout Standard
24106 \begin_inset Note Note
24109 \begin_layout Standard
24116 is used for separation, because otherwise the output will be ¡ and ¿ respective
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Standard
24137 <row topline="true">
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24141 \begin_layout Standard
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24152 \begin_layout Standard
24153 \begin_inset Formula $\textrm{\o}$
24162 <row topline="true">
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24166 \begin_layout Standard
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24177 \begin_layout Standard
24178 \begin_inset Formula $\textrm{\O}$
24187 <row topline="true">
24188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24191 \begin_layout Standard
24199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24202 \begin_layout Standard
24203 \begin_inset Formula $\textrm{\l}$
24212 <row topline="true">
24213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24216 \begin_layout Standard
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Standard
24228 \begin_inset Formula $\textrm{\L}$
24237 <row topline="true" bottomline="true">
24238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24241 \begin_layout Standard
24246 \begin_layout Standard
24259 \begin_layout Standard
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24276 \begin_layout Standard
24277 \begin_inset Formula $\textrm{!`}$
24286 <row bottomline="true">
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24290 \begin_layout Standard
24295 \begin_layout Standard
24308 \begin_layout Standard
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24325 \begin_layout Standard
24326 \begin_inset Formula $\textrm{?`}$
24335 <row bottomline="true">
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24339 \begin_layout Standard
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24350 \begin_layout Standard
24351 \begin_inset Formula $\textrm{\j}$
24369 \begin_layout Standard
24371 \begin_inset Formula $\textrm{\textrm{Å}}$
24375 \begin_inset Formula $\textrm{\textrm{Ø}}$
24378 can also be inserted via the math toolbar button
24379 \begin_inset Graphics
24380 filename ../images/math/digamma.png
24388 \begin_layout Standard
24389 An exception are the commands
24395 \begin_layout Standard
24412 \begin_layout Standard
24423 , because they can be inserted in LyX directly to text.
24426 \begin_layout Subsection
24428 \begin_inset LatexCommand label
24429 name "sub:Accents-in-Text"
24434 \begin_inset LatexCommand index
24435 name "Accents ! in text"
24442 \begin_layout Standard
24443 With the following commands all letters can be accented.
24444 The commands must be inserted in TeX-mode.
24447 \begin_layout Standard
24451 \begin_inset Tabular
24452 <lyxtabular version="3" rows="8" columns="2">
24454 <column alignment="block" valignment="top" leftline="true" width="0">
24455 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24456 <row topline="true" bottomline="true">
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24460 \begin_layout Standard
24466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24469 \begin_layout Standard
24476 <row topline="true">
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24480 \begin_layout Standard
24484 \begin_inset Quotes grd
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24495 \begin_layout Standard
24499 \begin_layout Standard
24514 <row topline="true">
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24518 \begin_layout Standard
24526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24529 \begin_layout Standard
24533 \begin_layout Standard
24548 <row topline="true">
24549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24552 \begin_layout Standard
24559 \begin_layout Standard
24573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24576 \begin_layout Standard
24580 \begin_layout Standard
24595 <row topline="true">
24596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24599 \begin_layout Standard
24607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24610 \begin_layout Standard
24614 \begin_layout Standard
24629 <row topline="true">
24630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24633 \begin_layout Standard
24640 \begin_layout Standard
24654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24657 \begin_layout Standard
24661 \begin_layout Standard
24676 <row topline="true" bottomline="true">
24677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24680 \begin_layout Standard
24687 \begin_layout Standard
24701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24704 \begin_layout Standard
24708 \begin_layout Standard
24723 <row bottomline="true">
24724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24727 \begin_layout Standard
24734 \begin_layout Standard
24748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24751 \begin_layout Standard
24755 \begin_layout Standard
24777 \begin_inset Tabular
24778 <lyxtabular version="3" rows="8" columns="2">
24780 <column alignment="block" valignment="top" leftline="true" width="0">
24781 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24782 <row topline="true" bottomline="true">
24783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24786 \begin_layout Standard
24792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24795 \begin_layout Standard
24802 <row topline="true">
24803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24806 \begin_layout Standard
24813 \begin_layout Standard
24827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24830 \begin_layout Standard
24834 \begin_layout Standard
24849 <row topline="true">
24850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24853 \begin_layout Standard
24861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24864 \begin_layout Standard
24868 \begin_layout Standard
24883 <row topline="true">
24884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24887 \begin_layout Standard
24891 \begin_inset LatexCommand index
24901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24904 \begin_layout Standard
24908 \begin_layout Standard
24923 <row topline="true">
24924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24927 \begin_layout Standard
24935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24938 \begin_layout Standard
24942 \begin_layout Standard
24957 <row topline="true" bottomline="true">
24958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24961 \begin_layout Standard
24968 \begin_layout Standard
24982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24985 \begin_layout Standard
24989 \begin_layout Standard
25004 <row bottomline="true">
25005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25008 \begin_layout Standard
25015 \begin_layout Standard
25029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25032 \begin_layout Standard
25036 \begin_layout Standard
25051 <row bottomline="true">
25052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25055 \begin_layout Standard
25062 \begin_layout Standard
25076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25079 \begin_layout Standard
25083 \begin_layout Standard
25107 \begin_layout Standard
25108 \begin_inset VSpace medskip
25117 also two different characters can be accented.
25126 \begin_layout Standard
25141 \begin_layout Standard
25153 \begin_layout Standard
25166 can in combination with vowels directly be inserted with the keyboard without
25168 The same applies for the tilde
25172 \begin_layout Standard
25173 This only applies for keyboards where the tilde is defined as accent.
25182 in combination with
25197 \begin_layout Standard
25240 , and accents inserted directly with the keyboard are also available in
25242 For the other accents there are special math commands to be used in formulas,
25244 \begin_inset LatexCommand ref
25245 reference "sub:Accents-for-one"
25252 \begin_layout Standard
25253 \begin_inset VSpace bigskip
25256 Furthermore, with the command
25263 \begin_inset LatexCommand index
25264 name "Commands ! T ! \\textbackslash textcircled"
25268 all numbers and letters can be set into a circle, quasi accented with a
25269 circle, similar to the the copyright symbol.
25272 \begin_layout Standard
25274 \begin_inset Tabular
25275 <lyxtabular version="3" rows="3" columns="2">
25277 <column alignment="center" valignment="top" leftline="true" width="0">
25278 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25279 <row topline="true" bottomline="true">
25280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25283 \begin_layout Standard
25289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25292 \begin_layout Standard
25294 \begin_inset Note Note
25297 \begin_layout Standard
25304 is only used as spacer.
25315 <row topline="true">
25316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25319 \begin_layout Standard
25327 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25330 \begin_layout Standard
25334 \begin_layout Standard
25349 <row topline="true" bottomline="true">
25350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25353 \begin_layout Standard
25364 raisebox{-1.5pt}{W}}
25369 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25372 \begin_layout Standard
25373 \begin_inset Formula $\raisebox{4.5mm}{}$
25380 \begin_layout Standard
25398 \begin_inset Formula $\raisebox{-2mm}{}$
25414 \begin_layout Standard
25415 One has to take care that the character fits in the circle.
25426 \begin_layout Standard
25428 \begin_inset LatexCommand ref
25429 reference "sub:Font-Sizes"
25438 specifies thereby the size of the circle.
25449 \begin_layout Standard
25451 \begin_inset LatexCommand ref
25452 reference "sub:Boxes-without-Frame"
25461 the character can be centered.
25464 \begin_layout Subsection
25466 \begin_inset LatexCommand index
25467 name "Minuscule numbers"
25474 \begin_layout Standard
25475 Minuscule numbers are created with the command
25482 \begin_inset LatexCommand index
25483 name "Commands ! O ! \\textbackslash oldstylenums"
25488 The command can be used in formulas and in TeX-mode.
25489 The command scheme is:
25492 \begin_layout Standard
25497 oldstylenums{number}
25500 \begin_layout Standard
25505 oldstylenums{0123456789
25508 \begin_inset Formula $\oldstylenums{0123456789}$
25514 \begin_layout Subsection
25515 Miscellaneous Special Characters
25516 \begin_inset LatexCommand label
25517 name "sub:Miscellaneous-Special-Characters"
25522 \begin_inset LatexCommand index
25523 name "Special characters ! miscellaneous"
25530 \begin_layout Standard
25531 The following characters can only be inserted to formulas by using commands:
25534 \begin_layout Standard
25536 \begin_inset Tabular
25537 <lyxtabular version="3" rows="4" columns="2">
25539 <column alignment="center" valignment="top" leftline="true" width="0">
25540 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25541 <row topline="true" bottomline="true">
25542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25545 \begin_layout Standard
25551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25554 \begin_layout Standard
25561 <row topline="true">
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25565 \begin_layout Standard
25572 \begin_layout Standard
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25589 \begin_layout Standard
25590 \begin_inset Formula $\mathcircumflex$
25599 <row topline="true">
25600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25603 \begin_layout Standard
25611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25614 \begin_layout Standard
25615 \begin_inset Formula $\_$
25624 <row topline="true" bottomline="true">
25625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25628 \begin_layout Standard
25633 \begin_layout Standard
25645 \begin_inset LatexCommand index
25655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25658 \begin_layout Standard
25659 \begin_inset Formula $^{\circ}$
25675 \begin_layout Standard
25676 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25677 contains the following line
25681 \begin_layout Standard
25682 More about this is described in
25683 \begin_inset LatexCommand ref
25684 reference "sub:Text-Characters-in"
25696 \begin_layout Standard
25701 DeclareInputtext{176}{
25711 f\SpecialChar \textcompwordmark{}
25715 \begin_layout Standard
25716 \begin_inset VSpace bigskip
25720 \begin_inset LatexCommand index
25725 is designed as accent, thus is looks alone a bit misplaced: ~
25728 addresses (URLs) sometimes a single tilde is needed.
25729 In this case the relation sign
25737 \begin_layout Standard
25739 \begin_inset LatexCommand ref
25740 reference "sec:Relations"
25751 is used in a formula.
25752 As a formula cannot be created in an URL-box (menu
25754 Insert\SpecialChar \menuseparator
25757 ), the URL is inserted as normal text with the font style '
25762 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25772 \begin_layout Standard
25779 can only be used together with the LaTeX-package
25784 \begin_inset LatexCommand index
25785 name "Packages ! hyperref"
25796 is written in the section
25802 Embedded\InsetSpace ~
25811 \begin_inset LatexCommand index
25812 name "Commands ! H ! \\textbackslash href"
25819 \begin_layout Standard
25820 As example an URL with a tilde:
25823 \begin_layout Standard
25826 http://www.lyx.org/
25827 \begin_inset Formula $\sim$
25833 \begin_layout Standard
25844 \begin_layout Standard
25848 href{http://www.lyx.org/~mustermann}{
25853 http://www.lyx.org/
25854 \begin_inset Formula $\sim$
25861 \begin_layout Standard
25871 \begin_layout Section
25873 \begin_inset LatexCommand label
25874 name "sec:Formula-Styles"
25879 \begin_inset LatexCommand index
25880 name "Formula ! styles"
25887 \begin_layout Itemize
25888 There are two different alignment styles:
25892 \begin_layout Description
25893 Centered is the predefined standard
25896 \begin_layout Description
25897 Indented for this the option
25901 must be inserted in the menu
25903 Document\SpecialChar \menuseparator
25908 Document\InsetSpace ~
25912 \begin_layout Standard
25917 is used, the indentation can be adjusted with the length
25924 \begin_inset LatexCommand index
25925 name "Commands ! M ! \\textbackslash mathindent"
25930 Should the distance be 15\InsetSpace \thinspace{}
25931 mm, the following command line is inserted in
25935 \begin_layout Standard
25945 \begin_layout Standard
25946 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25951 \begin_layout Itemize
25952 And two different numbering styles:
25956 \begin_layout Description
25957 Right is the predefined standard
25960 \begin_layout Description
25961 Left for this the option
25965 must be inserted in the menu
25967 Document\SpecialChar \menuseparator
25972 Document\InsetSpace ~
25977 \begin_layout Standard
25986 can also be used together.
25987 In this case both options are inserted, separated by a comma.
25990 \begin_layout Standard
25991 The chosen styles are used for all displayed formulas of the document.
25992 When both, centered and indented formulas should be created in a document,
25998 The indented formulas are then set in a flalign environment, see
25999 \begin_inset LatexCommand ref
26000 reference "sub:Flalign-Environment"
26007 \begin_layout Section
26009 \begin_inset LatexCommand label
26010 name "sec:Multiline-Formulas"
26015 \begin_inset LatexCommand index
26016 name "Formula ! multiline"
26023 \begin_layout Subsection
26027 \begin_layout Standard
26028 In LyX multiline formulas are created by pressing
26039 that is described in
26040 \begin_inset LatexCommand ref
26041 reference "sub:Standard-align-Environment"
26048 \begin_layout Standard
26049 There are other multiline formula environments that can be created via the
26052 Insert\SpecialChar \menuseparator
26056 These environments are described in the following sections.
26059 \begin_layout Standard
26060 In all multiline formula environments a new line is created by pressing
26066 To add or delete lines, the math toolbar buttons
26067 \begin_inset Graphics
26068 filename ../images/tabular-feature_append-row.png
26074 \begin_inset Graphics
26075 filename ../images/tabular-feature_delete-row.png
26080 , respectively, or the menu
26082 Edit\SpecialChar \menuseparator
26088 \begin_layout Subsubsection
26090 \begin_inset LatexCommand label
26091 name "sub:Line-Separation"
26096 \begin_inset LatexCommand index
26097 name "Formula ! multiline ! Line separation"
26104 \begin_layout Standard
26105 There is sometimes not enough space in multiline formulas between the lines:
26106 \begin_inset Formula \begin{eqnarray*}
26107 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}\\
26108 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*}
26115 \begin_layout Standard
26116 In LaTeX additional line space is specified as optional argument of the
26118 This is not yet possible in LyX
26122 \begin_layout Standard
26127 \begin_layout Standard
26131 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26140 \begin_layout Standard
26152 , therefore the whole formula must be inserted in TeX-mode.
26153 To add in our example space, the command
26161 is inserted at the end of the first line.
26166 \begin_layout Standard
26173 \begin_layout Standard
26175 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26178 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26185 \begin_layout Standard
26189 left(B^{2}+x_{0}^{2}
26197 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26202 \begin_layout Standard
26214 \begin_layout Standard
26215 \begin_inset VSpace bigskip
26218 To set the the line separation for all lines in a formula, the length
26225 \begin_inset LatexCommand index
26226 name "Commands ! J ! \\textbackslash jot"
26232 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26242 is the value 3\InsetSpace \thinspace{}
26244 To create 3\InsetSpace \thinspace{}
26245 mm additional line separation as in the previous example, the
26249 \begin_layout Standard
26259 \begin_layout Standard
26260 is inserted in TeX-mode before the formula.
26261 This requires that the LaTeX-package
26269 \begin_layout Standard
26274 is part of every LaTeX standard installation.
26280 \begin_inset LatexCommand index
26281 name "Packages ! calc"
26285 was loaded in LaTeX-preamble with the line
26288 \begin_layout Standard
26296 \begin_layout Standard
26301 \begin_layout Standard
26313 \begin_inset Formula \begin{eqnarray*}
26314 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}\\
26315 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*}
26322 \begin_layout Standard
26326 \begin_layout Standard
26337 To get back to the predefined distance,
26343 is set to the value 3\InsetSpace \thinspace{}
26347 \begin_layout Subsubsection
26349 \begin_inset LatexCommand label
26350 name "sub:Column-Separation"
26355 \begin_inset LatexCommand index
26356 name "Formula ! multiline ! Column separation"
26363 \begin_layout Standard
26364 Multiline formulas form a matrix.
26365 A formula in the eqnarray environment is for example a matrix with three
26367 By changing the column separation in this environment, the space beside
26368 the relation sign can be changed.
26371 \begin_layout Standard
26372 The column separation is specified with the length
26379 \begin_inset LatexCommand index
26380 name "Commands ! A ! \\textbackslash arraycolsep"
26386 column separation = 2\InsetSpace \thinspace{}
26398 \begin_layout Standard
26408 \begin_layout Standard
26409 inserted in TeX-mode, sets for all following formulas a column separation
26410 of 2\InsetSpace \thinspace{}
26412 To get back to the predefined distance,
26418 is set to 5\InsetSpace \thinspace{}
26422 \begin_layout Standard
26423 A formula with 2\InsetSpace \thinspace{}
26424 cm column separation:
26428 \begin_layout Standard
26440 \begin_inset Formula \begin{eqnarray*}
26442 C & \ne & A\end{eqnarray*}
26446 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26451 \begin_layout Standard
26463 \begin_inset Formula \begin{eqnarray*}
26465 C & \ne & A\end{eqnarray*}
26472 \begin_layout Subsubsection
26474 \begin_inset LatexCommand index
26475 name "Formula ! long"
26482 \begin_layout Standard
26483 Long formulas can be typeset using these methods:
26486 \begin_layout Itemize
26487 When one side of the equation is much shorther than the line width, this
26488 one is chosen for the left side and the right side is typeset over two
26493 \begin_layout Standard
26503 \begin_inset Formula \begin{eqnarray}
26504 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 \\
26505 & & -\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}
26513 \begin_layout Standard
26524 The minus sign at the beginning of the second line does normally not appear
26525 as operator because it is the first character of the line.
26526 Thus it would not be surrounded by space and could not be distinguished
26527 from the fraction bar.
26528 To avoid this, space was inserted behind the minus sign with the command
26539 \begin_layout Standard
26547 \begin_inset LatexCommand ref
26548 reference "sub:Variable-Space"
26558 \begin_inset LatexCommand index
26559 name "Commands ! H ! \\textbackslash hspace"
26566 \begin_layout Itemize
26567 When both sides of the equation are too long, the command
26574 \begin_inset LatexCommand index
26575 name "Commands ! L ! \\textbackslash lefteqn"
26580 It is inserted to the first column of the first line and effects that all
26581 further insertions overwrite the following columns:
26585 \begin_layout Standard
26595 \begin_inset Formula \begin{eqnarray}
26596 \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 \\
26597 & & -\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 \\
26598 & & =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}
26606 \begin_layout Standard
26617 After the insertion of
26623 , the cursor is in a purple box that is a bit shifted to the left from the
26625 In this the formula is inserted.
26629 \begin_layout Standard
26640 The content of the further lines is inserted to the second or another formula
26642 The greater the column number where it was inserted, the larger the indentation.
26646 \begin_layout Standard
26658 \begin_inset Note Greyedout
26661 \begin_layout Standard
26662 Note the following when using
26671 \begin_layout Itemize
26672 The formula doesn't use the full page width.
26673 When e.\InsetSpace \thinspace{}
26676 \begin_inset Formula $-B^{2}$
26679 is added to the first line in the above example, it would have been outside
26681 To better use the width, negative space can be inserted at the beginning
26685 \begin_layout Itemize
26686 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26691 \begin_layout Standard
26695 \begin_layout Standard
26699 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26708 \begin_layout Standard
26720 One can only set the cursor at the beginning of the line and move it with
26729 \begin_layout Itemize
26730 Other methods to set long formulas are offered by the environments described
26732 \begin_inset LatexCommand ref
26733 reference "sub:Multline-Environment"
26738 \begin_inset LatexCommand ref
26739 reference "sub:Multiline-Formula-Parts"
26746 \begin_layout Subsubsection
26748 \begin_inset LatexCommand label
26749 name "sub:Multiline-Brackets"
26754 \begin_inset LatexCommand index
26755 name "Brackets ! for multiline expressions"
26762 \begin_layout Standard
26763 For brackets spanning multiple lines the following problem occurs:
26764 \begin_inset Formula \begin{eqnarray*}
26765 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26766 & & \left.\cdots+B-D\right]\end{eqnarray*}
26773 \begin_layout Standard
26774 The closing bracket is smaller than the opening bracket because brackets
26775 with variable size may not span multiple lines.
26778 \begin_layout Standard
26779 To set the bracket size for the second line correctly, the first line is
26787 \begin_inset LatexCommand index
26788 name "Commands ! R ! \\textbackslash right"
26792 and the second line with
26800 \begin_layout Standard
26814 \begin_inset LatexCommand ref
26815 reference "sub:Automatic-Bracket-Size"
26827 \begin_inset LatexCommand index
26828 name "Commands ! L ! \\textbackslash left"
26850 \begin_layout Standard
26869 \begin_layout Standard
26888 \begin_layout Standard
26900 \begin_inset Formula $\downarrow$
26906 \begin_inset LatexCommand index
26907 name "Commands ! V ! \\textbackslash vphantom"
26911 is inserted, because the multiplication operator with its limits is the
26912 largest symbol in the first line and this should be the size for the bracket
26913 in the second line.
26916 \begin_layout Standard
26917 The result is this:
26918 \begin_inset Formula \begin{eqnarray*}
26919 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26920 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26927 \begin_layout Subsection
26931 \begin_layout Standard
26932 Align environments can be used for every kind of multiline formulas.
26933 They are specially useful to set several formulas side by side.
26936 \begin_layout Standard
26937 Align environments consist of columns.
26938 The odd columns are right aligned, the even ones left aligned.
26939 Every line in an Align environment can be numbered.
26942 \begin_layout Standard
26943 Align environments are created via the menu
26945 Insert\SpecialChar \menuseparator
26951 Edit\SpecialChar \menuseparator
26952 Math\SpecialChar \menuseparator
26953 Change Formula Type
26955 already existing existing formulas can be converted to Align environments.
26958 \begin_layout Standard
26959 To add or delete columns, the math toolbar buttons
26960 \begin_inset Graphics
26961 filename ../images/tabular-feature_append-column.png
26967 \begin_inset Graphics
26968 filename ../images/tabular-feature_delete-column.png
26973 , respectively, or the menu
26975 Edit\SpecialChar \menuseparator
26981 \begin_layout Subsubsection
26982 Standard align Environment
26983 \begin_inset LatexCommand label
26984 name "sub:Standard-align-Environment"
26989 \begin_inset LatexCommand index
26990 name "Formula ! multiline ! align environment"
26997 \begin_layout Standard
26998 This Align environment is created by presssing
27002 in a formula or by the menu
27004 Insert\SpecialChar \menuseparator
27005 Math\SpecialChar \menuseparator
27006 AMS align Environment
27011 \begin_layout Standard
27012 An example for two formulas set side by side, that are created with a four
27013 column align environment:
27014 \begin_inset Formula \begin{align*}
27015 A & =\sin(B) & C & =D\\
27016 C & \ne A & B & \ne D\end{align*}
27020 As it can be seen, the formulas in this environment are placed so as if
27029 \begin_layout Standard
27037 \begin_inset LatexCommand ref
27038 reference "sub:Variable-Space"
27049 before the first and after every even column.
27050 When the formula style
27056 \begin_layout Standard
27058 \begin_inset LatexCommand ref
27059 reference "sec:Formula-Styles"
27070 is used, the formula is set without the
27076 before the first column.
27079 \begin_layout Subsubsection
27080 Alignat Environment
27081 \begin_inset LatexCommand index
27082 name "Formula ! multiline ! alignat environment"
27089 \begin_layout Standard
27090 The alignat environment has no predefined column separation.
27091 It can be inserted manually with the spaces that are described
27092 \begin_inset LatexCommand ref
27093 reference "sub:Space"
27100 \begin_layout Standard
27101 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27102 cm space was inserted
27103 at the beginning of the second formula:
27104 \begin_inset Formula \begin{alignat*}{2}
27105 A & =\sin(B) & \hspace{1cm}C & =D\\
27106 C & \ne A & B & \ne D\end{alignat*}
27110 Because the column separation can be set separately for every column, this
27111 environment is especially suitable to set three and more formulas side
27115 \begin_layout Subsubsection
27116 Flalign Environment
27117 \begin_inset LatexCommand label
27118 name "sub:Flalign-Environment"
27123 \begin_inset LatexCommand index
27124 name "Formula ! multiline ! flalign environment"
27131 \begin_layout Standard
27132 In this environment the first two columns are always set as much as possible
27133 to the left and the last two ones to the right.
27135 \begin_inset Formula \begin{flalign*}
27136 A & =1 & B & =2 & C & =3\\
27137 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27144 \begin_layout Standard
27145 By creating a flalign environment with an odd number of columns where an
27146 empty TeX-brace is inserted to the last column, several formulas in a document
27147 can be set to the left, although the formula style
27152 As example the indented formula
27153 \begin_inset LatexCommand eqref
27154 reference "eq:VolInt"
27159 \begin_inset Formula \begin{flalign}
27160 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27164 The first two columns contain the formula.
27165 To indent it as with the formula style
27169 , 30\InsetSpace \thinspace{}
27170 pt space was inserted at the beginning of the first column.
27173 \begin_layout Subsection
27174 Eqnarray Environment
27175 \begin_inset LatexCommand index
27176 name "Formula ! multiline ! eqnarray environment"
27183 \begin_layout Standard
27184 When this environment has been created, three blue boxes appear.
27185 The content of the first box is right aligned, the content of the last
27187 The content of the middle box appears centered and a bit smaller, because
27188 it is designed to insert there only relation characters.
27189 \begin_inset Formula \begin{eqnarray*}
27190 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27192 A & = & A\end{eqnarray*}
27199 \begin_layout Subsection
27201 \begin_inset LatexCommand index
27202 name "Formula ! multiline ! gather environment"
27209 \begin_layout Standard
27210 This environment consists of only one centered column.
27211 Every line can be numbered.
27212 \begin_inset Formula \begin{gather}
27214 X=\textrm{-}1\end{gather}
27221 \begin_layout Subsection
27222 Multline Environment
27223 \begin_inset LatexCommand label
27224 name "sub:Multline-Environment"
27229 \begin_inset LatexCommand index
27230 name "Formula ! multiline ! multline environment"
27237 \begin_layout Standard
27238 The multline environment consists, like the gather environment, of only
27240 But the first line is left aligned, the last one right aligned.
27241 All other lines are centered.
27242 Therefore this environment is suitable for long formulas.
27244 \begin_inset LatexCommand eqref
27245 reference "eq:lefteqn"
27249 in the multline environment:
27250 \begin_inset Formula \begin{multline}
27251 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}\\
27252 -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}\\
27253 =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}
27260 \begin_layout Standard
27261 In the output only the the last (first) line of a multline environment appears
27262 numbered when the document numbering is right (left).
27266 \begin_layout Standard
27267 numbering styles see
27268 \begin_inset LatexCommand ref
27269 reference "sec:Formula-Styles"
27278 This is also the case when there is a formula number displayed after every
27283 \begin_layout Standard
27288 \begin_layout Standard
27292 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27301 \begin_layout Standard
27316 \begin_layout Standard
27322 \begin_inset LatexCommand index
27323 name "Commands ! S ! \\textbackslash shoveright"
27334 \begin_inset LatexCommand index
27335 name "Commands ! S ! \\textbackslash shoveleft"
27341 a centered line can be right or left aligned, respectively.
27342 The commands are used as follows:
27345 \begin_layout Standard
27350 shoveright{line content}
27356 shoveleft{line content}
27359 \begin_layout Standard
27360 \begin_inset VSpace medskip
27368 \begin_inset LatexCommand index
27369 name "Commands ! M ! \\textbackslash multlinegap"
27375 specifies the distance of the first line from the left page margin.
27376 Predefined is the length 0\InsetSpace \thinspace{}
27380 \begin_layout Standard
27381 As example the above formula where the command
27384 \begin_layout Standard
27394 \begin_layout Standard
27395 was inserted in TeX-mode before:
27399 \begin_layout Standard
27411 \begin_inset Formula \begin{multline}
27412 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}\\
27413 \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}}\\
27414 =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}
27422 \begin_layout Standard
27433 The second line was left aligned using
27442 \begin_layout Subsection
27443 Multiline Formula Parts
27444 \begin_inset LatexCommand label
27445 name "sub:Multiline-Formula-Parts"
27450 \begin_inset LatexCommand index
27451 name "Formula ! multiline ! formula parts"
27458 \begin_layout Standard
27459 To display only parts of a formula with multiple lines, one of the following
27460 environments are used:
27477 They can be inserted via the menu
27479 Insert\SpecialChar \menuseparator
27482 or by using the commands described in this section.
27485 \begin_layout Standard
27486 The first three have the same properties as the corresponding multiline
27487 formula environments, but it is possible to set further formula parts beside
27490 \begin_inset Formula \[
27491 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27492 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27493 \right\} \textrm{Uncertainty relations}\]
27500 \begin_layout Standard
27501 To get this formula, a displayed formula is created where the command
27506 \begin_inset LatexCommand index
27507 name "Commands ! A ! \\textbackslash aligned"
27514 A purple box appears around the blue formula box where now columns and
27515 lines can be added.
27516 Outside the multiline environment other formula parts can be set, like
27520 \begin_layout Standard
27521 The aligned environment is also suitable for long formulas whose lines are
27522 horizontally aligned.
27523 Using aligned in a displayed formula has the advantage that the formula
27524 number is vertically centered behind the lines.
27526 \begin_inset LatexCommand eqref
27527 reference "eq:kurzlang"
27531 in the aligned environment:
27532 \begin_inset Formula \begin{equation}
27533 \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}|}\\
27534 & -\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}
27542 \begin_layout Standard
27543 To use the environments
27562 \begin_inset LatexCommand index
27563 name "Commands ! A ! \\textbackslash alignedat"
27574 \begin_inset LatexCommand index
27575 name "Commands ! G ! \\textbackslash gathered"
27586 \begin_inset LatexCommand index
27587 name "Commands ! S ! \\textbackslash split"
27591 are inserted, respectively.
27592 The split environment has the same properties as the aligned environment
27593 but it can only have two columns.
27596 \begin_layout Subsection
27597 Text in multiline Formulas
27598 \begin_inset LatexCommand label
27599 name "sub:Text-in-multiline"
27604 \begin_inset LatexCommand index
27605 name "Text ! in formulas"
27610 \begin_inset LatexCommand index
27611 name "Formula ! multiline ! text"
27618 \begin_layout Standard
27619 In the Align environments, and the multline and gather environment, text
27620 can be inserted that will appear in a separate line and doesn't affect
27621 the column alignment.
27622 To do this, the command
27627 \begin_inset LatexCommand index
27628 name "Commands ! I ! \\textbackslash intertext"
27634 is used in the following scheme:
27637 \begin_layout Standard
27645 \begin_layout Standard
27646 The text should not be longer than a line because it cannot be hyphenated.
27647 As LyX doesn't yet support
27653 directly, the text is written as mathematical text.
27660 must hereby be at the beginning of a line and appears in the output above
27662 An example where the text was inserted at the beginning of the second line:
27663 \begin_inset Formula \begin{align}
27664 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27665 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27672 \begin_layout Section
27674 \begin_inset LatexCommand index
27675 name "Formula numbering"
27680 \begin_inset LatexCommand index
27681 name "Formula ! numbering|see{Formula numbering}"
27688 \begin_layout Subsection
27692 \begin_layout Standard
27693 Numbered formulas can be created with the menu
27695 Insert\SpecialChar \menuseparator
27696 Math\SpecialChar \menuseparator
27697 Numbered\InsetSpace ~
27702 Ctrl-Alt\InsetSpace ~
27706 Existing formulas can be numbered with the menu
27708 Edit\SpecialChar \menuseparator
27709 Math\SpecialChar \menuseparator
27710 Toggle\InsetSpace ~
27719 The formula number is displayed in LyX behind the formula as number sign
27721 The number sign is replaced in the output by the formula number.
27724 \begin_layout Standard
27725 When numbering is turned on in multiline formulas, all lines will be numbered.
27726 But the numbering can be controlled with the menu
27728 Edit\SpecialChar \menuseparator
27729 Math\SpecialChar \menuseparator
27730 Toggle\InsetSpace ~
27731 Numbering\InsetSpace ~
27743 \begin_layout Standard
27744 Except of inline formulas, all formulas can be numbered with two different
27746 \begin_inset LatexCommand ref
27747 reference "sec:Formula-Styles"
27754 \begin_layout Subsection
27756 \begin_inset LatexCommand label
27757 name "sub:Cross-References"
27762 \begin_inset LatexCommand index
27763 name "Cross-references ! to formulas"
27770 \begin_layout Standard
27771 All labeled formulas can be cross-referenced.
27772 A label is added by the menu
27774 Insert\SpecialChar \menuseparator
27777 or the toolbar button
27778 \begin_inset Graphics
27779 filename ../images/label-insert.png
27785 The cursor must hereby be inside a displayed formula.
27786 A dialog pops up displaying the prefix
27791 The label is inserted there behind the prefix.
27792 The predefined prefix means
27793 \begin_inset Quotes eld
27797 \begin_inset Quotes erd
27800 and makes it easier to find labels in large documents because it marks
27801 it as formula label to divide it from e.\InsetSpace \thinspace{}
27804 To change a label, the menu
27806 Insert\SpecialChar \menuseparator
27812 \begin_layout Standard
27813 The name of the label is displayed in LyX within two parentheses behind
27815 A formula with a label is always numbered.
27816 The label is deleted when the numbering is turned off.
27817 This is at the moment the only way to delete a label, see
27821 \begin_layout Standard
27825 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27834 \begin_layout Standard
27844 \begin_layout Standard
27845 Cross-references are inserted via the menu
27847 Insert\SpecialChar \menuseparator
27850 or with the toolbar button
27851 \begin_inset Graphics
27852 filename ../images/dialog-show-new-inset_ref.png
27858 A formula cross-reference appears in the output as formula number.
27859 When in the cross-reference dialog window the format
27863 is chosen, the cross-reference appears in the output as formula number
27866 By right-clicking on a cross-reference in LyX, one jumps
27867 to the formula that is referenced.
27870 \begin_layout Standard
27871 Here are as examples cross-references to formulas of the following subsections:
27872 \begin_inset Note Note
27875 \begin_layout Standard
27876 Note the different cross-reference types.
27884 \begin_layout Standard
27886 \begin_inset LatexCommand eqref
27892 \begin_inset LatexCommand eqref
27899 \begin_inset LatexCommand ref
27904 ) big Latin letters are used for the numbering in contrary to (
27905 \begin_inset LatexCommand ref
27913 \begin_layout Standard
27914 \begin_inset VSpace medskip
27917 When the argument of
27925 \begin_layout Standard
27933 \begin_inset LatexCommand ref
27934 reference "sub:User-defined-Numbering"
27945 contains a box like in
27946 \begin_inset LatexCommand ref
27947 reference "sub:Paragraph-Boxes"
27951 , the formula cannot be referenced.
27954 \begin_layout Subsection
27956 \begin_inset LatexCommand index
27957 name "Formula numbering ! subnumbering"
27964 \begin_layout Standard
27965 With the help of the commands
27969 begin{subequations}
27977 formulas can be subnumbered.
27978 Both commands are inserted in TeX-mode.
27981 \begin_layout Standard
27983 \begin_inset Formula \begin{equation}
27984 A=C-B\label{eq:a}\end{equation}
27992 \begin_layout Standard
27996 addtocounter{equation}{-1}
28005 \begin_layout Standard
28009 begin{subequations}
28015 \begin_inset VSpace -5mm
28019 \begin_inset Formula \begin{equation}
28020 B=C-A\label{eq:b}\end{equation}
28025 \begin_inset Formula \begin{equation}
28026 C=A+B\label{eq:c}\end{equation}
28033 \begin_layout Standard
28037 \begin_layout Standard
28049 \begin_layout Standard
28050 To create the example, the following is done:
28053 \begin_layout Enumerate
28054 first formula is inserted
28057 \begin_layout Enumerate
28062 addtocounter{equation}{-1}
28064 begin{subequations}
28065 \begin_inset LatexCommand index
28066 name "Commands ! A ! \\textbackslash addtocounter"
28074 is inserted after the first formula
28077 \begin_layout Enumerate
28078 second formula is inserted
28081 \begin_layout Enumerate
28082 third formula is inserted
28085 \begin_layout Enumerate
28092 is inserted after the third formula
28095 \begin_layout Standard
28096 Every formula between the commands
28108 is subnumbered as a, b,
28112 \begin_layout Standard
28121 c, \SpecialChar \ldots{}
28122 For multiline formulas every line will be subnumbered.
28123 All subnumbered formulas are treated as
28128 But as every numbered formula increases the counter
28132 by one, the command
28138 is needed to decrease it.
28139 Otherwise the formulas
28140 \begin_inset LatexCommand eqref
28146 \begin_inset LatexCommand eqref
28152 \begin_inset LatexCommand eqref
28157 would be numbered as
28158 \begin_inset LatexCommand eqref
28164 \begin_inset LatexCommand eqref
28170 \begin_inset LatexCommand eqref
28178 \begin_layout Standard
28179 By inserting the commands in TeX-mode, a space is created between the first
28181 To revert this -5\InsetSpace \thinspace{}
28182 mm vertical space is inserted after the command
28186 begin{subequations}
28189 When the formula style
28195 \begin_layout Standard
28197 \begin_inset LatexCommand ref
28198 reference "sec:Formula-Styles"
28209 is used, -7\InsetSpace \thinspace{}
28210 mm space is inserted instead.
28213 \begin_layout Standard
28214 Here is an example for a multiline formula where the numbering was turned
28215 off for the second line:
28219 \begin_layout Standard
28223 begin{subequations}
28229 \begin_inset Formula \begin{eqnarray}
28230 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28231 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28232 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28240 \begin_layout Standard
28252 \begin_layout Subsection
28253 User-defined Numbering
28254 \begin_inset LatexCommand label
28255 name "sub:User-defined-Numbering"
28260 \begin_inset LatexCommand index
28261 name "Formula numbering ! user-defined"
28268 \begin_layout Standard
28269 \begin_inset LatexCommand index
28270 name "Formula numbering ! self-defined delimiters"
28274 With the standard numbering parentheses are set around the formula number.
28275 To replace the parentheses for example by vertical bars, the following
28276 line is added to the LaTeX-preamble:
28279 \begin_layout Standard
28291 \begin_inset Note Note
28294 \begin_layout Standard
28295 This macro is already declared in the LaTeX-preamble for testing.
28296 To activate it, remove the percent sign at the beginning.
28304 \begin_layout Standard
28305 To use other characters, the vertical bars besides the
28309 are replaced by one ore more characters.
28310 To get only the formula number the vertical bars are omitted.
28313 \begin_layout Standard
28314 \begin_inset VSpace bigskip
28317 When there should be an expression of your choice instead of the consecutive
28318 formula number in parentheses behind the formula, the command
28325 \begin_inset LatexCommand index
28326 name "Commands ! T ! \\textbackslash tag"
28331 \begin_inset Formula \begin{equation}
28332 A+B=C\tag{something}\label{eq:tag}\end{equation}
28336 In this example the command
28344 was inserted to the formula.
28347 \begin_layout Standard
28356 is inserted instead, the star prevents the parentheses around the expression:
28357 \begin_inset Formula \[
28358 A+B=C\tag*{something}\]
28365 \begin_layout Standard
28366 \begin_inset VSpace bigskip
28369 To restart the formula numbering with new document parts or sections, the
28370 following command is used:
28373 \begin_layout Standard
28378 @addtoreset{equation}{part}
28381 \begin_inset LatexCommand index
28382 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28394 @addtoreset{equation}{section}
28397 \begin_layout Standard
28398 To be able to use these commands in TeX-mode, the
28399 \begin_inset Quotes eld
28403 \begin_inset Quotes erd
28406 character has to be made
28407 \begin_inset Quotes eld
28411 \begin_inset Quotes erd
28414 for LaTeX using the command
28428 So the command sequence in TeX-mode is:
28431 \begin_layout Standard
28440 @addtoreset{equation}{section}
28447 \begin_layout Standard
28448 In the LaTeX-preamble
28460 can be omitted as they are automatically internally inserted by LyX.
28463 \begin_layout Standard
28478 \begin_layout Standard
28483 is part of the LaTeX-package
28488 \begin_inset LatexCommand index
28489 name "Packages ! carlisle"
28493 that is part of every LaTeX standard installation.
28499 \begin_inset LatexCommand index
28500 name "Packages ! remreset"
28504 has to be loaded in the LaTeX-preamble with the line
28507 \begin_layout Standard
28512 usepackage{remreset}
28515 \begin_layout Standard
28523 \begin_inset LatexCommand index
28524 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28528 can be used with the same scheme as
28537 \begin_layout Standard
28538 \begin_inset VSpace bigskip
28541 Sometimes formulas should be numbered in the following form:
28544 \begin_layout Standard
28547 (section number.formula number)
28550 \begin_layout Standard
28551 The formula number should start with every section with
28552 \begin_inset Quotes eld
28556 \begin_inset Quotes erd
28562 \begin_layout Standard
28563 For this case there is the command
28570 \begin_inset LatexCommand index
28571 name "Commands ! N ! \\textbackslash numberwithin"
28575 , which is used with the following scheme:
28578 \begin_layout Standard
28583 numberwithin{counter}{sectioning}
28586 \begin_layout Standard
28587 Counter denotes what kind of numbering is affected, sectioning denotes what
28588 number is before the dot.
28591 \begin_layout Standard
28592 Thus in our case the following LaTeX-preamble or ERT line is used:
28595 \begin_layout Standard
28600 numberwithin{equation}{section}
28603 \begin_layout Standard
28604 This is the result:
28608 \begin_layout Standard
28612 numberwithin{equation}{section}
28618 \begin_inset Formula \begin{equation}
28619 A+B=C\end{equation}
28626 \begin_layout Standard
28627 To number e.\InsetSpace \thinspace{}
28629 tables so that the number of the part is the sectioning,
28635 numberwithin{table}{part}
28640 \begin_layout Standard
28641 To go back to the standard numbering or to prevent this kind of numbering
28642 when it is defined by the document class, the following command is inserted
28643 as ERT or to the LaTeX-preamble:
28646 \begin_layout Standard
28656 \begin_inset LatexCommand index
28657 name "Commands ! A ! \\textbackslash arabic"
28667 \begin_layout Standard
28699 \begin_layout Standard
28706 uses internally the command
28712 , described above, that also needs to be reverted.
28716 \begin_layout Standard
28723 \begin_layout Standard
28727 @removefromreset{equation}{section}
28730 \begin_layout Standard
28742 \begin_layout Subsection
28743 Numbering with Roman Numbers and Letters
28744 \begin_inset LatexCommand label
28745 name "sub:Numbering-with-Roman"
28750 \begin_inset LatexCommand index
28751 name "Formula numbering ! with letters"
28756 \begin_inset LatexCommand index
28757 name "Formula numbering ! with Roman numbers"
28764 \begin_layout Standard
28765 Formulas can also be numbered with Roman numbers and Latin letters.
28766 To number for example with small Roman numbers, the command
28769 \begin_layout Standard
28781 \begin_layout Standard
28782 is inserted before the formula in TeX-mode.
28790 \begin_inset LatexCommand index
28791 name "Commands ! R ! \\textbackslash renewcommand"
28795 redefines the predefined command
28811 \begin_layout Standard
28818 has the same scheme like the command
28824 that is described in
28825 \begin_inset LatexCommand ref
28826 reference "sec:User-defined-commands"
28840 is the formula counter.
28847 is used as prefix for a counter, the value of the counter is output as
28849 When a formula is numbered, LaTeX sets internally the command
28855 behind the formula.
28861 \begin_inset LatexCommand index
28862 name "Commands ! R ! \\textbackslash roman"
28868 outputs the counter as small Roman number.
28871 \begin_layout Standard
28872 All formulas behind the command
28882 are now numbered Roman.
28883 To switch to numbering with big Roman numbers, the command is inserted
28897 \begin_inset LatexCommand index
28898 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28904 \begin_inset Quotes eld
28908 \begin_inset Quotes erd
28911 with small Latin letters there is the command
28918 \begin_inset LatexCommand index
28919 name "Commands ! A ! \\textbackslash alph"
28923 , for big ones there is the command
28930 \begin_inset LatexCommand index
28931 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28938 \begin_layout Standard
28939 \begin_inset Note Greyedout
28942 \begin_layout Standard
28947 Only maximal 26 formulas can be numbered with Latin letters in one document.
28955 \begin_layout Standard
28959 \begin_layout Standard
28975 \begin_layout Standard
28976 \begin_inset Formula \begin{equation}
28977 A=\textrm{small roman}\label{eq:rom}\end{equation}
28985 \begin_layout Standard
28999 \begin_inset Formula \begin{equation}
29000 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
29008 \begin_layout Standard
29022 \begin_inset Formula \begin{equation}
29023 C=\textrm{small Latin}\label{eq:lat}\end{equation}
29031 \begin_layout Standard
29045 \begin_inset Formula \begin{equation}
29046 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
29053 \begin_layout Standard
29054 To switch back to the default numbering, insert the command:
29057 \begin_layout Standard
29067 \begin_inset LatexCommand index
29068 name "Commands ! A ! \\textbackslash arabic"
29075 \begin_layout Standard
29079 \begin_layout Standard
29093 \begin_inset Formula \begin{equation}
29094 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29101 \begin_layout Standard
29102 \begin_inset VSpace medskip
29105 As you see, formulas are numbered serially independent from the numbering
29107 When then numbering should start with
29108 \begin_inset Quotes eld
29112 \begin_inset Quotes erd
29115 when the style is changed, new equation counters have to be defined.
29116 A description about this can be found in the file
29120 \begin_layout Standard
29124 href{Formula-numbering.pdf}{
29129 Formula-numbering.pdf
29133 \begin_layout Standard
29141 \begin_inset Note Note
29144 \begin_layout Standard
29145 More about the command
29152 \begin_inset LatexCommand ref
29153 reference "sub:Links-in-DVI-"
29165 \begin_layout Section
29166 User-defined commands
29167 \begin_inset LatexCommand label
29168 name "sec:User-defined-commands"
29173 \begin_inset LatexCommand index
29174 name "User-defined commands"
29181 \begin_layout Standard
29182 Many LaTeX-commands are too long to be used frequently.
29183 But it is possible to define with the command
29190 \begin_inset LatexCommand index
29191 name "Commands ! N ! \\textbackslash newcommand"
29195 new shorter commands.
29198 \begin_layout Standard
29199 The command scheme of
29208 \begin_layout Standard
29213 newcommand{new command name}[number of arguments][optional
29223 \begin_layout Standard
29238 \begin_layout Standard
29245 {command definition}
29248 \begin_layout Standard
29249 \begin_inset Note Greyedout
29252 \begin_layout Standard
29257 Assure that the name of the new command is not already used in your document
29258 or by LaTeX-packages that you use.
29259 When you for example define the command
29271 , you get an error message because
29277 is already defined as command for
29278 \begin_inset Quotes eld
29282 \begin_inset Formula $\le$
29286 \begin_inset Quotes erd
29297 \begin_layout Standard
29298 \begin_inset Note Greyedout
29301 \begin_layout Standard
29306 The names of user-defined commands may only consist of Latin letters.
29314 \begin_layout Standard
29315 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29316 -\InsetSpace \thinspace{}
29317 9 and specifies how
29318 many arguments the new command should have.
29319 With the optional value a value for an optional argument can be predefined.
29320 When this is done, the
29328 rgument of the new command is automatically an optional one.
29331 \begin_layout Standard
29332 Here are some examples:
29335 \begin_layout Itemize
29336 To define the command
29348 , the LaTeX-preamble line is:
29352 \begin_layout Standard
29374 \begin_layout Itemize
29375 To define the command
29387 , the argument (that should be underlined) must be taken into account.
29388 For this the preamble line is:
29392 \begin_layout Standard
29417 \begin_layout Standard
29436 acts as argument placeholder, the
29440 behind it denotes that it is the placeholder for the first argument.
29443 \begin_layout Itemize
29450 one can e.\InsetSpace \thinspace{}
29462 \begin_layout Standard
29481 framebox#1#2{$#3$}}
29487 \begin_layout Standard
29502 The two Dollar signs creates the extra formula needed for
29509 \begin_inset LatexCommand ref
29510 reference "sub:Boxes-with-Frame"
29517 \begin_layout Itemize
29518 To create a new command for
29524 where the color for the box needn't to be specified, the argument for the
29525 color is defined optional:
29529 \begin_layout Standard
29548 fcolorbox{#2}{#1}{$#3$}}
29554 \begin_layout Standard
29565 When the color is not specified when using
29571 , the predefined color
29578 \begin_layout Standard
29579 A test of the new defined commands:
29582 \begin_layout Standard
29584 \begin_inset Tabular
29585 <lyxtabular version="3" rows="6" columns="2">
29587 <column alignment="center" valignment="top" leftline="true" width="0">
29588 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29589 <row topline="true" bottomline="true">
29590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29593 \begin_layout Standard
29599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29602 \begin_layout Standard
29604 \begin_inset Note Note
29607 \begin_layout Standard
29614 is only used as spacer.
29625 <row topline="true">
29626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29629 \begin_layout Standard
29636 \begin_layout Standard
29650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29653 \begin_layout Standard
29654 \begin_inset Formula $A\gr B$
29663 <row topline="true">
29664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29667 \begin_layout Standard
29675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29678 \begin_layout Standard
29679 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29688 <row topline="true">
29689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29692 \begin_layout Standard
29696 \begin_inset Formula $\to$
29702 \begin_inset Formula $\to$
29713 \begin_layout Standard
29727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29730 \begin_layout Standard
29731 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29740 <row topline="true">
29741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29744 \begin_layout Standard
29748 \begin_inset Formula $\to$
29759 \begin_layout Standard
29773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29776 \begin_layout Standard
29777 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29786 <row topline="true" bottomline="true">
29787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29790 \begin_layout Standard
29796 \begin_inset Formula $\to$
29807 \begin_layout Standard
29821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29824 \begin_layout Standard
29825 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29841 \begin_layout Section
29843 \begin_inset LatexCommand index
29851 \begin_layout Standard
29852 To create diagrams, the LaTeX-package
29858 \begin_layout Standard
29863 is part of every LaTeX standard installation.
29871 \begin_inset LatexCommand index
29872 name "Packages ! amscd"
29877 It is loaded in the LaTeX-preamble with the line
29880 \begin_layout Standard
29888 \begin_layout Standard
29889 Diagrams visualize relations and look like this:
29890 \begin_inset Formula \[
29891 \begin{CD}A@>>>B@>>>C\\
29893 F@<<<E@<<<D\end{CD}\]
29900 \begin_layout Standard
29901 To get them, the command
29906 \begin_inset LatexCommand index
29907 name "Commands ! C ! \\textbackslash CD"
29913 is inserted to a formula.
29914 A blue box appears with two dashed lines where further commands can be
29920 a new line is created.
29921 Horizontal relations are inserted in odd, vertical in even formula lines.
29924 \begin_layout Standard
29925 To create the relations there are the following commands:
29928 \begin_layout Itemize
29933 creates a left arrow,
29944 \begin_layout Itemize
29949 creates an up arrow,
29957 a vertical equal sign
29960 \begin_layout Itemize
29966 is a placeholder for non-existent relations
29969 \begin_layout Standard
29970 All arrows can be labeled as follows:
29973 \begin_layout Itemize
29974 Is text inserted between the first and second < or >, resp., it is placed
29976 When it is inserted between the second and third one, it appears under
29980 \begin_layout Itemize
29981 When text for vertical arrows is inserted between the first and second A
29982 or V, resp., it is placed left beside the arrow.
29983 When it is inserted between the second and third one, it appears right
29985 If the text contains an A or V, these letters must be set into a TeX-brace.
29988 \begin_layout Standard
29989 As example a diagram with all possible relations:
29992 \begin_layout Standard
29993 \begin_inset Formula \[
29994 \begin{CD}A@>j>>B@>>k>C@=F\\
29996 D@<<j<E@>k>>F@=C\end{CD}\]
30003 \begin_layout Standard
30004 The command for this is:
30014 \begin_layout Standard
30023 A@>j>>B@>>k>C@=F Ctrl-Enter
30029 \begin_layout Standard
30044 \begin_layout Standard
30057 \begin_layout Standard
30069 \begin_inset Formula $\to$
30080 \begin_layout Standard
30095 \begin_layout Standard
30108 \begin_layout Standard
30118 \begin_layout Standard
30124 \begin_layout Section
30129 \begin_layout Standard
30142 \begin_layout Standard
30143 Other useful math tips can be found in
30144 \begin_inset LatexCommand cite
30158 \begin_layout Standard
30166 \begin_inset Note Note
30169 \begin_layout Standard
30172 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30175 \begin_layout Standard
30178 texorpdfstring is in section
30179 \begin_inset LatexCommand ref
30180 reference "sub:Formulas-in-Section"
30190 \begin_inset LatexCommand index
30196 \begin_inset LatexCommand index
30197 name "Ions|see{Chemical characters}"
30204 \begin_layout Subsection
30205 Chemical Symbols and Equations
30206 \begin_inset LatexCommand label
30207 name "sub:Chemical-Symbols-and"
30212 \begin_inset LatexCommand index
30213 name "Chemical characters ! Symbols"
30218 \begin_inset LatexCommand index
30219 name "Chemical equations"
30224 \begin_inset LatexCommand index
30225 name "Symbols ! chemical"
30232 \begin_layout Standard
30233 An example text from chemistry:
30236 \begin_layout Quote
30238 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30241 -ion reacts with two
30242 \begin_inset Formula $\mathrm{Na^{+}}$
30245 -ions to sodium sulfate
30246 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30250 The chemical equation for this is:
30251 \begin_inset Formula \[
30252 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30259 \begin_layout Standard
30260 This chemical equation can directly be created as formula.
30261 To avoid that the symbols appear italic, everything is highlighted and
30262 changed by the shortcut
30267 to the upright font style.
30271 \begin_layout Standard
30277 \begin_inset LatexCommand ref
30278 reference "sub:Font-Styles"
30290 \begin_layout Subsection
30292 \begin_inset LatexCommand index
30293 name "Numbers ! negative"
30300 \begin_layout Standard
30301 Negative numbers often look ugly in formulas because the minus sign before
30302 the number is set with the same length as the minus operator sign.
30303 When writing the negative number in normal text, the minus sign appears
30307 \begin_layout Standard
30308 Thus, the problem disappears when converting the minus sign to mathematical
30312 \begin_layout Standard
30313 An example to visualize the problem:
30316 \begin_layout Standard
30318 \begin_inset Tabular
30319 <lyxtabular version="3" rows="3" columns="2">
30321 <column alignment="right" valignment="top" leftline="true" width="0">
30322 <column alignment="left" valignment="top" rightline="true" width="0">
30323 <row topline="true">
30324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30327 \begin_layout Standard
30333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30336 \begin_layout Standard
30343 <row topline="true" bottomline="true">
30344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30347 \begin_layout Standard
30353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30356 \begin_layout Standard
30357 \begin_inset Formula $x=-2$
30366 <row topline="true" bottomline="true">
30367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30370 \begin_layout Standard
30376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30379 \begin_layout Standard
30380 \begin_inset Formula $x=\textrm{-}2$
30396 \begin_layout Subsection
30397 Comma as Decimal Separator
30398 \begin_inset LatexCommand index
30406 \begin_layout Standard
30407 In LaTeX a comma inside a formula is used, according to the English convention,
30408 as number group separator.
30409 So there will be space added behind all commas in formulas.
30412 \begin_layout Standard
30413 To avoid this, the comma is highlighted and changed to mathematical text
30422 \begin_layout Standard
30423 To use all formula commas in the document as decimal separator, the file
30432 \begin_layout Standard
30437 is part of the LaTeX-package
30442 \begin_inset LatexCommand index
30443 name "Packages ! was\\vspace{4mm}"
30453 \begin_inset LatexCommand index
30454 name "Packages ! icomma"
30458 is loaded with the LaTeX-preamble line
30461 \begin_layout Standard
30469 \begin_layout Subsection
30471 \begin_inset LatexCommand label
30472 name "sub:Physical-Vectors"
30477 \begin_inset LatexCommand index
30478 name "Vectors ! physical"
30485 \begin_layout Standard
30486 Predefined vectors are offered by the LaTeX-package
30494 \begin_layout Standard
30499 should be part of every LaTeX standard installation.
30505 \begin_inset LatexCommand index
30506 name "Packages ! braket"
30510 that is loaded with the LaTeX-preamble line
30513 \begin_layout Standard
30521 \begin_layout Standard
30525 \begin_layout Standard
30535 \begin_inset Note Note
30538 \begin_layout Standard
30539 The following table will only be displayed when the LaTeX-package
30548 The following commands are defined:
30551 \begin_layout Standard
30553 \begin_inset Tabular
30554 <lyxtabular version="3" rows="4" columns="2">
30556 <column alignment="center" valignment="top" leftline="true" width="0">
30557 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30558 <row topline="true" bottomline="true">
30559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30562 \begin_layout Standard
30568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30571 \begin_layout Standard
30578 <row topline="true">
30579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30582 \begin_layout Standard
30592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30595 \begin_layout Standard
30596 \begin_inset Formula $\Bra{\psi}$
30605 <row topline="true">
30606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30609 \begin_layout Standard
30619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30622 \begin_layout Standard
30623 \begin_inset Formula $\Ket{\psi}$
30632 <row topline="true" bottomline="true">
30633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30636 \begin_layout Standard
30648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30651 \begin_layout Standard
30652 \begin_inset Formula $\Braket{\psi|\phi}$
30668 \begin_layout Standard
30675 assures that all vertical bars are set in the size of the surrounding brackets:
30676 \begin_inset Formula \[
30677 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30685 \begin_layout Standard
30695 \begin_inset Note Note
30698 \begin_layout Standard
30699 The following will be displayed when the LaTeX-package
30711 \begin_layout Standard
30712 You need to install the LaTeX-package
30716 to see the rest of this subsection in the output.
30719 \begin_layout Standard
30723 \begin_layout Standard
30735 \begin_layout Standard
30742 can also be achieved using the command
30748 , that is described in
30749 \begin_inset LatexCommand ref
30750 reference "sub:Automatic-Bracket-Size"
30757 \begin_layout Subsection
30758 Self-defined Fractions
30759 \begin_inset LatexCommand label
30760 name "sub:Self-defined-Fractions"
30765 \begin_inset LatexCommand index
30766 name "Fractions ! self-defined"
30773 \begin_layout Standard
30774 To define custom commands for fractions, the command
30781 \begin_inset LatexCommand index
30782 name "Commands ! G ! \\textbackslash genfrac"
30786 is used in the following scheme:
30789 \begin_layout Standard
30802 bracket}{fraction bar thickness}{style}
30808 \begin_layout Standard
30823 \begin_layout Standard
30830 {numerator}{denominator}
30833 \begin_layout Standard
30834 The style is a number in the range of 0\InsetSpace \thinspace{}
30835 -\InsetSpace \thinspace{}
30839 \begin_layout Standard
30841 \begin_inset Tabular
30842 <lyxtabular version="3" rows="5" columns="2">
30844 <column alignment="center" valignment="top" leftline="true" width="0">
30845 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30846 <row topline="true" bottomline="true">
30847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30850 \begin_layout Standard
30856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30859 \begin_layout Standard
30866 <row topline="true">
30867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30870 \begin_layout Standard
30876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30879 \begin_layout Standard
30880 display style formula
30886 <row topline="true">
30887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30890 \begin_layout Standard
30896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30899 \begin_layout Standard
30906 <row topline="true">
30907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30910 \begin_layout Standard
30916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30919 \begin_layout Standard
30926 <row topline="true" bottomline="true">
30927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30930 \begin_layout Standard
30936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30939 \begin_layout Standard
30953 \begin_layout Standard
30954 When no style is given, the size is adjusted to the surrounding environment
30955 like for the command
30964 \begin_layout Standard
30965 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30970 \begin_layout Standard
30971 \begin_inset VSpace medskip
30974 For example, the commands
30987 \begin_inset LatexCommand ref
30988 reference "sub:Fractions"
30992 are defined with the commands
30995 \begin_layout Standard
31004 genfrac{}{}{}{0}{#1}{#2}}
31007 \begin_layout Standard
31011 \begin_layout Standard
31020 genfrac{(}{)}{0pt}{1}{#1}{#2}}
31023 \begin_layout Standard
31024 \begin_inset VSpace medskip
31027 To define a fraction where the fraction bar thickness can be given as optional
31028 argument, the following line is inserted to the LaTeX-preamble:
31031 \begin_layout Standard
31040 genfrac{}{}{#1}{}{#2}{#3}}
31043 \begin_layout Standard
31045 \begin_inset Formula \begin{align*}
31046 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
31047 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
31051 As one can see, the distance of the numerator and the denominator to the
31052 fraction bar is round about three times the bar thickness.
31055 \begin_layout Subsection
31057 \begin_inset LatexCommand label
31058 name "sub:Canceled-Formulas"
31063 \begin_inset LatexCommand index
31064 name "Formula ! canceled"
31071 \begin_layout Standard
31072 To cancel formulas or formula parts, the LaTeX-package
31080 \begin_layout Standard
31085 is part of every LaTeX standard installation.
31091 \begin_inset LatexCommand index
31092 name "Packages ! cancel"
31096 has to be loaded with the LaTeX-preamble line
31099 \begin_layout Standard
31104 usepackage[samesize]{cancel}
31107 \begin_layout Standard
31108 There are four ways to cancel formulas:
31111 \begin_layout Standard
31113 \begin_inset Tabular
31114 <lyxtabular version="3" rows="5" columns="2">
31116 <column alignment="center" valignment="top" leftline="true" width="0">
31117 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31118 <row topline="true" bottomline="true">
31119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31122 \begin_layout Standard
31128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31131 \begin_layout Standard
31133 \begin_inset Note Note
31136 \begin_layout Standard
31149 are used here as spacer.
31160 <row topline="true">
31161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31164 \begin_layout Standard
31173 \begin_layout Standard
31187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31190 \begin_layout Standard
31191 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31200 <row topline="true">
31201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31204 \begin_layout Standard
31213 \begin_layout Standard
31227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31230 \begin_layout Standard
31231 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31240 <row topline="true" bottomline="true">
31241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31244 \begin_layout Standard
31253 \begin_layout Standard
31267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31270 \begin_layout Standard
31271 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31280 <row topline="true" bottomline="true">
31281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31284 \begin_layout Standard
31288 \begin_inset Formula $\to$
31299 \begin_layout Standard
31313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31316 \begin_layout Standard
31317 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31333 \begin_layout Standard
31340 is especially suitable to visualize the reduction of fractions within formulas:
31341 \begin_inset Formula \[
31342 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31349 \begin_layout Subsection
31350 Formulas in Section Headings
31351 \begin_inset LatexCommand label
31352 name "sub:Formulas-in-Section"
31357 \begin_inset LatexCommand index
31358 name "Formula ! in section headings"
31365 \begin_layout Standard
31366 When formulas are used in section headings, the following has to be taken
31370 \begin_layout Standard
31371 \begin_inset Note Greyedout
31374 \begin_layout Standard
31375 When the LaTeX-package
31380 \begin_inset LatexCommand index
31381 name "Packages ! hyperref"
31385 is used, PDF-bookmarks are automatically created for every section heading
31386 in the table of contents.
31387 If a section heading contains formulas, they are incorrectly displayed
31388 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31397 \begin_layout Standard
31398 Both problems can be solved by inserting at the end of the section heading
31399 a short title with the menu
31401 Insert\SpecialChar \menuseparator
31406 Short titles are used as alternative for multiline section headings to
31407 keep the table of contents clearly arranged.
31408 Only the short title appears in the table of contents and therefore also
31409 in the PDF-bookmark.
31412 \begin_layout Standard
31413 When formulas should be used in the table of contents but
31417 is used, one can use the following command in TeX-mode:
31420 \begin_layout Standard
31425 texorpdfstring{part}{alternative}
31426 \begin_inset LatexCommand index
31427 name "Commands ! T ! \\textbackslash texorpdfstring"
31434 \begin_layout Standard
31435 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31436 This can be characters, formulas, footnotes, but also cross-references.
31437 The alternative is used instead of the part for the bookmark.
31440 \begin_layout Standard
31441 Here are two example headings:
31442 \begin_inset VSpace -3mm
31449 \begin_layout Standard
31461 \begin_layout Subsubsection
31462 Heading without formula in table of contents
31463 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31467 \begin_inset OptArg
31470 \begin_layout Standard
31471 Heading without formula in table of contents
31479 \begin_layout Subsubsection
31480 Heading with formula in table of contents
31484 \begin_layout Standard
31494 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31501 \begin_layout Standard
31511 \begin_layout Standard
31515 \begin_layout Standard
31524 In the first heading a short title was used, in the second one
31533 \begin_layout Standard
31534 To get the same formatting as for the other headings, the complete heading
31537 boldmath environment
31543 \begin_layout Standard
31545 \begin_inset LatexCommand ref
31546 reference "sub:Bold-Formulas"
31558 \begin_layout Subsection
31559 Formulas in multi-column Text
31560 \begin_inset LatexCommand index
31561 name "Formula ! in multi-column text"
31568 \begin_layout Standard
31569 Formulas in multi-column text are often too wide to fit into a column and
31570 thus need to be set over the whole page width.
31571 This is done by using the LaTeX-package
31579 \begin_layout Standard
31584 is part of every LaTeX standard installation.
31590 \begin_inset LatexCommand index
31591 name "Packages ! multicol"
31595 , that is loaded with the LaTeX-preamble line
31598 \begin_layout Standard
31603 usepackage{multicol}
31606 \begin_layout Standard
31607 \begin_inset Note Greyedout
31610 \begin_layout Standard
31611 Note herby that the setting
31613 Two-column\InsetSpace ~
31618 Document\SpecialChar \menuseparator
31641 \begin_layout Standard
31642 Before the multi-column text the command
31645 \begin_layout Standard
31650 begin{multicols}{column number}
31653 \begin_layout Standard
31654 is written in TeX-mode.
31655 The column number is a number in the range of 2\InsetSpace \thinspace{}
31656 -\InsetSpace \thinspace{}
31658 Before the formula the multi-column text is ended by inserting the command
31661 \begin_layout Standard
31669 \begin_layout Standard
31673 \begin_layout Standard
31674 Due to the command some space is automatically added before the formula.
31675 To revert this, -6\InsetSpace \thinspace{}
31676 mm vertical space is inserted before the formula.
31677 When the formula style
31683 \begin_layout Standard
31685 \begin_inset LatexCommand ref
31686 reference "sec:Formula-Styles"
31697 is used, -9\InsetSpace \thinspace{}
31698 mm space is inserted instead.
31701 \begin_layout Standard
31702 As example a multi-column text with a displayed formula:
31705 \begin_layout Standard
31709 \begin_layout Standard
31713 begin{multicols}{2}
31718 Das Spektrum wird fouriertransformiert.
31719 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31720 , Lösungsmittel) zu trennen.
31721 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31722 nun das Aussehen des Ausgangssignals.
31723 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31724 über alle Phasen integrieren muss.
31726 \begin_inset Formula $S$
31729 unser normiertes Ausgangssignal and
31730 \begin_inset Formula $P$
31733 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31737 \begin_layout Standard
31747 \begin_inset VSpace -6mm
31751 \begin_inset Formula \begin{equation}
31752 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31760 \begin_layout Standard
31764 begin{multicols}{2}
31770 \begin_inset Formula $S_{0}$
31773 das Signal ohne Gradient ist and the Normierungsbedingung
31774 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31778 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31780 \begin_inset Formula $\nicefrac{\pi}{2}$
31783 \InsetSpace \thinspace{}
31784 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31785 das Signal zusätzlich abschwächt.
31786 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31788 \begin_inset Formula $T_{2}$
31794 \begin_layout Standard
31798 \begin_layout Standard
31810 \begin_layout Subsection
31811 Formulas with Description of Variables
31812 \begin_inset LatexCommand index
31813 name "Formula ! with description of variables"
31820 \begin_layout Standard
31821 To describe variables within a formula, like in formula
31822 \begin_inset LatexCommand eqref
31823 reference "eq:within"
31832 \begin_inset Formula $n$
31836 matrix is used with left aligned columns for the
31837 \begin_inset Formula $n$
31844 \begin_layout Standard
31846 \begin_inset LatexCommand ref
31847 reference "sec:Matrices"
31856 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31869 \begin_layout Standard
31871 \begin_inset LatexCommand ref
31872 reference "sub:Font-Sizes"
31884 \begin_layout Standard
31885 When the formula style
31891 \begin_layout Standard
31893 \begin_inset LatexCommand ref
31894 reference "sec:Formula-Styles"
31915 \begin_layout Standard
31922 only works in formulas with the style
31927 \begin_inset LatexCommand ref
31928 reference "sub:Variable-Space"
31937 is inserted before and after the matrix to have the same separation of
31938 the matrix from the equation and the side margin.
31941 \begin_layout Standard
31942 When the formula style
31946 is used, the method described in
31947 \begin_inset LatexCommand ref
31948 reference "sub:Flalign-Environment"
31952 is used to indent formulas.
31954 \begin_inset LatexCommand eqref
31955 reference "eq:within"
31959 consists of five columns whereas in the first two columns contain the equation,
31960 the third the matrix, and the last one an empty TeX-brace.
31961 \begin_inset Formula \begin{flalign}
31962 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31963 \rho & \textrm{density}\\
31964 V & \textrm{volume}\\
31965 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31972 \begin_layout Subsection
31973 Upright small Greek Letters
31974 \begin_inset LatexCommand label
31975 name "sub:Upright-small-Greek"
31980 \begin_inset LatexCommand index
31981 name "Greek letters ! upright"
31988 \begin_layout Standard
31989 Most of the math fonts only provide italic small Greek letters.
31990 But for symbols of elementary particles like pions and neutrinos, upright
31991 Greek letters are needed.
32000 \begin_layout Standard
32005 is part of the LaTeX-package
32010 \begin_inset LatexCommand index
32011 name "Packages ! was\\vspace{4mm}"
32021 \begin_inset LatexCommand index
32022 name "Packages ! upgreek"
32026 that is loaded with the LaTeX-preamble line
32029 \begin_layout Standard
32034 usepackage{upgreek}
32037 \begin_layout Standard
32043 \begin_layout Standard
32053 \begin_inset Note Note
32056 \begin_layout Standard
32057 The following table will only be displayed when the LaTeX-package
32066 They are created when the command for a small Greek letters is started
32072 For example the command
32079 \begin_inset Formula $\uptau$
32085 \begin_layout Standard
32086 With these commands reactions of elementary particles can be typeset:
32087 \begin_inset Formula \[
32088 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32095 \begin_layout Standard
32096 The upright letters are more bold and wider than the italic ones.
32097 They should therefore not be used for units like
32098 \begin_inset Quotes eld
32102 \begin_inset Quotes erd
32108 \begin_layout Standard
32112 \begin_layout Standard
32122 \begin_inset Note Note
32125 \begin_layout Standard
32126 The following will be displayed when the LaTeX-package
32138 \begin_layout Standard
32139 You need to install the LaTeX-package
32143 to see the rest of this subsection in the output.
32146 \begin_layout Standard
32150 \begin_layout Standard
32162 \begin_layout Subsection
32163 Text Characters in Formulas
32164 \begin_inset LatexCommand label
32165 name "sub:Text-Characters-in"
32170 \begin_inset LatexCommand index
32171 name "Text ! in formulas"
32178 \begin_layout Standard
32179 In some cases you might want to insert text characters directly into formulas.
32180 When for example the centered dot · is often used in formulas like
32181 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32184 , one would have to insert the command
32194 \begin_layout Standard
32196 \begin_inset LatexCommand ref
32197 reference "sub:Binary-Operators"
32206 all the time, because this character is defined in all encodings as text
32208 But the encoding can be changed by this LaTeX-preamble line:
32211 \begin_layout Standard
32216 Declare Inputtext{183}{
32226 f\SpecialChar \textcompwordmark{}
32230 \begin_layout Standard
32231 The character encoding (menu
32233 Document\SpecialChar \menuseparator
32234 Settings\SpecialChar \menuseparator
32237 ) specifies what character appears when a keyboard key is pressed.
32238 When the key for the character '·' is pressed, internally the command
32245 But this command is not available in a formula so that you would get LaTeX-erro
32247 With the changed encoding the right command is chosen automatically, depending
32248 on if the character was inserted into a formula or not.
32251 \begin_layout Standard
32252 The encoding of several characters is saved in definition files.
32253 Fore example the encoding
32257 is defined in the file
32261 that is in the installation folder of LaTeX.
32262 Encodings should only be changed via the LaTeX-preamble and not in the
32264 Otherwise own documents could not be edited by other LyX users working
32265 on other computers.
32268 \begin_layout Standard
32269 \begin_inset VSpace medskip
32272 Besides the centered dot, in this document the degree sign ° is defined
32273 with the following LaTeX-preamble line so that it can directly be inserted
32277 \begin_layout Standard
32282 DeclareInputtext{176}{
32292 f\SpecialChar \textcompwordmark{}
32296 \begin_layout Standard
32302 \begin_layout Section
32304 Typographic Advises
32305 \begin_inset LatexCommand index
32306 name "Typographic Advises"
32313 \begin_layout Standard
32314 This section is a summary of the most important typographic rules, listed
32319 \begin_layout Standard
32320 This collection was partly taken from the German semi-official dictionary
32322 \begin_inset Quotes eld
32326 \begin_inset Quotes erd
32330 \begin_inset LatexCommand cite
32335 that lists some of the ISO rules.
32343 \begin_layout Itemize
32352 \begin_layout Standard
32353 done with font styles, see
32354 \begin_inset LatexCommand ref
32355 reference "sub:Font-Styles"
32364 : 30\InsetSpace \thinspace{}
32367 Between the value and the unit is the smallest space, see
32368 \begin_inset LatexCommand ref
32369 reference "sub:Predefined-Space"
32376 \begin_layout Itemize
32377 Percent and perthousand signs are set like physical units:
32379 1,2\InsetSpace \thinspace{}
32384 \begin_layout Standard
32397 \begin_layout Itemize
32398 The degree sign follows directly on the value: 15°, but not when it is used
32399 in units: 15\InsetSpace \thinspace{}
32403 \begin_layout Itemize
32404 In numbers with more than four digits the smallest space is inserted before
32405 every third digit to group them:
32414 18\InsetSpace \thinspace{}
32415 473\InsetSpace \thinspace{}
32419 \begin_layout Itemize
32420 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32421 cm the multiplication sign
32422 \begin_inset Quotes eld
32426 \begin_inset Quotes erd
32430 It is available with the LaTeX-command
32436 , but can also directly be inserted with some keyboard definitions.
32439 \begin_layout Itemize
32440 Functions with names consisting of several letters are set upright to avoid
32442 \begin_inset LatexCommand ref
32443 reference "sub:Predefined-Functions"
32450 \begin_layout Itemize
32451 Indices consisting of several letters, are set upright:
32452 \begin_inset Formula $E_{\mathrm{kin}}$
32457 Components of matrices are set italic:
32458 \begin_inset Formula $\hat{H}_{kl}$
32464 \begin_layout Itemize
32465 The differentiation/integration operator 'd', the Euler's number 'e', and
32466 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32470 \begin_layout Standard
32476 \begin_layout Section
32478 \begin_inset LatexCommand index
32486 \begin_layout Standard
32487 Some characters and symbols can be created with several commands.
32488 Here is a list of the synonym commands:
32491 \begin_layout Standard
32492 \begin_inset VSpace bigskip
32498 \begin_inset Tabular
32499 <lyxtabular version="3" rows="12" columns="2">
32501 <column alignment="center" valignment="top" leftline="true" width="0pt">
32502 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32503 <row topline="true" bottomline="true">
32504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32507 \begin_layout Standard
32513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32516 \begin_layout Standard
32518 \begin_inset Note Note
32521 \begin_layout Standard
32528 is only used as spacer.
32539 <row topline="true">
32540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32543 \begin_layout Standard
32551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32554 \begin_layout Standard
32558 \begin_layout Standard
32571 \begin_layout Standard
32584 <row topline="true">
32585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32588 \begin_layout Standard
32596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32599 \begin_layout Standard
32608 <row topline="true">
32609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32612 \begin_layout Standard
32620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32623 \begin_layout Standard
32632 <row topline="true">
32633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32636 \begin_layout Standard
32644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32647 \begin_layout Standard
32654 <row topline="true">
32655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32658 \begin_layout Standard
32666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32669 \begin_layout Standard
32676 <row topline="true">
32677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32680 \begin_layout Standard
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33077 \begin_layout Standard
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33138 The LaTeX Companion
33141 Addison Wesley, 2004
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33158 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
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33174 of LaTeX's math abilities
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33183 LaTeX tips and tricks-
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33191 href{http://tug.org/TeXnik/}{
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33224 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
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33244 \begin_layout Standard
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33270 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
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33286 of all symbols available with LaTeX-packages
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33303 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
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33319 of the LaTeX-package
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33325 name "Packages ! hyperref"
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33370 reference "sub:Operator-Limits"
33375 \begin_inset LatexCommand index
33376 name "Commands ! M ! \\textbackslash mathclap"
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33395 Auflage, Duden 2001
33398 \begin_layout Subsubsection*
33399 \begin_inset LatexCommand printindex